{"id":"856.128.6.a","row":1252,"stored":{"file":"master_catalog.json","row":1252,"construction":null,"columns_sha256":null},"parameters":{"n":856,"k":128,"d":6,"N":169,"r":41,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100+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","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13\u00b7T14\u00b7T15\u00b7T16\u00b7T17\u00b7T18\u00b7T19\u00b7T20\u00b7T21\u00b7T22\u00b7T23\u00b7T24\u00b7T25\u00b7T26\u00b7T27\u00b7T28\u00b7T29\u00b7T30\u00b7T31\u00b7T32\u00b7T33\u00b7T34\u00b7T35\u00b7T36\u00b7T37\u00b7T38\u00b7T39\u00b7T40\u00b7T41\u00b7T42\u00b7T43\u00b7T44\u00b7T45\u00b7T46\u00b7T47\u00b7T48\u00b7T49\u00b7T50\u00b7T51\u00b7T52\u00b7T53\u00b7T54\u00b7T55\u00b7T56\u00b7T57\u00b7T58\u00b7T59\u00b7T60\u00b7T61\u00b7T62\u00b7T63\u00b7T64\u00b7T65\u00b7T66\u00b7T67\u00b7T68\u00b7T69\u00b7T70\u00b7T71\u00b7T72\u00b7T73\u00b7T74\u00b7T75\u00b7T76\u00b7T77\u00b7T78\u00b7T79\u00b7T80\u00b7T81\u00b7T82\u00b7T83\u00b7T84\u00b7T85\u00b7T86\u00b7T87\u00b7T88\u00b7T89\u00b7T90\u00b7T91\u00b7T92\u00b7T93\u00b7T94\u00b7T95\u00b7T96\u00b7T97\u00b7T98\u00b7T99\u00b7T100\u00b7T101\u00b7T102\u00b7T103\u00b7T104\u00b7T105\u00b7T106\u00b7T107\u00b7T108\u00b7T109\u00b7T110\u00b7T111\u00b7T112\u00b7T113\u00b7T114\u00b7T115\u00b7T116\u00b7T117\u00b7T118\u00b7T119\u00b7T120\u00b7T121\u00b7T122\u00b7T123\u00b7T124\u00b7T125\u00b7T126\u00b7T127","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45],[46],[47],[48],[49],[50],[51],[52],[53],[54],[55],[56],[57],[58],[59],[60],[61],[62],[63],[64],[65],[66],[67],[68],[69],[70],[71],[72],[73],[74],[75],[76],[77],[78],[79],[80],[81],[82],[83],[84],[85],[86],[87],[88],[89],[90],[91],[92],[93],[94],[95],[96],[97],[98],[99],[100],[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]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45],[46],[47],[48],[49],[50],[51],[52],[53],[54],[55],[56],[57],[58],[59],[60],[61],[62],[63],[64],[65],[66],[67],[68],[69],[70],[71],[72],[73],[74],[75],[76],[77],[78],[79],[80],[81],[82],[83],[84],[85],[86],[87],[88],[89],[90],[91],[92],[93],[94],[95],[96],[97],[98],[99],[100],[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]],"sk_fingerprint":"fa31dc30c9b4df7d","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,2,3,4,7,9,10,14,15,17,20,21,22,23,24,30,31,38,43,45,48,49,50,53,54,57,58,59,63,64,68,69,70,71,74,75,80,82,84,94,95,97,99,100,101,102,103,104,107,108,109,111,112,113,117,118,121,122,124,126,128,130,132,134,137,139,143,144,145,149,150,151,154,160,162,163,164,166],[2,4,6,10,11,18,19,25,26,28,29,31,32,33,36,37,38,40,42,45,46,48,50,53,54,55,56,57,60,61,66,67,71,74,75,76,78,80,81,86,87,90,93,94,95,96,97,100,101,102,103,104,105,108,109,110,111,112,115,117,119,120,121,122,123,125,128,129,131,132,133,135,138,141,143,144,145,146,147,148,150,151,152,153,155,156,157,159,160,161,167,168],[0,1,3,4,6,10,11,13,15,17,20,21,24,25,27,28,32,33,34,35,39,41,42,43,48,49,51,53,54,55,58,60,62,64,68,69,70,72,75,77,78,80,82,83,86,88,90,91,98,99,101,103,104,106,110,112,114,118,119,120,125,127,129,130,132,133,134,136,137,138,140,142,147,148,149,150,152,153,154,155,156,159,160,162,163,166,168],[4,24,123,125,136,139,145,146,147,148,149,155,157,159,161,165],[2,5,6,8,9,11,14,16,17,18,20,21,22,27,28,29,31,33,35,40,41,42,44,45,47,48,49,50,55,56,57,59,60,61,64,66,67,69,70,71,73,74,78,79,80,81,83,84,86,87,88,90,92,93,95,96,98,99,101,103,104,108,111,112,117,118,119,120,122,124,125,128,129,130,131,132,134,136,140,142,143,145,146,147,148,150,151,152,164,165,166,168],[0,1,2,3,5,10,11,13,15,16,17,21,23,29,32,33,36,37,38,39,40,42,43,44,45,46,49,50,51,52,53,54,56,60,61,63,64,70,72,75,77,79,80,83,84,86,87,88,89,92,101,102,108,111,114,115,117,119,120,121,122,124,125,126,128,130,131,133,135,137,144,145,148,150,152,154,156,157,159,160,162,164,167],[1,2,5,14,15,16,17,18,19,22,23,24,27,30,33,40,42,45,47,49,50,53,54,55,63,64,66,68,70,71,72,75,81,82,85,86,88,90,91,93,96,98,101,102,105,107,109,110,111,114,115,120,121,122,124,125,131,133,134,137,138,141,142,144,145,147,149,150,151,157,158,161,163,164,165,166,168],[0,1,2,7,9,10,12,13,15,16,17,18,19,23,24,25,27,29,31,34,40,41,42,44,45,47,48,49,51,52,53,54,56,57,58,60,61,62,67,68,69,71,73,75,76,77,78,79,83,86,88,89,95,98,102,103,107,112,113,115,116,117,119,121,122,125,129,130,131,134,143,144,147,149,152,156,159,160,161,162,163,165,166],[2,3,4,5,6,7,9,10,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,124,125,127,129,131,136,138,141,144,149,153,156,157,158,159,161,163,166,167],[1,2,3,5,6,7,9,11,12,14,15,16,18,21,28,36,39,40,45,49,50,51,52,54,55,57,58,59,61,63,67,70,74,75,76,77,78,79,84,85,86,88,89,90,91,92,94,96,97,99,102,103,106,108,109,111,115,119,122,125,126,128,133,134,136,138,139,140,142,143,144,146,147,148,149,150,151,152,154,155,157,158,159,166],[1,3,4,5,6,7,8,11,12,17,18,19,20,21,24,26,28,29,30,31,33,36,37,40,42,43,44,45,47,49,50,51,52,53,55,56,60,61,63,64,68,69,71,73,74,75,76,78,83,84,86,87,91,93,96,99,102,104,107,108,109,111,113,115,116,117,118,119,120,122,124,126,128,129,130,131,132,133,134,135,136,137,139,140,141,142,145,146,151,152,153,155,157,159,161,163,164,165,167],[1,4,8,12,15,16,18,19,20,31,33,34,38,43,46,48,49,51,52,53,55,56,57,59,64,66,67,68,75,77,82,83,84,88,92,93,95,96,97,98,102,104,105,107,112,113,114,116,117,119,123,124,126,128,129,130,131,132,133,136,140,144,149,150,155,156,160,166,167,168],[15,123,125,143,144,145,147,149,153,154,157,158,159,160,161,165],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,31,34,36,38,39,41,43,45,46,48,50,52,54,56,58,60,62,65,66,69,70,73,78,79,82,83,84,87,88,90,91,94,98,99,102,104,105,108,109,112,113,116,117,120,123,129,130,131,132,133,136,137,138,143,144,146,150,151,152,153,156,158,160,161,162,163,166,167,168],[1,5,8,9,10,12,13,14,17,18,21,22,23,25,27,28,30,34,35,37,38,43,44,45,49,50,51,52,54,56,57,59,64,68,70,73,78,82,84,85,86,88,89,90,92,93,94,99,100,101,102,103,104,109,110,114,116,117,119,120,128,129,130,131,133,136,137,138,142,143,144,146,147,149,150,151,156,157,159,160,162,163,165,168],[1,2,3,4,11,15,16,22,23,25,26,28,29,32,34,36,37,38,39,41,42,43,45,46,48,49,51,56,60,63,64,65,66,80,81,82,83,84,86,87,88,90,92,93,94,98,102,105,108,110,111,112,113,115,116,117,119,120,124,127,130,131,133,134,136,137,144,146,147,148,149,152,155,157,158,161,164,165,166,168],[0,5,6,7,8,12,18,19,20,21,25,27,28,30,32,33,34,39,40,41,43,44,45,48,50,51,53,54,55,57,58,59,61,62,64,65,66,68,69,71,73,75,78,82,85,86,87,88,91,93,94,96,98,99,101,103,107,111,115,116,117,118,121,122,124,125,126,127,128,136,140,141,142,143,148,152,154,157,159,160,162,164,165,166],[0,7,8,9,10,13,14,15,16,19,23,27,28,31,32,34,38,42,43,44,46,47,48,50,55,56,57,61,62,66,67,68,74,75,79,80,81,83,84,86,96,107,108,113,114,115,116,117,118,120,121,122,125,127,128,131,132,133,136,139,140,143,147,148,149,153,154,155,156,157,165,167],[0,1,2,4,6,7,11,12,14,15,21,26,27,28,29,30,31,32,33,34,40,42,48,51,52,53,56,58,63,69,70,72,76,82,83,86,87,88,90,94,95,97,98,99,100,101,104,108,109,112,118,120,122,123,125,126,127,129,130,131,134,135,137,138,142,144,147,149,151,155,156,157,159,163,164,165,167,168],[2,4,5,6,8,10,11,12,19,20,21,23,24,25,26,31,33,34,38,40,42,43,44,47,48,49,51,57,58,59,61,63,66,70,71,73,74,75,80,83,84,86,87,89,92,93,95,96,98,99,101,102,107,110,113,114,115,116,118,119,121,122,124,125,127,128,129,132,133,135,139,140,149,150,154,157,159,161],[0,6,9,12,13,14,17,23,24,30,31,32,34,36,37,39,41,42,48,50,57,58,60,61,64,67,68,69,70,71,72,73,75,76,77,80,84,86,91,94,97,98,99,100,101,104,108,109,111,112,114,115,116,117,118,120,121,127,128,129,131,132,136,139,140,141,144,145,146,147,148,151,154,155,156,161,162,163,167,168],[120,123,157,159,161,162,166],[2,4,11,12,14,15,16,17,18,19,20,22,23,26,30,32,33,36,38,39,45,46,48,49,53,55,56,57,58,59,61,62,63,65,67,68,69,73,75,78,80,84,87,88,89,90,93,94,95,97,105,108,109,110,113,114,115,116,117,119,122,123,125,127,129,132,133,134,135,137,139,140,141,144,145,148,149,150,151,152,155,157,161,163,164,166,167],[0,1,6,7,8,9,12,13,16,17,19,20,21,24,26,27,28,30,32,33,35,37,38,40,43,45,46,48,51,53,54,56,58,60,63,65,66,68,71,74,77,79,81,83,85,86,88,90,91,94,98,99,100,101,103,104,105,110,112,113,116,117,120,123,125,126,127,129,130,132,133,136,141,144,146,147,148,149,151,152,153,154,155,156,161,162,163,164,165,166],[2,3,4,5,6,7,9,11,13,14,19,22,23,27,30,33,35,37,39,40,41,42,43,46,48,50,53,56,57,58,59,60,61,63,65,66,69,70,71,73,74,75,76,77,80,82,86,87,94,96,99,100,102,106,107,113,115,116,119,124,126,127,128,130,131,132,133,134,135,136,137,140,141,142,143,145,149,151,154,158,159,162,164,165,166,167],[1,2,3,4,10,12,13,15,16,17,22,25,26,27,28,32,33,34,35,36,38,39,42,44,45,47,50,52,53,54,55,56,61,63,64,65,66,72,73,74,77,79,80,82,87,88,89,90,91,92,93,95,96,98,99,101,105,108,110,111,112,113,114,119,120,121,122,123,124,126,130,131,132,134,135,138,139,140,141,142,144,145,146,149,151,152,153,154,155,156,158,161,164,167,168],[0,5,8,9,11,12,13,14,22,26,27,29,30,36,39,42,47,48,49,50,52,53,54,55,57,58,59,60,63,64,65,67,72,73,74,75,78,79,80,82,84,85,86,90,91,92,96,98,99,100,105,106,107,109,111,112,113,115,119,120,121,124,125,127,129,132,133,135,136,140,141,143,144,145,147,148,149,151,154,155,158,160,166,168],[24,34,123,125,145,146,147,148,149,155,157,159,161,165],[0,2,4,6,9,11,13,15,16,21,22,24,27,29,31,32,35,36,37,38,40,41,42,43,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,76,81,82,84,85,86,87,90,93,94,96,99,101,102,103,105,107,109,112,114,116,118,120,121,123,124,126,128,129,130,133,134,135,136,139,141,143,144,146,150,153,156,158,160,165,167],[0,1,3,5,8,9,11,13,16,23,24,25,26,27,28,29,31,32,34,36,38,39,40,42,47,52,54,56,57,58,59,61,65,67,68,69,70,71,72,73,77,78,79,80,82,84,85,86,87,89,92,93,95,96,97,99,101,105,106,107,108,109,110,111,113,114,115,116,117,118,122,124,125,126,127,128,129,132,133,143,145,146,148,153,156,157,159,160,161,162,163,165,167],[8,9,10,11,16,19,20,23,24,27,29,31,33,35,36,37,38,41,42,45,46,47,48,49,73,74,75,78,79,82,83,84,86,89,91,92,93,95,96,99,100,103,108,109,110,111,122,123,124,127,129,132,135,138,141,142,144,145,146,147,148,149,151,152,155,156,157,158,162,164,166],[9,11,13,15,16,17,18,20,21,22,23,25,27,30,34,35,36,37,38,41,42,44,50,51,52,53,54,56,59,61,63,64,67,68,72,75,78,79,82,84,85,88,89,90,94,96,97,102,103,104,107,109,110,111,114,115,116,117,120,123,124,129,130,132,135,136,137,138,141,143,144,151,156,161,163],[0,1,3,7,9,12,19,20,21,23,25,26,27,28,29,30,31,33,35,36,37,38,42,43,44,47,48,49,50,52,53,57,58,59,61,65,66,67,69,71,72,73,75,77,79,80,81,84,85,87,88,89,91,92,93,95,99,100,101,103,105,108,112,113,115,119,123,124,128,132,133,134,136,137,138,140,143,144,145,146,147,151,152,153,154,155,158,161,165,168],[1,2,3,4,6,7,9,12,17,18,19,20,22,23,25,28,31,32,36,38,39,45,46,47,48,52,54,55,57,61,63,66,70,74,76,79,87,92,93,94,96,97,98,102,106,108,109,110,111,112,113,114,118,120,121,122,123,124,125,126,128,129,130,134,135,136,140,141,142,144,147,149,153,156,159,160,162,163,167],[1,3,5,6,8,10,13,14,17,20,23,24,26,28,30,36,37,43,50,51,60,61,62,63,66,67,68,69,72,73,74,75,77,78,79,80,81,82,83,86,87,88,89,90,93,96,99,101,103,105,106,108,110,113,114,117,119,126,128,130,132,133,134,135,136,143,145,147,149,150,152,153,157,158,159,160,165,166,168],[38,43,132,134,137,139,149,158,159,160,161,167],[2,4,9,10,11,14,16,18,20,21,22,24,27,28,29,30,32,33,36,38,40,42,44,46,47,48,51,55,61,62,63,64,66,68,69,71,73,74,75,76,77,78,79,80,82,84,87,88,89,90,92,95,99,101,106,109,110,111,113,114,115,116,117,119,120,122,125,126,128,129,130,132,133,135,136,140,141,142,144,145,146,147,152,157,158,163,165,167,168],[45,123,125,136,137,138,139,140,143,144,145,147,149,153,154,157,158,159,160,161,165],[0,2,5,6,10,11,22,23,25,26,28,29,32,34,36,38,44,45,46,48,49,54,56,59,60,62,64,67,68,72,76,77,78,79,80,85,87,89,91,92,102,103,104,105,108,109,110,111,113,115,116,119,120,125,128,129,130,131,133,135,136,137,138,139,140,142,145,147,149,151,152,154,156,157,159,160,161,162,166,168],[1,3,5,6,8,9,10,11,14,15,16,17,19,24,25,26,30,32,33,34,37,38,44,45,47,48,49,55,56,58,60,68,69,70,72,74,75,76,77,79,81,83,86,87,88,89,90,91,92,95,96,98,100,103,105,106,109,114,115,116,117,118,119,121,122,124,125,126,131,133,135,136,140,142,143,147,148,153,154,155,157,158,160,162,163,164,166,168],[0,1,2,5,6,7,11,13,14,15,17,22,26,27,29,32,33,34,35,36,38,42,43,44,46,47,48,49,50,52,53,56,58,60,61,63,66,67,69,70,72,73,74,78,80,81,82,83,84,87,88,89,90,91,93,94,98,101,104,108,109,110,111,113,114,115,116,117,118,121,124,126,127,129,131,134,138,139,143,144,145,148,149,152,153,156,157,159,161,162,168],[2,3,4,5,6,7,8,9,10,11,14,15,18,19,20,21,22,23,25,26,27,29,30,31,32,33,34,35,38,40,41,49,52,53,54,55,58,59,60,61,62,63,66,67,68,69,75,76,79,80,81,82,88,89,90,91,92,93,95,98,99,100,101,102,103,108,109,111,112,113,120,121,122,123,125,127,128,129,134,137,138,143,144,146,148,149,150,152,153,154,157,162,163,164,165,166,167,168],[1,2,3,4,5,6,8,9,10,12,16,18,20,21,23,25,27,31,37,38,39,40,42,47,50,52,54,55,57,59,63,66,67,69,72,74,76,77,78,82,83,84,87,88,89,91,94,95,96,97,99,100,102,105,106,107,111,115,116,121,123,126,128,132,134,135,137,145,147,149,152,154,156,157,159,160,161,162,163,167,168],[1,2,3,5,8,12,14,15,16,17,18,19,22,24,27,28,30,31,33,34,38,39,43,44,45,48,50,52,54,55,57,61,62,63,65,69,72,73,74,75,76,80,81,82,84,85,86,90,91,92,99,100,101,105,106,107,109,112,116,118,119,120,123,124,128,130,133,136,137,138,139,140,142,144,145,149,151,152,154,155,156,158,159,161,162,163,164,165,168],[4,5,8,11,12,14,16,19,20,22,25,26,27,29,30,33,34,35,36,37,39,41,43,44,46,48,50,52,53,56,57,58,59,60,61,63,64,66,68,70,71,72,73,74,81,82,83,84,86,88,91,95,98,99,103,106,107,112,114,117,118,122,124,127,128,132,134,136,138,139,140,142,144,145,146,147,148,149,153,156,160,161,164,165,166,167,168],[24,53,111,123,125,143,144,145,146,148,149,157,159,161,162,164,165],[1,4,5,6,9,15,18,20,25,27,28,31,33,37,38,39,45,46,47,49,51,52,53,55,57,58,63,66,67,68,71,77,79,83,85,86,90,92,93,95,97,103,104,105,107,109,110,111,112,113,115,116,122,123,128,131,134,141,143,144,146,149,150,154,155,156,157,158,161,162,163,164],[1,2,3,5,10,12,13,14,17,20,27,29,31,32,36,38,39,43,44,45,46,47,49,50,51,52,56,57,58,60,61,63,66,70,71,72,73,74,76,77,78,80,83,85,89,90,91,94,96,101,104,105,106,110,111,112,114,115,116,121,122,123,126,128,130,134,135,141,144,146,147,149,151,157,158,162,164,166],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,40,41,48,49,54,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,124,125,127,129,131,133,136,144,149,153,156,157,160,161,163,166,167],[1,2,3,4,6,7,11,12,13,15,22,28,29,30,32,33,34,36,37,38,39,40,44,46,47,48,50,51,53,54,57,58,60,61,63,64,65,67,75,78,79,80,82,87,91,92,93,94,96,97,98,100,101,104,105,106,110,112,117,122,123,126,128,129,132,133,134,135,138,139,140,141,142,143,146,147,149,150,151,154,155,156,160,162,163,165,166],[1,4,9,13,14,15,18,19,20,21,22,24,26,30,32,33,34,36,37,39,40,41,43,49,50,51,53,57,58,60,62,64,65,66,71,73,76,78,79,80,81,84,86,87,88,90,93,95,97,98,99,100,102,103,104,105,106,108,109,115,116,117,119,120,121,124,125,131,133,135,137,138,140,145,146,148,152,153,156,159,161,162,164,166],[0,2,3,5,8,9,10,12,13,14,17,19,20,22,23,27,30,31,33,35,38,41,45,46,48,49,51,57,59,61,62,63,64,69,70,72,73,75,78,79,80,81,83,87,90,91,92,93,95,97,101,103,104,105,106,113,117,121,124,125,126,129,132,134,137,138,141,142,146,147,148,149,150,153,156,157,158,159,161,162,164,165,168],[0,3,4,5,8,11,14,15,16,18,19,20,21,22,23,26,31,33,36,37,38,39,40,44,45,47,49,50,51,52,53,54,56,58,59,61,63,65,66,67,68,69,71,76,77,79,80,83,84,88,89,90,92,94,95,97,99,100,101,102,103,105,106,110,111,112,115,118,119,120,121,122,123,124,135,137,138,142,144,146,147,151,152,153,154,157,160,167],[1,3,4,7,8,11,12,14,16,18,20,23,25,26,28,29,31,33,34,36,39,41,42,45,47,48,50,52,54,56,58,62,63,70,71,72,73,74,77,78,86,87,93,95,98,99,100,101,102,104,105,106,107,110,111,112,113,116,117,118,119,120,121,122,124,125,126,128,129,133,134,139,140,145,148,149,151,153,154,157,158,161,163,168],[1,2,4,6,8,11,12,14,17,18,19,20,22,27,28,29,32,33,34,37,39,41,43,44,46,48,51,52,54,56,58,61,62,66,67,75,79,80,88,89,90,91,98,99,106,107,108,109,110,111,112,113,116,117,118,119,121,124,126,129,130,131,134,136,138,139,140,141,143,145,147,148,150,152,154,157,159,163,165],[2,3,4,7,8,9,13,14,19,21,23,24,25,26,27,28,29,32,34,35,41,44,45,47,49,54,56,58,59,60,61,62,64,65,67,69,70,71,72,74,77,78,80,81,84,85,87,88,90,92,93,96,98,103,105,106,110,113,114,118,119,120,122,123,124,125,126,127,128,129,132,136,138,142,144,146,147,148,149,150,151,153,154,155,156,157,159,162,164,167,168],[0,3,5,7,9,10,12,14,16,17,18,19,20,21,25,26,27,28,31,35,36,38,40,43,44,48,49,54,55,58,59,60,61,63,67,69,70,73,75,76,77,78,81,82,83,84,85,88,89,91,93,94,97,99,101,102,103,106,107,108,109,110,112,113,120,121,122,124,129,131,132,135,136,137,139,141,142,147,151,152,157,160,162,163,165],[1,5,6,7,9,10,11,12,14,15,17,18,20,22,23,24,25,29,30,31,33,35,36,37,39,40,41,43,46,50,52,53,55,58,64,65,66,67,68,70,71,72,73,74,76,77,79,80,82,84,86,87,88,92,95,99,100,101,104,105,106,110,111,112,113,115,116,117,118,121,123,125,127,129,130,133,134,135,137,139,140,142,144,148,149,150,152,157,159,167],[6,7,10,11,12,13,14,15,16,19,20,22,25,27,28,30,31,32,33,36,37,38,39,42,43,44,45,46,49,51,53,55,57,59,60,63,64,68,70,72,73,79,80,84,85,91,92,93,94,95,96,98,101,102,103,104,105,106,107,108,109,111,112,113,121,122,123,124,125,127,128,130,132,134,136,138,139,144,147,151,162,163,165,168],[0,1,3,5,8,9,11,13,18,19,21,24,25,27,28,29,30,31,32,35,36,37,41,42,46,47,48,50,54,55,56,58,63,64,65,66,68,71,72,73,74,75,76,77,78,82,86,87,88,90,92,93,97,100,101,103,105,110,111,113,118,126,127,130,131,132,134,137,138,139,142,143,144,145,146,147,150,151,152,154,156,158,159,161,162,164,165,166,167],[0,1,3,5,6,7,8,9,10,12,14,15,16,17,18,20,22,23,26,28,31,32,35,38,40,43,44,45,48,51,52,53,57,58,60,61,62,63,64,66,69,70,71,74,75,76,78,80,81,82,85,87,92,93,94,95,96,97,98,101,103,104,105,106,109,112,113,115,116,122,126,128,129,130,131,132,133,135,136,137,138,140,142,144,146,147,152,156,163,165,167,168],[0,1,14,15,16,18,20,23,24,25,26,28,29,32,33,35,36,39,40,42,44,46,47,54,55,56,57,58,59,62,64,66,70,74,76,83,84,85,86,87,90,91,102,103,105,107,109,110,111,112,115,117,119,120,123,124,127,129,130,131,132,133,134,135,137,138,141,143,144,147,150,155,157,158,159,160,163,165,168],[3,5,6,7,9,14,17,18,20,21,22,24,25,27,31,32,33,34,36,37,39,40,41,45,47,50,51,53,57,58,63,64,65,66,67,68,71,74,76,77,79,84,85,86,87,89,90,92,96,97,98,101,102,104,105,107,108,110,111,113,114,115,119,120,122,123,126,130,133,135,136,139,140,141,144,145,147,149,150,155,156,157,159,162,163,164,166,167,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,71,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,127,131,132,134,136,141,143,145,147,152,154,155,156,157,158,161,163,164,165,166,167],[123,124,157,158,159,163,166],[24,38,75,111,121,122,123,124,125,129,132,133,134,138,140,141,147,148,152,153,154,156,160,161,162,164,165,167],[122,123,156,157,159,165,166],[3,6,10,12,13,14,17,18,19,20,22,23,24,26,27,28,34,35,36,39,40,42,43,45,47,51,52,53,55,56,57,58,60,61,63,67,68,69,70,74,78,82,83,84,86,87,89,91,92,95,97,101,102,103,104,105,106,108,109,114,116,117,118,121,124,126,127,129,130,132,134,136,137,139,140,141,142,147,148,149,155,156,158,159,162,163,164,167],[1,3,5,7,9,11,12,14,16,17,18,19,24,31,32,33,34,35,36,37,39,40,41,46,48,51,53,55,57,59,61,62,65,66,69,70,74,75,76,77,81,82,84,85,88,89,92,93,95,98,99,100,101,104,107,109,110,113,114,117,118,123,125,126,127,128,131,132,134,139,140,141,142,143,145,146,147,148,151,154,155,156,157,158,159,161,162,163,164,165,166,167],[38,78,121,132,133,135,137,138,140,147,148,149,156,158,159,160],[0,1,2,3,4,5,6,7,8,10,12,14,16,18,21,23,24,25,26,27,38,40,42,44,47,49,50,52,54,55,56,57,62,65,66,69,70,71,73,74,76,79,81,82,85,87,88,91,92,94,96,97,100,101,106,107,108,109,111,112,115,117,118,120,124,127,128,131,135,136,137,139,140,142,143,145,148,150,153,157,160,162,165,166,168],[2,4,6,7,11,12,18,20,22,23,24,25,26,29,30,31,32,33,34,36,37,41,43,44,45,46,47,49,50,52,53,54,55,56,58,63,64,65,69,70,72,73,74,76,77,78,80,82,83,88,90,93,95,96,98,99,102,103,104,113,116,117,119,122,123,126,127,128,129,130,134,136,137,138,141,145,147,149,152,157,159,162,164,166],[1,2,3,4,5,7,9,10,11,12,13,15,16,17,19,21,22,23,25,27,29,30,31,36,44,48,50,56,58,62,63,64,67,73,75,76,79,80,84,85,89,93,95,96,97,98,101,103,104,106,107,111,113,116,117,118,121,122,124,125,129,132,134,136,137,138,139,140,142,144,145,146,147,151,153,155,156,158,160,162,165,166],[2,3,4,5,8,9,10,11,12,13,14,15,16,17,18,24,26,27,29,30,32,35,36,38,39,41,42,44,46,48,50,52,54,57,59,60,63,65,66,68,70,73,78,80,81,82,83,85,87,89,98,99,100,101,103,104,105,108,109,112,113,114,115,122,130,132,133,137,139,140,141,143,146,147,149,152,155,156,158,161,162,164,166,167],[123,125,157,159,165],[1,3,5,6,8,11,12,14,17,19,20,23,24,27,30,31,35,36,39,40,42,44,47,49,51,52,54,57,58,60,62,63,64,65,66,67,70,71,73,74,75,76,77,78,81,82,93,94,98,99,100,101,102,104,105,106,107,108,109,112,113,116,117,118,119,120,121,124,126,129,133,138,140,144,146,147,148,150,151,156,157,160,161,162,163,164,165,167],[2,3,4,5,6,7,10,11,12,13,14,15,19,20,21,24,25,26,27,29,30,32,33,34,37,38,40,43,44,46,49,51,53,54,57,59,61,63,65,67,68,71,74,75,78,79,81,83,87,89,90,91,94,95,98,99,103,104,105,106,107,108,109,112,113,114,115,116,117,121,122,125,131,133,136,138,139,140,141,142,143,144,145,146,148,149,151,155,156,158,159,163,167],[0,2,3,4,9,10,11,12,14,15,16,17,20,21,22,25,26,29,32,33,34,36,37,38,39,43,44,45,46,47,48,52,56,61,63,64,65,66,68,69,70,72,73,76,77,81,83,86,87,88,91,93,94,95,97,98,99,100,102,106,112,113,114,118,123,124,125,126,135,136,137,139,141,143,144,145,149,151,152,154,155,156,158,159,160,162,165,166,167,168],[0,1,3,5,6,7,8,12,13,15,17,19,23,27,28,29,30,31,32,33,34,39,40,41,42,43,45,47,50,51,52,54,55,56,58,60,61,63,64,65,68,70,71,74,75,76,77,80,83,86,89,91,92,94,95,98,101,102,103,104,105,106,108,110,111,112,114,115,119,120,123,125,126,128,131,135,136,139,141,142,143,145,147,148,149,150,154,160,161,162,163,168],[1,2,4,5,8,11,12,13,17,18,19,22,23,24,27,29,30,31,32,35,36,39,42,45,48,49,51,52,56,57,58,61,62,64,71,77,79,80,81,82,83,85,86,88,89,93,101,103,104,105,106,107,108,110,112,113,114,115,117,119,120,123,125,128,129,131,133,134,135,140,141,142,143,144,145,147,150,157,158,159,160,164,167],[0,1,3,7,8,9,11,12,13,14,16,18,19,20,26,27,29,30,31,35,42,44,45,49,52,57,58,59,61,62,63,65,66,67,68,70,71,76,79,83,87,89,91,92,93,94,97,98,99,100,102,107,108,109,115,118,121,125,126,131,132,143,147,148,151,153,156,157,161,162,163,164,165,166],[1,2,4,6,9,10,13,15,20,21,29,30,31,32,33,36,37,39,40,41,42,43,47,48,50,52,55,56,59,61,62,63,64,65,68,69,70,71,72,73,74,78,80,82,85,86,88,90,91,92,93,97,98,101,103,104,105,106,107,110,112,113,114,115,116,117,120,121,124,125,129,136,137,139,141,142,145,146,147,148,149,151,152,153,154,155,158,159,164,166,167,168],[0,2,4,5,6,7,8,9,13,14,18,20,23,24,25,27,33,35,36,40,47,49,50,51,52,53,54,55,58,61,66,68,71,72,75,78,79,80,83,84,85,87,89,90,91,95,101,104,105,106,107,108,110,111,113,114,116,117,120,121,122,126,130,132,138,144,147,149,150,152,157,163,164,165,166,168],[1,3,5,7,10,11,14,15,19,20,21,22,23,27,29,32,35,36,38,46,47,52,53,55,57,58,60,62,64,66,68,72,75,76,77,78,85,87,88,91,93,94,96,97,98,99,100,101,102,103,104,105,110,112,114,117,119,120,121,122,123,125,126,127,129,130,131,132,133,134,139,143,146,149,152,153,155,157,158,159,162,165,168],[24,94,111,123,125,129,133,135,138,141,143,145,153,154,157,159,162,164,165,167],[149,152,153,167],[0,2,3,4,6,7,8,12,16,20,25,36,38,39,40,42,43,44,46,47,48,50,51,52,54,55,57,58,59,61,62,63,64,69,72,73,74,76,78,81,83,84,89,90,93,94,96,98,99,101,105,108,110,112,117,118,119,123,125,127,130,132,133,134,137,138,139,144,146,147,148,149,150,151,152,154,155,157,159,160,161,167],[0,5,6,7,8,9,11,14,16,20,24,26,29,31,32,34,35,36,38,40,41,42,44,45,49,50,51,52,54,56,57,59,62,63,64,66,67,68,71,74,76,77,82,84,85,87,91,92,93,97,99,102,104,108,112,113,115,116,117,119,120,122,124,125,127,129,130,134,136,140,146,147,148,150,151,155,156,157,158,161,166,168],[3,5,6,7,9,14,16,18,19,22,25,26,29,30,31,37,40,42,44,45,48,51,54,58,59,60,62,63,65,67,71,72,73,74,75,76,77,78,82,83,85,86,88,89,90,92,94,95,96,98,100,107,108,113,116,117,119,121,122,128,130,131,132,134,140,141,143,144,147,148,149,150,151,156,157,159,160,163,165,166,167,168],[12,13,14,15,16,18,20,22,25,27,28,29,31,35,37,38,40,42,44,50,51,52,53,54,55,56,57,58,59,60,61,64,65,66,67,70,71,73,74,76,77,79,82,83,84,87,88,91,92,93,94,96,101,102,103,106,107,110,111,114,115,116,117,120,121,122,127,133,135,136,139,141,142,144,150,151,152,153,154,155,158,159,162,163,165,167,168],[1,7,8,10,11,12,13,14,21,24,27,31,34,35,37,38,42,43,45,48,51,52,53,54,55,57,58,62,68,70,75,76,78,80,81,82,84,86,91,94,96,98,99,100,104,105,106,109,112,113,114,117,120,121,122,126,129,132,133,134,135,137,138,139,142,143,145,146,148,149,151,152,154,155,156,157,158,159,160,161,165,167,168],[0,3,6,7,9,10,12,13,21,23,25,26,27,28,29,33,35,36,39,42,45,46,48,55,57,58,59,60,61,63,64,68,69,71,72,75,79,81,86,88,92,93,95,98,99,100,102,103,105,107,113,115,122,124,125,132,138,139,140,144,145,147,148,150,156,157,158,162,163,168],[1,6,9,10,11,12,13,14,17,19,20,21,23,28,29,31,32,33,34,36,37,38,39,40,43,44,45,46,47,49,51,57,59,60,61,65,67,68,69,70,71,74,78,79,84,87,91,92,93,95,96,98,99,102,103,104,105,106,107,108,109,110,111,113,118,122,124,129,130,133,135,136,137,138,140,142,144,145,146,147,148,151,159,161,165],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,112,114,117,118,122,124,127,129,131,134,135,138,140,143,145,152,154,155,158,159,161,163,165,166,167],[0,7,8,9,11,12,14,15,16,18,20,21,23,27,28,34,36,37,38,39,40,41,45,46,47,48,50,55,58,59,61,62,63,65,66,68,69,71,72,73,74,75,76,77,80,81,82,84,85,86,87,89,90,93,94,98,100,102,103,105,106,108,109,115,117,118,119,121,123,129,131,132,135,136,139,141,142,143,146,148,149,153,154,157,159,160,165,166,167],[0,3,6,7,8,10,16,17,19,21,22,25,26,27,30,32,33,34,35,36,37,41,44,45,46,47,48,49,51,53,56,57,58,61,64,65,67,68,70,71,72,73,75,78,79,80,83,85,90,91,92,96,97,100,103,104,106,107,108,109,110,111,112,115,116,117,120,123,124,125,126,127,130,132,137,140,146,147,148,149,151,153,155,157,158,160,168],[0,2,3,4,5,7,8,9,11,12,14,15,17,19,22,26,32,33,34,35,36,39,40,43,44,45,46,53,57,58,62,64,65,68,70,71,74,77,78,81,83,85,87,91,92,95,96,97,98,100,103,105,106,107,108,111,112,113,114,116,121,122,123,124,128,129,130,131,134,137,141,142,143,146,149,151,152,153,154,160,161,162,167,168],[1,2,4,6,8,11,13,15,16,18,19,20,23,24,26,28,30,31,33,35,37,38,41,43,45,47,49,51,52,54,56,58,61,63,65,66,69,71,73,78,79,81,83,84,87,89,90,92,94,97,99,100,103,105,106,111,113,114,117,119,122,124,127,128,130,131,135,136,140,142,143,146,147,149,152,155,156,158,159,160,161,162,167,168],[38,110,133,134,135,136,140,141,147,149,152,158,159,160,167],[24,111,123,151,157,158,159,160,163,164,166],[0,3,5,6,8,9,14,15,16,17,20,21,24,27,28,30,31,34,36,38,39,40,41,42,43,44,45,46,47,48,49,54,56,59,61,64,65,68,69,71,72,74,75,78,80,81,83,88,89,90,91,92,96,98,101,103,105,107,109,111,113,122,124,125,126,127,128,129,130,131,133,138,140,143,145,147,148,150,153,155,158,164,166,167,168],[0,1,2,4,6,7,8,10,11,15,17,18,19,22,24,26,28,31,33,34,35,36,38,41,42,44,45,46,47,49,50,55,56,57,58,59,61,63,66,67,68,74,76,78,80,81,82,86,87,89,95,96,98,99,100,101,102,105,106,107,108,109,111,112,113,114,115,116,121,122,124,125,127,128,130,133,135,142,143,145,146,147,148,150,151,152,155,158,159,160,161,162,164,166],[2,4,5,7,8,9,11,12,13,15,16,18,21,26,27,28,29,30,32,33,34,39,40,41,43,44,45,46,47,48,53,57,61,62,63,64,69,70,71,72,73,74,75,80,81,82,83,84,85,87,88,89,91,93,95,96,98,99,100,102,103,106,108,109,111,114,115,118,121,122,123,126,128,129,132,134,136,138,142,143,145,146,147,149,150,151,152,153,154,155,157,158,161,163,165,167],[0,2,4,5,6,7,8,11,12,13,17,24,27,28,34,36,39,43,44,46,47,48,49,51,53,54,55,59,60,63,65,70,73,74,76,78,83,84,88,89,98,99,100,108,110,112,113,118,122,124,125,126,127,130,131,133,135,136,139,141,142,143,144,146,149,156,157,167,168],[2,4,5,7,11,12,13,14,16,18,21,25,26,27,28,31,33,34,36,37,38,42,48,52,54,55,56,58,59,60,63,67,70,73,76,78,79,80,82,83,84,86,87,88,90,91,93,99,100,101,102,105,108,110,113,114,115,116,118,121,122,125,128,130,131,132,133,138,141,142,143,144,150,152,153,155,156,157,159,161,162,165,167,168],[6,7,9,10,12,14,17,20,23,25,28,29,30,31,32,39,41,43,44,46,49,50,52,54,55,56,57,60,61,62,63,64,65,66,67,71,72,73,75,77,80,81,83,86,87,88,89,92,93,94,95,97,99,101,102,103,105,106,109,111,112,113,114,115,118,120,121,124,125,126,128,129,130,131,133,134,136,140,141,142,143,145,146,147,148,153,154,155,156,159,163,165,166,168],[0,24,38,122,123,125,135,136,140,146,149,157,158,161,164,165],[0,4,5,12,15,19,20,23,24,26,28,31,33,34,35,36,37,38,39,43,45,46,47,51,53,54,57,58,59,60,61,62,64,68,69,74,75,80,81,84,88,89,91,92,93,94,95,98,99,101,106,107,109,113,114,116,117,118,119,120,122,126,127,129,130,132,134,135,136,137,139,140,142,144,145,148,149,154,155,157,164,166,168],[0,1,3,4,6,12,15,16,18,19,20,21,25,26,28,29,30,31,34,35,41,48,49,51,53,58,61,62,63,64,65,67,68,70,71,73,75,76,77,79,80,81,82,83,85,88,89,90,93,97,99,102,104,105,106,107,109,110,114,115,117,119,121,124,125,127,129,130,134,135,139,140,141,142,143,144,145,148,149,151,152,154,155,156,157,159,160,161,165,166],[4,5,6,8,11,12,13,14,15,16,17,19,20,22,24,26,28,32,38,43,44,46,48,50,51,56,57,59,61,66,69,71,72,73,74,75,77,78,79,81,84,88,89,91,92,93,94,95,96,97,98,99,101,102,105,107,108,109,111,114,115,116,118,121,124,126,127,130,131,133,135,139,140,143,147,148,151,153,154,155,156,159,160,163,165,167],[0,3,4,5,6,8,11,13,15,18,19,25,33,34,35,36,37,39,42,43,44,45,47,48,50,52,55,56,59,61,63,64,67,69,71,72,73,75,76,79,80,81,82,84,85,86,87,88,89,92,93,94,95,96,97,100,101,102,103,105,106,108,110,111,113,114,117,119,120,123,127,128,130,131,132,134,135,137,140,141,142,143,145,146,147,149,151,154,155,156,157,158,160,161,162,164,165,166,167,168],[2,3,7,8,11,13,14,16,19,21,22,25,28,32,33,35,37,42,43,44,45,46,47,48,49,55,57,59,61,62,64,67,69,76,77,78,79,80,81,82,84,87,89,90,91,93,95,96,99,100,103,104,107,108,111,114,115,116,117,120,121,124,125,128,129,131,132,133,135,136,137,138,140,141,142,143,145,146,150,151,152,154,158,160,161,164,165,167,168],[0,1,2,11,12,13,14,18,19,22,24,25,27,28,30,31,32,37,41,42,43,44,46,47,49,50,51,53,56,60,63,64,65,67,68,69,71,72,74,75,77,78,80,84,85,87,91,92,94,95,97,98,99,101,102,105,108,110,113,116,118,119,121,122,124,125,127,131,132,134,137,139,141,142,143,147,150,153,155,161,166,167,168],[1,2,3,4,5,7,14,16,17,19,20,24,26,29,30,31,36,39,40,41,42,43,45,46,47,49,50,56,59,60,61,62,63,64,67,73,75,77,78,79,80,81,83,89,90,91,92,93,94,99,100,102,103,105,111,112,114,115,116,117,118,121,128,130,132,133,134,135,137,138,139,141,145,146,148,149,151,158,159,160,165,166,168],[0,4,6,7,12,17,18,19,21,26,27,29,30,31,32,33,37,38,39,40,42,43,45,48,50,51,52,57,60,62,64,65,67,68,69,70,73,75,77,78,80,81,82,86,88,89,93,96,97,99,103,107,110,111,112,113,115,119,122,124,126,127,128,133,135,137,138,139,140,141,142,143,145,149,150,153,154,157,158,160,166,167],[0,2,3,4,5,7,8,9,10,11,13,18,19,20,22,23,25,29,31,33,36,38,39,41,42,44,45,48,51,55,58,59,61,62,63,65,66,68,69,70,72,75,76,79,80,82,84,87,90,91,93,94,96,98,99,100,101,105,110,114,116,118,119,120,123,125,126,127,128,130,131,135,137,138,139,142,143,145,147,150,153,154,155,156,158,161,165,166,167],[3,4,5,7,9,11,13,14,15,20,21,23,25,29,30,31,32,33,34,35,36,38,43,46,47,49,50,51,52,54,59,62,63,64,68,70,72,73,76,77,81,84,85,86,90,91,94,96,101,104,105,107,108,109,110,111,112,117,126,130,132,133,134,135,136,138,139,141,143,144,145,147,151,152,153,154,157,159,160,162,164,165],[1,2,4,6,9,11,15,16,18,19,20,23,24,25,26,30,31,33,34,36,38,40,42,45,47,49,50,53,54,57,59,61,63,64,67,69,70,72,73,77,80,81,85,87,89,90,94,95,97,99,100,103,105,107,109,110,111,113,114,117,119,121,122,123,124,126,130,131,134,137,138,139,144,145,146,150,151,154,155,156,157,160,161,162,163,165,166,167,168],[0,1,4,5,6,7,8,10,12,13,15,16,17,18,22,23,27,30,32,34,36,39,40,41,44,45,46,48,50,53,56,57,62,63,64,65,66,67,71,72,74,77,78,79,80,81,82,84,87,88,91,93,95,98,99,100,101,102,105,106,109,111,118,119,123,125,126,127,128,131,133,134,135,139,141,143,145,148,149,150,154,156,157,161,163,164,165,166,168],[0,4,6,7,8,12,15,17,18,21,24,25,26,27,31,32,36,38,41,42,43,45,49,50,51,53,54,55,56,60,63,66,70,72,74,75,77,78,80,81,82,83,86,90,91,94,96,97,99,100,101,102,103,106,114,119,121,124,126,131,132,133,135,137,138,139,140,141,142,146,147,148,149,151,153,154,158,159,160,162,164,165,166,167,168],[0,1,5,6,12,14,15,17,18,20,21,24,25,27,28,29,30,35,37,38,39,42,45,47,49,55,56,60,61,67,69,70,71,73,76,78,83,84,88,89,90,91,94,100,102,103,105,106,108,109,111,113,115,116,117,118,119,121,126,128,130,132,134,135,136,139,140,141,142,143,144,146,149,153,155,158,161,163,165,167,168],[0,2,4,5,8,10,12,13,18,22,23,26,29,30,32,33,36,37,39,41,44,45,46,48,52,53,54,56,60,61,63,65,68,69,70,72,73,74,77,81,82,83,85,86,87,91,93,95,96,98,100,101,105,107,108,109,111,112,114,118,119,121,122,129,131,132,133,134,135,138,139,140,146,148,149,150,151,152,153,154,156,158,160,161,163,164,165,168],[0,2,4,5,10,11,13,15,16,17,18,19,20,22,25,27,29,30,31,32,35,37,40,44,45,47,49,50,51,56,57,58,60,63,65,68,69,70,71,73,75,77,78,80,82,84,86,87,92,97,99,100,101,103,104,106,110,111,112,113,117,119,121,122,125,127,130,131,132,133,134,137,138,142,143,146,147,150,152,154,156,157,159,160,162,164,166],[1,5,8,9,10,12,13,14,17,18,19,21,22,23,24,25,27,28,30,34,35,37,43,44,45,49,50,51,52,54,56,57,59,64,68,70,73,78,82,84,85,86,88,89,90,92,93,94,99,100,101,102,103,104,109,110,114,116,117,119,120,121,123,125,128,129,130,131,132,135,136,140,142,148,149,150,156,158,159,161,162,163,164],[0,1,2,3,4,5,6,7,16,17,20,22,23,24,25,29,30,31,34,36,39,41,43,45,47,48,50,53,55,56,58,61,63,64,66,69,70,74,75,77,79,81,84,86,88,90,91,93,95,98,99,100,101,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,122,123,126,127,128,129,132,133,134,135,137,138,140,142,143,145,146,150,151,152,153,154,155,156,158,161,167],[2,3,4,7,8,9,12,15,17,18,21,22,23,27,29,30,31,39,41,46,47,48,49,50,52,58,60,62,63,64,65,67,69,70,71,72,73,75,77,79,80,81,82,84,90,93,95,96,99,100,101,104,105,108,112,113,117,118,126,128,129,131,132,136,137,142,143,146,153,154,157,159,162,165,166,167],[0,2,4,7,8,9,12,13,14,15,17,18,21,22,23,25,26,27,28,32,35,37,38,44,45,46,48,50,53,56,57,63,64,67,69,70,71,72,73,74,76,78,80,81,84,85,91,93,94,96,97,100,101,102,103,105,106,109,111,118,119,122,123,125,126,130,131,134,135,139,141,143,144,147,148,149,151,152,153,156,157,161,162,163,164,165,166,168],[1,2,4,5,6,7,8,9,10,11,12,15,16,17,18,20,24,25,26,28,29,30,32,42,45,46,47,48,49,51,52,54,57,58,59,60,61,62,64,68,69,72,74,76,79,81,83,85,86,87,91,95,98,99,100,102,103,106,107,108,110,113,115,118,119,120,122,128,134,138,143,145,146,148,149,151,152,153,154,156,158,159,160,162,163,167,168],[0,3,5,6,16,17,18,20,21,22,23,24,25,27,29,31,33,34,37,42,43,44,45,46,47,48,49,54,57,58,61,62,63,64,65,66,67,68,69,71,72,73,78,80,81,83,84,85,86,87,88,89,90,91,92,97,98,101,102,103,104,107,108,111,112,113,114,115,120,122,123,128,131,135,136,138,139,141,142,146,147,149,150,151,153,156,159,160,161,162,164,165,166],[2,4,5,7,10,14,16,17,18,19,23,30,34,35,37,40,44,49,50,51,52,54,55,56,58,59,60,62,63,64,69,70,71,72,73,74,75,76,78,81,84,88,90,91,92,95,96,97,98,100,101,102,106,108,109,111,112,113,115,116,117,119,121,124,125,126,128,130,134,135,136,141,142,144,146,147,148,149,150,151,152,157,160,161,162,163,164,165,166,167],[1,2,3,4,10,14,17,21,27,29,36,38,43,44,45,49,50,51,52,54,56,57,58,60,61,63,64,65,66,70,71,73,74,76,80,83,84,89,90,91,94,95,96,101,102,103,104,105,106,111,112,114,115,116,118,119,120,121,124,125,128,129,131,133,134,135,142,144,146,151,154,158,159,160,162,163,164,165,166,167],[0,1,2,4,5,6,8,9,11,12,13,15,16,18,19,21,25,26,27,28,29,31,32,33,36,41,42,43,44,47,48,49,51,52,53,55,59,63,66,68,69,70,74,75,78,82,84,88,91,92,94,95,97,101,103,104,105,107,110,115,116,117,118,120,121,122,124,126,130,131,134,139,140,141,144,145,146,147,148,149,151,152,155,156,157,159,160,161,165],[30,38,123,125,132,133,134,136,140,143,144,145,147,153,154,157,161,165],[2,3,4,5,8,9,14,15,17,21,23,26,28,29,35,37,38,39,41,42,44,46,47,50,51,56,57,60,61,62,63,66,67,72,75,76,78,79,81,84,87,89,90,92,97,99,101,103,106,107,108,109,112,113,118,119,120,122,123,124,127,128,129,131,132,135,136,138,140,141,142,144,145,149,150,153,154,156,157,158,161,162,164,167,168],[33,121,123,125,143,144,146,147,148,149,156,157,158,159,160,161,165],[2,3,4,5,9,10,13,14,17,18,20,23,24,25,28,32,33,34,35,37,38,42,43,44,45,46,47,48,49,50,51,52,53,55,57,58,60,62,63,68,69,70,73,76,77,79,82,83,86,87,90,92,96,97,98,99,104,105,106,107,108,109,110,111,113,115,116,118,121,124,125,126,128,129,130,131,132,133,135,137,139,140,141,142,143,144,145,146,147,150,151,152,154,158,159,162,168],[24,35,111,129,133,135,138,141,146,147,148,153,154,158,160,161,162,164,167],[0,2,3,4,5,7,9,10,11,15,17,18,23,25,29,31,32,33,35,36,39,40,43,44,45,46,47,48,51,52,53,56,58,60,61,63,66,67,69,70,82,84,85,88,90,91,95,96,97,98,100,103,104,105,106,108,114,117,121,123,125,126,127,128,129,132,134,139,140,142,144,149,150,151,152,153,157,158,160,163,164,165,166],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,39,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,125,127,131,132,134,137,140,141,145,152,154,155,156,159,160,163,164,166,167],[0,2,3,4,8,10,11,12,16,18,21,22,23,26,27,29,30,37,38,39,40,41,42,43,44,48,50,51,52,54,55,57,61,63,67,68,69,71,74,75,76,79,83,86,92,95,96,97,99,100,101,102,103,106,108,109,110,112,113,115,119,120,121,122,124,125,127,129,130,133,134,138,140,144,145,146,149,150,152,156,158,159,161,162,164,165],[0,1,3,6,8,9,11,14,16,17,18,23,27,28,29,31,32,34,35,36,38,39,40,41,42,43,44,46,47,49,50,51,53,56,60,62,63,65,66,67,69,70,71,73,74,78,82,83,84,86,87,88,90,91,92,93,95,96,97,98,103,106,108,109,112,113,115,118,122,125,126,127,129,130,132,138,139,141,143,145,149,151,155,156,158,159,163,164,166,167],[1,7,9,10,11,14,16,22,24,26,27,30,31,33,34,35,36,39,40,41,42,44,46,52,55,58,59,60,63,64,65,68,71,76,79,80,81,83,84,85,86,87,89,90,93,94,95,97,103,105,108,109,110,111,112,118,120,121,123,127,130,131,133,134,135,136,137,138,140,142,143,145,147,150,153,155,156,160,161,162,163,166,168],[0,1,5,7,9,11,14,15,21,22,25,26,28,29,30,31,36,37,38,39,42,43,44,46,49,50,51,52,53,58,61,62,63,67,69,70,72,73,74,76,77,78,79,82,83,84,86,87,88,89,91,94,96,97,100,102,104,107,108,109,110,111,112,113,114,115,117,118,120,121,122,123,125,126,128,129,130,134,135,138,142,144,146,147,150,155,157,159,161,162,163,164,167,168],[5,7,8,11,14,15,16,17,18,19,21,23,24,27,28,32,33,38,40,41,42,46,48,56,57,59,60,66,68,71,72,75,76,77,78,79,81,83,84,86,87,91,93,94,95,96,97,100,103,104,106,108,109,110,111,112,113,117,118,121,123,125,126,128,132,133,136,138,139,140,141,144,147,151,152,153,154,158,159,161,163,165,168],[0,4,6,7,9,10,11,12,14,15,17,18,21,31,33,35,36,37,39,43,44,45,48,49,51,52,53,55,59,60,61,62,63,64,66,67,69,70,71,72,75,76,77,79,80,82,83,84,88,90,91,93,95,96,97,99,100,101,102,103,106,108,109,110,111,114,119,120,121,122,123,124,128,129,130,132,140,142,143,144,146,147,148,149,150,151,152,154,155,157,158,159,161,164,165,166,167,168],[1,3,4,5,10,11,12,14,17,19,20,21,24,26,27,28,29,33,34,36,39,41,42,43,49,50,52,55,57,58,59,63,65,68,69,72,74,77,79,80,83,86,88,90,91,96,98,100,101,103,106,107,109,113,115,118,119,121,122,124,125,127,128,132,136,137,138,139,140,143,144,147,149,150,151,152,153,156,157,158,167],[24,38,50,123,125,134,135,136,140,141,145,146,147,148,155,157,158,160,161,165],[0,3,4,5,9,11,16,19,22,23,24,25,27,28,29,30,35,37,38,40,41,43,44,46,47,48,49,53,54,55,59,60,62,63,64,65,66,68,72,74,75,76,77,78,80,82,84,85,86,89,90,93,94,96,98,100,101,102,103,105,106,108,109,113,115,116,117,118,119,125,130,133,134,136,137,138,139,140,141,143,145,146,148,153,157,159,161,163,164,167],[0,2,3,6,9,14,16,19,23,24,28,29,32,33,34,35,36,38,42,43,44,46,48,49,54,56,57,58,59,61,63,64,65,66,67,68,70,73,74,75,77,78,81,84,85,86,87,89,91,93,94,95,96,98,99,100,101,105,106,107,108,109,110,113,114,115,119,120,122,123,125,127,129,131,132,137,138,140,142,144,150,152,155,156,158,159,161,162,163,164,165,166,167,168],[0,1,3,5,6,7,8,12,13,15,17,19,23,24,27,28,29,30,32,37,38,39,40,43,46,47,49,51,52,55,56,57,60,62,63,64,66,68,69,70,72,76,77,78,79,80,82,84,87,88,89,90,93,98,101,102,103,107,109,112,114,115,119,120,123,126,127,128,129,132,136,137,140,143,147,149,155,156,160,165,167,168],[4,7,10,11,13,15,16,18,19,20,21,24,27,31,32,35,37,43,44,46,49,50,51,52,53,54,55,57,58,59,62,63,66,68,73,78,83,85,88,89,94,98,99,100,102,104,106,110,112,115,116,117,118,119,121,122,125,127,130,132,133,134,136,139,140,143,145,146,147,150,152,153,156,159,162,163,164,166,168],[4,5,9,11,13,14,17,20,23,25,26,27,28,31,33,34,36,39,48,49,54,55,57,59,61,64,65,66,67,68,69,70,73,75,78,80,82,83,86,87,88,89,91,93,94,96,97,98,99,102,103,110,113,115,116,119,120,123,130,131,132,135,139,141,146,147,149,152,156,158,160,162,163,164,166,167],[0,5,10,12,13,14,17,19,20,25,26,29,31,32,36,40,41,43,44,45,48,50,51,52,55,57,58,60,61,64,66,67,68,71,72,73,75,76,77,81,84,85,87,88,89,91,96,97,98,102,104,109,114,116,117,118,122,125,127,128,130,135,136,141,143,145,146,147,149,151,152,157,158,162,163,166,167],[24,38,57,123,124,125,132,133,137,138,141,143,144,147,149,158,160,161,164,165],[1,2,3,5,8,10,11,13,14,15,16,19,21,24,26,27,28,31,34,36,37,39,42,46,51,54,56,57,62,63,65,69,70,71,72,73,74,77,82,83,84,88,90,91,93,95,96,97,98,100,101,103,104,105,107,108,109,110,115,116,117,119,120,123,124,130,131,132,133,134,135,136,139,140,141,143,145,146,147,150,152,153,154,156,158,160,161,162,165,166],[1,3,4,6,8,11,12,15,19,20,21,22,23,24,26,27,29,30,31,32,33,38,40,41,44,45,46,48,51,53,54,57,58,59,61,63,65,67,69,71,72,73,83,88,89,90,91,92,93,94,95,96,97,102,103,104,106,108,110,111,113,114,116,119,121,122,125,127,129,133,136,138,140,141,142,150,154,155,156,157,158,162,163,165,168],[4,6,10,11,13,14,17,19,20,21,22,23,25,26,29,30,35,37,38,40,41,42,45,46,48,50,51,52,53,54,57,61,62,64,71,72,75,79,81,83,86,89,91,96,99,102,103,109,112,113,117,118,122,127,128,129,130,131,132,133,134,135,138,140,142,143,145,146,148,149,151,152,156,158,159,160,161,162,165,166,168],[0,1,2,6,8,9,11,12,13,14,18,19,23,24,25,26,29,31,35,40,41,42,47,51,52,53,54,59,61,63,64,65,66,68,69,71,74,75,77,78,79,83,84,85,86,88,89,94,95,98,103,104,105,107,108,109,110,111,115,116,117,119,120,124,127,132,133,136,138,139,140,141,142,143,144,146,147,152,153,155,160,162,164,166,168],[24,38,62,122,135,136,140,147,159,160,164],[1,7,9,10,11,14,18,19,21,22,23,27,31,33,37,38,44,48,50,57,58,60,61,63,65,66,68,69,70,71,74,75,81,83,86,87,88,93,94,96,97,99,100,105,106,107,110,112,114,115,116,117,118,120,121,122,123,125,128,133,137,138,140,141,145,146,147,148,149,151,155,156,157,160,163,166],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,123,124,125,127,131,135,136,138,141,147,153,156,157,158,159,160,161,163,164,166,167],[0,1,2,3,4,6,9,11,12,13,14,15,16,18,19,25,26,27,28,29,31,33,36,37,38,40,41,43,44,48,49,51,52,55,56,58,59,62,64,67,68,69,70,71,72,74,76,77,78,80,82,83,85,92,95,97,98,102,104,107,108,109,111,114,115,116,119,121,122,123,124,125,129,133,135,137,141,143,145,149,150,151,152,154,156,157,158,160,162,163,166,168],[0,1,3,6,11,15,18,19,20,21,23,24,27,30,31,33,34,36,37,39,40,41,42,46,48,49,50,52,53,54,59,60,61,63,64,65,68,69,71,73,75,79,83,86,88,89,90,91,92,95,96,97,99,100,101,103,104,105,106,111,114,118,120,121,122,124,126,127,128,129,130,132,136,137,140,141,144,145,147,148,149,150,152,153,154,156,159,160,161,164,167],[0,2,3,4,9,10,11,13,16,17,23,24,27,28,30,31,34,36,37,38,40,41,42,49,50,51,53,56,58,59,60,63,64,65,66,69,70,72,74,75,78,81,83,85,86,87,88,90,92,94,95,96,101,106,111,115,118,121,122,123,124,125,128,130,131,133,137,138,139,140,141,143,144,145,148,149,150,154,155,156,162,164,167,168],[0,2,4,5,6,7,9,11,12,13,14,15,18,19,21,22,25,29,33,34,37,39,42,45,47,49,50,51,52,53,54,56,58,59,60,61,63,64,66,67,69,71,72,75,79,81,87,89,90,91,92,96,97,98,99,101,105,106,110,113,114,116,117,120,121,122,124,125,126,127,131,132,134,135,137,138,140,142,143,147,152,153,160,161,167],[3,5,9,10,11,14,16,18,19,23,24,25,27,29,30,33,34,36,37,44,47,53,54,55,57,58,64,66,72,76,77,78,81,83,84,86,88,89,90,91,96,98,99,100,101,102,105,106,107,108,109,111,115,116,118,119,121,122,125,126,127,128,131,135,136,138,141,143,146,151,156,164,165,166,168],[1,2,4,6,8,9,10,11,14,15,16,17,18,19,20,21,25,26,30,32,35,37,38,44,45,46,47,48,49,52,53,54,57,59,61,64,65,66,67,68,69,70,71,72,74,75,77,79,82,84,85,90,91,93,94,95,96,98,100,103,105,107,108,111,114,115,116,117,118,119,122,123,128,130,131,132,133,134,135,136,138,139,143,144,148,153,154,155,156,159,160,164,167,168],[0,2,4,7,8,9,10,11,12,13,16,17,18,20,21,26,28,30,33,39,40,43,45,46,49,50,52,54,55,58,59,60,61,62,63,70,72,74,78,80,82,83,90,92,94,96,97,98,99,102,103,108,109,111,113,115,116,119,121,123,124,125,127,135,136,137,139,140,141,142,146,148,153,155,156,157,158,160,162,164],[0,2,3,4,8,9,10,12,13,15,17,18,19,20,22,23,24,25,27,30,37,38,42,44,45,49,50,51,53,55,58,63,64,65,67,72,73,76,79,83,84,88,90,91,92,93,94,95,97,101,102,106,108,109,110,111,113,114,115,116,118,119,120,125,127,130,132,134,135,136,138,140,141,143,145,146,150,151,153,154,156,158,161,162,163,164,167],[6,7,8,9,10,11,12,13,17,18,19,20,22,24,27,30,31,33,35,37,38,41,43,45,46,47,48,49,50,51,54,55,56,57,58,59,68,69,74,75,76,77,79,81,83,84,86,88,90,94,95,97,98,100,102,104,105,106,107,108,109,111,118,119,120,121,124,127,130,131,132,139,143,146,147,148,149,150,151,152,155,159,160,163,164,165,167],[1,5,9,10,11,13,14,15,16,19,21,22,23,24,26,27,31,34,38,40,41,42,44,45,46,48,49,51,54,59,60,61,62,63,64,66,67,68,70,71,73,74,75,77,79,80,82,85,86,87,88,90,91,94,95,96,97,98,100,101,102,103,104,105,106,111,112,113,115,118,120,121,122,123,127,129,132,133,135,137,142,143,145,149,150,151,152,154,155,156,161],[149,153,154,168],[0,2,3,4,11,14,19,20,21,23,25,28,31,32,34,35,37,38,40,41,42,46,48,49,51,52,53,57,58,59,61,63,67,68,69,70,71,72,73,74,79,80,82,83,86,90,91,92,94,95,96,98,99,100,105,108,112,113,114,118,120,121,122,124,125,127,128,129,130,132,133,135,137,138,139,140,142,145,146,147,148,149,150,152,154,159,160,164,167,168],[24,38,79,134,135,139,140,147,148,149,155,159],[2,4,6,7,11,13,14,15,16,20,21,22,26,27,29,32,34,35,37,42,43,44,46,47,48,50,56,58,60,61,62,69,70,72,73,74,76,78,79,80,81,82,83,84,87,88,89,90,91,92,93,94,95,98,101,104,106,107,108,109,113,114,115,116,117,118,124,127,131,132,137,140,145,146,148,149,151,152,153,154,157,158,159,160,162,163,165],[0,7,8,9,11,12,14,15,17,19,20,21,23,25,26,28,35,38,39,40,41,42,43,44,46,47,48,50,55,58,59,61,62,63,64,66,71,73,74,77,80,81,83,84,85,86,87,88,90,92,93,99,101,102,103,105,106,107,108,109,110,114,117,121,126,128,129,131,132,133,134,135,142,143,146,147,148,149,151,153,157,162,163,168],[0,1,8,11,12,14,16,17,18,19,20,21,25,27,28,30,32,34,36,40,41,47,49,51,52,54,55,56,57,60,61,62,64,67,68,70,71,72,73,74,78,79,81,82,84,85,86,87,88,89,93,94,97,99,101,102,103,106,107,112,115,117,119,121,122,123,124,125,128,129,135,139,140,144,147,154,155,156,160,164,165,168],[2,4,5,6,8,10,11,12,19,20,21,23,25,26,27,31,33,34,40,42,43,44,47,48,49,51,57,58,59,61,63,66,70,71,73,74,75,80,83,84,85,86,87,89,92,93,95,96,98,99,101,102,107,110,113,114,115,116,118,119,121,122,125,127,129,135,136,139,143,144,147,149,154,158,165],[87,123,125,143,145,149,157,158,159,160,165,167],[1,2,4,5,6,7,10,11,12,14,18,20,22,27,32,33,34,35,39,40,41,43,44,46,47,48,49,51,52,54,56,60,61,62,63,64,65,67,68,71,73,74,76,78,79,80,86,88,89,92,97,98,100,101,102,105,106,108,109,110,111,112,113,117,119,122,140,141,145,148,151,158,159,160,161,163,168],[0,1,2,3,4,6,8,11,14,15,18,21,22,24,25,27,28,29,30,31,32,33,34,36,39,40,42,43,46,47,50,53,55,57,58,59,60,61,63,64,68,69,70,71,72,74,76,78,83,87,88,89,90,93,94,96,97,98,99,101,103,105,107,114,115,116,119,120,122,123,127,129,132,133,134,137,141,142,143,144,147,148,149,150,151,152,153,154,157,163,164,166,167,168],[0,1,2,3,4,7,8,11,16,17,18,19,21,22,24,25,26,32,34,35,36,37,39,40,41,42,45,47,48,58,61,67,68,71,72,73,74,75,79,82,85,86,87,88,89,101,102,104,107,108,109,110,112,113,114,115,117,118,121,124,125,126,128,129,131,132,135,137,138,139,140,145,146,148,150,151,152,153,156,163,165,168],[5,6,8,9,10,11,13,14,17,18,25,26,28,29,30,32,33,36,37,38,40,44,45,48,49,51,53,56,57,58,60,62,65,66,67,68,69,70,76,77,78,79,82,86,89,90,93,96,97,101,103,104,106,108,109,111,113,115,116,117,120,122,126,127,128,130,133,135,136,137,139,141,142,145,146,147,149,150,154,155,157,158,163,164,165,166,168],[0,3,8,11,18,19,20,22,26,27,28,29,31,36,37,40,44,45,46,47,48,49,51,52,54,55,56,57,59,60,63,65,68,69,70,72,73,74,80,81,83,84,85,86,89,91,96,99,100,101,102,104,105,108,110,114,115,117,119,120,121,122,123,125,127,129,130,131,132,134,136,139,140,142,144,145,147,149,151,152,153,155,156,157,159,161,162,163,166,168],[0,1,3,5,6,7,9,12,13,14,16,17,20,24,25,30,32,37,38,39,41,42,47,50,51,52,54,55,57,59,60,61,63,66,67,68,72,73,76,82,84,87,88,89,90,91,93,94,96,98,99,100,101,102,104,105,107,109,110,112,114,115,119,123,124,125,126,127,129,131,134,135,136,137,140,141,144,145,149,151,153,157,159,162,163,165,167,168],[0,3,6,7,8,10,16,17,19,21,22,25,26,27,30,32,33,34,35,36,37,41,44,45,46,47,48,49,51,53,56,57,58,61,64,65,67,68,70,71,72,73,75,78,79,80,83,85,90,91,92,95,96,97,100,103,104,106,108,109,110,111,112,115,116,117,120,121,123,124,125,126,127,130,132,137,140,142,146,147,148,151,153,155,156,157,158,160,163],[2,3,4,6,8,9,10,11,12,15,19,21,22,25,30,31,32,33,34,37,38,39,43,45,48,49,50,52,59,60,63,65,68,69,70,76,77,79,80,81,82,84,86,87,91,92,93,94,95,96,97,99,102,104,106,108,109,111,112,115,122,123,124,125,129,131,132,133,134,136,137,138,141,142,144,147,148,149,151,152,153,154,156,157,159,160,161,166,168],[0,1,3,5,11,12,16,18,19,20,21,23,24,25,26,27,30,31,32,35,36,37,38,39,41,43,47,48,49,53,55,60,62,64,65,68,70,77,80,85,87,88,89,91,92,93,94,96,97,98,99,102,103,107,109,110,111,112,113,115,116,118,119,120,123,125,126,127,128,130,131,132,133,136,137,140,141,143,145,146,148,153,154,160,161,164,165,168],[0,7,11,12,16,18,20,21,23,25,27,28,29,30,31,32,34,42,43,44,48,50,52,53,54,56,57,60,63,64,65,66,67,68,73,77,78,79,80,82,84,87,93,94,95,96,98,100,101,102,103,106,108,110,111,113,116,117,119,121,125,126,130,132,133,134,135,136,137,138,140,142,143,144,145,147,149,151,152,153,154,157,158,160,162,165,166,167],[1,5,6,7,9,13,14,15,16,19,21,24,25,26,27,28,29,30,31,32,33,34,35,36,38,40,45,49,50,51,53,57,58,59,61,64,69,70,71,73,74,75,76,77,81,83,84,88,90,92,96,98,99,105,106,107,108,110,111,112,117,120,121,124,126,128,129,130,132,135,136,137,138,141,142,143,144,145,147,149,151,152,158,164,165,168],[0,3,5,7,14,15,17,18,19,20,22,29,30,31,33,34,36,38,39,40,41,44,45,47,48,51,53,54,55,56,57,60,61,63,65,67,68,72,73,74,75,76,78,80,81,83,91,93,95,96,97,100,102,103,105,107,108,114,115,120,125,126,128,131,132,133,134,136,140,142,143,144,147,148,150,152,156,158,163,165,167,168],[0,1,2,3,4,5,6,7,8,9,10,11,17,18,19,20,23,25,26,29,31,32,36,37,38,40,41,44,45,46,48,50,52,55,57,58,60,66,67,68,69,70,71,72,73,74,75,76,77,80,81,85,87,88,92,93,95,98,99,100,101,102,104,106,109,111,112,114,116,118,121,123,126,127,130,140,141,144,145,146,147,150,153,155,157,158,159,160,163,165,166,167,168],[123,136,137,138,139,140,148,149,151,153,154,157,159,162,163,166],[1,5,6,7,8,9,10,14,16,19,21,26,30,37,39,40,41,42,44,45,49,50,51,53,55,59,60,61,62,63,64,68,70,72,73,77,82,83,84,85,86,88,89,91,92,93,95,96,97,99,100,101,102,109,110,112,113,114,118,120,123,124,129,130,131,133,134,135,136,138,139,140,141,142,144,145,147,148,150,151,152,153,154,163,165,168],[0,1,3,5,6,7,8,9,11,12,17,18,19,20,21,23,24,28,30,33,34,36,37,39,40,42,44,45,46,48,49,53,54,56,57,58,59,60,62,64,65,69,70,72,73,74,75,76,77,80,85,87,91,92,94,95,96,100,101,103,106,107,108,114,117,118,119,120,123,125,126,127,130,137,138,139,143,145,146,147,149,152,153,154,156,158,161,164,167,168],[2,4,10,12,17,18,19,20,21,23,24,25,26,27,28,30,31,32,33,35,36,37,39,41,43,44,45,46,52,54,60,63,64,65,68,71,72,75,77,80,81,82,84,87,88,89,91,92,93,97,98,99,102,103,106,109,114,117,118,119,120,129,131,133,136,139,142,143,149,150,151,153,154,155,157,158,160,161,162,164,166,168],[24,111,149,158,160,162,163,164],[5,7,12,14,16,19,20,21,24,27,29,30,31,32,34,37,40,41,42,45,47,49,54,56,67,69,70,71,72,74,78,79,80,83,84,86,87,92,94,98,99,100,104,106,108,109,110,111,114,120,122,133,134,135,138,141,142,144,145,146,147,149,153,154,155,156,161,162,163,166],[0,1,2,4,5,7,8,10,11,12,16,17,18,22,24,26,27,29,30,31,33,34,39,40,42,43,45,47,50,57,58,59,61,63,66,73,74,77,78,79,83,84,86,87,89,93,94,95,97,100,107,110,111,117,118,119,120,122,123,126,127,128,131,132,133,136,141,145,146,148,150,151,153,154,156,157,158,159,160,162,163,164,166],[1,5,6,7,9,10,11,12,14,15,16,17,18,19,22,25,27,28,29,37,39,40,44,46,51,55,59,60,61,63,66,70,73,75,76,77,79,80,82,84,86,87,88,92,93,94,99,102,103,104,108,110,111,112,115,117,118,119,120,121,122,126,131,136,137,138,139,140,144,145,148,149,150,152,154,156,158,159,162,163,165,167],[0,1,3,6,8,12,17,18,21,22,23,24,25,27,29,31,33,35,38,39,40,42,43,44,49,53,54,56,57,59,63,66,68,69,70,71,72,73,74,75,78,82,83,86,88,89,92,93,94,95,96,100,103,105,106,107,109,110,111,114,117,119,120,121,124,126,127,128,131,134,135,136,137,139,140,141,142,143,146,152,153,154,156,157,160,167,168],[0,1,2,4,5,6,8,9,10,12,13,14,16,17,18,20,21,22,24,25,26,28,29,31,32,33,34,35,37,39,41,42,43,45,48,52,56,60,63,66,68,69,70,72,74,76,79,81,82,84,85,87,90,94,95,97,98,99,100,105,106,107,108,111,112,118,119,123,128,129,132,134,135,137,138,139,142,146,147,150,152,156,157,161,165],[1,6,8,9,10,12,16,18,19,22,24,25,26,29,30,35,42,43,44,48,50,52,53,55,56,57,58,59,60,63,64,65,69,70,71,73,75,76,77,78,79,80,81,84,86,88,89,90,91,92,97,102,103,107,108,111,113,116,117,120,123,124,125,126,127,130,131,133,134,135,137,143,145,148,150,151,153,158,159,160,161,162,163,164,165,166,168],[0,1,3,4,5,6,7,8,10,12,13,14,15,16,18,20,21,22,23,26,34,36,43,45,46,47,48,49,50,52,58,60,62,65,68,69,70,73,74,78,79,80,83,84,86,87,90,91,93,94,98,99,101,102,103,104,105,108,112,113,117,118,120,121,125,126,127,129,130,131,135,136,140,147,148,149,150,153,155,157,160,162,163,165,168],[0,2,5,8,9,10,13,16,19,20,21,23,28,30,33,35,41,43,46,52,54,60,62,64,65,69,71,73,74,75,77,80,81,82,83,85,86,91,95,96,98,99,100,101,102,106,108,112,113,115,117,118,119,121,124,129,130,132,134,137,138,141,144,145,149,152,153,156,157,158,159,167,168],[2,3,4,6,7,8,10,11,15,16,22,25,27,29,30,35,36,37,38,39,40,41,44,47,53,54,55,56,58,60,61,63,64,65,66,67,69,70,71,74,75,78,79,81,82,83,86,87,88,91,95,99,101,104,105,107,108,111,113,114,115,118,120,122,125,128,131,133,135,136,139,140,141,142,147,148,149,151,152,153,160,162,163,167,168],[3,10,11,12,13,16,17,18,19,24,26,27,29,30,31,32,33,39,42,43,54,55,60,61,63,65,67,69,71,72,73,76,78,79,81,85,86,89,91,93,97,98,101,102,103,105,107,109,112,115,117,118,120,121,123,124,132,133,135,136,137,138,139,141,143,144,145,147,150,151,153,159,161,162,163,165,166,168],[0,2,3,4,5,11,12,13,14,16,18,19,21,25,26,30,32,34,36,37,38,39,40,45,46,48,49,51,54,55,56,61,62,64,65,67,70,71,72,76,79,81,82,83,84,89,90,92,94,96,97,98,104,106,107,109,111,115,116,117,118,120,121,122,124,125,126,128,129,133,136,137,138,140,144,145,148,149,150,151,154,156,159,160,162,163,166],[0,2,3,4,5,9,13,14,15,16,17,19,20,21,22,25,27,28,29,31,34,36,37,39,40,41,43,49,52,57,60,63,66,70,72,74,75,76,78,82,83,85,89,90,94,97,98,99,100,102,104,105,106,110,111,112,113,114,118,122,124,125,127,133,138,139,146,147,149,150,152,153,155,156,158,159,160,166],[6,24,123,125,136,138,139,144,145,146,147,148,152,157,159,161,164,165,167],[0,5,7,11,12,13,15,16,17,23,25,28,31,32,33,37,38,40,41,43,44,45,46,51,54,55,56,60,65,66,67,69,70,74,77,78,80,81,82,84,86,87,88,90,92,93,94,95,96,97,99,107,108,109,113,114,115,116,118,119,120,125,127,134,135,137,140,141,146,148,149,151,153,155,157,158,159,161,162,163,164,166,167],[4,7,8,10,11,13,15,16,18,19,20,21,27,31,32,35,37,43,44,46,49,50,51,52,53,55,57,58,59,62,63,66,68,73,78,83,85,88,89,94,98,99,100,102,104,106,110,112,115,116,117,118,119,121,122,123,125,127,130,131,132,133,134,136,139,140,143,145,146,147,150,152,153,154,156,157,158,159,162,163,164,168],[0,1,2,3,6,7,8,13,14,17,18,20,22,25,31,32,33,34,35,38,39,41,43,44,46,49,50,52,54,55,58,59,60,61,63,65,66,69,73,74,77,78,79,80,81,82,85,87,89,90,92,93,95,102,103,106,107,113,114,117,119,120,124,126,128,130,132,135,136,139,143,147,151,152,153,155,157,161,164,165,168],[1,2,4,6,11,12,13,16,18,20,23,25,28,29,30,31,32,33,34,35,38,39,40,43,45,46,47,55,57,58,61,62,64,67,68,72,73,74,75,78,79,81,88,89,92,97,99,101,102,103,104,105,106,107,110,112,115,117,119,122,124,128,130,132,135,140,141,142,143,144,145,146,147,148,150,153,155,157,161,162,164],[1,2,3,7,11,12,13,14,15,16,17,18,19,20,28,29,31,32,35,36,37,38,45,46,53,54,55,56,59,60,61,62,64,65,68,70,71,74,76,78,80,84,85,88,90,91,95,96,98,99,100,101,103,105,110,114,117,120,121,123,127,128,129,130,133,135,139,140,141,143,144,147,148,149,150,151,152,154,155,158,162,165,166,167,168],[0,1,6,7,14,16,17,19,20,21,24,25,26,27,32,33,34,36,41,42,45,46,48,50,52,54,57,59,60,63,64,67,68,70,72,74,78,80,81,84,86,88,90,91,92,93,94,95,98,99,100,101,103,104,105,106,107,112,113,116,117,121,128,129,130,135,136,137,138,139,141,142,144,146,147,148,150,151,153,154,155,156,157,158,162,164,165,166],[0,3,4,5,8,10,15,16,19,22,23,24,26,28,29,30,32,33,38,39,40,42,43,47,49,50,51,52,53,55,56,60,61,63,65,66,67,68,69,71,72,75,77,79,80,81,82,85,88,89,90,95,96,98,100,101,102,103,105,106,110,113,115,116,117,118,119,120,121,123,124,125,127,128,131,132,133,135,136,138,141,143,146,151,153,154,155,156,160,162,164],[0,1,3,6,8,9,10,15,19,21,22,23,24,26,27,31,34,38,40,41,42,44,45,46,47,49,50,51,53,54,55,56,58,59,60,63,67,71,72,74,75,78,82,84,88,94,98,100,101,103,105,108,110,113,114,115,116,121,122,123,124,126,128,131,132,133,136,139,140,143,149,150,151,152,153,154,158,162,164],[0,3,6,7,8,10,12,13,14,15,16,18,21,23,24,25,28,30,33,34,37,39,40,41,42,44,47,49,50,51,52,53,54,57,58,59,64,65,66,69,70,71,72,73,75,77,83,84,88,89,90,93,95,96,98,100,101,102,108,110,111,114,115,117,118,122,125,129,132,133,135,136,138,141,143,145,147,151,153,154,155,157,158,163,168],[0,1,6,7,8,9,10,11,12,13,14,15,16,18,19,20,23,25,27,28,29,31,32,33,39,42,43,46,48,50,52,55,56,58,61,70,71,75,77,80,82,85,86,89,92,93,95,96,97,98,99,103,104,107,109,110,112,114,116,118,120,122,123,125,126,128,129,134,135,138,141,142,143,145,146,147,151,153,160,161,165,166],[10,11,14,15,16,17,20,22,23,24,25,26,27,32,34,37,38,39,41,42,44,46,48,50,52,54,57,58,61,70,71,73,74,76,81,82,86,87,88,89,91,92,93,95,96,98,101,103,104,106,108,110,113,114,117,118,122,124,125,127,128,134,135,138,139,140,142,145,146,148,149,151,152,154,156,158,160,161,163,168],[21,38,111,129,132,133,134,137,138,139,140,141,146,147,148,149,153,154,158,159,160,161,162,167],[2,4,5,6,9,10,11,12,14,15,16,17,19,20,21,24,28,29,30,31,35,39,41,45,47,48,49,51,56,61,65,66,67,69,70,72,74,75,78,81,84,85,86,91,93,96,97,98,102,103,105,109,110,112,113,114,116,117,119,120,121,122,124,128,129,130,134,135,137,140,142,143,145,147,148,149,150,152,154,156,160,163,166,167,168],[0,1,2,4,9,10,11,15,16,17,19,21,23,24,26,27,29,33,34,39,40,41,42,43,44,46,47,49,50,52,53,55,60,65,66,71,72,73,74,75,76,78,79,81,82,83,88,93,94,95,96,100,101,102,106,108,110,113,116,117,119,120,121,124,126,127,134,137,139,140,142,143,144,148,149,151,153,156,157,160,161,162,163,164,167,168],[0,7,8,9,10,13,14,15,16,19,23,24,27,28,31,32,34,38,42,43,44,46,47,48,50,55,56,57,61,62,66,67,68,74,75,79,80,81,83,84,86,96,107,108,113,114,115,116,117,118,120,121,122,123,125,127,128,131,132,133,136,139,140,143,147,148,149,153,154,155,156,158,159,165,166,167],[0,2,3,4,5,6,8,10,11,15,16,20,21,23,26,27,28,30,33,34,36,37,41,43,48,50,54,55,57,58,62,63,64,67,74,77,79,84,87,88,89,91,93,95,96,98,99,103,104,108,109,111,112,118,120,121,123,124,125,126,128,132,133,135,136,137,139,140,141,143,144,145,146,147,149,151,153,155,156,159,160,161,164,167],[1,6,8,10,11,14,16,17,18,21,22,23,24,25,28,31,33,34,35,37,38,39,42,43,45,46,47,48,51,52,53,54,55,56,58,64,66,68,69,72,74,76,77,78,82,89,92,93,95,98,101,104,108,109,110,113,114,115,116,117,118,120,121,122,128,130,133,135,138,139,141,142,143,144,145,153,154,155,156,161,162,164,167,168],[27,38,123,124,125,132,133,136,140,143,144,147,161,165],[0,1,2,3,4,6,9,10,12,13,21,23,27,28,29,30,31,32,34,37,38,39,41,42,43,44,45,48,49,51,52,54,56,63,65,66,67,68,69,72,74,75,77,83,86,89,90,95,96,97,98,99,100,102,103,105,106,108,109,111,117,119,121,122,123,125,127,134,135,139,140,142,147,149,153,154,158,161,162,164,165,168],[0,1,5,6,8,9,13,14,17,20,21,22,23,25,27,28,30,31,38,39,41,42,43,44,45,46,47,51,52,56,57,58,61,62,65,66,67,70,73,74,80,82,87,89,90,91,92,93,101,103,104,107,108,109,113,114,118,119,120,121,124,125,126,127,129,130,131,132,133,135,137,146,147,150,156,157,160,163,164,165,167],[1,2,4,5,8,11,14,15,17,19,20,21,22,23,24,26,30,32,36,37,38,39,40,44,45,47,49,55,57,62,64,66,67,68,69,71,76,77,81,82,85,86,87,90,92,93,96,98,105,106,108,109,111,113,114,116,117,122,127,131,132,133,134,135,141,142,143,144,147,148,150,151,154,159,161,162,163,164,165],[2,4,6,7,8,9,10,12,16,18,19,20,21,23,30,32,34,36,37,38,39,40,42,46,48,49,50,51,53,54,61,63,66,67,69,70,73,74,75,77,80,85,86,91,93,94,95,96,100,101,102,106,109,115,116,120,122,124,125,126,129,130,136,137,138,139,140,143,144,146,147,149,151,155,156,158,161,162,163,167,168],[0,1,3,7,8,9,10,12,13,15,19,20,21,23,24,26,30,32,35,38,39,42,46,48,49,50,54,59,62,63,65,66,67,68,73,74,76,77,79,80,82,84,86,87,88,90,93,94,97,101,102,103,104,106,107,109,110,111,113,114,115,117,121,122,124,126,130,131,134,135,136,139,140,141,144,145,146,147,148,149,150,152,153,154,156,158,159,162,164,165,166,168],[0,1,3,5,8,9,11,13,16,23,25,26,27,28,29,31,32,38,39,40,42,47,52,54,56,57,58,59,61,65,67,68,69,70,71,72,73,77,78,79,80,82,84,85,86,87,89,92,95,96,97,99,101,105,106,107,108,109,110,111,113,114,115,116,117,118,122,123,124,125,127,129,132,133,143,144,145,146,148,149,153,155,156,158,161,162,163,164,165,166],[0,1,3,5,8,15,16,18,22,25,26,29,30,31,33,35,36,38,41,42,46,47,49,51,55,56,57,58,59,60,62,63,64,67,68,69,71,73,74,76,77,78,79,80,81,83,85,87,90,95,96,97,99,101,103,107,108,111,113,116,117,119,120,121,125,126,131,132,135,136,137,141,142,143,146,147,148,149,150,151,152,153,157,158,159,163,164,165],[24,36,123,125,144,145,146,147,148,152,157,159,161,164,165,167],[1,5,6,7,8,13,16,17,20,21,22,27,28,30,39,40,44,47,51,52,53,54,59,64,69,73,74,77,78,79,87,90,92,96,101,104,105,107,108,109,110,111,112,113,114,118,120,121,123,124,125,126,127,128,130,132,133,135,137,138,140,141,143,145,147,149,150,152,156,158,160,164,166],[123,154,155,157,166],[1,2,4,5,8,9,13,14,16,22,23,26,27,28,30,31,34,35,36,37,38,39,43,45,47,49,54,55,56,57,58,60,66,68,71,73,74,75,76,77,78,80,82,84,92,94,97,98,102,103,104,105,108,112,115,116,117,120,121,123,125,126,127,128,130,132,133,135,136,137,138,140,141,143,144,147,149,152,153,154,156,157,158,159,161,165,167],[1,3,5,6,8,10,12,15,16,17,18,22,23,24,25,26,27,29,30,33,34,35,36,37,38,39,40,47,48,51,53,55,56,59,61,63,64,66,68,70,74,76,79,80,81,82,83,86,87,88,89,90,91,92,93,94,102,103,104,106,109,110,112,114,117,118,120,123,124,128,130,131,132,136,137,140,141,143,144,147,149,150,151,154,155,159,160,161,162,163,167,168],[0,2,4,7,8,11,12,14,16,19,20,22,25,27,29,34,35,40,42,43,44,45,48,49,50,51,52,53,54,55,56,57,60,61,62,65,67,69,71,73,76,78,79,82,83,84,86,88,90,91,94,95,102,103,110,111,114,115,120,121,124,127,128,132,134,135,136,138,139,140,142,143,144,145,147,151,153,155,157,158,159,160,162,164],[3,5,6,7,8,9,11,13,16,17,20,22,23,27,28,31,33,34,35,37,39,40,41,43,44,46,50,51,52,55,58,59,61,62,64,65,66,67,69,71,72,73,74,75,76,77,78,82,84,85,88,94,95,96,97,99,101,106,109,111,112,113,114,117,118,119,120,121,126,127,128,131,132,137,138,140,142,149,152,155,156,158,161,162,163,165,166],[0,1,2,4,6,7,9,10,11,14,18,21,22,23,24,26,27,28,29,35,36,37,40,41,42,44,46,47,48,50,52,53,55,56,57,60,62,68,70,71,72,74,76,79,80,81,84,86,90,92,95,96,97,99,101,102,103,105,106,107,108,109,111,115,116,118,119,120,121,122,123,125,128,130,132,133,134,135,136,137,138,140,145,147,148,150,151,152,155,156,157,160,163,166,168],[0,1,3,7,8,10,11,13,14,15,16,17,23,26,27,29,30,31,32,33,37,38,39,42,44,46,47,49,53,55,58,62,64,65,67,68,69,72,73,74,75,77,78,80,81,82,84,86,87,88,90,92,94,95,96,97,99,103,104,106,107,109,110,112,113,115,119,120,121,122,123,124,125,126,128,129,131,134,135,136,140,141,142,144,151,152,155,156,157,160,161,162,163,164,165,166,167],[1,2,4,6,9,10,13,15,16,18,19,20,23,25,27,28,30,31,32,33,34,35,39,40,41,44,46,47,56,57,63,64,66,68,70,73,75,76,78,80,81,83,85,86,89,90,91,92,94,100,101,106,107,108,109,110,114,115,120,123,127,130,131,133,134,136,138,139,142,143,144,147,148,149,150,152,154,159,162,163,165,166,168],[2,4,5,7,9,12,14,15,17,18,21,22,23,25,26,28,29,31,32,33,34,35,37,38,39,43,51,52,53,54,55,56,61,63,66,68,69,70,71,75,78,82,83,84,85,87,88,89,90,92,93,95,96,97,99,100,101,104,105,106,113,114,115,116,121,123,124,131,132,133,135,137,138,139,141,143,144,145,148,149,150,155,156,160,161,162,164,166,167],[0,1,2,5,6,7,8,10,11,14,19,20,24,26,27,29,33,34,38,40,41,44,47,49,50,55,58,59,61,64,66,68,69,71,72,73,74,75,77,79,81,82,89,90,91,94,97,98,99,100,101,102,106,108,110,111,113,114,115,116,117,118,122,123,126,128,129,131,132,137,140,143,144,149,151,154,155,156,160,162,167,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,40,41,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,124,127,131,133,136,140,144,146,153,156,159,163,165,166,167],[0,1,2,5,10,13,14,15,16,17,18,19,20,22,23,24,25,27,29,30,33,34,36,37,38,40,43,44,45,46,47,48,49,50,52,53,56,58,62,64,65,69,71,72,75,76,82,83,84,85,86,87,89,90,92,95,96,100,101,103,104,106,107,108,109,110,111,113,114,115,116,117,119,120,123,124,125,126,127,130,131,132,134,135,136,140,141,144,145,146,147,150,152,157,159,160,161,162,167,168],[3,4,5,6,11,15,17,19,20,22,23,24,26,27,28,29,30,32,34,36,37,40,41,42,44,45,49,51,52,57,61,62,63,64,66,67,68,70,71,72,76,80,84,85,87,90,92,93,95,97,100,102,103,107,111,115,116,117,118,120,122,124,125,128,131,142,143,147,148,150,153,154,155,157,160,161,162,164,165,167],[0,1,2,4,8,9,11,12,14,15,17,18,23,25,29,31,33,34,35,37,38,39,40,41,45,46,47,49,50,51,52,53,57,59,60,61,64,66,68,69,73,77,78,81,89,91,92,93,94,96,98,99,102,103,107,108,111,112,113,115,117,120,124,125,128,129,132,133,136,138,140,141,142,143,144,147,149,151,152,155,156,160,161,165,166,168],[0,1,4,7,8,11,14,15,16,20,21,26,27,28,30,33,35,36,39,40,42,43,46,49,50,51,53,56,57,58,61,62,63,64,65,67,69,71,76,78,79,80,81,82,87,89,90,91,92,93,94,95,97,99,104,106,111,112,113,114,115,116,118,122,123,124,125,126,127,129,130,134,135,136,138,139,141,146,147,148,152,154,156,159,160,162,163,164,165,166],[1,5,6,7,9,10,11,13,16,19,21,24,25,28,32,33,35,38,39,43,44,45,47,50,59,62,67,71,73,77,78,79,86,88,89,90,92,93,94,95,97,98,99,100,102,103,105,106,107,109,111,113,117,118,119,121,125,127,128,130,131,132,133,136,139,140,141,144,145,147,149,152,153,154,155,158,161,168],[1,5,6,7,10,15,17,19,20,24,25,27,30,31,32,33,37,38,40,41,43,44,45,46,47,49,50,51,52,59,60,61,63,67,68,69,70,71,73,74,75,76,79,84,86,87,88,92,93,94,96,98,99,101,102,106,111,113,117,118,119,120,125,126,127,128,132,136,137,139,144,145,151,154,155,159],[0,1,3,4,5,7,8,9,10,12,13,14,17,18,19,21,22,23,26,27,28,29,30,33,37,38,39,41,42,43,45,47,51,55,57,59,60,61,63,67,71,72,74,75,76,77,79,80,81,84,88,90,97,101,103,104,105,107,108,109,112,113,114,116,117,118,121,123,124,125,127,129,131,132,133,135,136,137,141,146,150,153,154,155,159,164,165,167,168],[0,3,4,6,10,11,16,17,18,19,22,23,24,26,29,31,32,33,36,37,38,40,43,44,46,49,50,52,56,68,69,70,72,73,76,77,79,81,84,85,86,87,88,89,91,92,93,98,99,100,101,102,103,110,111,112,114,116,119,121,122,123,124,126,129,131,132,135,138,140,141,142,143,144,146,151,152,153,154,160,161,167],[24,58,111,121,122,124,132,133,139,140,145,148,153,154,155,156,157,160,162],[24,38,61,123,125,132,133,134,137,138,139,141,143,144,145,147,149,153,154,157,158,160,161,164,165],[0,1,6,7,8,9,10,11,24,25,28,31,35,37,38,39,40,42,45,47,48,51,52,55,57,59,61,62,63,65,66,68,70,74,75,76,77,80,81,83,85,87,89,90,91,93,95,96,97,98,99,103,104,105,106,107,108,109,110,111,114,115,118,119,120,122,123,124,125,126,127,128,131,132,134,137,140,143,144,145,150,151,152,153,155,156,158,161,164,166,168],[1,2,3,4,8,10,11,13,18,22,24,25,26,28,29,31,32,33,34,35,37,38,41,45,47,48,49,50,54,56,57,59,62,64,66,67,68,72,75,77,78,80,83,84,85,86,90,92,94,97,98,99,100,103,107,112,113,115,116,117,119,121,123,124,126,127,129,132,133,136,137,140,141,142,144,145,150,153,154,157,160,162,163,164,167,168],[1,7,9,10,11,12,13,15,16,17,18,21,25,27,28,31,32,33,35,36,37,39,40,42,44,45,47,48,49,52,55,58,59,60,62,65,66,67,68,70,75,78,79,81,82,84,87,88,89,90,91,93,94,95,96,97,98,100,102,105,106,107,110,113,116,117,118,123,125,129,130,131,132,133,134,135,137,138,141,143,145,148,149,153,156,157,158,159,161,163,165,167,168],[1,6,8,9,11,13,17,20,21,23,24,25,27,28,29,30,32,34,35,37,39,41,42,44,45,46,48,49,50,51,53,56,58,60,61,63,64,66,67,68,70,71,72,73,76,77,78,82,83,84,87,88,89,91,92,93,95,96,97,98,101,102,103,104,115,117,118,119,121,123,128,130,131,133,134,135,137,138,140,151,154,155,157,158,160,163,165,167],[0,1,2,3,4,7,9,10,18,20,22,26,29,30,32,39,40,41,42,45,46,48,52,53,56,57,58,60,62,63,66,67,69,71,73,74,76,77,78,79,82,83,84,91,93,94,96,97,101,103,105,106,112,113,114,115,116,119,123,127,128,129,130,132,133,134,135,136,137,138,139,141,143,144,145,147,149,150,152,154,156,158,159,160,165],[67,111,123,125,129,133,135,136,137,138,139,141,143,145,148,153,154,157,158,159,160,162,165,167],[1,2,4,5,6,7,8,11,12,13,14,15,18,20,22,26,27,30,32,34,35,36,37,41,42,43,44,45,48,49,50,52,56,57,59,61,62,65,68,71,72,76,80,82,83,86,88,90,93,97,98,103,104,105,109,111,112,113,116,118,121,124,125,126,129,132,135,138,141,142,143,145,146,147,149,150,154,155,157,158,159,160,162,163,165,166,167],[1,2,4,5,6,7,9,11,12,13,16,19,20,21,22,23,24,26,28,32,34,35,36,37,38,40,44,45,46,49,50,51,52,53,55,57,60,61,62,63,67,70,71,72,74,75,76,79,81,83,84,85,86,89,92,96,97,98,99,101,102,103,106,107,109,112,113,114,115,116,119,121,122,125,126,129,130,132,134,135,137,138,139,142,144,147,148,149,150,152,153,155,159,160,161,162,163,165,166,167,168],[6,7,10,11,16,17,19,20,21,22,23,24,29,30,31,32,38,39,40,41,44,45,50,51,54,55,63,65,67,68,70,71,72,74,78,79,81,83,85,87,88,91,92,97,99,100,104,106,109,110,113,114,116,118,120,121,123,127,128,130,131,133,136,138,139,143,144,145,146,150,151,155,157,161,162,163,164,166,167],[0,1,6,7,10,11,14,15,16,18,21,23,24,26,28,29,31,32,33,34,35,36,37,42,43,44,45,46,49,50,53,54,57,59,60,63,65,67,69,73,75,77,78,81,82,83,88,89,91,92,95,97,98,101,102,108,109,110,111,112,113,114,115,116,117,118,119,123,126,127,128,129,133,134,135,138,139,144,151,152,153,155,159,160,161,163,167],[0,1,3,7,8,10,11,12,18,19,20,21,22,26,27,28,31,34,36,37,38,39,40,44,47,48,49,51,54,55,56,60,62,66,68,69,72,73,74,76,77,78,80,85,86,87,89,90,91,93,95,97,101,102,106,108,109,110,111,113,117,118,119,120,121,122,127,128,129,131,133,134,136,143,144,145,147,150,153,154,155,156,157,159,161,162,165,166,167,168],[0,1,2,4,5,7,8,10,11,13,14,15,17,18,20,22,23,24,26,30,31,33,35,36,37,39,40,42,43,45,46,47,49,50,51,52,54,59,62,63,64,66,67,69,70,72,73,74,75,76,77,78,79,81,82,84,89,91,99,102,106,113,114,115,116,118,119,124,127,128,129,130,131,132,136,138,139,140,143,145,146,148,149,152,153,156,161,164,167],[0,1,6,7,10,11,12,13,16,17,18,20,21,22,23,31,32,36,37,38,39,44,45,64,65,66,67,72,73,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,93,95,98,99,100,101,103,104,105,106,107,108,109,110,111,121,122,123,126,128,129,130,134,137,138,139,140,142,144,147,152,154,156,157,158,159,162,163,166,167,168],[3,5,6,7,10,12,14,15,16,17,18,19,21,22,23,24,25,27,28,29,30,31,33,36,38,39,40,41,45,47,52,54,61,65,67,68,69,70,71,74,75,78,79,83,85,86,88,89,91,94,95,97,98,99,105,110,111,113,114,115,116,117,118,120,121,122,123,124,125,126,128,129,132,133,134,136,137,138,139,141,142,144,145,147,149,150,152,153,154,155,157,162,164,165,166],[123,127,149,154,157,159,166,168],[0,2,4,5,8,11,12,13,14,15,16,17,18,19,21,22,25,30,33,35,37,39,40,41,42,45,47,48,50,51,52,53,54,56,60,61,62,64,68,69,70,77,78,79,82,83,86,88,92,93,96,97,98,99,101,102,105,106,111,112,114,116,117,120,122,123,125,127,128,129,133,134,135,142,143,144,145,146,148,150,151,153,156,160,161,162,163],[1,5,9,13,16,17,18,19,20,21,22,25,26,28,29,31,35,36,37,38,43,44,45,46,47,49,52,54,55,57,60,62,63,65,66,67,69,72,75,76,78,80,81,82,86,94,96,97,98,105,108,110,112,114,115,117,120,121,122,124,126,127,129,133,135,136,138,143,148,149,150,151,152,155,160,163,166,167],[0,3,5,6,12,13,14,15,16,17,18,19,24,25,26,28,30,31,35,37,38,40,41,42,43,46,47,52,53,55,57,58,60,63,64,67,68,70,71,72,73,74,75,78,85,86,89,90,92,93,98,99,102,104,105,108,109,113,115,117,119,120,123,124,126,128,129,130,133,135,139,142,144,146,148,150,151,152,153,154,157,163,164,165],[0,2,4,5,8,11,12,13,14,15,17,18,20,21,22,23,25,27,28,32,34,35,36,37,38,40,44,45,46,48,50,51,55,56,63,64,70,72,73,74,76,78,80,85,91,93,94,97,98,100,101,102,103,105,106,113,115,118,119,122,130,131,132,133,137,138,140,144,147,149,152,155,156,157,159,161,164,166,168],[12,13,14,15,16,18,21,23,24,25,27,30,31,33,35,36,38,41,42,45,48,49,52,53,54,55,60,61,62,63,64,65,77,79,80,81,84,87,89,91,92,94,96,99,101,102,103,106,107,108,109,111,114,115,118,119,122,123,124,125,126,128,130,131,133,136,137,139,143,145,146,149,151,158,159,160,162,163,164,167],[24,38,81,133,134,135,138,139,140,147,148,149,152,159,164,167],[0,1,2,4,10,12,14,15,16,17,19,21,25,26,28,31,33,34,35,37,39,40,41,42,43,44,47,48,49,50,51,52,55,60,65,66,70,71,73,75,76,78,79,81,82,84,87,88,89,91,94,95,96,100,101,102,103,105,106,107,111,113,116,117,119,123,128,129,132,135,136,137,138,139,141,143,145,148,149,153,155,157,158,159,162,163,165,166],[0,3,5,6,8,11,13,14,16,17,18,19,20,21,22,23,24,33,34,35,39,44,45,47,49,51,53,55,57,59,61,64,65,66,67,70,71,75,77,79,81,86,88,91,92,93,95,97,98,100,103,104,105,106,107,108,109,110,122,123,125,126,127,129,134,136,137,138,140,142,144,146,147,148,153,154,155,156,157,161,162,165,166,167],[0,3,5,6,8,9,14,15,16,17,19,22,23,27,29,31,32,36,37,38,39,40,42,45,46,49,51,52,56,57,58,59,64,65,68,69,71,72,74,75,76,77,80,81,84,88,89,91,92,94,96,97,100,101,106,107,110,112,115,116,119,121,122,124,126,127,129,137,141,145,147,151,152,155,156,157,160,162,167,168],[2,4,5,6,9,12,16,20,22,23,24,25,26,28,30,32,33,35,38,41,44,46,47,49,53,54,56,57,59,60,61,62,64,65,67,68,69,70,71,76,77,79,80,82,88,89,90,91,92,94,95,96,100,102,103,104,106,107,109,110,112,113,115,119,120,121,122,124,128,129,130,131,132,143,149,150,151,152,153,154,157,160,161,162,163,164,167],[0,1,2,4,5,7,9,10,11,12,14,15,16,17,18,20,21,23,24,25,26,27,28,29,30,32,34,40,45,46,48,49,51,52,53,54,55,57,58,59,60,65,66,67,69,70,73,75,76,77,81,83,84,85,91,93,94,95,98,100,101,102,105,109,110,111,114,116,117,118,121,124,125,126,129,130,133,135,139,140,141,142,143,145,146,149,152,155,156,157,160,161,162,163,164,165,166,167,168],[0,2,3,4,5,6,8,9,10,13,16,19,22,26,29,30,31,32,33,34,39,40,41,42,43,45,46,47,48,51,54,56,57,58,59,60,64,66,70,73,74,78,80,83,86,87,91,93,94,99,101,105,106,107,110,111,112,113,115,117,118,119,121,122,123,125,126,131,132,140,141,143,145,147,153,156,158,160,162,164,165,168],[2,4,5,6,8,10,11,12,19,20,21,23,25,26,27,31,33,34,40,42,43,44,47,48,49,51,57,58,59,61,63,66,70,71,73,74,75,80,83,84,86,87,92,93,95,96,98,99,101,102,107,110,113,114,115,116,118,119,121,122,123,124,125,129,135,136,139,142,143,144,147,153,157,158,159,163,165,166,168],[38,90,122,135,140,147,148,149,158,159],[0,2,4,7,10,11,17,20,23,24,26,27,28,29,30,32,35,37,38,44,45,47,48,50,52,54,55,56,57,60,61,62,65,67,69,70,71,72,75,76,77,80,82,83,84,85,86,87,93,95,96,97,103,105,107,109,110,114,115,121,123,127,128,132,133,135,136,137,138,139,141,142,144,145,146,152,154,155,157,158,159,166],[24,121,149,151,156,158,160,164],[0,2,4,6,16,18,21,23,24,28,29,30,31,33,34,37,38,39,42,43,47,48,50,53,56,57,58,59,62,63,64,65,70,72,74,83,85,87,89,92,96,99,101,102,106,107,110,111,112,115,116,119,122,127,128,129,130,131,133,134,135,137,138,139,141,142,145,148,149,150,151,152,154,157,158,159,160,165,166],[24,123,126,149,153,157,158,159,160,164,166,167],[2,4,10,12,17,19,20,21,22,26,27,30,32,33,34,35,37,38,39,40,41,42,43,45,49,50,52,53,54,55,56,59,62,63,65,67,68,69,70,71,74,75,76,79,80,81,84,85,89,91,92,93,94,97,98,99,100,101,103,104,105,106,109,111,115,116,118,119,120,121,123,124,126,133,134,138,139,140,142,144,149,150,152,153,154,156,157,158,161,163,166,167],[24,38,96,123,125,147,148,157,161,164,165],[0,1,2,3,4,5,14,15,17,19,21,22,26,28,30,31,32,34,35,36,37,39,42,43,44,45,47,48,51,53,55,56,59,61,63,65,67,68,71,74,75,76,77,78,79,80,83,84,85,86,87,91,92,93,94,95,96,97,99,100,102,104,105,108,109,110,111,114,115,120,125,126,131,132,133,136,140,141,143,144,146,148,150,151,152,153,155,157,160,164,165,166],[10,11,14,15,17,18,19,21,22,24,26,28,29,32,35,36,39,41,43,45,54,55,58,59,62,65,66,69,70,72,73,75,83,86,87,90,91,92,93,94,95,96,97,98,100,101,105,106,109,110,112,114,116,118,122,124,127,128,129,131,133,136,138,140,141,145,149,151,152,153,154,155,156,157,159,160,162,163,164,167,168],[1,3,5,7,12,13,14,15,16,17,22,23,25,26,29,31,35,37,39,40,41,42,43,44,45,46,47,50,51,55,56,58,61,66,67,68,69,71,74,78,79,82,84,85,86,87,90,91,92,93,94,95,96,98,99,101,104,107,109,110,111,114,115,118,119,121,122,123,124,125,126,127,128,132,133,134,135,138,140,142,143,144,145,146,149,150,151,152,153,155,158,159,162],[5,6,8,9,10,11,12,15,16,19,24,25,26,28,29,30,32,33,36,37,38,40,42,43,48,49,50,52,54,55,59,61,62,64,68,69,71,73,74,77,78,80,82,83,86,88,90,91,92,94,104,107,108,109,110,113,114,121,125,128,130,132,144,146,148,153,162,164,165,166,167],[0,1,2,4,5,7,9,13,14,15,18,19,23,25,26,27,32,35,36,37,38,39,40,42,43,45,47,48,49,51,56,61,62,63,65,69,71,72,73,75,76,77,81,84,85,87,88,89,90,93,94,98,100,102,105,108,115,116,117,119,120,123,126,127,129,130,131,133,135,138,144,145,148,150,154,155,156,157,159,161,164,167,168],[1,2,4,5,8,11,12,13,17,18,19,20,21,27,28,31,32,33,35,37,39,40,41,42,44,50,52,59,61,63,64,66,67,70,73,74,76,77,79,80,85,86,87,101,102,103,104,105,106,107,109,112,113,114,115,116,118,123,126,127,129,130,133,134,136,138,146,147,148,149,152,154,155,157,158,160,161],[1,2,4,5,9,11,16,18,20,21,22,23,24,27,29,30,31,33,34,35,40,47,49,50,51,52,53,55,56,60,61,64,65,66,69,74,76,77,78,79,81,83,87,88,90,91,93,95,96,97,98,99,101,108,110,111,114,115,117,118,120,121,122,126,129,130,133,134,136,137,139,142,144,145,147,148,149,150,151,153,154,157,160,161,162,164,168],[0,7,9,10,11,15,18,20,22,23,24,25,27,28,29,30,31,32,33,35,38,40,43,47,48,49,50,51,52,54,58,59,60,62,64,65,68,70,72,73,74,76,77,80,81,82,83,84,86,93,99,101,102,103,104,105,108,109,111,113,118,127,128,129,131,132,133,136,137,151,152,158,159,163,166,167],[0,1,5,6,9,10,12,13,16,22,23,26,27,28,30,32,33,43,45,51,53,55,57,63,65,70,71,72,73,75,76,77,78,79,81,83,85,92,93,95,97,98,100,101,103,104,105,107,110,112,113,117,118,120,128,129,132,133,134,135,137,140,141,142,144,146,147,148,149,152,153,156,158,163,166,168],[3,7,8,9,10,15,16,18,21,24,25,32,35,39,42,44,45,49,50,51,52,57,61,62,63,64,66,67,68,70,71,72,76,79,81,82,83,87,91,93,94,96,98,99,101,103,106,107,108,109,110,112,113,114,116,117,118,120,122,125,126,127,128,129,132,133,134,136,140,142,143,146,150,151,152,153,155,157,158,160,162,164,165,166],[3,5,8,10,11,15,18,20,24,25,26,27,29,31,36,38,39,41,42,47,53,54,55,56,59,62,63,64,67,71,76,78,79,88,91,92,98,100,104,106,107,108,111,115,117,120,122,123,124,125,127,132,134,136,138,139,143,144,146,147,148,149,152,155,158,160,162,163,165,167],[2,3,4,5,6,7,9,11,13,14,16,18,21,22,25,28,29,30,31,35,36,38,39,42,43,44,45,48,49,50,51,52,53,55,57,59,60,63,65,67,68,72,73,74,75,77,78,83,85,86,89,90,91,94,95,96,98,101,102,104,106,108,109,112,113,125,126,130,131,132,134,137,138,140,142,143,144,146,147,151,155,158,159,163,166,167,168],[0,1,5,7,12,15,19,21,22,25,28,29,34,37,38,40,41,42,44,48,49,51,53,59,60,62,65,66,67,68,69,70,72,73,74,76,78,79,80,83,84,86,87,88,89,90,92,93,94,97,98,103,104,107,110,113,115,116,117,123,126,128,129,130,132,133,134,136,142,143,146,147,148,149,150,151,153,154,165,166,168],[0,3,6,7,8,10,18,19,20,23,25,26,27,30,31,32,33,35,37,38,40,41,42,45,47,49,50,51,52,53,55,56,58,59,62,63,67,68,70,71,72,74,78,81,82,83,85,86,87,88,89,90,92,93,97,98,100,101,104,105,106,107,109,111,113,117,118,120,121,124,125,126,128,129,130,134,135,136,138,141,143,147,149,150,155,157,158,161,164,165,166],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,113,114,117,118,121,122,127,131,134,136,137,143,145,148,152,154,155,156,157,158,159,161,163,165,166,167],[0,3,6,7,8,11,14,15,16,17,19,20,23,25,28,30,33,35,36,38,39,42,45,47,48,50,51,54,57,60,61,64,65,67,68,72,74,75,78,81,82,85,88,89,90,93,95,97,98,100,101,106,107,109,110,112,113,114,116,119,120,121,122,123,125,126,128,129,130,135,137,138,139,140,142,143,144,146,147,148,151,153,154,155,157,161,166],[1,3,5,6,9,10,13,15,16,17,19,25,26,27,29,30,31,32,38,42,43,47,49,51,52,54,57,58,60,62,65,66,68,70,72,73,76,77,78,81,82,83,90,91,92,95,98,99,100,101,102,104,107,108,110,111,113,117,118,120,127,131,135,136,140,141,142,143,144,149,150,151,152,153,154,155,157,161,163,165,168],[1,3,6,7,10,11,13,15,18,21,23,26,28,31,32,35,37,38,40,44,45,47,49,50,51,54,55,59,61,66,69,71,72,73,74,75,78,86,89,91,92,101,102,109,110,111,112,115,117,118,119,120,121,123,127,129,130,133,134,137,139,140,141,144,145,146,147,152,153,154,155,158,159,160,162,164,166],[24,117,123,125,136,137,139,140,141,143,145,148,157,159,164,165,167],[0,2,4,6,8,9,10,11,12,13,14,15,25,27,30,31,33,35,36,38,40,41,42,43,48,49,50,51,54,57,59,60,62,64,66,68,70,71,72,73,74,75,76,77,78,79,80,81,82,84,86,88,90,94,98,99,100,101,104,105,110,111,113,114,116,118,119,120,121,122,124,127,129,134,137,138,140,143,144,145,146,150,151,153,154,155,156,157,158,159,160,165,168],[1,7,8,14,16,17,18,19,20,22,23,24,26,28,31,32,35,39,41,42,46,48,49,53,54,58,59,61,62,66,67,69,70,72,76,78,79,83,84,87,90,91,93,94,95,99,101,105,106,107,108,109,112,114,115,116,117,118,119,121,127,128,129,135,136,137,140,141,142,146,147,150,151,154,155,156,157,158,159,160,161,162,164,166],[0,1,2,5,6,8,9,12,13,16,17,18,26,30,31,34,36,46,47,52,53,54,57,59,60,62,63,64,65,71,73,75,78,79,82,83,86,87,90,91,93,95,97,98,100,105,107,109,111,120,124,127,128,129,131,132,134,137,139,143,144,145,146,147,148,149,151,153,154,155,157,158,159,161,168],[0,1,4,5,6,8,9,11,13,16,18,20,21,23,25,26,29,30,31,32,35,36,37,38,40,41,42,43,45,48,50,52,53,55,56,57,61,62,64,65,66,67,69,73,76,77,78,82,83,85,87,90,91,93,94,97,98,99,103,104,105,106,109,110,111,113,118,120,122,124,125,128,130,131,133,134,135,137,143,146,147,148,149,150,151,155,157,158,159,160,161,166],[0,3,5,6,7,8,10,11,12,16,19,20,22,23,24,25,26,27,28,29,30,31,33,34,40,41,43,44,45,46,51,55,56,57,59,62,63,65,66,67,68,70,71,78,79,80,82,83,84,86,87,89,92,93,94,98,104,105,106,108,109,111,115,116,117,119,123,125,126,127,128,129,130,131,132,133,134,137,141,144,145,147,151,152,153,154,155,159,160,162,163,164,167],[0,2,3,4,6,8,15,17,18,20,21,22,25,28,30,34,36,37,39,40,43,44,45,49,50,54,55,57,59,62,64,65,66,67,69,70,73,74,75,76,77,78,82,83,88,90,91,93,95,99,101,102,104,105,106,108,114,117,120,122,127,128,129,130,131,135,137,138,143,144,146,148,150,153,161,162,167],[5,111,129,133,135,136,137,138,139,141,146,147,148,153,154,161,162,167],[0,1,5,6,7,8,10,14,15,17,19,22,23,24,25,28,29,35,36,38,39,40,47,48,50,51,52,53,54,55,56,57,59,60,62,63,67,69,70,72,75,76,78,81,82,83,86,88,90,91,92,93,95,96,99,100,101,102,103,104,107,116,119,122,125,126,129,130,132,139,140,141,142,143,145,147,151,152,156,157,158,159,162,164,166,167,168],[7,38,111,123,125,132,133,134,135,137,138,139,140,141,143,144,145,146,148,157,161,162,165],[1,2,3,5,10,11,13,14,15,17,18,21,24,26,27,29,30,32,35,36,37,39,40,41,42,44,45,47,51,52,53,55,56,57,58,60,61,64,66,67,68,75,77,79,80,81,85,88,90,91,92,93,98,103,104,105,106,110,111,114,119,122,125,127,128,131,135,136,137,138,140,141,143,147,148,149,150,151,152,153,154,156,159,160,162,163,164,165],[1,2,4,6,10,13,15,16,21,23,24,25,26,30,32,33,34,37,38,39,41,43,44,47,49,50,53,54,56,58,61,64,65,70,71,76,79,80,81,82,83,93,95,96,97,98,99,102,110,111,116,117,121,123,124,125,126,127,128,129,130,131,133,134,135,137,138,139,140,141,142,144,145,147,150,152,153,154,156,158,161,162,163,165,166,167],[1,2,3,7,12,14,15,20,26,27,28,30,31,32,35,36,37,38,40,41,42,43,45,46,50,51,52,56,58,60,61,62,64,65,68,74,75,76,78,79,81,82,89,90,91,95,97,98,99,100,101,102,104,106,107,110,112,113,114,116,121,122,123,129,132,137,141,142,144,145,149,150,151,152,153,154,157,161,163,164,166,168],[11,123,124,125,143,144,147,149,158,159,160,161,165],[3,4,6,7,9,13,14,17,23,24,25,26,28,29,30,32,33,34,35,37,40,42,46,47,49,50,55,56,57,60,62,63,65,67,68,69,71,72,73,74,76,77,78,81,84,87,88,89,91,94,96,97,98,101,107,109,111,113,119,120,122,123,124,126,127,128,129,131,133,134,135,137,138,140,141,143,145,146,147,148,149,152,156,158,159,160,161,163,166],[0,3,10,11,15,16,19,20,21,22,23,24,26,27,28,29,31,32,33,34,37,39,41,42,43,46,47,48,49,51,52,55,57,60,61,62,65,66,67,68,69,72,73,75,76,77,79,80,81,82,83,86,88,95,96,98,100,101,104,105,106,107,108,113,115,116,117,120,122,124,125,127,129,130,132,136,137,140,142,143,146,148,149,150,151,152,153,154,155,156,157,167,168],[1,3,4,6,8,10,12,14,15,16,17,18,19,20,21,22,23,25,26,27,32,33,35,37,40,43,45,50,51,52,53,63,65,66,68,70,72,73,75,76,77,78,79,80,81,82,83,84,85,91,94,95,96,98,101,108,109,110,111,120,123,124,126,127,130,131,133,134,138,139,140,142,143,145,147,151,153,156,162,163,164,166,167,168],[1,2,3,4,5,6,9,12,13,15,16,18,19,21,24,27,29,30,31,32,33,34,36,37,38,39,40,42,47,48,49,50,51,52,55,58,59,61,65,67,68,69,70,71,73,75,77,78,81,83,84,85,86,87,88,91,93,94,95,96,103,107,109,110,111,112,113,115,116,118,119,124,126,128,129,134,135,136,138,143,146,148,156,157,159,160,161,162,163,165,166,168],[1,2,4,5,9,11,17,19,20,22,25,28,30,31,33,36,37,38,40,42,43,44,45,46,47,48,49,51,53,56,57,59,60,62,64,71,72,75,77,78,79,82,87,89,91,93,94,95,96,99,100,101,104,105,109,110,111,112,113,114,115,116,118,120,122,125,130,131,135,137,141,144,145,146,147,150,152,154,155,156,159,160,161,162,167],[1,2,4,5,6,7,8,9,12,14,17,18,22,23,28,30,33,35,37,39,40,42,43,44,45,46,47,48,49,51,52,55,57,60,61,63,65,68,69,73,78,84,85,87,89,93,95,96,98,100,101,106,107,109,111,113,114,116,117,118,119,120,121,126,127,128,129,130,131,132,133,135,137,141,145,150,151,152,153,154,156,161,162,164,165,166],[19,24,38,121,123,125,132,133,135,137,138,140,143,144,146,147,148,149,156,157,158,160,161,164,165],[0,1,2,3,4,5,6,7,10,11,14,15,20,26,27,29,30,31,32,36,37,38,42,43,44,45,46,47,52,53,54,55,56,57,63,64,66,69,71,73,75,76,77,79,82,84,87,89,90,92,96,99,100,103,105,107,109,111,112,115,116,119,120,124,125,126,129,132,133,137,139,143,148,149,150,153,155,157,159,160,163,166,167,168],[1,7,8,9,11,12,16,17,18,25,26,27,28,30,31,32,34,36,37,42,43,45,47,50,51,52,56,58,62,66,67,69,70,71,72,73,75,77,79,83,86,87,88,92,94,95,96,98,99,100,101,102,104,110,115,116,118,119,120,123,124,126,127,128,130,137,138,139,140,141,142,143,144,146,152,155,157,159,160,164,166,168],[0,5,6,7,8,10,11,13,16,18,19,20,23,24,25,26,27,29,30,31,32,37,38,39,41,44,46,47,49,50,51,53,57,61,63,64,65,66,71,73,75,76,80,86,94,98,100,101,106,110,111,112,113,114,116,117,118,120,121,124,125,126,128,129,131,137,139,140,141,142,144,145,150,151,153,154,159,160,161,162,164,165,166,167],[23,111,123,125,136,137,138,139,141,143,144,145,146,148,157,158,159,160,161,162,165],[2,4,8,10,11,15,17,18,22,24,26,28,29,30,31,36,41,42,44,45,46,47,49,50,55,61,65,66,68,69,71,72,73,74,77,78,79,80,81,83,85,86,90,92,93,95,96,97,99,101,102,107,109,113,114,115,118,121,122,123,124,125,126,131,132,133,137,138,140,142,143,144,145,150,155,157,159,162,165,167],[0,2,4,7,8,10,12,15,16,17,18,22,23,24,25,27,29,30,32,35,37,38,39,40,43,45,46,47,54,55,63,64,66,68,70,74,77,78,83,86,87,88,89,90,92,93,94,97,99,100,110,112,113,114,115,116,117,121,125,126,127,128,129,131,133,134,137,139,141,143,145,147,149,151,153,154,161,162,163,165,166],[6,7,8,11,12,14,16,17,18,20,21,24,25,26,27,30,31,33,35,37,42,43,47,48,50,52,54,55,56,57,60,61,62,64,66,69,72,76,78,80,81,83,86,87,88,89,90,91,93,97,99,100,106,107,108,109,110,111,112,114,117,118,122,124,125,126,127,129,130,134,139,141,142,143,146,148,151,152,154,157,160,161,162,163,164,167],[24,28,111,121,122,124,132,133,136,141,145,148,149,153,154,155,156,157,160,162],[0,2,4,5,6,7,9,11,12,13,14,15,16,22,23,27,28,30,33,35,36,38,39,43,44,46,47,48,49,51,53,54,55,56,57,58,60,62,63,64,65,67,69,74,76,79,82,83,87,88,91,92,93,94,96,99,100,101,103,104,106,108,109,110,111,112,114,120,122,123,126,129,130,131,132,133,135,140,142,144,145,146,147,149,150,152,154,155,156,161,165],[6,7,8,11,13,15,17,19,21,22,26,27,28,29,30,31,33,38,40,43,44,47,48,51,53,58,59,62,65,67,69,70,71,72,73,74,77,78,79,80,81,82,84,86,89,90,92,94,96,97,100,101,102,103,108,109,112,115,116,118,120,122,126,129,130,133,134,137,138,143,144,150,151,153,156,161,165,168],[1,3,6,7,8,9,13,15,17,18,19,20,21,22,23,25,26,27,28,30,32,33,35,37,40,44,45,46,47,48,49,51,52,55,56,64,65,67,69,70,72,75,79,82,85,86,87,88,89,90,92,94,98,99,100,102,105,106,108,109,110,111,112,113,114,115,116,119,121,125,129,131,132,134,135,136,137,141,142,143,145,147,152,153,154,157,159,162,163,164,166],[1,3,5,7,10,11,14,15,19,20,21,22,23,24,27,29,32,33,35,36,38,46,47,52,53,55,57,58,60,62,64,66,68,72,75,76,77,78,85,87,88,91,92,93,94,96,97,98,99,100,101,102,103,104,105,110,112,114,117,119,120,121,122,126,127,129,130,131,132,133,134,139,144,147,148,149,150,151,152,153,155,158,159,161,162,164,166],[0,1,2,4,8,10,11,14,16,17,18,20,26,27,29,31,33,35,37,39,40,43,44,45,46,48,49,50,51,53,54,55,56,59,60,61,62,63,65,67,71,72,76,78,80,83,84,85,89,90,95,98,101,104,114,117,121,122,123,125,126,127,128,130,131,135,137,139,140,141,142,145,146,150,151,152,153,154,156,159,163,164,168],[1,2,3,4,5,6,8,9,11,13,18,21,25,26,27,30,32,33,35,37,40,43,48,50,52,53,54,61,62,63,64,67,68,69,71,73,74,77,78,79,80,82,83,84,86,93,94,95,97,102,105,108,109,112,113,114,117,118,119,124,125,128,130,131,132,134,135,137,138,139,141,142,144,146,149,151,152,153,154,156,158,161,162,163,166],[1,2,4,7,8,10,13,15,16,17,18,26,27,28,33,34,35,36,38,42,43,44,45,46,48,51,53,54,57,59,60,63,65,66,68,71,72,73,77,78,79,80,86,87,88,89,90,91,92,93,98,99,100,101,103,104,107,109,110,111,113,115,116,118,121,122,123,124,125,133,134,139,140,142,143,147,149,150,151,156,158,159,162,165],[1,5,6,7,9,10,11,13,17,19,21,22,23,24,28,29,30,31,33,35,36,38,39,40,41,42,44,45,46,48,49,51,52,53,54,59,64,69,75,77,82,83,84,86,87,89,90,91,93,95,99,100,101,103,104,105,107,112,113,114,118,120,121,122,123,125,126,128,129,130,133,137,140,142,143,144,146,148,150,151,155,159,160,162,166],[1,3,6,7,8,9,12,14,18,19,21,23,25,27,29,30,34,37,38,40,42,43,44,45,47,48,50,51,52,53,54,55,56,57,59,60,63,65,66,67,70,71,74,76,80,82,84,88,89,94,97,98,103,104,107,108,109,110,111,117,118,122,124,126,128,129,131,132,133,134,137,141,145,147,149,151,153,155,156,158,159,160,164,165],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,124,125,127,129,131,140,141,144,153,156,157,159,160,161,163,164,166,167],[2,4,5,6,10,15,18,23,24,25,27,30,31,35,39,40,41,47,48,49,51,55,56,57,58,60,61,63,67,68,69,71,73,77,78,80,81,82,83,87,88,89,90,91,92,94,95,99,100,101,103,104,105,106,110,112,113,114,116,117,119,123,126,129,133,134,136,139,140,142,144,145,146,148,149,151,152,156,157,158,159,162,164],[0,1,2,3,4,7,8,9,13,15,17,18,20,21,22,23,24,26,28,31,36,37,39,40,44,48,49,51,53,58,61,63,65,66,67,71,72,76,79,81,86,89,94,96,97,101,103,104,107,111,112,114,116,117,121,124,130,131,132,133,134,145,146,147,151,155,156,157,158,159,160,161,162,164,168],[1,2,4,5,6,7,8,9,10,11,13,14,17,20,21,24,25,30,31,34,35,38,39,42,44,45,47,48,59,60,63,64,70,71,72,73,77,79,80,84,85,87,89,90,92,93,95,96,97,101,103,104,107,111,112,113,114,115,117,118,120,121,126,127,128,130,131,132,134,136,137,138,139,141,142,144,145,147,148,150,151,154,160,162,165],[46,122,123,125,136,141,146,149,157,158,159,161,165],[0,2,3,7,9,15,16,17,20,25,27,29,30,32,37,40,41,45,47,48,50,56,59,60,61,64,66,70,71,73,76,82,83,86,87,88,92,94,95,96,97,99,101,102,103,105,108,109,110,111,113,119,121,124,125,128,129,132,133,135,136,137,142,144,147,148,149,151,153,156,158,159,163,164,167],[0,5,9,10,11,13,17,21,22,23,24,26,27,29,30,31,32,34,35,37,38,39,40,44,46,47,48,49,53,54,55,57,58,59,60,64,66,67,68,72,78,81,85,86,87,89,90,92,93,97,100,105,106,107,108,110,111,112,116,118,119,121,122,123,124,125,126,127,128,129,132,133,134,137,144,145,146,147,148,150,151,153,156,157,158,159,161,162,163,165,168],[0,1,3,4,6,7,8,9,11,13,16,17,21,24,26,31,32,35,36,37,41,43,44,45,46,47,48,49,50,54,55,56,59,60,61,63,64,65,66,67,68,71,72,79,80,81,83,84,85,86,87,88,91,93,96,98,99,102,104,106,107,110,112,114,115,116,117,119,121,122,123,124,126,128,129,130,131,132,135,136,137,138,140,141,143,145,147,148,149,153,154,157,160,161,163,164,165],[1,2,8,9,10,11,12,15,16,17,18,19,21,22,25,26,28,29,30,31,32,34,36,39,41,44,45,47,49,51,54,55,59,61,62,64,68,69,70,71,74,77,78,80,82,83,85,88,89,90,91,92,93,94,96,99,103,105,106,117,118,120,121,122,123,124,126,131,132,136,137,140,141,142,143,146,147,149,150,152,153,156,158,160,161,163,164,166,168],[38,51,111,129,132,133,134,136,138,140,146,147,148,153,154,158,159,160,161,162,167],[0,2,3,4,5,6,8,9,11,12,20,22,23,24,25,26,27,28,30,32,37,38,39,41,42,49,50,53,54,60,65,67,71,72,75,77,78,82,83,85,87,88,89,93,94,96,100,101,103,105,108,109,110,112,113,115,117,118,119,120,124,125,128,129,131,134,136,137,139,145,146,147,148,149,150,152,153,155,157,158,160,162,163,166],[3,4,5,6,11,12,13,14,16,17,19,20,21,23,26,29,32,33,35,36,37,38,42,47,50,52,55,58,60,61,65,66,67,68,70,71,72,77,81,84,88,91,92,94,95,97,98,99,101,102,103,104,106,107,109,113,116,118,119,120,122,124,128,130,132,134,135,137,138,139,140,141,144,145,152,154,155,159,161,163,165,167,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,55,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,125,127,131,134,136,137,145,152,154,155,156,160,163,166,167],[1,2,5,6,8,11,12,15,17,18,19,21,22,25,26,29,32,33,34,36,38,39,41,42,44,47,49,50,52,54,59,61,63,65,66,68,70,72,74,77,80,82,84,87,89,91,92,94,97,98,101,102,104,107,108,113,114,117,118,123,125,127,128,130,132,136,137,143,144,145,147,150,151,152,154,155,156,157,158,160,161,162,164,165,166,167,168],[0,1,2,7,10,12,13,15,16,17,18,19,23,26,28,30,31,34,38,39,43,47,48,49,51,52,53,54,56,58,60,61,63,64,65,67,68,69,70,72,73,75,76,77,78,80,81,82,84,85,86,88,89,94,96,97,99,102,103,104,105,106,111,114,116,117,119,121,125,128,131,132,134,137,138,139,141,143,150,152,153,155,156,157,158,159,160,162,163,164,167],[2,3,4,5,8,9,10,11,16,18,20,22,24,27,28,30,31,32,33,40,41,42,43,46,49,50,53,54,56,60,63,64,66,69,70,72,74,76,77,78,79,80,81,82,83,86,87,91,96,99,101,102,106,107,110,111,122,124,125,130,133,134,136,137,138,140,141,143,145,147,150,153,155,156,158,162,164,165,166],[0,1,2,4,5,6,9,10,11,13,14,15,17,21,24,26,29,32,35,40,44,49,53,54,58,59,62,64,65,67,70,71,75,78,79,80,81,87,88,89,94,96,101,102,105,108,110,111,114,116,117,119,122,123,124,126,127,132,133,134,136,137,140,146,147,148,149,153,154,155,157,161,163,164,166],[0,3,5,6,8,10,13,15,16,17,18,25,29,30,31,33,35,36,39,41,42,44,46,47,48,49,56,57,58,59,60,62,63,64,65,66,67,68,69,72,75,76,77,80,81,84,86,88,90,91,92,94,95,96,97,100,101,105,106,109,110,111,113,115,117,119,120,121,124,127,128,129,130,131,132,133,134,137,140,143,144,145,147,148,149,153,154,156,158,161,162,165,167,168],[0,2,3,4,6,7,9,13,16,19,20,28,33,34,35,36,38,39,40,45,48,50,51,53,56,58,59,62,64,65,66,68,69,70,72,73,75,79,83,84,85,87,88,89,93,94,99,100,101,102,103,106,108,109,112,113,115,118,121,122,126,127,128,129,133,136,137,139,142,146,148,151,152,153,155,157,159,162,163,165],[0,2,4,7,9,10,12,14,17,18,19,20,22,25,27,29,31,32,33,34,35,40,41,42,43,44,45,46,47,54,55,56,57,58,59,62,63,65,67,68,70,74,76,77,79,81,83,85,87,88,93,95,96,97,103,104,105,112,113,114,115,116,117,120,121,125,127,128,129,130,132,135,137,138,139,140,141,144,148,151,153,154,155,156,158,159,160,161,163,165,168],[0,1,2,4,6,7,9,12,13,14,17,23,24,27,28,29,30,31,32,33,34,39,40,41,42,43,45,47,48,49,52,56,58,62,63,66,68,69,70,72,76,82,83,84,87,92,94,95,97,98,99,100,101,104,108,109,114,116,120,122,123,127,130,131,133,134,135,139,141,142,143,145,148,149,151,152,159,162,163,164,168],[5,7,8,10,12,13,14,15,18,21,22,27,28,31,32,33,34,36,40,42,43,44,45,48,49,51,52,55,56,60,61,63,74,78,79,80,83,86,89,91,93,96,97,98,99,100,102,103,105,106,110,111,112,113,116,119,123,125,127,128,129,131,138,139,142,144,148,149,150,151,152,154,155,157,158,160,163,165,166],[5,6,8,9,13,15,20,23,25,28,29,32,33,34,35,39,40,47,49,52,53,55,56,58,59,60,61,66,67,69,72,74,76,77,78,79,82,83,87,89,91,93,95,96,99,104,106,110,111,113,114,120,121,122,124,125,128,131,133,134,135,137,140,142,145,146,149,151,154,167],[24,68,136,138,139,148,152,158,160,164,167],[38,69,111,132,133,134,135,137,138,139,140,141,147,148,149,158,159,160,162],[24,38,70,123,125,136,140,147,149,157,161,164,165],[0,3,5,6,8,11,12,15,24,25,26,27,33,36,37,40,41,42,43,47,49,50,52,54,56,58,60,63,65,66,68,74,77,78,81,82,83,88,89,93,100,101,102,104,107,109,110,113,114,117,118,121,123,126,129,130,134,141,145,147,148,151,155,158,159,165,167,168],[1,2,3,4,9,13,16,17,19,22,27,30,31,33,34,36,37,38,43,44,45,46,47,48,50,51,52,56,58,59,61,63,66,68,69,70,72,73,76,77,82,83,85,86,87,89,91,92,93,94,95,96,98,99,101,103,106,110,115,116,117,118,120,122,124,125,128,129,131,133,134,135,137,139,140,141,142,143,144,145,146,147,148,150,154,157,158,160,161,164,165,167,168],[1,3,5,7,9,11,12,14,19,25,26,27,31,33,35,36,38,39,40,43,44,46,47,52,53,54,55,58,59,62,65,66,69,70,73,74,75,77,78,81,82,83,88,89,90,92,93,94,95,97,99,101,108,109,110,111,120,123,124,125,128,129,131,134,135,139,141,148,149,150,151,152,154,157,158,159,162,163,166],[0,1,8,9,16,19,21,23,24,27,30,32,33,35,36,39,41,43,44,46,47,48,49,50,51,54,55,56,57,58,59,64,65,66,67,68,69,72,73,75,78,80,82,85,87,89,91,93,94,97,99,101,102,103,110,118,119,120,122,124,126,127,128,129,131,132,134,137,138,140,142,143,144,146,148,149,150,151,154,155,156,158,159,160,162,164,165,168],[1,3,6,7,9,11,12,13,17,18,24,25,26,28,29,30,33,34,36,38,39,42,44,46,47,48,49,51,52,59,60,62,63,64,65,66,69,73,75,77,78,80,82,83,87,89,90,96,99,100,101,102,103,104,106,110,111,112,114,116,117,121,122,126,127,128,129,132,133,135,136,139,140,143,144,148,151,152,154,159,160,167],[0,2,3,4,5,6,8,10,11,15,16,20,21,23,24,25,26,27,28,30,33,34,36,37,41,43,48,50,54,55,57,58,62,63,64,67,74,76,77,79,84,87,88,89,91,93,95,96,98,99,103,104,108,109,111,112,118,120,121,122,124,125,126,128,130,132,133,135,136,137,139,140,141,143,144,145,146,147,149,150,151,153,155,157,158,160,161,164,166,167],[3,7,11,12,13,14,20,21,22,24,25,26,28,29,32,33,34,38,39,40,41,43,44,45,47,48,49,51,52,53,54,59,60,61,63,67,70,72,74,78,80,84,85,86,88,89,92,93,94,95,96,97,99,100,101,104,105,107,108,109,112,113,115,118,120,121,122,124,125,128,129,131,132,133,134,135,136,138,139,140,141,142,145,146,147,149,150,152,154,156,158,160,161,162,164,165,166],[2,4,5,6,11,12,13,15,16,17,18,20,21,23,24,26,30,32,34,38,43,47,48,49,51,55,59,60,61,64,69,75,79,80,82,83,85,89,91,93,94,95,96,100,102,104,109,112,114,115,117,118,119,122,125,126,127,133,135,144,145,148,151,153,156,158,159,163,165,166,167,168],[1,3,6,7,10,11,13,15,16,17,20,22,26,28,32,34,35,36,37,38,42,45,46,47,48,49,51,52,54,57,62,63,64,65,66,69,71,72,78,80,81,82,87,88,92,93,96,98,102,103,105,107,108,109,111,112,113,117,119,120,122,123,124,127,128,130,132,133,134,136,138,140,142,143,144,145,150,152,153,156,157,159,160,161,162,164,165,166],[38,80,111,123,125,129,132,133,134,137,138,139,140,141,143,145,147,148,149,153,154,157,162,165,167],[0,1,2,3,4,5,8,10,13,14,16,20,22,24,26,27,28,29,30,31,35,36,39,40,41,42,43,46,47,55,56,59,61,66,67,71,74,75,76,77,79,83,86,87,88,89,90,92,95,96,97,98,99,102,104,105,108,109,110,111,113,114,116,118,122,123,124,125,126,128,131,134,136,137,143,144,145,147,152,155,156,158,160,163,164,165,167,168],[0,1,2,3,4,5,9,10,13,15,19,20,21,24,25,26,28,29,34,35,38,39,40,42,44,46,47,48,49,50,51,55,56,59,61,62,63,64,65,66,67,71,72,74,79,80,82,83,84,86,88,93,94,97,98,100,102,104,105,106,107,108,109,113,114,117,119,121,124,125,128,129,130,132,133,135,137,141,143,144,146,149,152,154,157,158,159,160,161,162,165,167,168],[0,2,3,4,5,6,8,10,11,15,16,20,21,23,24,25,26,27,28,30,33,34,36,37,41,43,48,50,54,55,57,58,62,63,64,67,74,77,79,83,84,87,88,89,91,93,95,96,98,99,103,104,108,109,111,112,118,120,121,124,126,128,132,133,135,136,137,139,140,141,143,144,145,146,147,149,150,151,153,155,156,157,158,160,161,164,167],[0,2,4,7,8,10,12,15,16,17,18,22,23,25,26,27,29,30,32,35,37,38,39,40,43,45,46,47,54,55,63,64,66,68,70,74,77,78,83,84,86,87,88,89,90,92,93,94,97,99,100,110,112,113,114,115,116,117,121,126,127,129,131,133,134,137,139,141,143,145,147,149,151,153,154,158,161,162,163,165],[0,1,2,3,4,7,8,9,13,15,16,17,19,20,22,24,25,26,27,29,31,34,35,38,39,40,42,43,44,45,46,49,50,51,52,53,55,57,58,59,62,63,67,69,74,75,79,82,83,88,90,96,98,100,101,105,107,108,109,111,113,114,121,122,124,125,126,129,130,132,135,136,139,141,142,145,147,148,151,152,153,159,164,166,167,168],[0,7,8,9,10,13,14,15,16,19,20,21,22,25,26,28,31,34,35,36,39,40,42,46,53,54,55,56,59,60,61,62,64,65,66,67,69,70,71,73,75,76,79,80,82,84,86,87,88,89,91,94,95,98,100,102,103,104,106,107,108,109,111,112,113,115,116,118,119,120,121,123,124,125,126,128,130,131,134,139,143,144,145,146,147,150,152,155,156,159,160,161,162,163,167,168],[0,1,3,5,10,12,14,15,18,19,20,22,23,24,26,28,29,30,32,36,39,44,46,48,49,50,51,53,55,60,64,66,68,69,72,73,75,76,78,80,84,86,88,90,92,94,95,97,102,103,105,110,113,118,120,121,123,124,125,127,132,133,134,135,136,137,139,141,148,149,150,151,152,154,157,158,164,165,166,167],[0,3,6,7,8,9,10,11,13,15,16,17,18,19,20,22,24,25,26,29,30,31,33,34,35,38,43,45,50,52,55,56,58,59,62,63,64,65,67,69,70,75,78,79,80,87,89,91,92,93,97,98,102,103,105,106,108,109,116,118,120,122,123,126,128,131,132,136,138,141,142,148,150,154,155,156,157,159,163,164,165,167],[0,1,5,7,8,10,14,15,18,21,23,26,28,31,32,35,37,38,40,44,45,48,49,51,53,54,56,58,59,62,63,64,65,66,69,70,73,74,75,76,77,78,80,81,83,84,86,87,88,89,92,93,94,97,98,103,108,112,115,123,126,133,136,140,142,143,144,145,146,147,151,156,157,158,159,161,163,165],[24,121,123,149,151,157,158,159,160,164,166,168],[93,123,152,157,159,164,166],[1,2,3,4,5,7,9,12,13,14,17,18,20,21,23,24,25,28,29,31,32,33,34,41,43,48,51,52,53,54,55,56,58,60,61,62,64,65,66,67,68,70,73,74,76,82,83,84,85,88,90,91,92,93,98,100,104,105,106,109,114,116,122,123,124,126,128,129,130,135,136,139,140,141,142,143,144,145,148,150,152,158,160,163,164,165,168],[24,126,152,158,160,164,167],[0,2,3,4,5,7,10,12,14,15,16,19,20,21,22,25,26,29,30,33,35,36,37,38,39,40,41,42,43,44,48,51,54,56,57,60,62,64,65,66,67,69,70,71,74,79,80,81,85,86,94,95,106,109,111,113,116,117,119,120,123,125,127,130,131,132,133,137,138,140,141,142,144,146,147,148,149,150,152,153,154,155,158,160,161,164,165,166],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,103,104,105,112,114,117,118,121,122,127,131,132,134,137,140,141,143,145,147,148,149,152,154,155,156,157,160,161,163,165,166,167],[0,7,10,12,14,15,16,17,19,20,22,23,24,25,26,27,30,31,34,35,36,39,41,42,44,45,48,50,52,53,55,56,57,58,59,60,62,63,64,67,68,69,70,72,75,77,78,79,80,82,83,84,86,90,91,92,97,98,102,103,105,108,109,111,112,113,114,117,118,119,121,122,123,124,125,126,127,128,129,130,131,132,134,135,137,141,142,143,144,147,155,156,157,158,163,164,165,168],[1,3,5,7,17,18,20,23,26,27,28,38,39,41,43,45,46,47,52,53,54,57,59,60,64,65,68,69,70,73,76,77,78,83,85,86,88,90,95,98,102,103,104,106,109,116,117,118,119,120,124,125,126,128,132,134,136,138,139,140,141,143,145,146,149,154,157,159,163,165,166,167,168],[24,38,100,111,121,122,123,124,125,132,133,134,136,139,141,147,153,154,155,156,160,161,162,165],[1,2,3,4,9,13,17,20,22,23,25,26,27,29,30,31,32,33,34,35,37,41,42,43,44,49,53,54,55,57,60,62,67,68,69,71,74,77,78,80,83,84,85,87,88,89,90,91,94,95,96,97,98,101,103,107,114,116,117,119,125,127,128,129,130,132,134,135,136,138,140,142,143,145,147,152,154,155,158,161,163,164,165,166],[38,102,111,121,122,123,124,125,129,132,133,134,136,139,141,147,149,152,153,154,156,158,161,162,165,167],[1,2,4,5,9,11,16,18,20,21,22,23,24,27,29,30,31,33,34,35,40,47,49,50,51,52,53,55,56,60,61,64,65,66,69,74,76,77,78,79,81,83,87,88,90,91,93,95,96,97,98,99,101,103,108,110,111,114,115,117,118,120,121,122,126,129,130,133,134,138,140,142,144,145,147,150,157,160,161,163,164,168],[0,1,6,7,12,13,14,15,17,18,19,21,22,24,25,27,30,34,35,36,37,39,44,45,46,48,50,52,54,57,58,61,62,64,67,69,71,72,73,76,77,78,79,80,81,82,83,86,87,91,92,95,96,98,101,104,106,107,110,122,123,124,127,128,130,131,132,135,138,140,142,144,145,146,147,148,152,157,158,159,161,163,165,167],[0,2,3,4,5,6,8,9,11,13,14,15,17,20,21,22,24,26,29,30,31,32,33,34,39,42,43,44,48,50,54,56,57,58,59,60,62,68,70,71,72,73,75,76,77,78,81,85,86,88,89,90,91,92,94,97,98,99,102,105,107,109,112,118,122,127,128,129,130,132,134,135,136,137,139,140,143,146,149,150,151,152,155,156,157,161,163,166,167],[0,3,10,11,12,14,20,23,24,25,27,28,32,34,35,36,37,38,40,41,42,44,46,47,48,49,51,52,55,57,58,59,64,65,67,69,70,73,74,75,77,79,80,83,84,85,86,89,90,91,96,99,100,101,102,105,106,107,110,112,113,114,115,116,119,120,121,122,125,126,127,128,131,133,134,135,139,140,141,148,149,150,151,152,154,155,157,158,162,164,166,167],[1,5,9,10,11,12,16,18,20,22,23,24,25,26,27,28,32,35,39,40,41,42,47,51,54,59,60,61,62,67,68,69,71,74,76,77,78,79,83,87,90,94,95,97,101,104,107,109,110,111,112,114,115,116,118,119,123,124,132,138,139,140,143,145,148,151,152,154,155,156,159,160,161,164,166,167],[0,2,4,7,9,10,12,14,17,18,19,20,22,24,25,27,29,31,32,33,34,35,38,40,41,42,43,44,45,46,47,54,55,56,57,58,59,63,65,67,68,70,74,76,77,79,81,83,85,87,88,95,96,97,103,104,105,108,112,113,114,115,116,117,120,121,123,125,127,128,129,130,131,132,136,137,138,139,141,142,144,147,148,151,153,154,155,157,158,159,161,163,165,166,168],[1,3,5,7,8,9,14,15,19,20,21,22,23,24,25,26,29,33,36,37,39,41,42,44,47,48,50,53,54,55,56,57,58,59,60,61,66,67,68,69,71,72,74,75,77,79,81,84,85,86,87,91,92,95,96,97,98,99,100,101,102,103,104,105,108,111,112,114,117,119,122,123,124,125,126,127,128,132,134,135,136,137,138,144,149,151,152,156,157,159,160,161,162,163],[0,1,2,4,5,7,10,15,17,18,20,22,23,24,26,27,29,30,31,32,33,34,35,36,39,40,42,43,45,46,48,49,51,52,53,54,59,62,63,64,66,67,69,70,71,73,74,75,76,77,78,79,81,82,83,86,90,91,94,99,102,104,106,107,109,113,114,115,116,118,119,120,126,128,130,131,132,133,135,136,139,140,141,146,148,149,152,155,161,162,164,165,166,167],[111,149,151,162],[0,3,5,6,8,10,12,14,16,18,21,23,24,25,26,29,33,34,35,38,50,51,52,53,54,55,58,59,62,63,68,69,79,80,81,82,84,85,88,89,90,93,94,97,99,101,105,107,108,110,112,113,114,117,118,121,122,123,124,125,126,128,129,130,133,136,142,143,144,145,146,150,153,154,156,158,159,162,163,164,165,166],[1,5,10,14,17,18,19,21,22,23,24,27,30,31,33,34,36,37,38,40,44,46,50,57,61,63,66,68,69,70,71,75,80,81,82,85,86,87,88,91,93,95,98,100,101,104,109,110,112,114,119,120,121,122,124,125,127,129,130,131,132,134,137,138,140,141,145,146,147,148,151,152,157,158,159,160,161,162,165,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,117,118,121,122,124,127,129,131,133,136,148,149,153,156,159,160,163,164,165,166,167],[1,2,3,4,6,7,8,10,11,12,17,18,19,21,25,28,31,33,34,38,39,40,41,42,44,45,46,48,49,51,52,53,54,58,60,61,63,64,65,66,68,69,71,74,75,76,77,78,80,84,85,87,88,89,90,92,93,96,101,103,104,106,107,109,110,113,114,117,120,121,122,126,127,128,129,131,132,134,135,138,140,141,144,145,146,147,157,158,159,166,167,168],[0,7,8,10,11,12,13,15,17,22,24,25,26,27,28,29,32,33,37,39,42,43,45,47,50,51,53,55,56,57,61,63,68,70,82,83,88,91,93,94,95,96,100,101,102,103,105,106,107,112,114,115,116,118,124,126,128,129,130,131,133,135,136,142,143,144,145,147,155,156,158,162,164,167,168],[1,7,9,10,11,14,16,18,20,21,22,24,25,26,27,29,31,32,33,35,36,37,41,42,44,45,46,47,49,51,52,53,54,55,56,59,65,66,68,69,72,73,78,79,81,82,83,85,87,88,89,90,94,95,97,105,106,107,110,111,113,117,119,122,123,124,126,127,128,129,130,131,132,133,134,138,139,140,144,145,147,148,149,150,152,161,164,166,168],[0,5,6,7,8,9,10,15,16,18,21,26,28,30,34,35,37,40,41,43,49,50,51,52,55,56,57,58,62,63,64,66,67,68,71,72,74,75,77,81,83,87,91,93,94,98,102,104,108,111,115,118,119,120,123,124,125,127,128,129,130,131,132,133,134,137,140,141,142,145,146,151,152,154,157,158,159,160,161,162,166,167],[0,2,3,4,7,9,10,14,15,17,20,21,22,23,30,31,43,45,48,49,50,53,54,57,58,59,63,64,68,69,70,71,74,75,80,82,84,94,95,97,99,100,101,102,103,104,107,108,109,111,112,113,117,118,121,123,124,125,126,128,130,132,134,135,136,137,139,140,143,144,145,146,149,150,151,154,157,158,160,161,162,163,165,166],[3,5,7,9,10,12,15,17,18,20,23,24,25,27,30,32,33,34,36,41,42,45,46,49,50,53,55,57,58,60,64,65,66,67,70,71,72,73,74,75,76,77,78,79,80,81,82,84,85,86,87,92,93,95,100,101,102,108,109,110,111,114,115,118,119,120,121,124,127,128,133,134,135,137,143,144,147,149,150,151,153,154,156,158,160,161,163,166,168],[3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,124,127,131,135,136,138,141,144,146,153,156,163,164,165,166,167],[0,1,3,4,6,10,11,13,15,17,20,21,24,25,27,28,32,33,34,35,39,41,42,43,48,49,51,53,54,55,58,60,62,64,68,69,70,72,75,77,78,80,82,83,86,88,90,91,98,99,101,103,104,106,110,112,114,118,119,120,121,123,127,129,130,132,133,134,140,142,143,144,146,149,150,152,153,154,155,157,158,161,162,163,165,166,168],[2,5,6,8,9,11,14,16,17,18,20,21,22,24,27,28,29,31,33,35,40,41,42,44,45,47,48,49,50,55,56,57,59,60,61,64,66,67,69,70,71,73,74,78,79,80,81,83,84,86,87,88,90,92,93,95,96,98,99,101,103,104,108,112,117,118,119,120,122,124,125,128,130,131,132,133,134,135,137,138,139,140,141,142,143,145,149,150,151,152,153,154,158,160,161,162,165,166,167,168],[0,1,2,3,5,10,11,13,15,16,17,21,23,29,32,33,36,37,38,39,40,42,43,44,45,46,49,50,51,52,53,54,56,60,61,63,64,70,72,75,77,79,80,83,84,86,87,88,89,92,101,102,108,111,114,115,117,119,120,121,122,123,124,126,128,130,131,133,135,136,137,138,139,146,147,150,154,156,158,161,162,164,165],[1,2,5,14,15,16,17,18,19,22,23,27,30,33,38,40,42,45,47,49,50,53,54,55,63,64,66,68,70,71,72,75,81,82,85,86,88,90,91,93,96,98,101,102,105,107,109,110,114,115,120,121,122,123,124,131,132,135,139,140,142,143,146,147,148,150,151,160,162,163,166,168],[8,38,136,140,149,159],[0,1,3,4,5,6,10,11,13,16,18,20,24,25,26,28,30,37,38,42,44,45,47,51,52,53,57,60,62,64,65,67,68,69,70,71,72,75,76,78,82,83,84,85,86,88,89,90,92,94,95,96,97,98,102,104,105,107,113,114,115,116,118,119,123,127,129,130,132,136,141,143,144,145,147,154,155,161,162,164,165,167],[1,2,3,5,6,7,9,11,12,14,15,16,18,21,24,28,36,39,40,45,49,50,51,52,54,55,57,58,59,61,63,67,70,74,75,76,77,78,79,84,85,86,88,89,90,91,92,94,96,97,99,102,103,106,108,109,111,115,119,122,123,124,126,128,133,134,136,138,139,140,142,146,148,149,150,151,152,154,155,157,158,161,164,165,166],[12,38,111,121,122,124,132,133,134,140,141,145,148,153,154,155,156,157,159,160,162,164],[1,3,4,5,6,7,8,11,12,17,18,19,20,21,24,26,28,29,30,31,33,36,37,38,40,42,43,44,45,47,49,50,51,52,53,55,56,60,61,63,64,68,69,71,73,74,75,76,78,83,84,86,87,91,93,96,99,102,104,107,108,109,111,113,115,116,117,118,119,120,122,124,126,128,129,130,131,133,135,137,139,141,142,145,146,149,151,152,153,155,157,158,160,163,164,165],[1,4,8,12,15,16,18,19,20,24,31,33,34,43,46,48,49,51,52,53,55,56,57,59,64,66,67,68,75,77,82,83,84,88,92,93,95,96,97,98,102,104,105,107,111,112,113,114,116,117,119,121,122,123,126,128,130,131,134,136,138,141,145,148,150,152,153,154,155,157,158,159,160,162,164,166,168],[16,24,122,123,125,146,157,159,160,161,164,165],[0,1,8,10,13,14,16,17,18,21,22,26,27,28,29,30,36,37,38,39,40,43,45,46,49,50,52,60,61,62,64,66,69,72,77,78,83,85,87,88,91,92,96,97,98,99,102,103,108,109,113,114,116,118,120,122,124,125,127,130,132,133,134,135,140,141,143,144,145,148,149,150,151,153,154,155,156,157,158,161,162,168],[2,3,4,5,6,7,9,11,12,15,17,18,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,124,127,131,133,138,140,141,144,146,153,156,158,159,160,163,164,165,166,167],[1,5,8,9,10,12,13,14,17,18,21,22,23,25,27,28,30,34,35,37,43,44,45,49,50,51,52,54,56,57,59,64,68,70,73,78,82,84,85,86,88,89,90,92,93,94,99,100,101,102,103,104,109,110,114,116,117,119,120,121,123,125,128,129,130,131,132,135,136,140,142,148,149,150,151,159,160,161,162,163,168],[20,24,38,123,125,134,135,139,140,145,146,147,148,149,155,157,158,160,161,165],[1,2,3,4,11,15,16,22,23,24,25,26,28,29,32,34,36,37,39,41,42,43,45,46,48,49,51,56,60,63,64,65,66,80,81,82,83,84,86,87,88,90,92,93,94,98,102,105,108,110,112,113,115,116,117,119,120,124,127,129,130,131,132,136,138,139,140,141,144,152,153,154,155,157,158,159,162,165,166,167,168],[22,38,123,125,133,134,135,138,139,140,144,145,146,147,148,152,157,161,165,167],[0,5,6,7,8,12,18,19,20,21,24,25,27,28,30,32,33,34,39,40,41,43,44,45,48,50,51,53,54,55,57,58,59,61,62,64,65,66,68,69,71,73,75,78,82,85,86,87,88,91,93,94,96,98,99,101,103,107,115,116,117,118,121,122,123,124,126,127,128,137,138,139,140,142,144,145,146,149,152,154,160,161,166],[0,7,8,9,10,13,14,15,16,19,23,27,28,31,32,34,38,42,43,44,46,47,48,50,55,56,57,61,62,66,67,68,74,75,79,80,81,83,84,86,96,107,108,113,114,115,116,117,118,120,121,122,125,127,128,131,132,133,136,139,140,143,147,148,153,154,155,156,157,158,160,165,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,25,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,125,127,131,134,140,141,145,149,152,154,155,156,158,163,164,166,167],[0,1,3,5,9,14,17,19,20,21,23,32,33,37,41,42,49,51,52,53,54,61,63,64,65,69,73,76,77,79,83,84,85,86,87,88,92,95,96,98,99,100,101,103,105,108,109,114,117,120,121,124,126,130,133,134,135,137,140,141,142,147,151,153,155,159,160,161,164,165,166,168],[2,4,5,6,8,10,11,12,19,20,21,23,25,26,31,33,34,40,42,43,44,47,48,49,51,57,58,59,61,63,66,70,71,73,74,75,80,83,84,86,87,89,92,93,95,96,98,99,101,102,107,110,113,114,115,116,118,119,121,122,123,127,128,129,135,136,139,143,144,147,149,150,154,157,158,159,160,164,165],[0,6,9,12,13,14,17,23,24,30,31,32,34,36,37,39,41,42,48,50,57,58,60,61,64,67,68,69,70,71,72,73,75,76,77,80,84,86,91,94,97,98,99,100,101,104,108,109,112,114,115,116,117,118,120,122,124,127,128,129,131,133,139,140,144,146,147,151,153,157,158,161,163,164,167,168],[120,123,149,157,159,162,166,167],[2,4,11,12,14,15,16,17,18,19,20,22,23,24,26,30,32,33,36,38,39,45,46,48,49,53,55,56,57,58,59,61,62,63,65,67,68,69,73,75,78,80,84,87,88,89,90,93,94,95,97,105,108,109,110,111,113,114,115,116,117,119,121,123,124,125,127,133,134,135,136,137,138,139,140,150,151,153,154,155,156,160,161,162,163,166],[0,1,6,7,8,9,12,13,16,17,19,20,21,24,26,27,28,30,32,33,35,37,40,43,45,46,48,51,53,54,56,58,60,63,65,66,68,71,74,77,79,81,83,85,86,88,90,91,94,98,99,100,101,103,104,105,110,112,113,116,117,120,126,127,129,130,134,140,141,143,145,146,148,151,152,155,156,157,162,163,164,166],[2,3,4,5,6,7,9,11,13,14,19,22,23,24,27,30,33,35,37,38,39,40,41,42,43,46,48,50,53,56,57,58,59,60,61,63,65,66,69,70,71,73,74,75,76,77,80,82,86,87,94,96,99,100,102,106,107,113,115,116,119,122,123,124,125,126,127,128,130,131,132,133,134,136,137,141,142,143,145,146,149,151,154,157,159,161,162,166,167],[1,5,6,7,9,10,11,13,16,19,20,22,23,24,25,29,30,31,32,33,35,36,37,39,40,41,42,44,45,47,48,49,50,52,53,55,58,63,66,70,74,80,84,85,87,88,89,91,93,94,95,97,98,99,101,103,104,108,110,111,113,117,118,119,120,121,125,126,127,129,130,135,136,139,140,142,144,148,151,153,156,157,159,161,163,164,166,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,123,124,127,131,135,141,144,146,153,156,163,164,165,166,167],[0,5,8,9,11,12,13,14,22,26,27,29,30,36,39,42,47,48,49,50,52,53,54,55,57,58,59,60,63,64,65,67,72,73,74,75,78,79,80,82,84,85,86,90,91,92,96,98,99,100,105,106,107,109,111,112,113,115,119,120,123,124,127,129,132,133,135,136,140,141,145,146,149,151,154,155,156,157,159,161,165,166,168],[0,2,4,6,9,11,13,15,16,21,22,27,29,31,32,35,36,37,38,40,41,42,43,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,76,81,82,84,85,86,87,90,93,94,96,99,101,102,103,105,107,109,111,112,114,116,118,120,121,123,124,126,128,130,134,136,138,139,143,144,147,148,149,150,154,156,161,162,164,165],[0,1,3,5,8,9,11,13,16,23,24,25,26,27,28,29,31,32,34,36,38,39,40,42,47,52,54,56,57,58,59,61,65,67,68,69,70,71,72,73,77,78,79,80,82,84,85,86,87,89,92,93,95,96,97,99,101,105,106,107,108,109,110,111,113,114,115,116,117,118,122,123,124,126,127,128,129,132,133,143,144,147,152,153,156,158,162,163],[8,9,10,11,16,19,20,23,27,29,31,33,35,36,37,41,42,45,46,47,48,49,73,74,75,78,79,82,83,84,86,89,91,92,93,95,96,99,100,103,108,109,110,122,124,125,127,129,133,134,136,138,140,142,143,147,151,152,155,156,160,161,165,166],[38,149,155,159],[2,3,4,5,6,7,12,13,16,18,19,21,22,25,26,28,29,31,35,36,40,42,44,48,49,50,51,52,53,58,59,63,65,67,68,70,73,75,77,78,88,89,92,102,105,107,109,110,111,112,115,116,118,120,121,122,124,125,127,129,130,131,134,135,136,138,140,143,144,145,149,151,152,154,155,159,160,161,164,166,167],[0,1,2,4,5,6,11,15,17,21,25,33,34,35,36,40,41,42,43,44,47,50,52,53,54,56,57,59,64,66,67,69,70,71,75,80,81,82,87,88,89,90,91,93,94,95,96,97,99,100,101,104,108,113,114,115,117,118,119,121,122,125,127,128,129,131,132,133,134,136,137,138,141,143,145,146,147,149,151,152,154,155,156,157,159,163,165,166,167,168],[1,2,3,4,6,7,9,12,17,18,19,20,22,23,24,25,28,31,32,36,38,39,45,46,47,48,52,54,55,57,61,63,66,70,74,76,79,87,92,93,94,96,97,98,102,106,108,109,110,111,112,113,114,118,120,121,122,126,128,129,130,134,135,137,138,141,142,143,149,153,156,160,161,162,163,164,165,167],[1,3,5,6,8,10,13,14,17,20,23,24,26,28,30,36,37,38,43,50,51,60,61,62,63,66,67,68,69,72,73,74,75,77,78,79,80,81,82,83,86,87,88,89,90,93,96,99,101,103,105,106,108,110,111,113,114,117,119,121,122,124,126,128,130,135,139,141,143,147,148,149,150,152,154,155,156,158,162,164,165,166,168],[2,4,9,10,11,14,16,18,20,21,22,27,28,29,30,32,33,36,40,42,44,46,47,48,51,55,61,62,63,64,66,68,69,71,73,74,75,76,77,78,79,80,82,84,87,88,89,90,92,95,99,101,106,109,110,113,114,115,116,117,119,120,121,124,125,126,128,130,134,135,139,140,142,146,147,148,149,153,154,156,159,162,163,164,165,168],[0,2,5,6,10,11,22,23,24,25,26,28,29,32,34,36,38,44,45,46,48,49,54,56,59,60,62,64,67,68,72,76,77,78,79,80,85,87,89,91,92,102,103,104,105,108,109,110,111,113,115,116,119,120,122,123,128,129,130,131,133,135,137,138,139,140,141,142,145,146,147,149,151,152,154,156,162,164,165,166,168],[1,2,4,7,8,10,12,14,16,20,23,25,27,28,29,31,32,33,38,40,41,44,45,47,54,55,60,61,64,65,68,69,73,74,75,76,81,82,83,84,85,86,87,88,89,91,94,95,97,98,100,104,106,109,112,115,116,119,121,123,126,127,129,133,134,136,138,142,143,145,146,147,149,152,153,158,162,164,167,168],[0,1,3,4,9,12,13,14,19,20,22,23,24,28,30,31,32,33,35,36,37,38,40,41,42,43,44,46,47,50,52,53,54,60,63,64,65,66,67,69,74,77,78,79,80,81,83,85,87,88,89,91,92,93,96,97,98,101,103,105,108,109,110,111,112,113,115,116,126,129,133,134,136,138,139,140,143,145,146,148,149,152,157,158,160,161,162,163,164,165,166,167,168],[2,3,4,5,6,7,8,9,10,11,14,15,18,19,20,21,22,23,25,26,27,29,30,31,32,33,34,35,40,41,49,52,53,54,55,58,59,60,61,62,63,66,67,68,69,75,76,79,80,81,82,88,89,90,91,92,93,95,98,99,100,101,102,103,108,109,111,112,113,120,122,127,128,129,132,133,134,135,136,137,138,140,141,147,149,150,152,153,154,156,161,162,163,164,166,167,168],[1,2,3,4,5,6,8,9,10,12,16,18,20,21,23,24,25,27,31,37,39,40,42,47,50,52,54,55,57,59,63,66,67,69,72,74,76,77,78,82,83,84,87,88,89,91,94,95,96,97,99,100,102,105,106,107,111,115,116,121,125,126,128,132,136,137,140,141,146,148,152,154,155,156,158,159,162,163,165,167,168],[1,2,3,5,8,12,14,15,16,17,18,19,22,27,28,30,31,33,34,39,43,44,45,48,50,52,54,55,57,61,62,63,65,69,72,73,74,75,76,80,81,82,84,85,86,90,91,92,99,100,101,105,106,107,109,111,112,116,118,119,120,123,124,128,129,130,132,134,137,139,142,144,145,146,147,148,151,152,153,155,156,158,163,165,167,168],[4,5,8,11,12,14,16,19,20,22,25,26,27,29,30,33,34,35,36,37,38,39,41,43,44,46,48,50,52,53,56,57,58,59,60,61,63,64,66,68,70,71,72,73,74,81,82,83,84,86,88,91,95,98,99,103,106,107,112,114,117,118,122,123,124,125,127,128,132,133,135,138,139,141,142,149,152,153,156,157,160,164,166,168],[1,4,5,6,9,15,18,20,25,27,28,31,33,37,38,39,45,46,47,49,51,52,53,55,57,58,63,66,67,68,71,77,79,83,85,86,90,92,93,95,97,103,104,105,107,109,110,111,112,113,115,116,122,123,128,131,134,136,140,143,144,146,150,154,155,156,157,160,161,162,163,164],[1,4,6,7,9,10,11,13,14,15,19,23,26,28,30,32,34,36,37,38,39,40,41,43,44,45,46,47,48,50,51,52,54,57,60,63,64,65,66,71,74,76,78,79,80,82,83,84,89,91,92,97,101,103,106,110,111,115,116,117,118,125,126,127,128,130,131,135,136,137,141,144,145,146,147,151,152,154,155,156,157,162,163,167],[1,2,3,4,6,7,11,12,13,15,22,24,28,29,30,32,33,34,36,37,39,40,44,46,47,48,50,51,53,54,57,58,60,61,63,64,65,67,75,78,79,80,82,87,91,92,93,94,96,97,98,100,101,104,105,106,110,112,117,122,124,125,126,128,129,134,135,137,139,140,142,144,146,149,150,151,154,155,156,158,161,162,163,164,166],[1,4,9,13,14,15,18,19,20,21,22,24,26,30,32,33,34,36,37,39,40,41,43,49,50,51,53,57,58,60,62,64,65,66,71,73,76,78,79,80,81,84,86,87,88,90,93,95,97,98,99,100,102,103,104,105,106,108,109,111,115,116,117,119,120,122,125,131,132,135,137,138,139,146,152,154,155,157,158,159,161,166],[0,2,3,5,8,9,10,12,13,14,17,19,20,22,23,27,30,31,33,35,38,41,45,46,48,49,51,57,59,61,62,63,64,69,70,72,73,75,78,79,80,81,83,87,90,91,92,93,95,97,101,103,104,105,106,113,117,121,124,125,126,129,132,134,136,138,139,140,142,146,147,148,150,153,156,157,158,159,162,164,165,167,168],[0,3,4,5,8,11,14,15,16,18,19,20,21,22,23,24,26,31,33,36,37,38,39,40,44,45,47,49,50,51,52,53,54,56,58,59,61,63,65,66,67,68,69,71,76,77,79,80,83,84,88,89,90,92,94,95,97,99,100,101,102,103,105,106,110,112,115,118,119,120,123,129,132,135,137,138,139,140,142,145,146,147,148,149,151,156,162,164],[1,3,4,7,8,11,12,14,16,18,20,23,25,26,28,29,31,33,34,36,38,39,41,42,45,47,48,50,52,54,56,58,62,63,70,71,72,73,74,77,78,86,87,93,95,98,99,100,101,102,104,105,106,107,110,111,112,113,116,117,118,119,120,121,122,123,124,126,128,129,132,137,138,140,141,143,144,147,148,151,158,163,165,168],[1,2,4,6,8,11,12,14,17,18,19,20,22,24,27,28,29,32,33,34,37,38,39,41,43,44,46,48,51,52,54,56,58,61,62,66,67,75,79,80,88,89,90,91,98,99,106,107,108,109,110,111,112,113,116,117,118,119,121,122,124,126,129,130,131,134,135,138,139,141,143,145,148,149,150,152,154,157,160,163,164,165],[5,6,8,11,12,13,14,15,17,20,21,25,30,31,32,35,37,38,40,44,45,47,48,59,60,62,67,69,71,73,74,78,79,80,81,82,87,88,93,94,97,98,104,106,110,112,113,117,119,120,123,125,126,128,131,134,136,137,141,142,143,144,145,146,149,150,151,152,153,156,157,159,160,161,162,163,164,165,166,168],[0,2,4,6,10,11,14,15,16,18,21,23,24,25,29,30,34,35,36,37,41,43,44,55,56,59,60,63,64,65,67,69,72,75,76,78,79,81,83,88,89,90,91,92,93,96,99,101,102,104,105,106,107,108,109,110,113,114,117,118,120,122,123,125,127,129,132,137,138,139,142,149,151,152,153,156,158,159,161,162,164,165,166,167],[1,5,6,7,9,10,11,12,14,15,17,18,20,22,23,24,25,29,30,31,33,35,36,37,39,40,41,43,46,50,52,53,55,58,64,65,66,67,68,70,71,72,73,74,76,77,79,80,82,84,86,87,88,92,95,99,100,101,104,105,106,110,111,112,113,115,116,117,118,123,125,127,129,130,133,134,135,136,138,139,140,142,144,150,152,156,157,159,167],[6,7,10,11,12,13,14,15,16,19,20,22,24,25,27,28,30,31,32,33,36,37,38,39,42,43,44,45,46,49,51,53,55,57,59,60,63,64,68,70,72,73,79,80,84,85,91,92,93,94,95,96,98,101,102,103,104,105,106,107,108,109,111,112,113,121,122,123,124,125,127,128,130,132,134,138,144,147,148,151,155,158,160,162,163,165,168],[0,1,3,5,8,9,11,13,18,19,21,25,27,28,29,30,31,32,35,36,37,41,42,46,47,48,50,54,55,56,58,63,64,65,66,68,71,72,73,74,75,76,77,78,82,86,87,88,90,92,93,97,100,101,103,105,110,113,118,123,125,126,127,129,130,131,132,133,134,135,136,141,142,144,146,147,148,150,151,152,153,156,157,158,161,166],[0,1,3,5,6,7,8,9,10,12,14,15,16,17,18,20,22,23,26,28,31,32,35,38,40,43,44,45,48,51,52,53,57,58,60,61,62,63,64,66,69,70,71,74,75,76,78,80,81,82,85,87,92,93,94,95,96,97,98,101,103,104,105,106,109,112,113,115,116,122,126,128,129,130,131,132,133,135,137,139,140,142,144,146,147,148,149,156,163,165,168],[0,1,14,15,16,18,20,23,25,26,28,29,32,33,35,36,38,39,40,42,44,46,47,54,55,56,57,58,59,62,64,66,70,74,76,83,84,85,86,87,90,91,102,103,105,107,109,110,112,115,117,119,120,123,124,127,129,130,131,139,140,143,144,148,150,155,157,158,160,162,163,164,165,168],[3,5,6,7,9,14,17,18,20,21,22,24,25,27,31,32,33,34,36,37,38,39,40,41,45,47,50,51,53,57,58,63,64,65,66,67,68,71,74,76,77,79,84,85,86,87,89,90,92,96,97,98,101,102,104,105,107,108,110,111,113,114,115,119,120,122,125,126,130,133,135,139,141,144,145,149,150,155,156,158,159,160,161,162,163,164,165,166,167,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,124,127,129,131,136,138,141,147,153,156,160,163,165,166,167],[24,123,149,159,160,163,164,166],[38,73,111,121,122,123,124,125,132,133,134,140,141,147,148,149,153,154,155,156,158,161,162,164,165],[38,74,123,125,132,134,136,140,143,145,147,157,165,167],[24,123,149,156,157,158,159,164,165,166],[2,4,5,7,9,10,11,13,14,15,18,22,29,30,31,35,36,37,39,41,42,43,45,47,48,49,51,52,53,54,55,57,60,63,64,65,67,68,69,72,73,74,77,78,79,83,85,86,87,89,90,91,94,95,96,101,102,106,108,109,112,116,121,122,126,130,131,132,135,138,139,142,143,145,147,149,152,154,156,161,162,164,165,166],[1,2,4,6,14,15,16,18,20,23,26,27,28,29,30,32,33,35,36,39,46,49,51,53,54,55,56,57,58,59,62,64,66,69,72,73,74,75,76,79,81,88,89,90,93,94,95,96,97,98,99,100,101,103,105,107,109,110,112,113,121,124,126,128,132,133,134,138,139,142,143,145,146,147,148,149,151,153,154,155,158,159,162,165],[0,1,2,3,4,5,6,7,8,10,12,14,16,18,21,23,25,26,27,40,42,44,47,49,50,52,54,55,56,57,62,65,66,69,70,71,73,74,76,79,81,82,85,87,88,91,92,94,96,97,100,101,106,107,108,109,111,112,115,117,118,120,124,127,128,131,134,136,137,142,143,145,147,150,153,155,157,159,160,162,165,166,168],[2,4,6,7,11,12,18,20,22,23,25,26,29,30,31,32,33,34,36,37,38,41,43,44,45,46,47,49,50,52,53,54,55,56,58,63,64,65,69,70,72,73,74,76,77,78,80,82,83,88,90,93,95,96,98,99,102,103,104,111,113,116,117,119,122,125,126,127,128,130,132,133,136,139,140,143,148,149,152,153,154,158,159,160,165,166,167],[1,2,3,4,5,7,9,10,11,12,13,15,16,17,19,21,22,23,25,27,29,30,31,36,38,44,48,50,56,58,62,63,64,67,73,75,76,79,80,84,85,89,93,95,96,97,98,101,103,104,106,107,111,113,116,117,118,121,122,124,125,129,132,133,135,136,137,142,144,145,146,148,149,151,152,153,155,156,159,162,165,166,167],[2,3,4,5,8,9,10,11,12,13,14,15,16,17,18,26,27,29,30,32,35,36,38,39,41,42,44,46,48,50,52,54,57,59,60,63,65,66,68,70,73,78,80,81,82,83,85,87,89,98,99,100,101,103,104,105,108,109,111,112,113,114,115,122,130,132,133,136,138,140,143,146,147,148,149,152,155,156,160,161,166,167],[1,2,4,7,8,9,14,15,24,26,28,29,34,35,36,37,39,41,42,44,47,48,51,52,56,57,60,61,62,63,66,67,71,72,74,75,76,78,79,81,84,85,90,92,93,96,97,98,99,100,101,102,103,106,107,108,109,113,114,116,119,120,122,124,126,127,129,131,133,134,138,141,143,144,145,146,147,148,150,151,152,154,155,159,162,166],[9,10,13,14,17,21,23,24,25,28,31,32,33,38,41,43,44,46,48,51,53,56,57,58,59,63,64,67,68,70,71,72,73,74,75,77,78,81,82,83,84,85,87,89,91,92,95,96,97,98,99,106,107,108,109,113,115,116,118,124,125,127,129,136,139,142,143,144,145,146,148,149,151,153,155,165,166],[0,2,3,4,9,10,11,12,14,15,16,17,20,21,22,24,25,26,29,32,33,34,36,37,39,43,44,45,46,47,48,52,56,61,63,64,65,66,68,69,70,72,73,76,77,81,83,86,87,88,91,93,94,95,97,98,99,100,102,106,112,113,114,118,123,125,126,132,133,135,137,139,140,141,143,144,145,147,151,152,154,155,156,157,158,160,162,164,165,166,167,168],[0,1,3,5,6,7,8,12,13,15,17,19,23,27,28,29,30,31,32,33,34,39,40,41,42,43,45,47,50,51,52,54,55,56,58,60,61,63,64,65,68,70,71,74,75,76,77,80,83,86,89,91,92,94,95,98,101,102,103,104,105,106,108,110,112,114,115,119,120,121,122,124,126,128,131,132,133,135,139,142,143,145,147,150,153,155,156,159,163,164,165,168],[1,2,4,5,8,11,12,13,17,18,19,22,23,24,27,29,30,31,32,35,36,39,42,45,48,49,51,52,56,57,58,61,62,64,71,77,79,80,81,82,83,85,86,88,89,93,101,103,104,105,106,107,108,110,112,113,114,115,117,119,120,128,129,131,133,134,135,140,141,142,144,147,150,164,165],[0,1,3,7,8,9,11,12,13,14,16,18,19,20,24,26,27,29,30,31,35,42,44,45,49,52,57,58,59,61,62,63,65,66,67,68,70,71,76,79,83,87,89,91,92,93,94,97,98,99,100,102,107,108,109,111,115,118,122,123,124,126,129,131,136,138,141,143,147,151,152,154,157,158,159,163,166,167],[38,89,132,133,134,136,140,147,153,154,158,159,160],[1,2,4,6,9,10,13,15,20,21,24,29,30,31,32,33,36,37,38,39,40,41,42,43,47,48,50,52,55,56,59,61,62,63,64,65,68,69,70,71,72,73,74,78,80,82,85,86,88,90,91,92,93,97,98,101,103,104,105,106,107,110,112,113,114,115,116,117,120,121,122,124,125,129,135,136,137,139,140,141,142,145,146,151,152,153,154,155,158,160,166,167,168],[0,3,8,11,12,13,14,15,17,18,19,25,26,28,29,30,31,33,34,35,36,37,38,41,47,48,50,51,52,53,55,56,64,65,66,68,70,71,73,75,77,78,80,82,83,87,89,91,92,94,95,96,97,101,103,106,107,108,110,111,112,113,116,118,120,121,124,126,127,129,130,131,134,136,141,143,144,145,149,150,154,155,157,160,161,164,167,168],[1,2,4,6,9,10,12,14,17,21,22,24,26,28,30,31,32,34,35,36,37,40,41,46,47,48,49,52,53,54,55,56,57,60,61,62,65,66,68,70,73,75,76,78,79,82,84,87,88,90,91,92,93,98,99,100,101,102,110,118,119,120,122,124,126,129,130,132,133,134,135,139,141,143,146,147,148,152,155,156,160,161,162,163,164,165,166,167,168],[121,149,156,168],[24,93,155,158,160],[0,2,3,4,6,7,8,12,16,20,24,25,36,39,40,42,43,44,46,47,48,50,51,52,54,55,57,58,59,61,62,63,64,69,72,73,74,76,78,81,83,84,89,90,93,94,96,98,99,101,105,108,110,111,112,117,118,119,123,125,127,130,135,136,137,138,139,140,141,144,146,148,149,150,151,152,154,155,157,160,161,162,164,167],[0,5,6,7,8,9,11,14,16,20,24,26,29,31,32,34,35,36,40,41,42,44,45,49,50,51,52,54,56,57,59,62,63,64,66,67,68,71,74,76,77,82,84,85,87,91,92,93,97,99,102,104,108,112,113,115,116,117,119,120,122,123,124,127,129,130,134,136,140,146,150,151,155,156,160,165,166,168],[2,4,11,12,14,15,16,17,18,20,22,23,25,27,28,34,38,41,42,44,45,49,51,56,59,60,61,62,63,64,67,70,71,74,75,76,78,79,83,84,86,88,89,95,97,98,100,103,104,105,107,108,112,113,114,116,118,119,127,128,130,137,144,145,149,150,151,152,154,155,158,159,160,161,164,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,98,103,104,105,112,114,117,118,121,122,124,127,129,131,140,141,147,148,153,156,160,163,165,166,167],[12,13,14,15,16,18,20,22,24,25,27,28,29,31,35,37,38,40,42,44,50,51,52,53,54,55,56,57,58,59,60,61,64,65,66,67,70,71,73,74,76,77,79,82,83,84,87,88,91,92,93,94,96,101,102,103,106,107,110,111,114,115,116,117,120,121,122,124,127,133,135,137,138,139,140,141,142,144,148,149,150,151,152,153,154,155,157,159,160,162,163,164,165,167,168],[1,7,8,10,11,12,13,14,21,24,27,31,34,35,37,42,43,45,48,51,52,53,54,55,57,58,62,68,70,75,76,78,80,81,82,84,86,91,94,96,98,99,100,104,105,106,109,111,112,113,114,117,120,123,124,125,126,129,135,136,137,138,141,142,143,145,146,147,148,151,152,153,157,159,160,162,164,167,168],[38,101,123,125,132,134,137,139,143,145,147,148,157,165,167],[0,3,6,7,9,10,12,13,21,23,24,25,26,27,28,29,33,35,36,38,39,42,45,46,48,55,57,58,59,60,61,63,64,68,69,71,72,75,79,81,86,88,92,93,95,98,99,100,102,103,105,107,111,113,115,121,123,129,133,134,136,138,140,141,144,145,148,150,152,153,154,157,158,160,161,163,164,165,167,168],[103,136,137,138,139,140,148,153,154],[1,6,9,10,11,12,13,14,17,19,20,21,23,24,28,29,31,32,33,34,36,37,38,39,40,43,44,45,46,47,49,51,57,59,60,61,65,67,68,69,70,71,74,78,79,84,87,91,92,93,95,96,98,99,102,103,104,105,106,107,108,109,110,111,113,118,124,129,130,133,135,137,138,140,141,142,144,145,146,147,149,151,158,159,161,164,165],[0,2,3,4,5,6,8,14,16,17,18,19,21,24,26,29,30,31,36,38,39,45,46,47,49,50,54,55,56,59,62,63,64,66,68,69,70,71,74,75,76,79,80,81,86,87,89,92,93,96,97,98,100,102,104,106,108,109,112,114,115,119,124,125,127,129,132,133,135,139,140,141,142,143,146,154,156,159,160,161,163,164,165],[0,3,6,7,8,10,16,17,19,21,22,25,26,27,30,32,33,34,35,36,37,38,41,44,45,46,47,48,49,51,53,56,57,58,61,64,65,67,68,70,71,72,73,75,78,79,80,83,85,90,91,92,96,97,100,103,104,106,107,108,109,110,111,112,115,116,117,120,121,123,124,125,126,127,130,133,135,136,137,141,146,148,151,153,155,156,157,159,168],[0,2,3,4,5,7,8,9,11,12,14,15,17,19,22,24,26,32,33,34,35,36,38,39,40,43,44,45,46,53,57,58,62,64,65,68,70,71,74,77,78,81,83,85,87,91,92,95,96,97,98,100,103,105,106,107,108,111,112,113,114,116,121,122,123,124,128,129,130,131,135,136,137,140,142,143,146,147,149,151,152,153,154,155,159,160,161,162,167,168],[1,2,4,6,8,11,13,15,16,18,19,20,23,26,28,30,31,33,35,37,41,43,45,47,49,51,52,54,56,58,61,63,65,66,69,71,73,78,79,81,83,84,87,89,90,92,94,97,99,100,103,105,106,113,114,117,119,122,123,124,125,127,128,129,130,131,132,133,134,135,138,142,145,146,149,152,153,154,155,156,157,159,161,164,165,168],[112,123,125,136,140,141,148,157,159,161,165],[0,2,4,7,8,11,12,14,16,19,21,23,24,26,29,36,37,38,39,42,43,44,45,46,47,58,59,68,69,70,71,73,74,75,77,78,79,80,81,82,83,84,85,88,89,91,94,97,98,101,104,107,109,111,112,113,114,117,118,121,124,125,126,128,129,130,133,134,136,137,138,140,147,150,152,153,154,156,157,158,159,160,161,163,165,168],[0,1,3,5,8,9,10,12,18,20,22,23,24,27,29,30,33,35,36,37,38,40,42,44,45,46,47,48,50,54,55,57,59,63,64,65,66,67,68,70,72,73,74,76,77,78,79,80,81,84,85,86,87,89,90,92,94,95,97,98,99,100,101,102,103,104,106,107,108,109,111,113,115,116,117,118,125,128,129,130,131,135,136,142,143,145,146,147,150,151,152,153,155,156,160,161,162,163,164,165,167],[2,4,5,7,8,9,11,12,13,15,16,18,21,24,26,27,28,29,30,32,33,34,38,39,40,41,43,44,45,46,47,48,53,57,61,62,63,64,69,70,71,72,73,74,75,80,81,82,83,84,85,87,88,89,91,93,95,96,98,99,100,102,103,106,108,109,111,114,115,118,121,122,123,124,126,128,129,133,134,136,137,141,142,143,145,146,148,150,151,152,153,154,155,158,159,161,163,164,165,167],[111,116,121,122,123,124,125,132,133,139,140,149,153,154,155,156,159,160,161,162,164,165],[0,2,4,5,6,7,8,11,12,13,17,24,27,28,34,36,39,43,44,46,47,48,49,51,53,54,55,59,60,63,65,70,73,74,76,78,83,84,88,89,98,99,100,108,110,112,113,118,122,123,124,126,127,130,131,133,135,137,140,142,144,145,146,148,149,156,158,159,160,165,168],[2,4,5,7,11,12,13,14,16,18,21,24,25,26,27,28,31,33,34,36,37,38,42,48,52,54,55,56,58,59,60,63,67,70,73,76,78,79,80,82,83,84,86,87,88,90,91,93,99,100,101,102,105,108,110,111,113,114,115,116,118,123,124,128,129,130,131,133,138,139,140,141,142,143,144,150,154,155,157,158,164,168],[6,7,9,10,12,14,17,20,23,25,28,29,30,31,32,38,39,41,43,44,46,49,50,52,54,55,56,57,60,61,62,63,64,65,66,67,71,72,73,75,77,80,81,83,86,87,88,89,92,93,94,95,97,99,101,102,103,105,106,109,111,112,113,114,115,118,120,121,124,125,126,128,129,130,131,132,136,137,138,139,140,142,143,145,146,155,156,158,160,163,165,166,168],[1,2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,122,123,124,125,127,129,131,132,134,137,138,141,145,146,148,152,154,155,157,158,159,163,166,167],[0,2,3,6,7,9,11,17,27,29,30,33,35,36,39,40,41,43,45,46,47,48,49,51,53,56,57,59,60,62,65,68,69,70,72,73,74,75,77,79,80,81,82,85,88,89,90,91,93,95,96,97,98,99,101,103,104,105,106,107,109,112,113,116,119,120,121,122,124,126,129,130,131,132,134,137,138,139,140,141,142,145,146,148,153,154,155,156,157,163,165,167,168],[0,1,3,4,6,12,15,16,18,19,20,21,25,26,28,29,30,31,34,35,41,48,49,51,53,58,61,62,63,64,65,67,68,70,71,73,75,76,77,79,80,81,82,83,85,88,89,90,93,97,99,102,104,105,106,107,109,110,114,115,117,119,123,124,127,129,130,134,135,136,137,138,139,140,141,142,145,146,147,151,152,154,155,158,166],[4,5,6,8,11,12,13,14,15,16,17,19,20,22,26,28,32,38,43,44,46,48,50,51,56,57,59,61,66,69,71,72,73,74,75,77,78,79,81,84,88,89,91,92,93,94,95,96,97,98,99,101,102,105,107,108,109,111,114,115,116,118,121,123,124,125,126,127,130,131,133,135,136,140,143,145,146,151,153,154,156,157,160,161,163,167],[0,3,4,5,6,8,11,13,15,18,19,24,25,33,34,35,36,37,39,42,43,44,45,47,48,50,52,55,56,59,61,63,64,67,69,71,72,73,75,76,79,80,81,82,84,85,86,87,88,89,92,93,94,95,96,97,100,101,102,103,105,106,108,110,113,114,117,119,120,123,127,128,129,130,131,132,133,134,136,138,139,140,142,143,145,148,149,151,153,155,156,157,165,166,168],[2,3,7,8,11,13,14,16,19,21,22,25,28,32,33,35,37,42,43,44,45,46,47,48,49,55,57,59,61,62,64,67,69,76,77,78,79,80,81,82,84,87,89,90,91,93,95,96,99,100,103,104,107,108,111,114,115,116,117,120,121,123,124,128,129,131,132,133,135,137,139,140,141,142,143,144,147,148,149,150,151,154,157,159,164,168],[0,1,2,11,12,13,14,18,19,22,25,27,28,30,31,32,37,38,41,42,43,44,46,47,49,50,51,53,56,60,63,64,65,67,68,69,71,72,74,75,77,78,80,84,85,87,91,92,94,95,97,98,99,101,102,105,108,110,111,113,116,118,119,121,122,123,124,127,131,133,135,138,140,142,144,145,146,147,148,150,153,155,157,158,160,162,164,165,166,167,168],[1,2,3,4,5,7,14,16,17,19,20,24,26,29,30,31,36,38,39,40,41,42,43,45,46,47,49,50,56,59,60,61,62,63,64,67,73,75,77,78,79,80,81,83,89,90,91,92,93,94,99,100,102,103,105,111,112,114,115,116,117,118,121,128,130,132,133,134,135,136,137,138,139,140,141,145,146,148,149,151,158,160,165,166,168],[0,2,3,5,9,11,15,18,20,21,23,28,32,33,34,39,41,42,43,45,49,50,51,52,54,56,57,58,60,61,62,67,68,69,72,75,78,79,80,81,84,85,86,88,89,90,92,93,94,99,104,105,107,110,111,113,114,115,117,118,119,121,123,124,125,126,128,131,132,133,134,135,136,137,138,139,140,142,143,149,150,152,153,155,156,157,158,159,163,164],[0,6,8,10,12,13,15,17,18,22,25,26,27,28,30,33,34,36,37,39,40,42,44,45,49,51,54,55,56,59,62,63,64,66,68,69,73,75,76,77,80,85,87,91,92,93,97,98,99,100,101,103,104,110,112,116,117,119,120,121,122,124,126,128,129,130,135,136,137,139,141,142,143,144,145,147,150,154,155,157,159,163,165],[3,4,5,7,9,11,13,14,15,20,21,23,24,25,29,30,31,32,33,34,35,36,38,43,46,47,49,50,51,52,54,59,62,63,64,68,70,72,73,76,77,81,84,85,86,90,91,94,96,101,104,105,107,108,109,110,111,112,117,123,124,125,126,130,132,133,134,135,136,138,139,141,145,149,151,152,153,154,157,160,161,162],[1,2,4,6,9,11,15,16,18,19,20,23,24,25,26,30,31,33,34,36,40,42,45,47,49,50,53,54,57,59,61,63,64,67,69,70,72,73,77,80,81,85,87,89,90,94,95,97,99,100,103,105,107,109,110,113,114,117,119,123,126,130,131,132,133,137,138,139,140,141,144,146,148,149,150,151,153,159,161,163,164,165,166,167,168],[0,1,4,5,6,7,8,10,12,13,15,16,17,18,22,23,27,30,32,34,36,38,39,40,41,44,45,46,48,50,53,56,57,62,63,64,65,66,67,71,72,74,77,78,79,80,81,82,84,87,88,91,93,95,98,99,100,101,102,105,106,109,111,118,119,123,125,126,127,128,131,132,133,135,136,139,140,141,143,145,148,149,150,154,156,157,158,159,160,163,164,165,166,167,168],[0,4,6,7,8,12,15,17,18,21,25,26,27,31,32,36,41,42,43,45,49,50,51,53,54,55,56,60,63,66,70,72,74,75,77,78,80,81,82,83,86,90,91,94,96,97,99,100,101,102,103,106,111,114,119,122,126,129,131,134,135,137,139,142,144,145,146,147,149,151,152,156,157,160,165,166,168],[0,1,5,6,12,14,15,17,18,20,21,24,25,27,28,29,30,35,37,38,39,42,45,47,49,55,56,60,61,67,69,70,71,73,76,78,83,84,88,89,90,91,94,100,102,103,105,106,108,109,111,113,115,116,117,118,119,121,123,125,126,128,130,132,134,135,136,139,140,141,142,145,146,147,149,154,155,157,159,160,163,167,168],[0,2,4,5,8,10,12,13,18,22,23,24,26,29,30,32,33,36,37,39,41,44,45,46,48,52,53,54,56,60,61,63,65,68,69,70,72,73,74,77,81,82,83,85,86,87,91,93,95,96,98,100,101,105,107,108,109,111,112,114,118,119,121,123,125,129,131,132,133,134,135,138,139,140,148,150,151,152,153,154,156,157,158,159,163,168],[2,3,4,5,6,7,9,11,12,15,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,122,123,124,125,127,129,131,134,135,136,137,138,140,141,145,146,148,152,154,155,157,160,163,166,167],[0,3,6,7,9,10,12,13,16,18,22,23,24,25,26,28,32,34,35,41,44,45,47,48,50,51,54,57,60,61,63,64,68,69,71,72,75,78,79,80,85,86,87,90,94,96,99,100,101,105,106,110,111,113,114,118,119,122,124,125,130,132,134,137,140,141,142,143,144,147,149,150,152,153,154,157,158,162,163,165,167],[1,5,8,9,10,12,13,14,17,18,19,21,22,23,24,25,27,28,30,34,35,37,38,43,44,45,49,50,51,52,54,56,57,59,64,68,70,73,78,82,84,85,86,88,89,90,92,93,94,99,100,101,102,103,104,109,110,114,116,117,119,120,128,129,130,131,133,136,137,138,142,143,144,146,147,150,157,158,159,162,163,164,165],[0,1,2,3,4,5,6,7,16,17,20,22,23,25,29,30,31,34,36,38,39,41,43,45,47,48,50,53,55,56,58,61,63,64,66,69,70,74,75,77,79,81,84,86,88,90,91,93,95,98,99,100,101,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,122,125,126,127,128,129,132,133,137,138,139,142,143,147,148,150,151,152,153,154,156,157,160,165,167],[2,3,4,7,8,9,12,15,17,18,21,22,23,24,27,29,30,31,38,39,41,46,47,48,49,50,52,58,60,62,63,64,65,67,69,70,71,72,73,75,77,79,80,81,82,84,90,93,95,96,99,100,101,104,105,108,111,112,113,117,118,126,128,131,133,134,136,138,139,140,141,142,143,147,148,157,161,164,165,166],[0,2,4,7,8,9,12,13,14,15,17,18,21,22,23,25,26,27,28,32,35,37,44,45,46,48,50,53,56,57,63,64,67,69,70,71,72,73,74,76,78,80,81,84,85,91,93,94,96,97,100,101,102,103,105,106,109,111,118,119,122,126,130,131,133,138,140,141,143,145,146,151,153,156,162,163,164,166,167,168],[1,2,4,5,6,7,8,9,10,11,12,15,16,17,18,20,25,26,28,29,30,32,42,45,46,47,48,49,51,52,54,57,58,59,60,61,62,64,68,69,72,74,76,79,81,83,85,86,87,91,95,98,99,100,102,103,106,107,108,110,111,113,115,118,119,120,122,123,125,128,134,136,137,139,141,144,149,151,152,153,154,156,157,158,160,161,163,164,165,167,168],[0,2,4,7,9,11,12,15,16,18,19,21,22,24,25,26,28,30,33,40,41,42,43,44,45,46,47,56,57,62,63,66,67,68,69,70,71,77,78,79,80,81,82,83,86,87,88,89,91,94,96,98,101,102,105,107,108,111,113,115,117,118,120,121,125,127,128,134,135,136,138,139,140,142,145,146,147,149,150,151,152,153,154,155,158,159,160,161,162,163,165,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,124,125,127,129,131,133,138,140,141,144,153,156,157,160,161,163,166,167],[2,4,5,7,10,14,16,17,18,19,23,24,30,34,35,37,38,40,44,49,50,51,52,54,55,56,58,59,60,62,63,64,69,70,71,72,73,74,75,76,78,81,84,88,90,91,92,95,96,97,98,100,101,102,106,108,109,111,112,113,115,116,117,119,121,123,126,128,130,132,133,134,135,140,141,142,143,146,148,150,151,152,157,158,162,163,166,167],[1,2,3,4,10,14,17,21,27,29,36,38,43,44,45,49,50,51,52,54,56,57,58,60,61,63,64,65,66,70,71,73,74,76,80,83,84,89,90,91,94,95,96,101,102,103,104,105,106,112,114,115,116,118,119,120,122,125,128,129,131,132,134,135,136,141,142,144,145,146,148,149,151,153,155,156,157,159,160,163,165,166,167],[0,1,2,4,5,6,8,9,11,12,13,15,16,18,19,21,24,25,26,27,28,29,31,32,33,36,41,42,43,44,47,48,49,51,52,53,55,59,63,66,68,69,70,74,75,78,82,84,88,91,92,94,95,97,101,103,104,105,107,110,111,115,116,117,118,120,126,129,130,131,132,134,136,138,139,140,146,147,149,151,153,154,155,159,161,162,164,165,167],[2,3,4,5,8,9,14,15,17,21,23,24,26,28,29,35,37,39,41,42,44,46,47,50,51,56,57,60,61,62,63,66,67,72,75,76,78,79,81,84,87,89,90,92,97,99,101,103,106,107,108,109,112,113,118,119,120,124,125,127,128,129,131,132,136,138,141,142,144,145,146,150,153,154,156,162,165,167,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,32,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,122,123,124,125,127,129,131,132,134,136,138,141,145,146,148,152,154,155,157,158,159,163,166,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,124,127,131,135,141,144,146,149,153,156,159,163,164,165,166,167],[2,3,4,5,9,10,13,14,17,18,20,23,25,28,32,33,34,35,37,38,42,43,44,45,46,47,48,49,50,51,52,53,55,57,58,60,62,63,68,69,70,73,76,77,79,82,83,86,87,90,92,96,97,98,99,104,105,106,107,108,109,110,111,113,115,116,118,121,123,124,126,128,129,130,131,132,133,135,137,139,140,141,142,143,144,148,150,151,152,154,155,157,158,161,162,165,168],[0,2,3,4,5,7,9,10,11,15,17,18,23,25,29,31,32,33,35,36,39,40,43,44,45,46,47,48,51,52,53,56,58,60,61,63,66,67,69,70,82,84,85,88,90,91,95,96,97,98,100,103,104,105,106,108,114,117,121,126,127,128,129,132,134,139,140,142,145,146,147,148,150,151,153,159,161,163,164,166,167],[24,37,38,111,123,125,132,133,134,135,136,140,141,143,144,145,146,148,157,158,160,161,162,164,165],[0,5,6,7,8,9,10,15,16,17,18,19,20,21,22,28,31,34,39,42,43,44,49,50,51,52,55,56,57,58,63,64,65,67,68,69,70,71,72,73,74,75,76,77,82,83,84,85,86,90,94,95,99,100,101,102,104,105,106,108,109,110,113,114,115,117,118,119,120,123,130,131,133,134,138,141,145,146,149,150,152,153,157,162,163,164,165,166,167],[0,1,3,6,8,9,11,14,16,17,18,23,24,27,28,29,31,32,34,35,36,38,39,40,41,42,43,44,46,47,49,50,51,53,56,60,62,63,65,66,67,69,70,71,73,74,78,82,83,84,86,87,88,90,91,92,93,95,96,97,98,103,106,108,109,112,113,115,118,122,123,124,126,127,129,130,132,136,137,139,140,141,144,145,147,151,155,156,158,161,163,165,166,167],[1,7,9,10,11,14,16,22,24,26,27,30,31,33,34,35,36,38,39,40,41,42,44,46,52,55,58,59,60,63,64,65,68,71,76,79,80,81,83,84,85,86,87,89,90,93,94,95,97,103,105,108,109,110,112,118,120,122,123,124,127,130,131,132,135,137,138,139,140,141,142,143,147,148,149,150,154,157,159,161,163,164,166,168],[0,1,5,7,9,11,14,15,21,22,25,26,28,29,30,31,36,37,39,42,43,44,46,49,50,51,52,53,58,61,62,63,67,69,70,72,73,74,76,77,78,79,82,83,84,86,87,88,89,91,94,96,97,100,102,104,107,108,109,110,111,112,113,114,115,117,118,120,121,122,123,125,126,128,129,130,132,135,137,138,139,142,144,146,147,150,155,157,158,160,162,163,164,168],[24,38,44,111,121,122,124,129,132,133,134,136,139,141,144,145,148,152,153,154,156,157,158,159,162,164,167],[5,7,8,11,14,15,16,17,18,19,21,23,24,27,28,32,33,38,40,41,42,46,48,56,57,59,60,66,68,71,72,75,76,77,78,79,81,83,84,86,87,91,93,94,95,96,97,100,103,104,106,108,109,110,111,112,113,117,118,121,126,128,132,133,137,141,143,145,151,152,157,160,163,168],[0,4,6,7,9,10,11,12,14,15,17,18,21,24,31,33,35,36,37,39,43,44,45,48,49,51,52,53,55,59,60,61,62,63,64,66,67,69,70,71,72,75,76,77,79,80,82,83,84,88,90,91,93,95,96,97,99,100,101,102,103,106,108,109,110,111,114,119,120,121,124,125,128,129,130,132,136,140,141,142,143,144,147,148,150,151,152,154,155,158,160,166,167,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,47,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,122,123,124,125,127,129,131,134,135,138,140,145,146,148,152,154,155,157,160,163,166,167],[1,2,6,7,9,10,14,15,21,23,30,31,33,36,37,39,40,42,43,48,50,52,54,55,56,57,59,61,63,64,68,69,70,73,74,80,82,83,84,85,86,88,91,92,94,97,98,100,101,104,105,106,107,109,112,113,114,115,117,119,122,125,128,131,132,133,137,138,139,143,146,147,150,151,152,157,159,160,163,164,165,166],[38,49,121,123,125,132,133,135,136,140,141,143,144,146,147,148,149,156,157,161,165],[0,3,4,5,9,11,16,19,22,23,25,27,28,29,30,35,37,40,41,43,44,46,47,48,49,53,54,55,59,60,62,63,64,65,66,68,72,74,75,76,77,78,80,82,84,85,86,89,90,93,94,96,98,100,101,102,103,105,106,108,109,111,113,115,116,117,118,119,125,129,130,132,137,139,141,143,145,147,154,157,162,163],[0,2,3,6,9,14,16,19,23,24,28,29,32,33,34,35,36,42,43,44,46,48,49,54,56,57,58,59,61,63,64,65,66,67,68,70,73,74,75,77,78,81,84,85,86,87,89,91,93,94,95,96,98,99,100,101,105,106,107,108,109,110,113,114,115,119,120,122,127,129,131,132,133,134,135,136,137,138,141,142,145,146,147,148,149,150,155,156,157,158,159,162,163,164,166,168],[0,1,3,5,6,7,8,12,13,15,17,19,23,27,28,29,30,32,37,38,39,40,43,46,47,49,51,52,55,56,57,60,62,63,64,66,68,69,70,72,76,77,78,79,80,82,84,87,88,89,90,93,98,101,102,103,107,109,111,112,114,115,119,120,125,126,127,128,129,132,136,137,140,144,145,146,147,148,149,155,156,157,159,160,161,162,164,167,168],[4,7,10,11,13,15,16,18,19,20,21,24,27,31,32,35,37,43,44,46,49,50,51,52,53,54,55,57,58,59,62,63,66,68,73,78,83,85,88,89,94,98,99,100,102,104,106,110,112,115,116,117,118,119,121,122,125,127,130,132,133,134,139,141,143,145,146,147,150,152,153,156,158,159,160,162,163,164,166,168],[2,3,6,7,12,13,14,15,19,25,29,30,33,36,37,39,40,41,55,56,57,58,59,66,67,68,69,72,75,77,78,79,80,83,84,85,86,87,88,89,90,91,92,93,98,99,102,104,105,110,112,113,114,115,116,117,118,119,120,121,122,125,127,130,132,134,135,136,137,139,141,145,146,147,149,154,155,160,162],[0,2,3,4,6,7,9,10,11,13,14,15,23,25,27,28,30,32,34,36,37,43,44,45,49,50,51,52,54,55,56,57,60,65,66,67,68,70,71,75,76,79,81,82,87,88,89,90,91,92,94,98,102,103,105,109,112,116,121,123,124,128,129,130,131,133,135,141,143,144,145,146,147,149,151,152,153,156,158,160,161,162],[1,2,3,5,8,10,11,13,14,15,16,19,21,24,26,27,28,31,34,36,37,39,42,46,51,54,56,57,62,63,65,69,70,71,72,73,74,77,82,83,84,88,90,91,93,95,96,97,98,100,101,103,104,105,107,108,109,110,111,115,116,117,119,120,121,122,123,130,131,134,135,136,141,143,146,147,148,149,150,152,155,157,160,161,164,165,166],[1,3,4,6,8,11,12,15,19,20,21,22,23,24,26,27,29,30,31,32,33,38,40,41,44,45,46,48,51,53,54,57,58,59,61,63,65,67,69,71,72,73,83,88,89,90,91,92,93,94,95,96,97,102,103,104,106,108,110,111,113,114,116,119,121,122,125,127,129,133,137,138,139,142,150,154,155,156,157,158,161,162,163,165,167,168],[4,6,10,11,13,14,17,19,20,21,22,23,24,25,26,29,30,35,37,38,40,41,42,45,46,48,50,51,52,53,54,57,61,62,64,71,72,75,79,81,83,86,89,91,96,99,102,103,109,111,112,113,117,118,121,124,127,128,130,131,133,134,135,138,139,142,143,144,146,149,151,153,154,157,158,159,161,164,165,166,167,168],[0,1,2,6,8,9,11,12,13,14,18,19,23,24,25,26,29,31,35,38,40,41,42,47,51,52,53,54,59,61,63,64,65,66,68,69,71,74,75,77,78,79,83,84,85,86,88,89,94,95,98,103,104,105,107,108,109,110,111,115,116,117,119,120,123,124,125,127,134,136,137,140,142,145,146,152,154,155,157,160,161,162,164,165,166,168],[1,2,3,4,5,6,10,12,14,15,17,18,20,21,22,24,26,28,29,30,33,34,40,41,44,49,50,54,56,57,60,63,64,66,68,69,71,72,73,74,75,77,79,81,82,83,84,85,86,87,88,90,92,93,99,100,103,104,106,107,110,115,116,120,121,123,124,125,127,128,129,131,132,133,134,140,143,146,151,152,154,156,157,161,165,167],[65,121,136,137,138,148,156],[0,1,2,3,4,6,9,11,12,13,14,15,16,18,19,24,25,26,27,28,29,31,33,36,37,38,40,41,43,44,48,49,51,52,55,56,58,59,62,64,67,68,69,70,71,72,74,76,77,78,80,82,83,85,92,95,97,98,102,104,107,108,109,111,114,115,116,119,121,122,123,124,125,129,133,135,136,137,139,141,143,145,148,150,151,152,154,155,156,157,162,163,166,168],[0,1,3,6,11,15,18,19,20,21,23,27,30,31,33,34,36,37,39,40,41,42,46,48,49,50,52,53,54,59,60,61,63,64,65,68,69,71,73,75,79,83,86,88,89,90,91,92,95,96,97,99,100,101,103,104,105,106,114,118,120,121,122,123,124,125,126,127,128,130,132,133,135,138,139,140,143,144,147,150,152,156,157,160,161,162,165],[0,2,3,4,9,10,11,13,16,17,23,24,27,28,30,31,34,36,37,38,40,41,42,49,50,51,53,56,58,59,60,63,64,65,66,69,70,72,74,75,78,81,83,85,86,87,88,90,92,94,95,96,101,106,111,115,118,121,122,123,124,125,128,130,131,133,136,137,140,141,143,144,145,149,150,152,154,155,156,162,164,168],[0,2,4,5,6,7,9,11,12,13,14,15,18,19,21,22,24,25,29,33,34,37,38,39,42,45,47,49,50,51,52,53,54,56,58,59,60,61,63,64,66,67,69,71,72,75,79,81,87,89,90,91,92,96,97,98,99,101,105,106,110,111,113,114,116,117,120,121,122,124,125,126,127,131,133,139,141,142,143,148,149,152,153,159,160,161,162,164,167],[3,5,9,10,11,14,16,18,19,23,24,25,27,29,30,33,34,36,37,38,44,47,53,54,55,57,58,64,66,72,76,77,78,81,83,84,86,88,89,90,91,96,98,99,100,101,102,105,106,107,108,109,111,115,116,118,119,121,122,123,126,127,128,131,135,138,140,141,143,146,147,149,151,156,157,158,160,161,164,166,168],[1,3,5,7,8,10,12,14,16,18,21,23,25,27,28,29,31,32,34,35,40,41,44,45,46,47,52,53,56,57,58,59,66,67,68,69,71,73,74,75,91,92,93,95,97,98,100,104,107,108,111,112,115,116,119,121,123,127,128,130,133,135,138,139,141,144,145,147,148,149,152,153,157,158,159,160,161,163,165,166,168],[0,3,5,6,8,10,13,15,16,18,19,21,23,27,29,31,33,34,37,38,39,41,43,45,46,48,50,52,55,56,59,60,62,63,64,65,73,74,77,78,79,80,83,84,85,98,99,102,104,105,108,109,111,112,113,114,115,116,117,118,119,122,123,125,129,131,135,137,138,139,140,142,146,147,148,149,155,157,158,162,163,164,165,166,167],[24,124,157,158,160,163,164],[0,2,3,4,8,9,10,12,13,15,17,18,19,20,22,23,24,25,27,30,37,42,44,45,49,50,51,53,55,58,63,64,65,67,72,73,76,79,83,84,88,90,91,92,93,94,95,97,101,102,106,108,109,110,113,114,115,116,118,119,120,121,122,123,124,127,130,133,135,136,138,143,145,146,147,148,150,151,155,163,165,167],[6,7,8,9,10,11,12,13,17,18,19,20,22,24,27,30,31,33,35,37,41,43,45,46,47,48,49,50,51,54,55,56,57,58,59,68,69,74,75,76,77,79,81,83,84,86,88,90,94,95,97,98,100,102,104,105,106,107,108,109,111,118,119,120,121,123,124,125,127,130,131,134,136,139,140,145,146,148,150,151,152,155,157,159,160,163,164],[1,5,9,10,11,13,14,15,16,19,21,22,23,26,27,31,34,40,41,42,44,45,46,48,49,51,54,59,60,61,62,63,64,66,67,68,70,71,73,74,75,77,79,80,82,85,86,87,88,90,91,94,95,96,97,98,100,101,102,103,104,105,106,112,113,115,118,120,124,125,127,134,135,137,138,140,141,142,143,145,147,148,150,151,153,155,160,162,164,165,167],[24,122,156,158,164],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,76,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,122,124,127,129,131,134,135,136,137,138,140,141,143,145,148,149,152,154,155,158,159,161,163,165,166,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,123,124,125,127,131,133,138,140,141,153,156,157,161,163,164,166,167],[0,2,3,4,11,14,19,20,21,23,25,28,31,32,34,35,37,40,41,42,46,48,49,51,52,53,57,58,59,61,63,67,68,69,70,71,72,73,74,79,80,82,83,86,90,91,92,94,95,96,98,99,100,105,108,112,113,114,118,120,122,124,125,127,128,129,130,139,142,145,146,149,150,152,154,156,158,164,167,168],[2,4,6,7,11,13,14,15,16,20,21,22,24,26,27,29,32,34,35,37,38,42,43,44,46,47,48,50,56,58,60,61,62,69,70,72,73,74,76,78,79,80,81,82,83,84,87,88,89,90,91,92,93,94,95,98,101,104,106,107,108,109,111,113,114,115,116,117,118,123,124,125,127,129,131,133,134,138,139,141,143,146,147,151,152,159,163,164,167],[0,7,8,9,11,12,14,15,17,19,20,21,23,25,26,28,35,39,40,41,42,43,44,46,47,48,50,55,58,59,61,62,63,64,66,71,73,74,77,80,81,83,84,85,86,87,88,90,92,93,99,101,102,103,105,106,107,108,109,110,114,117,121,126,128,129,131,132,138,139,140,142,143,146,149,151,152,153,157,158,159,160,162,163,167,168],[0,1,8,11,12,14,16,17,18,19,20,21,24,25,27,28,30,32,34,36,40,41,47,49,51,52,54,55,56,57,60,61,62,64,67,68,70,71,72,73,74,78,79,81,82,84,85,86,87,88,89,93,94,97,99,101,102,103,106,107,111,112,115,117,119,121,122,123,124,125,128,129,135,136,137,138,140,141,144,147,148,149,154,155,156,158,162,165,168],[123,125,149,157,159,161,165,166],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,83,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,127,131,134,140,141,143,145,149,152,154,155,156,157,159,160,161,163,164,165,166,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,124,127,129,131,133,138,140,141,149,153,156,158,159,163,165,166,167],[2,4,5,6,8,10,11,12,19,20,21,23,24,25,26,27,31,33,34,38,40,42,43,44,47,48,49,51,57,58,59,61,63,66,70,71,73,74,75,80,83,84,85,86,87,89,92,93,95,96,98,99,101,102,107,110,113,114,115,116,118,119,121,122,124,125,127,129,132,133,135,139,140,143,144,149,154,157,158,159,164,165],[86,111,121,122,123,124,125,132,133,136,141,148,153,154,155,156,159,160,161,162,164,165],[1,2,4,5,6,7,10,11,12,14,18,20,22,24,27,32,33,34,35,39,40,41,43,44,46,47,48,49,51,52,54,56,60,61,62,63,64,65,67,68,71,73,74,76,78,79,80,86,88,89,92,97,98,100,101,102,105,106,108,109,110,112,113,117,119,121,123,124,125,129,132,136,138,140,145,149,151,152,153,154,156,160,162,163,164,165,167,168],[0,1,2,3,4,6,8,11,14,15,18,21,22,24,25,27,28,29,30,31,32,33,34,36,38,39,40,42,43,46,47,50,53,55,57,58,59,60,61,63,64,68,69,70,71,72,74,76,78,83,87,88,89,90,93,94,96,97,98,99,101,103,105,107,114,115,116,119,120,122,123,127,129,136,137,140,141,142,143,144,148,150,151,152,157,158,159,160,163,164,166,167,168],[0,1,2,3,4,7,8,11,16,17,18,19,21,22,25,26,32,34,35,36,37,38,39,40,41,42,45,47,48,58,61,67,68,71,72,73,74,75,79,82,85,86,87,88,89,101,102,104,107,108,109,110,112,113,114,115,117,118,121,122,124,125,126,128,129,131,132,137,138,139,145,146,147,150,151,152,153,156,159,160,163,164,165,168],[2,3,4,7,8,10,12,13,14,15,18,19,20,23,24,25,27,31,32,33,34,36,41,44,45,51,53,54,57,60,61,62,64,66,67,68,69,72,73,76,78,84,85,86,89,92,93,94,101,105,106,108,109,111,112,113,114,115,116,118,120,124,126,128,129,130,131,132,133,134,135,137,138,139,142,143,146,150,152,157,158,160,161,164,167,168],[0,2,4,5,6,7,8,9,12,15,17,18,22,23,24,30,34,36,38,41,44,45,46,47,51,52,55,57,58,59,60,61,63,64,68,69,74,77,79,80,81,82,83,86,89,90,91,92,94,97,99,100,101,102,103,108,110,112,115,118,119,120,122,124,129,130,132,134,135,136,139,140,141,142,144,145,148,149,151,152,155,158,160,162,164,167,168],[24,149,152,155,158,160],[0,1,3,5,6,7,9,12,13,14,16,17,20,25,30,32,37,38,39,41,42,47,50,51,52,54,55,57,59,60,61,63,66,67,68,72,73,76,82,84,87,88,89,90,91,93,94,96,98,99,100,101,102,104,105,107,109,110,111,112,114,115,119,124,126,127,131,133,134,136,137,138,140,143,144,151,154,163,164,168],[0,3,6,7,8,10,16,17,19,21,22,24,25,26,27,30,32,33,34,35,36,37,38,41,44,45,46,47,48,49,51,53,56,57,58,61,64,65,67,68,70,71,72,73,75,78,79,80,83,85,90,91,92,95,96,97,100,103,104,106,108,109,110,112,115,116,117,120,121,123,124,125,126,127,130,133,134,135,136,137,141,142,146,148,149,151,153,155,156,157,158,159,160,162,163,164],[2,3,4,6,8,9,10,11,12,15,19,21,22,25,30,31,32,33,34,37,39,43,45,48,49,50,52,59,60,63,65,68,69,70,76,77,79,80,81,82,84,86,87,91,92,93,94,95,96,97,99,102,104,106,108,109,111,112,115,122,124,129,131,132,133,134,136,137,138,141,142,144,151,152,153,154,156,158,159,165,166,168],[0,1,2,4,6,7,9,15,16,17,18,21,24,25,28,29,32,34,35,36,39,40,43,47,53,54,55,56,58,60,61,62,68,72,73,79,80,82,84,87,88,89,90,91,93,98,99,102,104,105,107,109,110,111,113,114,115,116,117,119,120,121,122,123,125,126,128,130,133,134,136,146,147,149,152,153,155,156,157,158,160,163,166,167,168],[0,2,3,4,5,6,9,15,16,17,18,19,21,25,26,32,37,38,40,41,42,43,44,49,50,52,53,57,58,60,61,63,66,67,68,70,72,78,80,85,87,90,92,93,95,97,98,100,101,102,104,105,106,108,110,111,112,113,114,116,118,119,122,124,125,126,127,129,130,131,132,133,134,135,136,137,138,141,142,143,144,145,148,151,152,154,156,157,158,162,163],[24,99,124,136,137,138,140,148,157,158,160,164],[1,5,6,7,9,13,14,15,16,19,21,24,25,26,27,28,29,30,31,32,33,34,35,36,40,45,49,50,51,53,57,58,59,61,64,69,70,71,73,74,75,76,77,81,83,84,88,90,92,96,98,99,105,106,107,108,110,112,117,120,122,123,125,126,128,129,130,133,134,135,137,138,139,142,143,144,145,149,151,152,153,154,155,156,161,162,168],[0,3,5,7,14,15,17,18,19,20,22,29,30,31,33,34,36,39,40,41,44,45,47,48,51,53,54,55,56,57,60,61,63,65,67,68,72,73,74,75,76,78,80,81,83,91,93,95,96,97,100,102,103,105,107,108,114,115,120,123,126,128,131,133,136,137,139,140,142,144,145,149,150,152,156,157,158,163,168],[0,1,2,3,4,5,6,7,8,9,10,11,17,18,19,20,23,24,25,26,29,31,32,36,37,40,41,44,45,46,48,50,52,55,57,58,60,66,67,68,69,70,71,72,73,74,75,76,77,80,81,85,87,88,92,93,95,98,99,100,101,102,104,106,109,112,114,116,118,122,124,125,126,127,129,130,132,133,134,136,139,140,144,145,146,149,150,152,154,155,156,157,158,159,161,162,163,164,166,168],[24,104,122,136,141,148,158,164],[1,2,3,4,8,10,11,12,14,15,16,17,20,21,23,24,27,28,29,31,34,39,42,44,45,48,50,51,53,54,55,56,58,59,60,62,63,65,68,79,83,86,88,89,90,91,93,94,95,99,100,101,102,103,104,105,109,110,113,117,120,122,123,127,130,133,136,139,141,142,143,144,147,148,149,150,151,153,155,158,159,161,166,167,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,106,112,114,117,118,121,123,124,125,127,131,133,136,140,148,153,156,157,161,163,164,166,167],[0,1,3,5,6,7,8,9,11,12,17,18,19,20,21,23,24,28,30,33,34,36,37,38,39,40,42,44,45,46,48,49,53,54,56,57,58,59,60,62,64,65,69,70,72,73,74,75,76,77,80,85,87,91,92,94,95,96,100,101,103,106,107,108,114,117,118,119,120,121,123,125,126,127,130,132,133,135,136,137,138,139,140,141,143,145,146,149,152,153,154,159,160,161,164,167,168],[24,38,108,134,135,136,140,141,147,149,155,159],[24,38,109,111,123,125,129,132,133,134,136,138,140,143,145,147,149,153,154,157,158,160,162,164,165,167],[2,4,10,12,17,18,19,20,21,23,24,25,26,27,28,30,31,32,33,35,36,37,38,39,41,43,44,45,46,52,54,60,63,64,65,68,71,72,75,77,80,81,82,84,87,88,89,91,92,93,97,98,99,102,103,106,109,114,117,118,119,120,129,131,134,135,139,140,141,142,143,147,149,150,151,152,153,154,155,157,159,161,162,164,166,167,168],[5,7,12,14,16,19,20,21,24,27,29,30,31,32,34,37,40,41,42,45,47,49,54,56,67,69,70,71,72,74,78,79,80,83,84,86,87,92,94,98,99,100,104,106,108,109,110,111,114,120,122,123,125,133,134,135,136,138,140,142,144,145,146,147,148,153,154,155,156,157,159,162,163,165,166],[0,1,3,6,8,9,10,15,16,18,19,20,22,23,24,28,33,37,39,41,42,43,45,47,48,49,50,54,56,57,59,63,64,65,66,70,72,74,78,82,83,85,86,87,89,90,92,93,95,96,100,103,104,105,107,110,111,112,114,119,120,121,123,126,128,132,133,134,137,141,143,146,149,150,151,152,153,155,158,161,162,165,167],[1,2,3,4,10,14,16,18,20,22,23,25,26,30,31,34,39,41,44,46,48,49,51,54,55,56,58,59,60,63,64,65,66,72,75,76,80,85,86,87,88,90,93,96,97,99,102,105,108,110,111,114,115,119,120,124,126,127,129,133,137,138,139,140,144,145,150,152,153,154,162,166],[24,38,115,124,132,133,137,138,141,147,148,157,159,164],[0,1,3,6,8,12,17,18,21,22,23,24,25,27,29,31,33,35,38,39,40,42,43,44,49,53,54,56,57,59,63,66,68,69,70,71,72,73,74,75,78,82,83,86,88,89,92,93,94,95,96,100,103,105,106,107,109,110,114,117,119,120,122,123,125,126,127,128,131,132,133,134,135,136,137,141,142,143,146,152,155,157,159,161,162,164,165,167,168],[0,1,2,4,5,6,8,9,10,12,13,14,16,17,18,20,21,22,24,25,26,28,29,31,32,33,34,35,37,39,41,42,43,45,48,52,56,60,63,66,68,69,70,72,74,76,79,81,82,84,85,87,90,94,95,97,98,99,100,105,106,107,108,111,112,118,119,125,128,129,132,134,135,136,138,140,141,142,143,145,146,147,148,149,150,152,156,158,159,160,161,167],[24,111,118,121,122,123,124,125,129,132,139,140,149,152,153,154,156,158,159,161,162,164,165,167],[1,6,8,9,10,12,16,18,19,22,24,25,26,29,30,35,38,42,43,44,48,50,52,53,55,56,57,58,59,60,63,64,65,69,70,71,73,75,76,77,78,79,80,81,84,86,88,89,90,91,92,97,102,103,107,108,111,113,116,117,120,123,124,125,126,127,130,131,132,135,138,139,141,143,145,147,149,150,151,154,161,162,163,164,165,166,168],[0,1,3,4,5,6,7,8,10,12,13,14,15,16,18,20,21,22,23,26,34,36,38,43,45,46,47,48,49,50,52,58,60,62,65,68,69,70,73,74,78,79,80,83,84,86,87,90,91,93,94,98,99,101,102,103,104,105,108,112,113,117,118,120,121,122,123,126,127,129,130,131,146,147,148,149,150,153,155,161,162,163,168],[0,3,4,6,7,8,10,11,12,13,15,16,17,21,26,27,29,31,33,34,35,37,38,40,43,46,48,49,52,56,58,60,61,62,69,70,71,72,74,75,79,80,81,83,84,86,90,91,92,94,95,97,98,99,100,101,102,103,104,105,106,108,113,114,115,119,121,122,123,125,127,130,131,144,146,148,153,154,155,156,158,160,163,164,166,168],[5,8,9,10,12,16,17,19,20,22,23,25,26,28,31,34,35,36,39,44,47,48,49,53,55,60,63,66,67,69,71,72,73,74,75,77,78,81,83,84,85,86,87,88,90,91,92,94,95,96,97,99,101,103,107,108,111,112,113,115,117,120,121,122,124,125,127,128,133,138,139,140,142,144,146,147,148,149,151,152,156,158,162,165,166,168],[3,10,11,12,13,16,17,18,19,26,27,29,30,31,32,33,39,42,43,54,55,60,61,63,65,67,69,71,72,73,76,78,79,81,85,86,89,91,93,97,98,101,102,103,105,107,109,112,115,117,118,120,124,125,132,133,135,139,141,145,146,148,150,151,153,156,157,162,163,164,166,168],[0,2,3,4,5,11,12,13,14,16,18,19,21,25,26,30,32,34,36,37,38,39,40,45,46,48,49,51,54,55,56,61,62,64,65,67,70,71,72,76,79,81,82,83,84,89,90,92,94,96,97,98,104,106,107,109,111,115,116,117,118,120,121,122,123,124,126,128,129,133,137,138,139,140,144,146,147,150,151,154,155,156,157,158,161,162,163,164,165,166],[0,2,3,4,5,9,13,14,15,16,17,19,20,21,22,25,27,28,29,31,34,36,37,39,40,41,43,49,52,57,60,63,66,70,72,74,75,76,78,82,83,85,89,90,94,97,98,99,100,102,104,105,106,110,112,113,114,118,122,124,125,127,129,135,136,137,141,148,150,152,154,155,156,158,159,160,161,162,166,167],[0,5,7,11,12,13,15,16,17,23,25,28,31,32,33,37,40,41,43,44,45,46,51,54,55,56,60,65,66,67,69,70,74,77,78,80,81,82,84,86,87,88,90,92,93,94,95,96,97,99,107,108,109,111,113,114,115,116,118,119,120,123,127,132,133,138,139,143,144,145,151,153,155,158,159,163,164,165,166,167],[4,7,8,10,11,13,15,16,18,19,20,21,24,27,31,32,35,37,38,43,44,46,49,50,51,52,53,55,57,58,59,62,63,66,68,73,78,83,85,88,89,94,98,99,100,102,104,106,110,112,115,116,117,118,119,121,122,123,125,127,130,131,132,133,134,139,143,145,146,147,149,150,152,153,154,156,157,160,162,163,168],[2,3,4,5,6,7,11,12,15,17,19,20,23,24,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,122,123,125,127,131,132,134,136,141,145,149,152,154,155,156,158,159,163,166,167],[0,1,4,5,8,9,11,12,13,14,15,18,19,22,23,24,25,26,27,28,29,30,32,33,35,37,39,40,43,44,46,48,50,52,55,56,59,60,63,64,66,69,70,72,74,78,80,81,84,87,89,93,94,95,96,97,102,104,105,106,107,112,113,118,119,120,121,122,123,125,126,127,128,129,130,131,132,135,138,139,141,143,144,147,149,151,152,155,156,159,160,163,165,166,167,168],[1,2,4,6,11,12,13,16,18,20,23,25,28,29,30,31,32,33,34,35,38,39,40,43,45,46,47,55,57,58,61,62,64,67,68,72,73,74,75,78,79,81,88,89,92,97,99,101,102,103,104,105,106,107,110,112,115,117,119,122,123,125,128,130,132,135,140,141,142,145,146,148,150,153,155,157,158,159,160,162,164,165],[1,2,3,7,11,12,13,14,15,16,17,18,19,20,24,28,29,31,32,35,36,37,45,46,53,54,55,56,59,60,61,62,64,65,68,70,71,74,76,78,80,84,85,88,90,91,95,96,98,99,100,101,103,105,110,111,114,117,120,122,123,124,127,128,129,130,132,134,135,139,143,144,145,147,149,150,151,152,153,156,157,159,165,166,167,168],[13,24,38,132,134,136,140,149,159,161,164,167],[0,1,6,7,14,16,17,19,20,21,24,25,26,27,32,33,34,36,38,41,42,45,46,48,50,52,54,57,59,60,63,64,67,68,70,72,74,78,80,81,84,86,88,90,91,92,93,94,95,98,99,100,101,103,104,105,106,107,111,112,113,116,117,122,124,128,130,132,133,134,135,136,137,139,140,142,145,146,147,149,150,151,152,155,158,159,160,164,165,166,167],[0,3,4,5,8,10,15,16,19,22,23,26,28,29,30,32,33,38,39,40,42,43,47,49,50,51,52,53,55,56,60,61,63,65,66,67,68,69,71,72,75,77,79,80,81,82,85,88,89,90,95,96,98,100,101,102,103,105,106,110,113,115,116,117,118,119,120,121,124,127,128,131,132,133,135,136,138,141,144,145,146,147,149,151,155,156,157,159,160,161,162,165],[0,1,3,6,8,9,10,15,19,21,22,23,24,26,27,31,34,38,40,41,42,44,45,46,47,49,50,51,53,54,55,56,58,59,60,63,67,71,72,74,75,78,82,84,88,94,98,100,101,103,105,108,110,113,114,115,116,121,124,125,126,128,131,132,133,136,139,140,143,146,149,150,151,152,153,154,157,159,161,162,164,165],[0,2,4,5,8,9,10,11,13,14,16,17,18,19,20,21,24,25,26,27,29,31,33,39,42,44,47,48,50,51,52,53,56,57,59,61,66,69,71,75,79,82,83,85,88,89,92,93,94,95,97,98,100,101,102,103,104,105,108,110,111,112,115,123,124,127,131,132,133,134,137,140,143,146,147,148,149,151,152,153,164,166,167,168],[0,1,2,3,4,5,8,10,13,14,16,17,18,25,26,30,32,33,34,37,39,40,41,42,43,46,49,50,52,54,55,64,65,71,72,73,75,79,80,84,86,89,90,93,94,95,98,99,105,107,109,110,116,117,120,121,122,123,124,125,126,127,128,129,131,133,134,135,140,142,143,144,145,147,151,156,159,160,161,163,167],[24,38,121,125,132,133,135,137,138,140,143,144,146,147,148,149,151,158,159,160,161,164,165,166,168],[10,11,14,15,16,17,20,22,23,24,25,26,27,32,34,37,39,41,42,44,46,48,50,52,54,57,58,61,70,71,73,74,76,81,82,86,87,88,89,91,92,93,95,96,98,101,103,104,106,108,110,113,114,117,118,122,123,124,127,128,138,142,147,151,152,154,155,156,157,158,160,163,164,165,168],[2,4,5,6,9,10,11,12,14,15,16,17,19,20,21,28,29,30,31,35,38,39,41,45,47,48,49,51,56,61,65,66,67,69,70,72,74,75,78,81,84,85,86,91,93,96,97,98,102,103,105,109,110,112,113,114,116,117,119,120,121,122,123,124,125,128,129,130,133,137,138,139,142,143,144,146,149,150,154,156,157,158,161,163,164,165,166,168],[0,1,2,4,9,10,11,15,16,17,19,21,23,24,26,27,29,33,34,39,40,41,42,43,44,46,47,49,50,52,53,55,60,65,66,71,72,73,74,75,76,78,79,81,82,83,88,93,94,95,96,100,101,102,106,108,110,111,113,116,117,119,120,121,123,124,125,126,127,134,136,138,140,141,142,145,146,151,153,156,158,159,163,164,165,167,168],[0,7,8,9,10,13,14,15,16,19,23,27,28,31,32,34,38,42,43,44,46,47,48,50,55,56,57,61,62,66,67,68,74,75,79,80,81,83,84,86,96,107,108,113,114,115,116,117,118,120,121,122,123,125,127,128,131,132,133,136,139,140,143,147,148,153,154,155,156,158,159,164,165,166,167],[0,7,8,9,10,12,16,17,19,21,24,29,31,33,36,40,43,49,50,55,56,57,61,62,63,65,67,70,72,73,74,82,85,87,88,89,90,91,92,93,94,95,97,98,99,105,108,109,111,114,117,120,122,124,126,127,128,131,132,133,134,135,136,137,139,143,144,146,147,151,152,153,154,159,161,163,164,166],[1,2,3,4,5,7,8,9,10,12,14,15,16,18,19,20,21,22,25,26,27,29,30,33,35,38,39,40,41,42,43,45,46,47,49,51,52,53,55,61,65,66,68,69,70,73,74,76,78,79,84,85,89,90,93,94,95,96,97,98,101,103,105,108,109,110,112,113,115,116,120,123,124,125,127,128,129,130,131,135,139,140,142,143,145,149,154,155,157,158,162,163,166,168],[0,1,2,3,4,6,9,10,12,13,21,23,24,27,28,29,30,31,32,34,37,38,39,41,42,43,44,45,48,49,51,52,54,56,63,65,66,67,68,69,72,74,75,77,83,86,89,90,95,96,97,98,99,100,102,103,105,106,108,109,117,119,123,124,125,127,132,133,134,135,136,139,140,141,142,145,147,148,149,155,156,157,158,160,161,164,165,168],[24,120,149,158,160,161,164,167],[0,1,5,6,8,9,13,14,17,20,21,22,23,25,27,28,30,31,38,39,41,42,43,44,45,46,47,51,52,56,57,58,61,62,65,66,67,70,73,74,80,82,87,89,90,91,92,93,101,103,104,107,108,109,111,113,114,118,119,120,122,125,126,127,130,131,133,135,136,137,138,141,144,145,146,147,148,149,150,152,153,154,158,160,162,163,164,165],[1,2,4,5,8,11,14,15,17,19,20,21,22,23,26,30,32,36,37,39,40,44,45,47,49,55,57,62,64,66,67,68,69,71,76,77,81,82,85,86,87,90,92,93,96,98,105,106,108,109,111,113,114,116,117,122,123,125,127,131,135,136,140,141,142,145,148,149,150,151,153,157,158,159,160,162,163],[31,38,122,123,125,135,140,146,157,160,161,165],[3,5,8,10,11,15,16,17,18,21,26,27,28,29,31,32,36,39,41,42,46,50,51,53,56,58,63,64,65,66,67,69,72,74,75,79,80,82,84,86,90,91,92,93,95,97,100,101,102,103,104,105,106,109,112,114,115,116,117,118,120,123,126,127,130,131,132,134,137,139,140,141,143,144,145,147,148,151,152,154,156,157,158,159,160,161,162,164,166,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,124,127,131,135,141,144,146,153,156,157,158,160,163,165,166,167],[0,1,3,7,8,9,10,12,13,15,19,20,21,23,26,30,32,35,38,39,42,46,48,49,50,54,59,62,63,65,66,67,68,73,74,76,77,79,80,82,84,86,87,88,90,93,94,97,101,102,103,104,106,107,109,110,111,113,114,115,117,122,123,124,125,126,130,131,134,135,136,139,140,141,143,145,149,150,152,153,154,157,158,161,162,166,168],[0,1,3,5,8,9,11,13,16,23,25,26,27,28,29,31,32,38,39,40,42,47,52,54,56,57,58,59,61,65,67,68,69,70,71,72,73,77,78,79,80,82,84,85,86,87,89,92,95,96,97,99,101,105,106,107,108,109,110,111,113,114,115,116,117,118,122,124,127,129,132,133,143,144,147,153,156,157,159,160,162,163,166],[0,1,3,5,8,15,16,18,22,25,26,29,30,31,33,35,36,38,41,42,46,47,49,51,55,56,57,58,59,60,62,63,64,67,68,69,71,73,74,76,77,78,79,80,81,83,85,87,90,95,96,97,99,101,103,107,108,113,116,117,119,120,121,125,126,129,131,132,133,136,137,138,142,143,150,151,152,154,157,158,159,161,162,163,164,165,167],[1,5,6,7,8,13,16,17,20,21,22,27,28,30,38,39,40,44,47,51,52,53,54,59,64,69,73,74,77,78,79,87,90,92,96,101,104,105,107,108,109,110,112,113,114,118,120,121,124,126,127,128,130,134,136,137,138,144,146,147,148,150,152,156,157,158,160,161,162,164,165,166],[24,38,123,149,154,155,157,158,159,160,164,166],[1,3,6,7,8,11,12,13,14,15,16,17,19,20,22,24,29,35,36,39,40,41,43,45,47,48,55,57,60,61,64,65,66,68,70,71,72,74,75,76,78,79,80,85,90,96,98,102,108,114,115,116,118,120,122,126,128,130,131,133,134,135,136,138,143,144,145,147,153,155,157,161,163,165,166],[1,2,4,7,8,9,10,11,16,18,19,20,22,25,28,31,33,35,36,39,41,47,49,51,53,54,55,58,59,63,65,66,68,72,73,74,76,77,80,81,83,84,85,86,87,88,89,91,93,96,97,102,105,106,109,110,120,121,122,125,127,128,129,130,132,136,137,143,147,150,151,153,154,155,156,157,162,164,166,168],[0,2,4,7,8,11,12,14,16,19,20,22,25,27,29,34,35,40,42,43,44,45,48,49,50,51,52,53,54,55,56,57,60,61,62,65,67,69,71,73,76,78,79,82,83,84,86,88,90,91,94,95,102,103,110,111,114,115,120,121,123,125,127,128,132,134,135,137,139,142,145,151,153,155,157,161,162,164,165],[3,5,6,7,8,9,11,13,16,17,20,22,23,24,27,28,31,33,34,35,37,38,39,40,41,43,44,46,50,51,52,55,58,59,61,62,64,65,66,67,69,71,72,73,74,75,76,77,78,82,84,85,88,94,95,96,97,99,101,106,109,112,113,114,117,118,119,120,122,124,126,127,128,131,133,134,136,137,138,139,140,141,142,145,148,149,152,153,154,157,159,161,163,165,166],[0,1,2,4,6,7,9,10,11,14,18,21,22,23,26,27,28,29,35,36,37,38,40,41,42,44,46,47,48,50,52,53,55,56,57,60,62,68,70,71,72,74,76,79,80,81,84,86,90,92,95,96,97,99,101,102,103,105,106,107,108,109,111,115,116,118,119,120,121,122,123,125,128,130,133,135,136,138,139,140,145,147,148,149,150,151,152,155,156,157,159,160,161,163,164,166,167,168],[0,1,3,7,8,10,11,13,14,15,16,17,23,26,27,29,30,31,32,33,37,39,42,44,46,47,49,53,55,58,62,64,65,67,68,69,72,73,74,75,77,78,80,81,82,84,86,87,88,90,92,94,95,96,97,99,103,104,106,107,109,110,111,112,113,115,119,120,123,125,126,128,131,132,133,135,139,140,142,145,148,149,151,153,154,155,159,161,163,164,165,166],[1,2,4,6,9,10,13,15,16,18,19,20,23,24,25,27,28,30,31,32,33,34,35,39,40,41,44,46,47,56,57,63,64,66,68,70,73,75,76,78,80,81,83,85,86,89,90,91,92,94,100,101,106,107,108,109,110,114,115,120,125,127,130,131,133,134,137,140,142,145,148,150,152,153,157,161,162,163,164,166,168],[2,4,5,7,9,12,14,15,17,18,21,22,23,25,26,28,29,31,32,33,34,35,37,38,39,43,51,52,53,54,55,56,61,63,66,68,69,70,71,75,78,82,83,84,85,87,88,89,90,92,93,95,96,97,99,100,101,104,105,106,113,114,115,116,121,122,124,125,131,132,133,135,136,137,138,139,143,144,145,146,148,149,150,155,156,157,158,159,160,162,164,165,166,167],[0,1,3,4,8,9,10,12,14,15,17,23,24,28,30,31,33,37,38,44,47,48,50,54,55,56,59,65,66,68,69,70,71,74,75,81,84,85,89,91,92,96,98,99,100,101,102,103,104,105,106,108,110,111,112,113,115,116,124,125,126,127,128,132,134,135,137,138,143,144,145,146,148,151,152,156,157,158,160,162,163,164,166,168],[0,1,2,5,10,13,14,15,16,17,18,19,20,22,23,25,27,29,30,33,34,36,37,40,43,44,45,46,47,48,49,50,52,53,56,58,62,64,65,69,71,72,75,76,82,83,84,85,86,87,89,90,92,95,96,100,101,103,104,106,107,108,109,110,111,113,114,115,116,117,119,120,121,124,126,127,130,131,133,134,143,145,148,150,152,156,158,159,162,164,165,167,168],[3,4,5,6,11,15,17,19,20,22,23,24,26,27,28,29,30,32,34,36,37,38,40,41,42,44,45,49,51,52,57,61,62,63,64,66,67,68,70,71,72,76,80,84,85,87,90,92,93,95,97,100,102,103,107,111,115,116,117,118,120,122,123,124,128,131,134,135,136,140,141,142,143,145,146,149,150,153,154,160,162,167],[0,1,2,4,8,9,11,12,14,15,17,18,23,25,29,31,33,34,35,37,39,40,41,45,46,47,49,50,51,52,53,57,59,60,61,64,66,68,69,73,77,78,81,89,91,92,93,94,96,98,99,102,103,107,108,112,113,115,117,120,124,125,128,134,141,142,143,144,146,148,151,152,153,154,155,156,158,159,162,165,166,167,168],[24,38,52,123,125,133,134,135,136,140,141,144,145,146,147,148,152,157,158,160,161,164,165,167],[0,1,4,7,8,11,14,15,16,20,21,26,27,28,30,33,35,36,39,40,42,43,46,49,50,51,53,56,57,58,61,62,63,64,65,67,69,71,76,78,79,80,81,82,87,89,90,91,92,93,94,95,97,99,104,106,112,113,114,115,116,118,122,124,126,127,129,130,134,135,136,138,139,141,143,144,145,147,149,152,154,156,157,158,161,163,164,166],[1,5,6,7,9,10,11,13,16,19,21,25,28,32,33,35,38,39,43,44,45,47,50,59,62,67,71,73,77,78,79,86,88,89,90,92,93,94,95,97,98,99,100,102,103,105,106,107,109,111,113,117,118,119,121,125,127,128,130,131,132,133,139,144,145,147,152,153,154,155,158,161,164,168],[1,2,3,4,9,10,11,12,23,25,26,28,29,32,33,34,38,43,44,45,46,47,48,50,51,52,54,56,58,59,60,63,64,65,67,68,69,71,72,74,75,76,77,82,85,86,87,88,90,93,97,98,99,101,102,103,104,105,106,111,112,113,114,119,120,121,122,123,126,128,131,132,134,139,144,149,151,152,156,159,160,163,166,167],[0,1,2,6,8,10,11,13,14,15,18,20,21,22,24,31,33,34,38,39,40,42,43,45,47,48,49,51,54,55,56,57,58,59,60,63,64,65,67,70,71,73,74,75,76,80,81,82,85,88,92,94,96,101,107,108,109,113,116,122,132,135,137,141,144,146,149,150,154,155,156,157,158,159,161,163,165,166,168],[0,3,4,6,10,11,16,17,18,19,22,23,24,26,29,31,32,33,36,37,40,43,44,46,49,50,52,56,68,69,70,72,73,76,77,79,81,84,85,86,87,88,89,91,92,93,98,99,100,101,102,103,110,111,112,114,116,119,121,122,125,126,129,131,133,135,137,140,142,146,147,151,152,153,154,160,165,167],[24,59,136,137,139,140,141,149,158,160,161,164,167],[60,111,121,122,124,129,132,139,140,144,145,148,149,152,153,154,156,157,158,162,167],[0,1,6,7,8,9,10,11,24,25,28,31,35,37,39,40,42,45,47,48,51,52,55,57,59,61,62,63,65,66,68,70,74,75,76,77,80,81,83,85,87,89,90,91,93,95,96,97,98,99,103,104,105,106,107,108,109,110,111,114,115,118,119,120,123,124,125,126,127,128,131,132,134,135,136,137,143,144,145,147,149,150,151,152,153,155,156,159,161,164,166,168],[1,5,6,7,8,9,10,12,13,15,17,18,19,20,22,23,24,25,27,30,32,33,35,40,45,47,50,57,58,59,61,62,65,66,67,68,70,73,75,78,79,80,82,83,86,96,98,99,100,104,105,107,113,114,115,116,118,119,121,122,123,126,131,133,134,136,138,140,142,143,144,147,148,150,152,153,155,157,158,160,161,162,165,166,168],[1,2,3,4,5,6,10,13,16,18,19,20,21,23,25,26,29,30,32,33,34,35,36,38,39,41,42,44,45,47,52,54,55,56,59,60,61,62,64,66,67,68,72,73,75,77,78,81,85,87,88,89,91,92,93,95,98,100,102,103,104,106,107,110,112,113,114,116,121,124,127,129,130,132,133,134,136,137,143,145,147,148,158,165,166,168],[1,6,8,9,11,13,17,20,21,23,25,27,28,29,30,32,34,35,37,39,41,42,44,45,46,48,49,50,51,53,56,58,60,61,63,64,66,67,68,70,71,72,73,76,77,78,82,83,84,87,88,89,91,92,93,95,96,97,98,101,102,103,104,115,117,118,119,123,128,130,131,133,134,135,136,140,148,149,151,154,155,156,157,163,164,165,167],[0,1,2,3,4,7,9,10,18,20,22,26,29,30,32,39,40,41,42,45,46,48,52,53,56,57,58,60,62,63,66,67,69,71,73,74,76,77,78,79,82,83,84,91,93,94,96,97,101,103,105,106,112,113,114,115,116,119,123,127,128,129,130,132,133,134,135,137,138,141,143,144,145,147,148,149,150,152,154,155,156,158,159,160,164,165],[1,2,4,5,6,7,8,11,12,13,14,15,18,20,22,24,26,27,30,32,34,35,36,37,41,42,43,44,45,48,49,50,52,56,57,59,61,62,65,68,71,72,76,80,82,83,86,88,90,93,97,98,103,104,105,109,111,112,113,116,118,121,124,125,126,129,132,135,136,139,141,142,143,145,146,147,148,150,152,154,155,157,159,162,163,164,165,166],[1,2,4,5,6,7,9,11,12,13,16,19,20,21,22,23,24,26,28,32,34,35,36,37,40,44,45,46,49,50,51,52,53,55,57,60,61,62,63,67,70,71,72,74,75,76,79,81,83,84,85,86,89,92,96,97,98,99,101,102,103,106,107,109,111,112,113,114,115,116,119,121,122,125,126,129,130,133,140,141,142,144,149,150,152,153,155,158,161,163,165,166,167,168],[6,7,10,11,16,17,19,20,21,22,23,29,30,31,32,39,40,41,44,45,50,51,54,55,63,65,67,68,70,71,72,74,78,79,81,83,85,87,88,91,92,97,99,100,104,106,109,110,113,114,116,118,120,121,125,127,128,130,131,133,138,139,140,143,144,145,146,147,150,151,155,162,163,165,166,167],[0,1,2,3,4,5,9,10,12,14,16,17,18,19,20,21,27,30,32,33,35,36,38,40,41,42,43,44,45,46,48,50,53,56,57,58,59,60,61,63,64,67,69,70,72,75,78,79,81,83,84,85,88,89,90,91,94,95,96,98,101,102,103,104,105,108,109,110,111,113,115,116,119,121,122,123,126,128,129,131,132,133,135,136,138,139,141,143,144,145,147,151,153,154,156,157,159,165,166],[0,1,2,4,5,6,8,9,10,15,17,18,21,22,23,24,29,30,36,39,41,44,47,51,55,58,60,61,62,64,65,66,68,69,70,74,76,78,79,80,82,84,86,87,89,91,92,93,94,95,96,101,102,103,104,105,106,108,109,110,111,112,113,114,119,120,124,128,133,134,138,141,143,144,145,150,154,155,157,158,159,161,162,163,164,168],[124,149,157,158],[0,1,2,4,5,7,8,10,11,13,14,15,17,18,20,22,23,26,30,31,33,35,36,37,38,39,40,42,43,45,46,47,49,50,51,52,54,59,62,63,64,66,67,69,70,72,73,74,75,76,77,78,79,81,82,84,89,91,99,102,106,111,113,114,115,116,118,119,121,122,123,125,127,128,129,130,131,133,134,136,138,139,141,143,145,146,147,152,154,155,160,162,164,165,167],[0,1,6,7,10,11,12,13,16,17,18,20,21,22,23,24,31,32,36,37,39,44,45,64,65,66,67,72,73,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,93,95,98,99,100,101,103,104,105,106,107,108,109,110,111,121,122,125,126,128,129,130,132,136,137,138,139,142,143,144,145,152,154,156,159,160,162,163,164,165,166,168],[3,5,6,7,10,12,14,15,16,17,18,19,21,22,23,24,25,27,28,29,30,31,33,36,39,40,41,45,47,52,54,61,65,67,68,69,70,71,74,75,78,79,83,85,86,88,89,91,94,95,97,98,99,105,110,113,114,115,116,117,118,120,126,128,136,137,139,140,142,144,145,148,149,150,155,156,157,158,161,164,166,167],[24,123,127,149,153,157,158,159,160,164,166,168],[122,149,160,165],[0,3,6,7,8,9,13,14,16,18,20,21,22,23,25,26,27,28,29,31,33,34,35,39,42,45,47,49,50,51,52,53,58,60,62,65,68,69,72,73,78,83,84,85,86,88,90,93,94,98,99,101,102,103,104,106,111,116,118,120,123,124,125,128,131,133,136,137,138,140,141,142,144,146,150,151,152,153,154,155,156,159,162,164,165,166,167],[1,2,3,4,6,7,11,12,13,15,16,18,21,22,23,25,27,30,34,35,36,38,40,41,43,44,45,46,47,48,52,55,56,57,58,60,61,62,63,64,66,67,69,70,73,75,76,77,78,79,80,81,84,85,86,90,92,98,103,104,108,110,115,118,120,122,123,125,126,129,131,135,136,140,141,143,148,150,151,152,153,155,156,157,158,161],[0,3,5,6,12,13,14,15,16,17,18,19,25,26,28,30,31,35,37,40,41,42,43,46,47,52,53,55,57,58,60,63,64,67,68,70,71,72,73,74,75,78,85,86,89,90,92,93,98,99,102,104,105,108,109,113,115,117,119,120,121,123,124,126,128,129,130,132,137,138,139,140,142,144,146,147,149,150,151,152,153,154,156,157,159,163,165],[0,2,4,5,8,11,12,13,14,15,17,18,20,21,22,23,25,27,28,32,34,35,36,37,40,44,45,46,48,50,51,55,56,63,64,70,72,73,74,76,78,80,85,91,93,94,97,98,100,101,102,103,105,106,113,115,118,119,122,130,131,132,133,134,135,137,138,139,144,148,149,152,156,157,158,160,161,166,168],[12,13,14,15,16,18,21,23,24,25,27,30,31,33,35,36,41,42,45,48,49,52,53,54,55,60,61,62,63,64,65,77,79,80,81,84,87,89,91,92,94,96,99,101,102,103,106,107,108,109,114,115,118,119,122,124,126,128,129,130,131,132,134,136,138,140,141,146,147,148,149,151,153,154,157,158,159,160,163,164,165],[82,111,136,137,138,139,141,148,162],[24,123,125,157,158,159,160,161,164],[0,1,3,5,6,7,9,10,11,14,16,20,21,23,24,25,27,29,30,33,35,39,42,43,44,47,50,51,52,54,55,56,58,60,61,64,66,71,72,75,76,77,78,81,85,87,88,89,90,91,92,95,97,100,101,102,104,106,107,111,112,113,114,116,118,119,121,122,123,127,128,129,131,132,134,135,136,137,138,139,140,148,149,152,153,154,156,161,162,167],[0,2,4,7,8,9,12,13,14,15,16,18,21,22,26,27,28,29,30,31,33,35,37,39,40,41,44,45,47,48,51,53,54,55,56,57,58,59,66,67,71,72,73,75,81,82,84,85,86,88,90,91,93,94,95,96,98,100,106,107,108,109,110,112,114,117,118,121,123,124,125,126,131,133,134,136,137,141,142,144,146,147,148,154,155,157,159,160,161,162,163,164],[0,3,5,6,8,9,14,15,16,17,19,22,23,27,29,31,32,36,37,39,40,42,45,46,49,51,52,56,57,58,59,64,65,68,69,71,72,74,75,76,77,80,81,84,88,89,91,92,94,96,97,100,101,106,107,110,112,115,116,119,121,122,126,127,129,132,133,136,137,140,141,145,149,151,152,155,156,158,159,162,167,168],[2,4,5,6,9,12,16,20,22,23,25,26,28,30,32,33,35,38,41,44,46,47,49,53,54,56,57,59,60,61,62,64,65,67,68,69,70,71,76,77,79,80,82,88,89,90,91,92,94,95,96,100,102,103,104,106,107,109,110,111,112,113,115,119,120,123,125,128,129,130,131,133,136,141,143,148,150,151,152,155,156,157,158,159,160,163,164,165,167],[0,1,2,4,5,7,9,10,11,12,14,15,16,17,18,20,21,23,25,26,27,28,29,30,32,34,40,45,46,48,49,51,52,53,54,55,57,58,59,60,65,66,67,69,70,73,75,76,77,81,83,84,85,91,93,94,95,98,100,101,102,105,109,110,111,114,116,117,118,121,123,124,126,129,130,133,135,139,140,141,142,146,149,152,155,156,159,160,161,162,163,166,168],[0,2,3,4,5,6,8,9,10,13,16,19,22,26,29,30,31,32,33,34,39,40,41,42,43,45,46,47,48,51,54,56,57,58,59,60,64,66,70,73,74,78,80,83,86,87,91,93,94,99,101,105,106,107,110,112,113,115,117,118,119,124,126,129,131,136,138,140,143,145,147,148,152,154,158,159,161,164,167,168],[2,4,5,6,8,10,11,12,19,20,21,23,24,25,26,27,31,33,34,38,40,42,43,44,47,48,49,51,57,58,59,61,63,66,70,71,73,74,75,80,83,84,86,87,92,93,95,96,98,99,101,102,107,110,113,114,115,116,118,119,121,122,123,124,125,129,132,133,134,135,139,140,142,143,144,154,157,158,163,164,165,166,168],[0,3,5,6,9,10,12,15,19,24,31,32,34,35,40,41,44,45,47,49,50,52,55,57,58,60,62,64,67,69,71,73,75,76,79,80,83,86,87,90,92,93,94,95,104,107,109,110,112,115,117,118,121,122,123,124,128,129,131,133,134,135,137,139,142,143,144,146,147,157,159,161,163,164,165,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,94,96,97,103,104,105,112,114,117,118,121,123,124,125,127,131,135,141,147,148,149,153,156,157,159,161,163,166,167],[0,2,4,6,16,18,21,23,24,28,29,30,31,33,34,37,38,39,42,43,47,48,50,53,56,57,58,59,62,63,64,65,70,72,74,83,85,87,89,92,96,99,101,102,106,107,110,112,115,116,119,122,123,125,127,128,130,131,134,137,139,142,143,148,149,150,151,152,153,162,166,167],[123,126,152,153,157,159,166],[2,4,10,12,17,19,20,21,22,26,27,30,32,33,34,35,37,39,40,41,42,43,45,49,50,52,53,54,55,56,59,62,63,65,67,68,69,70,71,74,75,76,79,80,81,84,85,89,91,92,93,94,97,98,99,100,101,103,104,105,106,109,115,116,118,119,120,121,123,124,126,132,135,136,138,139,141,142,144,147,149,150,152,153,154,156,157,159,160,161,162,163,166,167],[0,1,6,7,9,11,12,14,20,21,22,23,24,27,29,32,35,36,38,39,40,41,42,43,44,45,47,49,51,53,54,55,58,59,63,64,67,68,70,71,72,73,74,75,76,78,80,82,83,86,87,90,91,93,95,99,100,102,103,108,109,110,111,112,115,117,118,120,121,122,125,126,127,133,134,136,137,144,145,146,147,150,151,153,154,156,161,163,164,167],[2,3,4,5,6,7,9,10,12,14,18,20,21,22,23,27,30,31,32,34,35,36,37,38,39,40,43,45,48,49,55,56,59,61,62,64,66,69,75,77,79,82,83,84,85,86,87,91,93,95,98,100,101,103,104,106,109,110,116,117,121,128,133,136,138,145,147,148,149,151,152,154,155,157,158,159,160,162,165,166,168],[1,3,5,7,12,13,14,15,16,17,22,23,25,26,29,31,35,37,39,40,41,42,43,44,45,46,47,50,51,55,56,58,61,66,67,68,69,71,74,78,79,82,84,85,86,87,90,91,92,93,94,95,96,98,99,101,104,107,109,110,111,114,115,118,119,121,122,123,125,126,127,128,132,133,134,135,136,137,142,143,144,145,146,148,150,151,152,153,155,157,158,159,162],[5,6,8,9,10,11,12,15,16,19,25,26,28,29,30,32,33,36,37,40,42,43,48,49,50,52,54,55,59,61,62,64,68,69,71,73,74,77,78,80,82,83,86,88,90,91,92,94,104,107,108,109,110,111,113,114,122,123,124,128,130,133,134,136,139,141,144,146,147,148,149,154,155,156,160,161,164,166,167],[0,1,2,4,5,7,9,13,14,15,18,19,23,24,25,26,27,32,35,36,37,39,40,42,43,45,47,48,49,51,56,61,62,63,65,69,71,72,73,75,76,77,81,84,85,87,88,89,90,93,94,98,100,102,105,108,115,116,117,119,120,125,126,127,129,130,131,132,133,134,135,137,138,139,143,144,147,150,154,155,156,158,159,160,161,165,168],[1,2,4,5,8,11,12,13,17,18,19,20,21,27,28,31,32,33,35,37,38,39,40,41,42,44,50,52,59,61,63,64,66,67,70,73,74,76,77,79,80,85,86,87,101,102,103,104,105,106,107,109,111,112,113,114,115,116,118,121,122,124,125,126,127,130,132,138,139,141,146,148,149,153,155,156,157,160,162,165,167],[1,2,4,5,9,11,16,18,20,21,22,23,27,29,30,31,33,34,35,40,47,49,50,51,52,53,55,56,60,61,64,65,66,69,74,76,77,78,79,81,83,87,88,90,91,93,95,96,97,98,99,101,108,110,111,114,115,117,118,120,121,122,126,129,130,133,134,138,140,142,144,145,147,149,150,151,157,158,161,162,168],[0,7,9,10,11,15,18,20,22,23,24,25,27,28,29,30,31,32,33,35,38,40,43,47,48,49,50,51,52,54,58,59,60,62,64,65,68,70,72,73,74,76,77,80,81,82,83,84,86,93,99,101,102,103,104,105,108,109,111,113,118,122,127,128,129,131,132,133,137,141,148,149,151,152,158,159,160,163,166,167],[0,1,2,3,4,7,10,11,13,15,16,17,19,20,22,29,31,32,33,34,37,40,41,43,45,48,49,51,53,54,55,56,57,58,61,63,64,71,75,76,78,81,82,83,84,90,93,94,95,96,98,100,101,107,110,113,114,120,122,124,127,128,131,132,133,137,138,141,142,143,144,145,146,147,148,149,153,154,155,156,158,159,160,161,164,165,167,168],[2,4,5,6,8,10,11,12,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,34,35,37,39,40,41,42,44,45,48,50,51,52,54,56,57,58,62,63,65,66,67,68,71,73,76,77,81,83,84,85,87,90,91,92,93,97,98,99,101,104,105,106,107,108,109,110,113,116,120,121,122,123,124,126,128,129,131,132,134,142,143,146,148,149,150,151,152,155,156,161,162,163,164,165,167],[24,38,107,121,132,133,135,136,140,141,147,149,156,159,164],[3,5,8,10,11,15,18,20,24,25,26,27,29,31,36,39,41,42,47,53,54,55,56,59,62,63,64,67,71,76,78,79,88,91,92,98,100,104,106,107,108,111,115,117,120,122,123,124,125,127,132,135,138,139,140,141,143,144,146,148,149,152,159,162,163,164,165,167],[2,3,4,5,6,7,9,11,13,14,16,18,21,22,25,28,29,30,31,35,36,39,42,43,44,45,48,49,50,51,52,53,55,57,59,60,63,65,67,68,72,73,74,75,77,78,83,85,86,89,90,91,94,95,96,98,101,102,104,106,108,109,111,112,113,123,126,129,130,131,133,136,137,142,144,145,146,151,153,154,155,157,158,159,162,163,165,166,168],[0,1,5,7,12,15,19,21,22,24,25,28,29,34,37,40,41,42,44,48,49,51,53,59,60,62,65,66,67,68,69,70,72,73,74,76,78,79,80,83,84,86,87,88,89,90,92,93,94,97,98,103,104,107,110,113,115,116,117,123,126,128,129,130,132,135,140,141,142,143,146,148,150,151,152,153,154,159,164,165,166,167,168],[0,3,6,7,8,10,18,19,20,23,24,25,26,27,30,31,32,33,35,37,38,40,41,42,45,47,49,50,51,52,53,55,56,58,59,62,63,67,68,70,71,72,74,78,81,82,83,85,86,87,88,89,90,92,93,97,98,100,101,104,105,106,107,109,111,113,117,118,120,121,123,124,126,128,129,130,134,135,138,140,143,147,148,149,150,155,159,160,166],[0,2,4,5,8,9,12,14,16,24,25,26,27,29,31,33,34,35,36,37,38,39,40,41,42,45,47,49,50,51,56,57,58,60,67,68,70,73,74,75,77,78,79,81,84,88,89,92,93,94,95,96,98,100,101,103,104,105,106,107,109,110,113,116,117,118,119,120,123,124,125,126,127,128,130,131,133,135,136,137,138,139,140,142,143,144,146,147,151,154,155,156,157,159,160,161,163,164,165,167],[1,3,5,6,9,10,13,15,16,17,19,25,26,27,29,30,31,32,42,43,47,49,51,52,54,57,58,60,62,65,66,68,70,72,73,76,77,78,81,82,83,90,91,92,95,98,99,100,101,102,104,107,108,110,111,113,117,118,120,124,127,131,132,133,135,136,137,138,140,142,143,144,147,148,150,151,152,153,154,155,158,159,160,161,163,165,168],[1,3,6,7,10,11,13,15,18,21,23,24,26,28,31,32,35,37,38,40,44,45,47,49,50,51,54,55,59,61,66,69,71,72,73,74,75,78,86,89,91,92,101,102,109,110,112,115,117,118,119,120,122,124,125,127,129,130,132,134,137,141,144,145,146,147,149,152,156,160,161,164,165,166],[0,2,4,6,8,9,10,11,12,13,14,15,25,27,30,31,33,35,36,38,40,41,42,43,48,49,50,51,54,57,59,60,62,64,66,68,70,71,72,73,74,75,76,77,78,79,80,81,82,84,86,88,90,94,98,99,100,101,104,105,110,113,114,116,118,119,120,123,125,127,132,134,137,138,139,143,144,145,146,150,151,152,155,157,158,161,162,167,168],[1,7,8,14,16,17,18,19,20,22,23,26,28,31,32,35,38,39,41,42,46,48,49,53,54,58,59,61,62,66,67,69,70,72,76,78,79,83,84,87,90,91,93,94,95,99,101,105,106,107,108,109,112,114,115,116,117,118,119,121,127,128,129,132,133,134,135,136,138,139,140,142,146,148,150,151,153,155,156,157,158,160,161,162,166],[0,1,2,5,6,8,9,12,13,16,17,18,26,30,31,34,36,38,46,47,52,53,54,57,59,60,62,63,64,65,71,73,75,78,79,82,83,86,87,90,91,93,95,97,98,100,105,107,109,111,120,122,123,124,125,127,128,129,131,132,134,135,136,137,139,140,143,144,145,147,148,151,153,154,155,158,159,160,165,168],[0,1,2,3,7,8,12,13,15,16,17,18,19,21,25,27,28,32,34,35,36,42,43,45,49,50,52,53,54,55,57,58,62,66,67,69,70,72,76,78,79,83,84,87,91,92,93,96,98,99,106,109,110,111,112,113,114,117,120,123,127,128,129,130,132,133,135,138,141,143,145,147,149,150,151,152,154,158,161,163,164,167],[0,2,4,8,9,10,15,16,17,22,24,25,33,37,38,43,44,45,46,48,49,51,54,55,57,58,59,61,62,63,64,66,67,68,71,72,73,77,78,80,83,85,86,87,89,90,93,96,97,98,103,106,108,109,111,112,114,115,116,118,119,121,123,124,125,126,128,129,130,132,133,134,135,136,137,138,145,146,147,149,151,152,154,155,156,158,159,162,164,165,166],[3,24,121,123,125,136,137,138,143,144,146,147,148,149,156,157,159,161,164,165],[0,2,3,4,6,8,15,17,18,20,21,22,25,28,30,34,36,37,39,40,43,44,45,49,50,54,55,57,59,62,64,65,66,67,69,70,73,74,75,76,77,78,82,83,88,90,91,93,95,99,101,102,104,105,106,108,114,117,120,122,123,125,127,128,129,130,131,135,136,137,138,139,143,144,145,147,150,153,155,157,158,159,160,162,164,165,167],[0,1,5,6,7,8,10,14,15,17,19,22,23,25,28,29,35,36,38,39,40,47,48,50,51,52,53,54,55,56,57,59,60,62,63,67,69,70,72,75,76,78,81,82,83,86,88,90,91,92,93,95,96,99,100,101,102,103,104,107,116,119,122,123,126,129,130,132,136,138,140,141,142,143,144,146,148,149,151,156,158,161,162,165,166,168],[1,2,3,5,10,11,13,14,15,17,18,21,26,27,29,30,32,35,36,37,38,39,40,41,42,44,45,47,51,52,53,55,56,57,58,60,61,64,66,67,68,75,77,79,80,81,85,88,90,91,92,93,98,103,104,105,106,110,111,114,119,122,125,127,128,131,135,137,138,141,143,147,148,149,150,151,152,153,154,156,158,162,163,165],[1,3,5,7,9,10,11,12,13,16,17,19,20,21,25,27,28,29,31,32,33,39,40,43,44,47,48,50,53,71,72,73,76,77,80,81,83,84,85,90,92,93,94,95,98,99,102,103,104,105,110,111,112,114,116,118,122,124,126,128,129,130,132,133,135,136,137,138,139,140,142,144,147,150,153,155,159,161,162,165],[1,4,5,6,9,11,14,17,19,23,24,29,32,34,35,36,42,43,45,46,48,49,50,51,52,54,60,62,68,70,72,73,74,75,76,77,78,81,84,85,89,91,92,94,95,96,98,99,100,101,102,103,105,106,107,110,113,116,117,118,124,125,127,131,132,136,137,138,142,145,149,150,151,152,154,156,159,160,167,168],[3,4,6,7,9,13,14,17,23,25,26,28,29,30,32,33,34,35,37,38,40,42,46,47,49,50,55,56,57,60,62,63,65,67,68,69,71,72,73,74,76,77,78,81,84,87,88,89,91,94,96,97,98,101,107,109,113,119,120,121,123,126,127,128,129,131,132,135,137,138,143,146,147,152,153,154,155,157,160,161,162,163,166],[0,3,10,11,15,16,19,20,21,22,23,26,27,28,29,31,32,33,34,37,38,39,41,42,43,46,47,48,49,51,52,55,57,60,61,62,65,66,67,68,69,72,73,75,76,77,79,80,81,82,83,86,88,95,96,98,100,101,104,105,106,107,108,113,115,116,117,120,122,124,125,127,129,130,134,137,142,143,146,148,149,150,151,152,153,154,155,156,157,159,161,164,168],[14,38,111,121,122,124,129,132,133,134,138,140,141,144,145,148,152,153,154,156,157,159,160,162,167],[1,3,4,6,8,10,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,32,33,35,37,40,43,45,50,51,52,53,63,65,66,68,70,72,73,75,76,77,78,79,80,81,82,83,84,85,91,94,95,96,98,101,108,109,110,111,120,124,125,126,127,130,131,133,134,138,139,140,142,144,151,154,156,157,159,161,162,163,165,166,167,168],[1,2,3,4,5,6,9,12,13,15,16,18,19,21,24,27,29,30,31,32,33,34,36,37,38,39,40,42,47,48,49,50,51,52,55,58,59,61,65,67,68,69,70,71,73,75,77,78,81,83,84,85,86,87,88,91,93,94,95,96,103,107,109,110,111,112,113,115,116,118,119,122,123,124,125,126,128,129,134,135,136,138,143,148,149,156,158,160,162,163,166,168],[1,3,6,7,12,15,22,23,25,26,27,29,33,34,36,38,41,42,43,44,45,46,47,51,53,54,57,58,59,60,61,62,65,70,71,73,75,78,84,85,87,89,90,91,92,93,95,97,99,100,101,103,109,110,111,113,115,116,117,120,123,124,127,129,130,134,136,138,140,144,147,148,150,156,157,158,159,160,161,162,163,164,166],[1,3,8,11,14,15,18,19,20,22,26,27,29,31,33,34,35,39,41,42,43,44,45,46,47,51,52,54,55,56,57,58,60,63,64,68,69,70,72,77,78,79,82,87,89,90,92,93,94,95,97,98,100,101,103,104,105,106,107,109,111,112,113,116,119,120,124,126,128,129,130,132,135,137,138,140,144,145,146,149,150,151,152,154,159,161,162,163,164,167],[0,1,2,3,4,5,6,7,10,11,14,15,20,26,27,29,30,31,32,36,37,42,43,44,45,46,47,52,53,54,55,56,57,63,64,66,69,71,73,75,76,77,79,82,84,87,89,90,92,96,99,100,103,105,107,109,111,112,115,116,119,120,123,124,126,129,132,133,134,135,137,140,143,145,146,147,149,150,153,159,160,161,163,164,165,166,167,168],[1,7,8,9,11,12,16,17,18,25,26,27,28,30,31,32,34,36,37,38,42,43,45,47,50,51,52,56,58,62,66,67,69,70,71,72,73,75,77,79,83,86,87,88,92,94,95,96,98,99,100,101,102,104,110,111,115,116,118,119,120,123,124,126,127,128,129,130,132,133,134,142,143,144,147,148,152,153,154,155,157,158,161,162,164,166,167,168],[0,5,6,7,8,10,11,13,16,18,19,20,23,25,26,27,29,30,31,32,37,39,41,44,46,47,49,50,51,53,57,61,63,64,65,66,71,73,75,76,80,86,94,98,100,101,106,110,111,112,113,114,116,117,118,120,121,123,124,126,128,129,131,133,134,135,137,138,141,142,146,147,148,149,150,151,152,153,154,157,158,159,162,166],[3,5,6,7,8,9,10,12,18,19,20,22,23,27,34,36,37,40,42,44,45,46,47,48,50,54,55,56,58,64,66,68,69,70,71,74,78,80,81,82,83,84,86,93,94,95,99,101,102,103,104,105,107,109,112,113,115,117,124,126,127,132,133,134,137,138,141,142,143,144,150,152,154,156,157,159,160,162,163,165,166],[0,3,5,6,8,9,10,11,16,18,19,20,22,25,26,28,31,32,34,35,38,39,41,43,45,46,47,48,49,55,56,58,61,63,65,66,68,72,73,74,78,79,82,83,84,85,86,87,88,89,93,96,99,100,103,104,105,110,113,115,116,118,122,123,124,126,128,134,137,138,139,140,143,144,145,147,149,151,154,156,157,158,162,164,165,167],[6,7,8,11,12,14,16,17,18,20,21,24,25,26,27,30,31,33,35,37,38,42,43,47,48,50,52,54,55,56,57,60,61,62,64,66,69,72,76,78,80,81,83,86,87,88,89,90,91,93,97,99,100,106,107,108,109,110,111,112,114,117,118,122,123,126,127,129,130,132,133,134,136,139,140,141,142,144,146,147,148,149,151,152,154,157,160,162,163,164,165,167],[24,158,160,161,162,164,167],[29,111,121,122,124,129,132,136,138,141,144,145,148,152,153,154,156,157,158,162,167],[0,2,4,5,6,7,9,11,12,13,14,15,16,22,23,24,27,28,30,33,35,36,39,43,44,46,47,48,49,51,53,54,55,56,57,58,60,62,63,64,65,67,69,74,76,79,82,83,87,88,91,92,93,94,96,99,100,101,103,104,106,108,109,110,111,112,114,120,122,125,126,129,130,131,134,135,136,142,143,146,149,150,152,153,155,156,157,158,160,164],[6,7,8,11,13,15,17,19,21,22,26,27,28,29,30,31,33,40,43,44,47,48,51,53,58,59,62,65,67,69,70,71,72,73,74,77,78,79,80,81,82,84,86,89,90,92,94,96,97,100,101,102,103,108,109,112,115,116,118,120,123,125,126,129,130,133,134,135,137,138,140,143,144,146,149,150,151,153,156,157,160,168],[1,2,4,5,8,11,12,13,18,21,22,25,29,31,32,33,34,35,38,41,44,45,46,47,51,52,54,55,58,61,67,69,73,75,77,84,86,87,88,89,96,97,98,99,100,102,103,104,106,108,109,110,111,113,115,116,117,118,119,121,122,123,124,127,135,137,138,142,143,146,147,148,153,155,160,162,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,121,124,127,131,135,141,144,146,149,153,156,158,160,163,165,167],[1,3,5,7,10,11,14,15,19,20,21,22,23,27,29,32,33,35,36,38,46,47,52,53,55,57,58,60,62,64,66,68,72,75,76,77,78,85,87,88,91,92,93,94,96,97,98,99,100,101,102,103,104,105,110,112,114,117,119,120,122,123,125,126,127,129,130,131,132,133,134,139,143,146,150,151,152,153,155,156,157,158,162,165,166],[0,1,2,4,8,10,11,14,16,17,18,20,26,27,29,31,33,35,37,39,40,43,44,45,46,48,49,50,51,53,54,55,56,59,60,61,62,63,65,67,71,72,76,78,80,83,84,85,89,90,95,98,101,104,114,117,121,122,126,127,128,130,131,135,137,139,140,141,142,147,148,150,151,152,153,154,155,156,157,158,160,161,163,165,168],[1,2,3,4,5,6,8,9,11,13,18,21,25,26,27,30,32,33,35,37,40,43,48,50,52,53,54,61,62,63,64,67,68,69,71,73,74,77,78,79,80,82,83,84,86,93,94,95,97,102,105,108,109,111,112,113,114,117,118,119,124,125,128,129,130,131,132,133,134,137,139,142,144,147,148,149,151,152,156,158,163,166,167],[1,2,4,7,8,10,13,15,16,17,18,24,26,27,28,33,34,35,36,38,42,43,44,45,46,48,51,53,54,57,59,60,63,65,66,68,71,72,73,77,78,79,80,86,87,88,89,90,91,92,93,98,99,100,101,103,104,107,109,110,111,113,115,116,118,121,122,124,133,134,139,140,142,143,144,145,146,148,150,151,152,156,157,158,161,162,164,167],[1,5,6,7,9,10,11,13,17,19,21,22,23,24,28,29,30,31,33,35,36,39,40,41,42,44,45,46,48,49,51,52,53,54,59,64,69,75,77,82,83,84,86,87,89,90,91,93,95,99,100,101,103,104,105,107,111,112,113,114,118,120,121,122,126,128,129,130,132,134,135,136,137,141,142,145,150,151,155,157,159,160,161,165,166],[24,38,154,158,159,160,164],[1,2,4,5,8,11,14,15,17,18,20,21,24,25,26,28,31,41,42,43,44,45,47,49,50,51,52,53,55,57,58,59,60,61,63,64,66,67,71,72,73,74,76,77,79,80,85,88,89,90,92,96,98,105,107,108,109,110,111,112,114,121,123,124,125,126,127,128,129,133,140,147,149,151,152,153,154,160,163,164,165,166,167],[41,123,124,125,136,137,138,140,143,144,147,149,158,159,160,161,165],[24,38,42,111,121,122,124,132,133,134,136,139,141,145,148,149,153,154,155,156,157,158,159,162],[2,4,5,6,10,15,18,23,25,27,30,31,35,38,39,40,41,47,48,49,51,55,56,57,58,60,61,63,67,68,69,71,73,77,78,80,81,82,83,87,88,89,90,91,92,94,95,99,100,101,103,104,105,106,110,112,113,114,116,117,119,123,126,129,132,133,136,137,140,142,144,145,146,148,149,151,152,156,157,158,161,162,167],[0,1,2,3,4,7,8,9,13,15,17,18,20,21,22,23,24,26,28,31,36,37,38,39,40,44,48,49,51,53,58,61,63,65,66,67,71,72,76,79,81,86,89,94,96,97,101,103,104,107,112,114,116,117,122,129,130,131,136,139,141,144,146,147,148,151,152,153,154,155,158,161,164,167,168],[1,2,4,5,6,7,8,9,10,11,13,14,17,20,21,25,30,31,34,35,38,39,42,44,45,47,48,59,60,63,64,70,71,72,73,77,79,80,84,85,87,89,90,92,93,95,96,97,101,103,104,107,111,112,113,114,115,117,118,120,121,123,125,126,127,128,130,131,132,134,140,141,142,143,148,150,151,153,157,159,160,161,162,164],[0,4,5,6,11,12,16,19,23,25,26,28,31,32,34,45,47,49,50,54,58,59,60,65,66,71,72,76,77,79,83,84,85,86,87,88,90,95,99,101,102,104,108,109,110,111,112,113,114,117,118,119,121,122,123,127,128,131,132,133,134,136,137,138,140,142,144,145,146,147,149,151,152,153,154,155,156,157,159,166],[0,2,3,4,6,7,10,12,13,15,19,20,21,22,24,28,32,35,38,39,41,44,46,47,53,55,56,57,59,60,61,65,66,67,68,70,73,77,78,79,81,82,84,86,87,89,93,94,96,100,103,104,106,107,108,110,111,114,116,117,119,122,123,125,126,128,129,131,132,134,136,137,140,145,147,148,149,150,151,157,158,161,162,166,167,168],[0,1,3,4,6,7,8,9,11,13,16,17,21,26,31,32,35,36,37,38,41,43,44,45,46,47,48,49,50,54,55,56,59,60,61,63,64,65,66,67,68,71,72,79,80,81,83,84,85,86,87,88,91,93,96,98,99,102,104,106,107,110,112,114,115,116,117,119,122,124,125,126,128,129,130,131,133,137,138,144,145,146,153,154,156,158,163],[1,2,8,9,10,11,12,15,16,17,18,19,21,22,25,26,28,29,30,31,32,34,36,38,39,41,44,45,47,49,51,54,55,59,61,62,64,68,69,70,71,74,77,78,80,82,83,85,88,89,90,91,92,93,94,96,99,103,105,106,117,118,120,121,122,124,125,126,131,132,134,135,137,142,143,145,148,149,150,152,153,155,156,157,158,160,163,165,166,168],[0,2,3,4,5,6,8,9,11,12,20,22,23,25,26,27,28,30,32,37,39,41,42,49,50,53,54,60,65,67,71,72,75,77,78,82,83,85,87,88,89,93,94,96,100,101,103,105,108,109,110,112,113,115,117,118,119,120,123,124,128,129,131,133,135,137,139,140,141,144,150,153,155,161,162,163,164,165,166,167],[3,4,5,6,11,12,13,14,16,17,19,20,21,23,26,29,32,33,35,36,37,38,42,47,50,52,55,58,60,61,65,66,67,68,70,71,72,77,81,84,88,91,92,94,95,97,98,99,101,102,103,104,106,107,109,111,113,116,118,119,120,122,123,124,125,128,130,132,134,135,137,138,139,140,141,143,146,148,152,154,155,157,158,160,162,163,167,168],[24,54,136,140,141,164],[1,3,4,7,8,9,18,20,21,22,23,24,25,27,28,30,31,32,33,36,37,38,39,40,42,44,47,48,50,52,56,58,59,63,64,66,68,73,74,79,80,85,87,89,90,91,96,98,101,102,103,105,107,108,112,113,121,122,124,128,129,130,131,132,133,137,143,145,147,150,151,152,153,154,155,160,162,163,165,168],[0,1,2,7,10,12,13,15,16,17,18,19,23,26,28,30,31,34,39,43,47,48,49,51,52,53,54,56,58,60,61,63,64,65,67,68,69,70,72,73,75,76,77,78,80,81,82,84,85,86,88,89,94,96,97,99,102,103,104,105,106,111,114,116,117,119,121,123,124,128,131,133,134,139,144,147,149,150,152,153,155,156,157,158,159,160,161,162,163,164,165,167],[2,3,4,5,8,9,10,11,16,18,20,22,27,28,30,31,32,33,40,41,42,43,46,49,50,53,54,56,60,63,64,66,69,70,72,74,76,77,78,79,80,81,82,83,86,87,91,96,99,101,102,106,107,110,121,125,130,132,134,136,137,138,139,141,143,147,148,149,150,154,157,158,160,164,165,166],[0,1,2,4,5,6,9,10,11,13,14,15,17,21,26,29,32,35,40,44,49,53,54,58,59,62,64,65,67,70,71,75,78,79,80,81,87,88,89,94,96,101,102,105,108,110,111,114,116,117,119,122,123,124,126,127,132,133,134,139,141,146,147,148,149,153,154,155,157,158,160,163,166,167],[0,3,5,6,8,10,13,15,16,17,18,25,29,30,31,33,35,36,39,41,42,44,46,47,48,49,56,57,58,59,60,62,63,64,65,66,67,68,69,72,75,76,77,80,81,84,86,88,90,91,92,94,95,96,97,100,101,105,106,109,110,113,115,117,119,120,122,127,128,130,131,133,134,137,139,143,147,149,152,157,161,165,168],[0,2,3,4,6,7,9,13,16,19,20,24,28,33,34,35,36,39,40,45,48,50,51,53,56,58,59,62,64,65,66,68,69,70,72,73,75,79,83,84,85,87,88,89,93,94,99,100,101,102,103,106,108,109,112,113,115,118,121,122,123,125,126,127,128,129,132,134,136,138,141,142,143,144,145,146,147,148,151,152,154,155,158,159,160,161,162,163,164],[0,2,4,7,9,10,12,14,17,18,19,20,22,25,27,29,31,32,33,34,35,38,40,41,42,43,44,45,46,47,54,55,56,57,58,59,62,63,65,67,68,70,74,76,77,79,81,83,85,87,88,93,95,96,97,103,104,105,112,113,114,115,116,117,120,121,122,125,127,128,129,130,132,136,137,138,139,141,144,147,148,151,153,154,155,156,160,161,163,165,168],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,63,64,65,70,72,73,77,79,82,84,85,90,92,94,96,97,103,104,105,112,114,117,118,122,124,127,129,131,132,134,137,138,141,143,145,147,148,149,152,154,155,158,161,163,164,165,166,167],[0,1,3,5,11,13,14,15,19,20,24,26,32,33,37,38,39,42,43,45,47,52,54,61,62,63,64,65,66,68,69,73,76,77,79,83,85,87,90,95,96,98,99,100,101,103,105,108,109,112,116,117,118,120,121,122,124,125,130,133,134,136,138,139,142,143,145,147,148,149,151,152,153,156,157,161,162,164,166,167,168],[5,7,8,10,12,13,14,15,18,21,22,24,27,28,31,32,33,34,36,40,42,43,44,45,48,49,51,52,55,56,60,61,63,74,78,79,80,83,86,89,91,93,96,97,98,99,100,102,103,105,106,110,111,112,113,116,119,121,123,125,127,128,129,131,136,137,139,142,144,149,150,151,152,154,155,156,157,163,164,165,166],[66,136,139,148,149,155,164],[5,6,8,9,13,15,20,23,25,28,29,32,33,34,35,39,40,47,49,52,53,55,56,58,59,60,61,66,67,69,72,74,76,77,78,79,82,83,87,89,91,93,95,96,99,104,106,110,113,114,120,121,122,123,124,128,129,131,134,136,138,139,140,141,142,143,146,148,151,153,157,158,159,160,162,165],[0,2,4,7,8,9,17,19,20,23,25,28,29,30,31,33,34,36,38,42,43,47,48,50,52,60,61,63,64,66,68,70,72,73,74,78,79,81,83,84,85,88,89,90,92,93,94,96,97,100,101,102,103,105,107,109,110,112,113,122,123,126,127,129,130,131,132,136,143,148,149,151,152,154,156,157,158,159,160,161,163,166,168],[1,5,6,7,11,12,13,15,16,20,22,23,24,26,28,29,33,36,40,41,43,44,45,46,47,49,50,51,52,54,59,63,64,65,66,68,69,76,79,83,84,86,87,89,90,91,93,95,97,98,99,101,104,105,106,110,112,114,115,116,120,121,125,127,128,133,134,135,136,137,138,139,140,142,143,144,145,146,148,149,150,153,154,156,157,160,161,163,166,168],[1,3,5,7,9,11,12,14,19,24,25,26,27,31,33,35,36,39,40,43,44,46,47,52,53,54,55,58,59,62,65,66,69,70,73,74,75,77,78,81,82,83,88,89,90,92,93,94,95,97,99,101,108,109,110,120,121,122,128,129,131,132,133,135,139,140,147,149,150,151,152,153,155,156,157,158,159,160,161,163,165,166],[0,1,8,9,16,19,21,23,27,30,32,33,35,36,38,39,41,43,44,46,47,48,49,50,51,54,55,56,57,58,59,64,65,66,67,68,69,72,73,75,78,80,82,85,87,89,91,93,94,97,99,101,102,103,110,118,119,120,122,123,124,125,126,127,128,129,131,136,137,138,142,144,145,146,147,148,150,151,154,155,156,157,159,162,167,168],[1,3,6,7,9,11,12,13,17,18,24,25,26,28,29,30,33,34,36,39,42,44,46,47,48,49,51,52,59,60,62,63,64,65,66,69,73,75,77,78,80,82,83,87,89,90,96,99,100,101,102,103,104,106,110,112,114,116,117,123,124,125,126,127,128,134,135,136,138,139,141,143,144,147,149,151,153,156,158,159,160,161,162,165],[24,127,149,153,154,158,160,164],[0,7,8,9,10,12,16,17,19,21,24,25,29,31,33,36,40,43,49,50,55,56,57,61,62,63,65,67,70,72,73,74,76,82,85,87,88,89,90,91,92,93,94,95,97,98,99,105,108,109,111,114,117,120,121,125,126,127,128,129,130,131,132,133,134,138,139,144,146,147,148,150,151,152,153,154,157,158,159,163,165],[2,4,5,6,9,13,14,15,17,19,21,22,23,24,25,27,30,31,32,33,37,38,39,43,44,45,47,51,52,53,56,58,59,60,63,64,65,67,73,74,77,78,79,80,82,86,88,89,90,93,95,99,100,101,103,107,108,109,113,114,115,117,120,122,123,127,128,129,132,134,135,136,139,142,145,146,147,149,150,152,153,154,157,162,163,164,165,167],[2,4,5,6,11,12,13,15,16,17,18,20,21,23,26,30,32,34,43,47,48,49,51,55,59,60,61,64,69,75,79,80,82,83,85,89,91,93,94,95,96,100,102,104,109,112,114,115,117,118,119,121,122,125,126,127,132,137,138,140,144,145,147,151,153,158,163,164,165,166,167,168],[1,3,6,7,10,11,13,15,16,17,20,22,26,28,32,34,35,36,37,42,45,46,47,48,49,51,52,54,57,62,63,64,65,66,69,71,72,78,80,81,82,87,88,92,93,96,98,102,103,105,107,108,109,111,112,113,117,119,120,122,123,124,127,128,130,132,133,135,136,138,139,142,143,144,145,147,148,149,150,152,153,155,156,157,158,161,162,165,166],[0,1,2,3,4,5,8,10,13,14,16,20,22,26,27,28,29,30,31,35,36,38,39,40,41,42,43,46,47,55,56,59,61,66,67,71,74,75,76,77,79,83,86,87,88,89,90,92,95,96,97,98,99,102,104,105,108,109,110,111,113,114,116,118,122,123,124,125,126,128,131,133,135,136,137,138,139,140,143,144,145,148,155,156,158,159,160,163,165,168],[0,1,2,3,4,5,9,10,13,15,19,20,21,24,25,26,28,29,34,35,38,39,40,42,44,46,47,48,49,50,51,55,56,59,61,62,63,64,65,66,67,71,72,74,79,80,82,83,84,86,88,93,94,97,98,100,102,104,105,106,107,108,109,111,113,114,117,119,121,124,125,128,129,130,132,133,135,136,138,139,143,144,146,148,152,154,157,158,159,160,161,165,167,168],[24,123,149,157,158,159,160,161,164,165],[0,7,8,9,10,12,16,17,19,21,25,29,31,33,36,40,43,49,50,55,56,57,61,62,63,65,67,70,72,73,74,82,83,85,87,88,89,90,91,92,93,94,95,97,98,99,105,108,109,111,114,117,120,122,124,126,127,128,131,132,133,134,135,136,137,139,144,146,147,150,151,152,153,154,159,160,163,164,165,166],[0,3,5,6,8,9,10,11,16,18,19,20,22,24,25,28,31,32,34,35,38,39,41,43,45,46,47,48,49,55,56,58,61,63,65,66,68,72,73,74,78,79,82,83,85,86,87,88,89,93,96,99,100,103,104,105,110,113,115,116,118,122,124,126,134,137,138,139,140,143,145,147,151,154,156,158,159,160,161,162,164,166,167],[38,85,124,132,133,136,140,147,157,158,159,160],[0,1,2,3,4,7,8,9,13,15,16,17,19,20,22,25,26,27,29,31,34,35,38,39,40,42,43,44,45,46,49,50,51,52,53,55,57,58,59,62,63,67,69,74,75,79,82,83,88,90,96,98,100,101,105,107,108,109,113,114,123,126,129,130,133,135,139,142,145,147,151,152,154,155,156,158,161,162,164,165,166,167,168],[0,7,8,9,10,13,14,15,16,19,20,21,22,24,25,26,28,31,34,35,36,39,40,42,46,53,54,55,56,59,60,61,62,64,65,66,67,69,70,71,73,75,76,79,80,82,84,86,87,88,89,91,94,95,98,100,102,103,104,106,107,108,109,111,112,113,115,116,118,119,120,121,124,126,128,130,131,134,139,144,146,147,149,150,152,155,156,157,160,161,162,163,164,165,168],[88,111,121,122,123,124,125,129,132,136,138,141,148,149,152,153,154,156,159,160,161,162,165,167],[0,1,3,5,10,12,14,15,18,19,20,22,23,26,28,29,30,32,36,38,39,44,46,48,49,50,51,53,55,60,64,66,68,69,72,73,75,76,78,80,84,86,88,90,92,94,95,97,102,103,105,110,113,118,120,121,123,124,125,127,135,137,139,140,141,147,148,150,151,152,153,157,158,159,165,166,167],[0,3,6,7,8,9,10,11,13,15,16,17,18,19,20,22,24,25,26,29,30,31,33,34,35,43,45,50,52,55,56,58,59,62,63,64,65,67,69,70,75,78,79,80,87,89,91,92,93,97,98,102,103,105,106,108,109,116,118,120,123,126,128,131,132,135,136,138,140,141,142,147,150,154,155,156,157,158,163,164,165,167],[2,3,4,5,6,7,9,11,12,15,17,19,20,23,26,27,28,29,30,31,34,37,38,40,41,48,49,54,56,58,61,64,65,70,72,73,77,79,82,84,85,90,91,92,94,96,97,103,104,105,112,114,117,118,122,124,127,129,131,132,134,136,138,141,143,145,147,149,152,154,155,158,161,163,164,165,166,167],[0,1,2,3,4,6,8,9,10,11,12,14,17,18,19,20,21,27,29,30,32,34,35,41,44,45,51,53,59,61,62,63,66,69,72,74,75,76,78,79,80,81,82,83,85,86,87,88,89,90,93,96,98,104,105,108,114,115,117,118,121,124,125,126,127,131,133,135,136,140,141,142,143,144,145,146,148,151,153,158,165,166,167],[93,123,149,152,155,157,159,166],[1,2,3,4,5,7,9,12,13,14,17,18,20,21,23,24,25,28,29,31,32,33,34,41,43,48,51,52,53,54,55,56,58,60,61,62,64,65,66,67,68,70,73,74,76,82,83,84,85,88,90,91,92,93,98,100,104,105,106,109,111,114,116,122,124,125,126,128,130,133,136,138,139,140,142,144,148,149,150,152,153,154,157,159,162,163,164,167,168],[38,95,111,132,133,134,135,136,140,141,147,149,158,159,160,162],[0,2,3,4,5,7,10,12,14,15,16,19,20,21,22,24,25,26,29,30,33,35,36,37,39,40,41,42,43,44,48,51,54,56,57,60,62,64,65,66,67,69,70,71,74,79,80,81,85,86,94,95,106,109,111,113,116,117,119,120,127,130,131,132,133,137,138,140,141,142,144,146,150,152,153,154,155,157,158,160,166],[0,2,3,4,5,6,9,10,11,14,16,22,25,28,29,35,36,37,38,39,40,42,44,45,49,50,52,53,54,55,57,59,60,61,62,63,65,67,68,69,73,75,78,80,83,85,86,91,94,96,98,102,104,108,109,111,113,119,123,125,126,128,130,132,134,135,137,140,142,143,144,148,149,153,155,157,166,167,168],[1,3,5,7,17,18,20,23,26,27,28,38,39,41,43,45,46,47,52,53,54,57,59,60,64,65,68,69,70,73,76,77,78,83,85,86,88,90,95,98,102,103,104,106,109,116,117,118,119,120,125,126,128,132,134,137,139,141,143,145,146,148,149,154,159,163,165,166,167,168],[1,2,3,4,9,13,17,20,22,23,24,25,26,27,29,30,31,32,33,34,35,37,38,41,42,43,44,49,53,54,55,57,60,62,67,68,69,71,74,77,78,80,83,84,85,87,88,89,90,91,94,95,96,97,98,101,103,107,114,116,117,119,123,127,128,129,130,135,136,137,138,139,140,142,148,149,152,154,155,157,160,161,163,166,167],[1,2,4,5,9,11,16,18,20,21,22,23,27,29,30,31,33,34,35,40,47,49,50,51,52,53,55,56,60,61,64,65,66,69,74,76,77,78,79,81,83,87,88,90,91,93,95,96,97,98,99,101,103,108,110,111,114,115,117,118,120,121,122,126,129,130,133,134,136,137,139,142,144,145,147,148,149,150,153,154,157,158,161,163,168],[0,1,6,7,12,13,14,15,17,18,19,21,22,24,25,27,30,34,35,36,37,39,44,45,46,48,50,52,54,57,58,61,62,64,67,69,71,72,73,76,77,78,79,80,81,82,83,86,87,91,92,95,96,98,101,104,106,107,110,123,124,127,128,130,131,132,135,136,138,140,141,142,144,145,146,147,152,157,158,159,160,161,163,165,167],[0,7,8,12,13,14,19,21,22,23,24,27,28,32,33,37,39,40,41,42,43,44,49,50,57,59,60,61,62,64,65,68,71,75,76,78,79,81,82,84,86,88,89,91,96,98,99,102,103,104,107,109,114,117,124,128,130,131,132,136,137,138,139,145,146,150,151,154,156,157,159,160,164,165],[0,2,4,5,6,7,9,10,14,15,17,19,24,25,26,29,30,31,32,35,36,38,42,44,46,47,51,52,54,55,56,57,59,61,67,69,72,74,75,80,82,83,86,89,91,92,94,97,99,100,101,102,103,104,106,107,110,113,115,116,117,118,119,120,122,123,124,126,128,134,135,136,139,141,149,150,151,152,153,154,155,156,160,161,162,163,164],[1,5,9,10,11,12,16,18,20,22,23,25,26,27,28,32,35,38,39,40,41,42,47,51,54,59,60,61,62,67,68,69,71,74,76,77,78,79,83,87,90,94,95,97,101,104,107,109,110,111,112,114,115,116,118,119,121,123,124,133,135,136,138,139,141,143,145,147,148,151,152,154,155,160,161,166,167],[0,2,4,7,9,10,12,14,17,18,19,20,22,24,25,27,29,31,32,33,34,35,40,41,42,43,44,45,46,47,54,55,56,57,58,59,63,65,67,68,70,74,76,77,79,81,83,85,87,88,95,96,97,103,104,105,108,112,113,114,115,116,117,120,121,123,125,127,128,129,130,131,132,134,135,137,138,139,140,142,144,148,149,151,153,154,157,160,161,163,164,165,166,168],[1,3,5,7,8,9,14,15,19,20,21,22,23,24,25,26,29,33,36,37,38,39,41,42,44,47,48,50,53,54,55,56,57,58,59,60,61,66,67,68,69,71,72,74,75,77,79,81,84,85,86,87,91,92,95,96,97,98,99,100,101,102,103,104,105,108,112,114,117,119,122,124,126,127,128,129,133,135,137,140,143,144,145,147,151,152,153,154,156,159,160,161,163,165,167],[0,1,2,4,5,7,10,15,17,18,20,22,23,26,27,29,30,31,32,33,34,35,36,38,39,40,42,43,45,46,48,49,51,52,53,54,59,62,63,64,66,67,69,70,71,73,74,75,76,77,78,79,81,82,83,86,90,91,94,99,102,104,106,107,109,113,114,115,116,118,119,120,126,128,130,131,132,134,139,146,147,148,149,155,159,161,162,165,166],[0,3,5,6,8,10,12,14,16,18,21,23,25,26,29,33,34,35,38,50,51,52,53,54,55,58,59,62,63,68,69,79,80,81,82,84,85,88,89,90,93,94,97,99,101,105,107,108,110,112,113,114,117,118,121,122,124,126,128,129,130,133,140,141,142,143,144,145,146,148,149,150,153,154,156,157,160,161,162,163,166],[1,2,3,4,6,7,9,10,11,12,14,15,18,20,21,22,26,28,29,33,36,38,41,44,46,48,49,50,54,56,57,58,63,64,65,66,68,69,71,72,73,75,77,79,80,81,84,86,87,88,90,91,92,93,94,95,96,97,98,100,101,103,105,109,110,117,118,119,120,124,125,129,130,132,136,138,140,141,143,146,147,149,151,154,155,156,160,162,163,166,167,168],[1,2,3,4,6,7,8,10,11,12,17,18,19,21,25,28,31,33,34,39,40,41,42,44,45,46,48,49,51,52,53,54,58,60,61,63,64,65,66,68,69,71,74,75,76,77,78,80,84,85,87,88,89,90,92,93,96,101,103,104,106,107,109,110,113,114,117,120,121,122,124,126,127,128,129,131,133,134,135,137,140,144,145,146,148,160,166,167,168],[0,7,8,10,11,12,13,15,17,22,25,26,27,28,29,32,33,37,39,42,43,45,47,50,51,53,55,56,57,61,63,68,70,82,83,88,91,93,94,95,96,100,101,102,103,105,106,107,111,112,114,115,116,118,121,122,123,125,126,128,129,130,131,132,135,136,139,140,142,143,144,145,147,153,154,159,161,164,165,167,168],[1,7,9,10,11,14,16,18,20,21,22,25,26,27,29,31,32,33,35,36,37,41,42,44,45,46,47,49,51,52,53,54,55,56,59,65,66,68,69,72,73,78,79,81,82,83,85,87,88,89,90,94,95,97,105,106,107,110,111,113,117,119,122,124,125,126,127,128,129,130,131,132,133,134,136,137,138,141,143,144,147,150,152,157,159,161,165,166,167,168],[0,5,6,7,8,9,10,15,16,18,21,26,28,30,34,35,37,40,41,43,49,50,51,52,55,56,57,58,62,63,64,66,67,68,71,72,74,75,77,81,83,87,91,93,94,98,102,104,108,115,118,119,120,121,122,127,128,130,131,133,134,137,139,141,142,145,146,149,151,153,156,157,158,165,166],[24,38,119,132,133,134,137,138,139,141,147,148,149,153,154,159,164]]},"distance":{"d":6,"is_exact":true,"upper":6,"witness":[29,130,228,346,446,563],"A_d":null,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,1],[11,1],[12,1],[13,1],[14,1],[15,1],[16,1],[17,1],[18,1],[19,1],[20,1],[21,1],[22,1],[23,1],[24,1],[25,1],[26,1],[27,1],[28,1],[29,1],[30,1],[31,1],[32,1],[33,1],[34,1],[35,1],[36,1],[37,1],[38,1],[39,1],[40,1],[41,1],[42,1],[43,1],[44,1],[45,1],[46,1],[47,1],[48,1],[49,1],[50,1],[51,1],[52,1],[53,1],[54,1],[55,1],[56,1],[57,1],[58,1],[59,1],[60,1],[61,1],[62,1],[63,1],[64,1],[65,1],[66,1],[67,1],[68,1],[69,1],[70,1],[71,1],[72,1],[73,1],[74,1],[75,1],[76,1],[77,1],[78,1],[79,1],[80,1],[81,1],[82,1],[83,1],[84,1],[85,1],[86,1],[87,1],[88,1],[89,1],[90,1],[91,1],[92,1],[93,1],[94,1],[95,1],[96,1],[97,1],[98,1],[99,1],[100,1],[101,1],[102,1],[103,1],[104,1],[105,1],[106,1],[107,1],[108,1],[109,1],[110,1],[111,1],[112,1],[113,1],[114,1],[115,1],[116,1],[117,1],[118,1],[119,1],[120,1],[121,1],[122,1],[123,3],[124,1],[125,1],[126,1],[127,1],[149,1],[151,3],[152,1],[153,1],[154,1],[155,1],[156,2],[157,3],[158,1],[159,3],[160,1],[161,1],[162,2],[163,2],[164,1],[165,1],[166,3],[167,1],[168,2]],"CZ":[[123,149],[123,156],[123,162],[123,163],[123,168],[149,151],[149,156],[149,157],[149,159],[149,166],[149,168],[151,156],[151,162],[151,163],[151,168],[156,157],[156,159],[156,166],[156,168],[157,162],[157,163],[157,168],[159,162],[159,163],[159,168],[162,163],[162,166],[163,166],[166,168]]},"rotation_powers":[[0,5],[2,3],[3,3],[7,3],[8,7],[10,5],[11,5],[12,5],[13,7],[14,3],[16,3],[17,3],[21,3],[22,7],[24,5],[25,5],[26,3],[27,7],[28,5],[29,5],[30,5],[31,7],[32,3],[33,3],[34,7],[36,7],[38,3],[40,5],[41,7],[42,7],[44,7],[45,3],[46,5],[48,7],[50,3],[51,3],[52,5],[53,7],[54,7],[55,3],[56,7],[57,5],[58,3],[59,5],[61,5],[62,5],[63,7],[64,5],[65,7],[67,3],[70,7],[71,5],[72,3],[73,3],[75,3],[76,5],[77,5],[78,7],[80,5],[81,7],[82,3],[83,3],[84,3],[86,3],[87,3],[88,3],[90,7],[91,3],[92,5],[93,7],[94,5],[95,5],[96,7],[100,5],[101,7],[106,7],[108,7],[109,5],[110,3],[111,3],[112,5],[114,7],[115,7],[117,5],[123,5],[128,3],[133,7],[134,7],[135,7],[144,3],[158,7],[159,7],[160,3],[161,7],[164,3],[165,5],[168,3],[171,3],[172,7],[179,3],[180,3],[184,3],[186,3],[190,3],[191,3],[192,3],[193,3],[194,3],[198,3],[199,3],[200,3],[203,3],[204,7],[206,3],[207,3],[209,3],[212,5],[213,3],[214,3],[215,3],[216,3],[217,5],[218,7],[219,5],[222,3],[223,3],[224,3],[225,3],[227,3],[231,7],[232,3],[234,3],[236,3],[238,3],[243,3],[245,3],[246,3],[248,3],[251,3],[252,3],[253,3],[256,3],[257,3],[259,7],[261,3],[262,7],[263,3],[264,3],[265,3],[266,3],[269,3],[270,3],[273,7],[275,3],[276,3],[279,3],[280,3],[281,3],[285,3],[286,3],[290,3],[292,3],[293,3],[294,3],[295,3],[296,3],[297,3],[299,3],[301,3],[304,3],[309,3],[310,3],[311,3],[312,3],[313,3],[316,3],[318,3],[321,3],[322,3],[324,3],[326,3],[327,3],[328,3],[329,3],[330,3],[331,3],[332,3],[336,3],[337,3],[338,3],[343,3],[345,3],[349,3],[351,3],[353,3],[356,3],[357,3],[361,3],[362,3],[366,3],[371,3],[372,3],[374,3],[375,3],[376,3],[377,3],[379,3],[380,3],[381,3],[385,3],[387,3],[391,3],[395,3],[397,3],[398,3],[403,3],[405,3],[406,3],[407,3],[408,3],[413,3],[414,3],[415,3],[418,3],[419,3],[421,3],[422,7],[423,3],[424,5],[425,3],[430,3],[433,3],[434,5],[435,5],[436,3],[438,3],[439,3],[440,3],[441,3],[442,3],[443,3],[444,3],[448,3],[450,3],[451,5],[452,5],[454,5],[455,3],[458,3],[462,3],[465,3],[467,3],[471,3],[473,3],[474,3],[475,3],[476,3],[478,3],[480,3],[481,3],[483,3],[485,3],[487,3],[490,3],[491,3],[492,3],[493,3],[496,3],[500,3],[502,3],[503,3],[504,3],[505,3],[510,3],[511,3],[514,3],[516,3],[517,3],[519,3],[524,3],[525,3],[526,3],[529,3],[530,3],[531,3],[532,3],[533,3],[534,3],[535,3],[537,3],[539,3],[543,3],[547,3],[548,3],[550,3],[552,3],[553,3],[555,3],[556,3],[557,3],[558,3],[559,3],[571,3],[574,3],[575,3],[577,3],[578,3],[580,3],[581,3],[582,3],[584,3],[586,3],[588,3],[592,3],[594,3],[595,3],[597,3],[598,3],[600,3],[601,3],[602,3],[604,3],[605,3],[606,3],[608,3],[610,3],[612,3],[613,3],[615,3],[619,3],[622,3],[623,3],[627,3],[629,3],[633,3],[635,3],[636,3],[637,3],[638,3],[644,3],[645,3],[647,3],[652,3],[655,3],[658,3],[660,3],[661,3],[662,3],[663,3],[664,3],[670,3],[671,3],[674,3],[675,3],[676,3],[677,3],[678,3],[679,3],[680,3],[681,3],[682,3],[683,3],[685,3],[690,3],[691,3],[695,3],[697,3],[698,3],[699,3],[701,3],[703,3],[706,3],[707,3],[711,3],[712,3],[713,3],[714,3],[716,3],[718,3],[719,3],[721,3],[722,3],[725,3],[726,3],[731,3],[732,3],[734,3],[735,3],[738,3],[740,3],[741,3],[742,3],[743,3],[744,3],[745,3],[746,3],[755,3],[756,3],[757,3],[758,3],[759,3],[760,3],[763,3],[764,3],[765,3],[766,3],[770,3],[772,3],[774,3],[776,3],[778,3],[779,3],[780,3],[781,3],[784,3],[786,3],[787,3],[788,3],[792,3],[794,3],[797,3],[800,3],[801,3],[802,3],[803,3],[804,3],[812,3],[813,3],[816,3],[818,3],[820,3],[821,3],[822,3],[824,3],[825,3],[827,3],[828,3],[829,3],[831,3],[834,3],[835,3],[836,3],[839,3],[840,3],[844,3],[845,3],[847,3],[849,3],[850,3],[852,3],[855,3]]},"metrics":{"gamma":1.0605441996301026,"gamma_t":null,"gamma_rho":1.0605441996301026,"gamma_claim":1.0605441996301026,"gamma_t_claim":null,"gamma_rho_claim":1.0605441996301026,"v_ex":128,"rate":0.14953271028037382,"t_count":null,"poly_degree":null,"effective_width":128},"provenance":{"regimes":["AI search (gamma frontier): from Wills parent codes"],"discovery":"AI search","strongest_claim":"built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows","sources":[{"regime":"AI search (gamma frontier): from Wills parent codes","file":"gamma_frontier_release/protocols/paired_column_contraction_856_128_6.json","label":"paired_column_contraction_856_128_6","N":169,"d":6,"d_is_exact":true,"origin":"Wills-derived code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_856_128_6 (source catalogue id paired_column_contraction_856_128_6); construction: Wills-derived code with physical paired-column contraction; matrix 7e6f962b4b5462a4...; the release states d=6 (exact), gamma=1.0605441996301026 (exact)","notes":"matrix gamma_frontier_release/matrices/7e6f962b4b5462a4f55591e62ebd541c0af167388223182935149d8a56578015.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"}]}