{"id":"1023.21.5.a","row":1340,"stored":{"file":"master_catalog.json","row":1340,"construction":null,"columns_sha256":null},"parameters":{"n":1023,"k":21,"d":5,"N":41,"r":20,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13\u00b7T14\u00b7T15\u00b7T16\u00b7T17\u00b7T18\u00b7T19\u00b7T20","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20]],"sk_fingerprint":"55751bc1b83a8676","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,2,6,8,9,11,12,16,17,19,21,31],[2,3,5,6,7,9,11,13,14,15,16,18,22,34],[3,4,5,9,10,12,16,20,21,22,31,32,33,34],[1,5,6,7,8,10,14,16,17,18,20,23,37],[0,2,4,8,9,14,15,17,18,21,23,31,33,35,37],[5,6,8,10,11,12,15,17,19,20,22,23,34,35,36,37],[2,3,5,6,7,12,14,15,18,21,22,23,31,32,34,36,37],[2,3,5,6,7,10,13,14,15,16,18,19,24,40],[4,10,11,15,17,19,21,24,31,34,37,40],[2,3,6,7,8,10,11,13,20,22,24,34,36,38,40],[0,1,3,5,7,8,12,14,16,19,20,21,22,24,31,32,33,36,37,38,40],[2,5,7,8,12,13,15,16,20,23,24,37,38,39,40],[1,3,4,5,8,9,10,12,14,17,18,19,21,23,24,31,33,34,35,38,39,40],[1,2,4,8,12,14,15,16,17,18,19,20,22,23,24,34,35,37,39,40],[0,2,3,4,6,9,13,14,17,19,21,22,23,24,31,32,39,40],[2,3,4,6,8,10,19,25,33,36],[0,1,9,13,16,17,21,25,31,33,35,36,39],[3,8,10,12,14,18,19,20,22,25,33,34,36,37,40],[1,2,3,4,8,10,12,13,18,21,22,25,31,32,34,35,36,37,39,40],[4,5,6,11,12,18,20,23,25,31,33,34,36,37,39],[0,1,2,3,7,8,11,13,14,15,16,17,18,20,21,23,25,34,36,37],[3,4,5,6,7,8,10,11,12,13,14,18,22,23,25,31,33,35,39,40],[1,2,7,10,13,14,16,17,19,21,22,23,25,32,33,35,40],[4,7,11,12,13,14,15,16,17,18,24,25,31,32,33,34,35,36,40],[2,3,4,7,8,11,12,19,20,21,24,25,32,33,36,37,39,40],[2,5,8,12,15,16,17,19,20,22,24,25,31,32,33,35,37,38],[0,1,2,4,5,6,7,8,10,11,12,13,16,17,19,20,21,22,24,25,34,38,39],[4,6,7,8,10,12,15,19,23,24,25,32,33,35,36,37,38,40],[1,2,6,7,8,12,13,15,17,19,21,23,24,25,31,32,34,35,36,38,39,40],[1,4,5,6,7,8,9,10,13,15,22,23,24,25,32,33,34,36],[0,1,2,3,6,7,12,15,21,22,23,24,25,31,33,36,37,39],[0,1,2,3,4,5,6,9,12,18,20,26,36,39],[2,3,4,5,6,9,11,12,13,14,16,17,20,21,26,34,39],[0,1,3,4,6,7,8,9,15,16,17,18,19,22,26,32,34,35,36,38,39],[0,1,2,5,6,7,11,12,13,14,16,21,22,26,33,35,38,39],[0,1,4,9,10,11,14,15,18,19,20,23,26,33,37,39,40],[1,2,4,6,7,9,10,11,14,17,19,20,21,23,26,34,35,36,37,39,40],[0,3,4,5,6,10,11,14,16,17,20,22,23,26,32,33,34,36,37,38,39,40],[0,1,2,9,10,13,15,17,18,20,21,22,23,26,33,35,37,38,39,40],[0,2,5,7,8,13,15,16,17,18,20,24,26,32,34,35,36,37,39,40],[0,2,7,9,10,11,15,16,17,21,24,26,32,34,35,39,40],[0,1,2,4,6,7,8,10,11,15,16,17,18,22,24,26,37,39,40],[3,4,5,6,7,10,11,12,16,20,21,22,24,26,32,33,36,39,40],[0,2,3,4,5,6,7,8,11,13,14,15,17,19,20,23,24,26,32,33,34,35,38],[0,1,2,4,5,6,8,10,11,12,14,16,17,21,23,24,26,32,34,36,37,38],[0,7,8,9,10,13,14,15,18,22,23,24,26,33,35,38],[2,3,4,5,7,10,13,16,19,20,21,22,23,24,26,32,33,36,37,38],[1,4,5,7,8,9,11,13,18,19,20,25,26,33,34,35,37,38,39],[0,6,8,10,13,15,16,17,18,19,20,21,25,26,33,36,37,38],[3,5,6,10,11,13,15,16,17,19,20,22,25,26,32,33,39,40],[2,3,6,7,9,10,12,13,14,16,19,21,22,25,26,34,35,36,40],[2,3,6,10,11,12,14,15,19,23,25,26,31,35,36,38,40],[0,2,5,10,12,14,15,18,19,21,23,25,26,31,33,34,35,38,39,40],[3,5,6,7,8,9,10,12,13,14,15,18,20,22,23,25,26,31,32,34,35,37],[1,2,3,5,6,7,9,10,11,12,13,15,16,19,20,21,22,23,25,26,31,35,36,37,39],[1,4,6,9,12,17,20,24,25,26,31,33,34,35,38,39,40],[1,3,5,6,12,13,17,19,20,21,24,25,26,31,33,34,36,37,38,40],[1,2,4,5,7,8,9,11,12,13,15,18,19,20,22,24,25,26,31,32,33,36,37,38,39],[0,3,5,6,11,12,13,14,16,21,22,24,25,26,31,35,38],[2,3,5,6,7,8,10,11,12,13,16,17,19,20,23,24,25,26,35,36,37,39],[1,2,4,5,6,8,11,13,14,15,16,17,18,20,21,23,24,25,26,33,35],[1,2,3,6,7,8,11,12,17,22,23,24,25,26,32,34,35,36,39,40],[0,1,3,6,7,9,11,12,14,17,21,22,23,24,25,26,34,35,37,40],[2,4,5,6,10,11,13,15,27,32,35,39],[0,1,5,7,13,14,15,17,18,19,20,21,27,31,32,33,35,36,37,39],[1,2,3,5,6,7,12,15,22,27,32,35,37],[1,2,4,5,6,8,13,16,17,18,21,22,27,31,35,36],[0,2,3,4,5,8,10,12,14,15,17,19,20,23,27,31,32,34,37,38,39],[3,5,6,8,9,12,15,18,21,23,27,32,34,35,36,38,39],[0,7,8,9,11,12,14,17,22,23,27,31,32,34,35,36,38],[0,1,5,12,20,21,22,23,27,33,34,37,38],[1,2,4,5,6,8,9,10,12,14,15,16,17,20,24,27,32,33,35,40],[1,3,4,5,6,9,13,15,16,17,20,21,24,27,31,32,34,35,36,40],[1,3,5,8,10,11,13,14,18,20,22,24,27,32,33,35,36,37,38,39,40],[0,3,6,7,12,14,18,20,21,22,24,27,31,33,34,35,37,38,39,40],[0,1,2,7,8,11,14,15,20,23,24,27,31,32,33,34,37,39,40],[0,5,7,10,11,15,17,19,21,23,24,27,32,33,35,36,37,39,40],[0,2,6,7,9,11,12,17,18,22,23,24,27,31,32,33,34,35,38,40],[2,3,4,6,9,10,12,15,16,21,22,23,24,27,36,38,40],[2,5,7,10,14,17,19,20,25,27,32,33,36,37,38,39,40],[0,1,5,6,8,9,12,13,16,18,21,25,27,31,32,35,38,40],[4,7,8,9,11,12,14,16,17,18,19,22,25,27,32,33,36,37,38],[3,4,5,6,9,11,15,20,21,22,25,27,31,33,35,38,39],[0,1,2,5,6,7,9,10,11,14,15,16,17,18,23,25,27,32,33,35,36,40],[1,3,5,6,8,10,11,12,13,14,15,18,20,21,23,25,27,31,32,33,35,37,39,40],[0,2,3,6,7,13,14,16,17,22,23,25,27,32,33,39],[0,1,2,3,6,7,8,10,12,16,18,20,21,22,23,25,27,31,36,37],[3,6,7,8,9,10,11,17,18,19,20,24,25,27,31,34,35,36,37,38],[2,5,6,7,12,17,18,21,24,25,27,33,37,38,39],[1,5,6,7,9,10,11,12,13,16,17,18,19,20,22,24,25,27,31,34,35,37,39,40],[0,5,6,7,8,10,11,12,13,15,17,18,21,22,24,25,27,32,36,37,40],[0,1,3,4,5,6,8,9,10,15,16,17,18,23,24,25,27,31,34,36,38],[0,2,3,4,13,14,15,17,18,19,20,21,23,24,25,27,38,39],[0,1,2,3,4,6,7,9,10,12,15,16,17,18,20,22,23,24,25,27,31,34,35,36,39,40],[1,2,4,5,7,9,10,11,13,14,15,21,22,23,24,25,27,32,33,35,40],[0,1,2,4,8,9,11,14,15,16,19,20,26,27,31,32,34,35,36,37,38,40],[2,3,7,8,14,16,19,21,26,27,31,32,33,35,36,38,40],[0,3,5,7,8,9,10,13,14,16,17,18,19,22,26,27,31,34,36,39,40],[0,2,3,5,6,7,8,11,13,16,18,20,21,22,26,27,31,32,36,37,39,40],[4,5,6,7,8,11,13,15,17,18,19,20,23,26,27,32,33],[0,9,10,11,12,19,20,21,23,26,27,32,33,34,35,37],[4,5,10,15,17,18,22,23,26,27,33,36,37,38,39],[1,2,3,8,12,15,16,18,19,21,22,23,26,27,32,34,35,36,38,39],[0,1,3,9,13,14,15,18,19,24,26,27,31,33,36,38,39],[0,1,3,4,5,6,8,9,11,12,13,14,16,17,20,21,24,26,27,31,36,38,39],[0,1,3,4,6,7,10,14,15,17,19,22,24,26,27,31,32,33,35,37,38],[2,12,14,16,17,18,19,21,22,24,26,27,31,33,35,37,38],[2,3,7,8,9,11,12,15,23,24,26,27,34,35,37,38,40],[1,2,5,6,13,16,17,18,21,23,24,26,27,34,37,38,40],[1,4,5,7,11,12,16,17,18,19,22,23,24,26,27,32,34,35,38,39,40],[0,1,2,4,5,8,11,12,14,16,18,19,20,21,22,23,24,26,27,33,34,38,39,40],[2,3,4,5,6,8,9,11,12,13,14,15,16,17,25,26,27,31,32,33,35,37,38],[0,1,2,4,5,6,9,11,14,16,19,21,25,26,27,31,32,34,38,39],[2,4,8,10,11,13,15,17,18,20,22,25,26,27,31,33,37,39,40],[4,5,6,7,9,10,17,19,20,21,22,25,26,27,31,32,33,34,35,40],[0,3,8,9,11,13,16,20,23,25,26,27,31,32,36,39,40],[3,4,6,10,19,21,23,25,26,27,31,32,34,36,37,40],[0,1,2,3,6,8,11,14,22,23,25,26,27,31,38],[0,4,5,6,8,9,10,11,14,15,18,19,20,21,22,23,25,26,27,31,32,33,34,37,38,39],[1,2,3,10,11,12,13,15,16,17,19,24,25,26,27,32,35,38,39,40],[1,2,3,4,6,7,9,11,14,16,19,21,24,25,26,27,32,33,38,40],[3,4,6,7,9,10,11,15,19,20,22,24,25,26,27,36,38],[0,1,2,6,8,9,12,14,16,17,19,21,22,24,25,26,27,32,35,36,38,39],[0,1,3,6,9,11,12,14,15,17,20,23,24,25,26,27,32,33,36,37,38,39],[0,5,7,8,12,14,15,17,20,21,23,24,25,26,27,32,33,36,37,38],[0,1,4,8,9,11,14,15,17,18,20,22,23,24,25,26,27,33,36,37,38,40],[1,2,4,7,8,9,10,11,14,17,19,20,21,22,23,24,25,26,27,32,36,37,38,39,40],[1,3,5,6,10,11,12,13,14,18,28,32,38],[2,5,8,9,10,12,15,16,17,18,20,21,28,31,32,35,38],[1,2,5,6,8,12,13,14,16,17,20,22,28,32,34,36,38,39,40],[0,1,2,6,7,9,10,14,17,18,19,20,21,22,28,31,33,34,35,36,38,39,40],[0,1,4,7,8,9,13,14,15,16,23,28,35,38,40],[0,1,2,7,13,16,17,18,21,23,28,31,33,35,38,40],[0,4,6,7,9,10,11,13,16,17,18,19,22,23,28,34,38,39],[1,3,5,7,8,12,16,18,19,20,21,22,23,28,31,32,34,38,39],[0,1,3,4,6,9,11,12,13,14,15,16,18,20,24,28,31,32,37,40],[1,2,3,5,7,8,12,13,17,19,20,21,24,28,32,34,35,40],[0,3,6,12,14,17,22,24,28,31,32,34,37,38,39],[0,1,4,8,13,14,19,20,21,22,24,28,33,35,38,39],[1,4,6,7,8,9,10,11,13,18,20,23,24,28,31,35,37,38,39],[0,2,3,4,5,7,8,9,11,12,14,16,17,18,19,21,23,24,28,33,34,35,38,39],[1,2,3,7,9,11,13,14,15,16,17,20,22,23,24,28,31,34,36,37,40],[1,2,3,6,7,15,17,18,21,22,23,24,28,32,36,40],[1,2,3,4,5,6,7,8,9,11,13,14,15,17,18,19,20,25,28,33,35,38],[4,7,9,13,18,19,20,21,25,28,31,33,35,38,39],[2,4,5,7,10,11,12,13,14,15,17,22,25,28,33,34,35,36,37,38,39],[0,2,4,5,6,8,10,11,12,16,17,18,21,22,25,28,31,32,34,35,36,37,38],[0,2,6,7,9,10,13,15,18,20,23,25,28,31,32,33,34,38,39,40],[0,4,5,6,7,9,12,13,15,17,18,19,21,23,25,28,32,34,35,38,40],[0,10,15,17,18,19,22,23,25,28,31,32,33,35,37,38,40],[1,3,4,7,8,9,11,14,17,20,21,22,23,25,28,33,37,38,39,40],[0,4,8,9,10,11,15,16,20,24,25,28,32,33,34,37,40],[2,6,7,8,9,15,18,20,21,24,25,28,31,32,33,39,40],[0,2,7,8,9,14,15,17,18,22,24,25,28,32,33,38,39,40],[0,1,2,3,4,5,6,7,12,13,14,15,16,17,21,22,24,25,28,31,34,37,38,40],[1,3,4,9,10,12,13,14,15,16,19,20,23,24,25,28,31,33,35,37,38],[0,2,4,6,9,11,12,13,17,21,23,24,25,28,34,38,39],[7,9,10,13,15,16,17,19,20,22,23,24,25,28,31,33,34,36,39],[5,6,7,8,11,12,13,17,19,21,22,23,24,25,28,32,33,35,36,37],[0,3,5,6,11,12,14,15,17,18,20,26,28,31,32,33,34,39,40],[0,1,3,6,8,9,11,12,13,14,16,17,20,21,26,28,31,32,33,35,36,39,40],[0,3,7,8,9,11,14,15,16,17,18,19,22,26,28,31,33,35,36,38],[2,10,12,13,16,19,21,22,26,28,31,32,34,38],[1,2,4,6,8,9,12,15,17,20,23,26,28,31,34,35,36,39,40],[1,2,3,5,6,8,9,10,13,17,18,21,23,26,28,31,33,35,39,40],[3,4,5,9,10,11,12,17,22,23,26,28,31,32,35,36,38],[0,1,2,3,5,7,9,12,13,16,17,20,21,22,23,26,28,31,34,35,38],[1,2,4,6,9,10,12,15,18,24,26,28,33,35,38,39],[0,1,2,3,7,9,10,11,12,13,14,15,16,18,19,20,21,24,26,28,33,36,37,38,39],[3,5,6,7,10,13,15,18,20,22,24,26,28,32,33,34,38,40],[1,2,3,4,10,11,14,15,17,18,19,21,22,24,26,28,34,35,36,37,38,40],[0,3,4,7,8,9,13,16,18,20,23,24,26,28,32,36],[1,3,4,6,7,8,12,13,14,15,17,18,19,21,23,24,26,28,32,33,37],[0,3,5,15,16,19,20,22,23,24,26,28,34,39,40],[0,2,6,7,10,12,13,14,15,17,18,21,22,23,24,26,28,32,34,36,37,39,40],[1,2,4,8,9,11,13,14,15,18,19,20,25,26,28,31,37,38,39,40],[2,4,10,11,13,14,17,19,21,25,26,28,31,34,36,37,38,40],[4,5,6,11,14,15,17,19,22,25,26,28,31,32,34,35,36,40],[0,2,3,4,6,10,11,12,15,16,17,18,21,22,25,26,28,31,33,35,39,40],[0,1,3,5,8,9,12,13,19,23,25,26,28,32,33,34,35,36,37,38,40],[0,1,4,5,9,13,17,19,21,23,25,26,28,32,37,38,39,40],[0,1,6,7,8,10,11,13,14,15,18,19,22,23,25,26,28,33,35,36,39,40],[2,4,5,6,7,10,11,12,13,15,16,19,20,21,22,23,25,26,28,32,33,34,40],[0,1,2,4,5,6,11,14,24,25,26,28,31,37,39],[1,2,3,8,10,11,13,14,16,19,20,21,24,25,26,28,31,36],[0,1,2,3,6,7,9,10,14,19,22,24,25,26,28,31,32,34,35],[0,3,4,7,8,10,13,14,17,19,20,21,22,24,25,26,28,31,33,34,35,36,37,39],[1,3,4,5,11,12,13,16,18,23,24,25,26,28,32,33,34,35,36,37,38,39],[0,3,4,6,9,10,12,13,15,16,17,18,20,21,23,24,25,26,28,32,34,38],[2,3,8,9,10,11,12,13,18,22,23,24,25,26,28,33,35,38],[6,9,12,15,17,20,21,22,23,24,25,26,28,32,33,36,37,38,39],[3,4,5,6,12,13,14,15,16,17,27,28,31,33,35,36,37,38,39,40],[1,2,4,5,8,9,10,11,12,15,19,20,21,27,28,38,39,40],[1,2,5,12,17,18,20,22,27,28,31,33,35,38,39],[0,1,2,6,8,9,10,12,13,14,15,16,19,20,21,22,27,28,32,33,36,37,38,39],[1,3,4,5,8,11,12,13,14,16,19,23,27,28,32,33,34,35,36,37,39],[1,2,3,5,6,8,10,13,17,21,23,27,28,31,32,33,34,35,39],[1,3,5,6,7,11,13,14,15,17,18,19,22,23,27,28,32,33,34,36,39,40],[0,4,7,9,10,11,14,15,16,17,19,20,21,22,23,27,28,31,34,37,39,40],[0,1,4,5,7,8,10,11,13,14,18,20,24,27,28,35,36],[1,2,7,9,12,14,16,17,18,19,20,21,24,27,28,31,33,34],[0,1,4,5,10,14,15,19,20,22,24,27,28,35,36,37,38,40],[0,3,5,8,9,10,13,15,16,19,20,21,22,24,27,28,31,32,34,37,38,40],[0,7,10,13,14,15,16,18,19,23,24,27,28,31,32,34,35,36,39,40],[1,2,3,5,7,8,9,10,14,15,16,17,21,23,24,27,28,32,35,39,40],[0,1,2,3,7,11,13,14,19,20,22,23,24,27,28,31,32,34,37,38,39],[0,1,2,3,7,10,13,16,17,19,20,21,22,23,24,27,28,33,36,37,38,39],[1,3,4,5,6,7,8,10,11,16,18,19,25,27,28,31,32,35,36,39],[2,4,7,9,10,11,12,13,14,15,20,21,25,27,28,32,33,35,37],[1,5,7,10,11,12,13,16,17,19,22,25,27,28,31,32,35,39],[0,1,5,6,7,11,12,13,14,17,18,19,21,22,25,27,28,35,36,37],[1,3,4,5,7,9,10,11,15,16,17,18,20,23,25,27,28,31,35,36,38,40],[1,2,3,6,7,9,10,13,14,15,16,17,20,21,23,25,27,28,37,38,39,40],[2,3,5,6,8,10,11,16,17,18,22,23,25,27,28,31,36,38,40],[0,1,2,4,5,15,17,21,22,23,25,27,28,32,33,35,37,38,39,40],[0,1,2,3,5,6,7,8,10,13,15,17,18,19,24,25,27,28,31,33,34,36,37,38,40],[1,3,4,5,6,7,10,11,12,14,15,16,17,19,20,21,24,25,27,28,37,38,39,40],[0,3,5,6,8,9,11,12,16,17,22,24,25,27,28,31,33,34,36,37,40],[0,1,4,6,8,9,12,21,22,24,25,27,28,32,33,37,39,40],[0,1,2,3,4,6,7,9,17,23,24,25,27,28,31,32,33,34,36,37,38],[4,6,7,9,10,13,15,18,19,21,23,24,25,27,28,32,33,35,37,38,39],[0,1,2,4,6,7,9,14,15,18,22,23,24,25,27,28,31,32,33,34,35,37],[0,1,2,4,5,6,7,8,9,12,13,16,17,18,20,21,22,23,24,25,27,28,36,37,39],[0,1,2,3,8,9,16,17,19,20,26,27,28,31,35,36,38,40],[0,2,3,5,6,7,8,9,12,13,14,16,17,18,19,20,21,26,27,28,31,33,34,36,37,38,40],[0,2,3,4,5,6,7,9,13,14,15,17,18,19,20,22,26,27,28,31,32,37],[4,5,8,10,11,15,18,21,22,26,27,28,31,34,35],[0,1,3,7,8,14,17,18,20,23,26,27,28,32,33,34,35,40],[0,1,4,5,6,9,10,11,13,14,21,23,26,27,28,32,33,35,37,40],[0,1,2,4,5,6,7,9,12,18,22,23,26,27,28,33,34,35,37,38],[5,10,12,13,16,18,20,21,22,23,26,27,28,32,35,38],[1,3,7,9,10,11,14,15,16,17,18,24,26,27,28,32,33,34,36,39],[0,1,4,9,10,11,13,14,16,17,18,19,21,24,26,27,28,32,34,35,36,39],[1,2,5,7,9,10,15,18,22,24,26,27,28,33,34,35,36,37,39,40],[4,8,9,12,13,14,17,21,22,24,26,27,28,32,33,34,36,37,39,40],[1,2,3,4,5,6,9,18,19,20,23,24,26,27,28,31],[0,2,3,4,5,6,7,8,10,12,15,21,23,24,26,27,28,31],[2,3,4,6,7,15,17,19,22,23,24,26,27,28,31,32,36,37,40],[4,5,6,10,11,13,15,17,18,19,20,21,22,23,24,26,27,28,31,33,36,37,40],[1,2,5,7,9,10,12,13,18,25,26,27,28,31,32,33,34,36,38],[2,5,6,8,9,10,12,13,14,17,19,20,21,25,26,27,28,31,32,36,37,38,39],[1,4,6,8,9,11,12,14,16,17,18,20,22,25,26,27,28,31,33,34,35],[0,1,2,3,4,5,7,8,9,12,13,15,17,21,22,25,26,27,28,31,32,33,35,37,39],[5,8,9,13,14,17,18,23,25,26,27,28,31,34,39],[3,4,5,6,7,8,9,10,11,14,15,16,17,18,21,23,25,26,27,28,31,35,37],[1,3,4,6,9,11,12,14,15,17,20,22,23,25,26,27,28,31,32,34,38,39],[0,2,3,5,7,8,9,12,15,16,18,19,21,22,23,25,26,27,28,31,33,35,37,38],[0,2,3,4,5,6,7,9,11,14,15,16,17,18,24,25,26,27,28,31,32,34,36,39,40],[2,6,8,13,14,16,17,18,19,21,24,25,26,27,28,31,32,33,34,36,40],[0,1,2,4,6,7,9,14,16,17,18,22,24,25,26,27,28,31,34,35,36,39,40],[0,6,11,12,15,20,21,22,24,25,26,27,28,31,32,34,35,36,40],[0,1,3,8,11,15,17,19,20,23,24,25,26,27,28,31,33,34,39,40],[3,5,7,8,9,10,15,16,17,21,23,24,25,26,27,28,31,33,34,35,40],[0,1,2,3,5,7,8,11,12,15,16,18,19,20,22,23,24,25,26,27,28,31,32,33,34,36,39,40],[0,1,5,9,10,11,14,15,17,18,21,22,23,24,25,26,27,28,31,34,35,36,40],[0,1,2,3,4,6,8,9,11,12,13,14,16,18,29,31,34,35],[0,1,2,4,5,6,7,9,10,13,15,16,18,20,21,29,34,35,37,39,40],[1,2,4,5,6,7,9,10,11,15,17,18,22,29,31,35,38],[0,4,5,6,9,10,11,15,16,17,21,22,29,32,33,35,37,38,39,40],[0,2,3,4,6,7,10,11,14,15,17,19,20,23,29,31,32,33,34,36,37,39],[0,1,2,3,5,6,10,13,14,18,21,23,29,32,34,35,36,40],[1,3,4,5,6,7,8,10,11,13,15,16,18,22,23,29,31,32,33,35,37,38,39],[0,1,2,5,6,12,17,21,22,23,29,33,38,40],[0,4,5,9,10,15,17,19,20,24,29,31,33,34,36,38],[1,5,6,7,8,10,11,15,16,17,18,20,21,24,29,33,36,38,39,40],[1,2,6,9,10,11,14,16,19,22,24,29,31,33,38],[1,3,4,5,7,10,11,13,14,15,16,17,18,21,22,24,29,32,34,38,39,40],[0,1,6,7,8,9,10,13,14,16,17,18,19,20,23,24,29,31,32,34,35,37],[1,3,8,12,13,14,15,16,17,19,20,21,23,24,29,32,33,37,39,40],[1,3,4,5,8,9,10,13,15,19,20,22,23,24,29,31,32,37],[2,3,4,6,7,10,12,13,14,15,16,17,18,19,20,21,22,23,24,29,34,35,37,39,40],[0,1,2,3,5,6,9,10,13,15,16,17,18,20,25,29,33,34,35,36,40],[0,1,2,5,6,7,12,13,15,16,17,19,20,21,25,29,31,33,34,36,37],[6,7,8,9,12,14,15,18,20,22,25,29,33,35,36,37,38],[0,1,2,5,6,11,12,13,14,16,18,19,21,22,25,29,31,32,36,38,40],[0,1,2,3,5,6,7,10,12,13,14,17,18,23,25,29,31,32,37,40],[0,2,3,4,5,6,8,9,11,13,16,19,21,23,25,29,32,33],[1,2,3,6,7,8,10,12,13,15,17,19,20,22,23,25,29,31,32,34,35,36,38],[0,1,4,5,6,8,9,10,11,12,17,21,22,23,25,29,34,35,36,37,38,40],[0,1,2,3,4,6,7,10,12,13,14,19,24,25,29,31,32,35,38,40],[2,3,5,10,13,14,16,17,21,24,25,29,32,34,38],[1,2,3,5,7,10,11,12,13,14,15,22,24,25,29,31,32,34,35,36,37,38],[1,4,5,6,8,11,12,13,15,16,19,20,21,22,24,25,29,33,36,37,38,40],[0,1,2,3,5,12,13,15,17,18,23,24,25,29,33,34,36,37,39,40],[1,2,6,7,8,13,15,16,17,19,21,23,24,25,29,31,36,37,39],[4,6,7,10,13,16,19,22,23,24,25,29,33,35,36,39],[1,2,4,11,14,15,19,20,21,22,23,24,25,29,31,32,33,34,35,36,39,40],[0,4,6,9,11,14,15,17,19,26,29,31,34,36,38],[0,2,4,6,8,12,13,16,18,20,21,26,29,31,37,38,39,40],[2,4,6,8,9,10,12,13,16,18,22,26,29,31,32,35,36,38],[0,1,2,3,4,5,6,8,11,12,13,15,17,18,20,21,22,26,29,31,33,34,35,37,38,39,40],[0,2,4,8,9,11,13,14,23,26,29,31,32,34,35,36,37,38,39,40],[0,1,3,8,15,17,18,21,23,26,29,31,32,33,38],[1,2,3,4,7,9,14,15,16,18,19,20,22,23,26,29,31,35,37,38,39,40],[0,1,2,3,5,7,8,10,11,12,17,18,19,21,22,23,26,29,31,32,34,36,38],[0,4,5,6,8,11,12,13,14,16,19,20,24,26,29,31,32,33,37],[1,2,3,10,11,12,13,14,15,16,17,18,19,21,24,26,29,31,32,33,36,37,39,40],[1,3,5,7,8,12,15,17,18,19,22,24,26,29,31,33,34,35,36,37,38],[1,3,4,5,6,7,8,13,16,18,19,21,22,24,26,29,31,32,34,35,37,38,39,40],[0,2,6,9,10,14,16,23,24,26,29,31,33,35,38,40],[5,9,12,13,21,23,24,26,29,31,36,38,39],[4,9,11,16,18,19,20,22,23,24,26,29,31,32,33,34,35,40],[1,3,4,6,8,9,11,12,13,15,16,17,19,20,21,22,23,24,26,29,31,33,34,36,39],[1,3,6,11,12,17,18,19,25,26,29,33,35,37,40],[1,2,3,5,6,10,11,12,14,17,18,21,25,26,29,33,34,36],[0,3,6,8,11,13,18,19,22,25,26,29,32,33,34],[1,6,11,13,15,17,18,19,21,22,25,26,29,35,36,37,40],[2,3,11,12,14,18,19,20,23,25,26,29,31,32,33,34],[1,4,5,8,10,12,13,14,15,16,21,23,25,26,29,31,32,36,37,40],[0,7,8,10,17,22,23,25,26,29,31,33,36,37,40],[4,7,8,10,11,13,14,15,17,18,21,22,23,25,26,29,31,32,33,34],[2,4,5,7,12,13,14,15,19,20,24,25,26,29,31,36,38,40],[0,1,3,5,6,7,9,12,15,16,18,21,24,25,26,29,31,35,38],[0,3,5,6,10,11,12,13,14,16,17,22,24,25,26,29,31,32,34,35,37],[0,3,4,8,9,11,12,13,14,15,18,19,21,22,24,25,26,29,31,33,34,36,37,40],[1,7,9,10,11,12,13,14,15,17,19,20,23,24,25,26,29,32,34,35,36,37,39],[0,1,2,6,7,8,10,14,15,17,19,21,23,24,25,26,29,32,33,34,35,37,39,40],[0,4,6,7,9,10,11,12,16,17,18,19,20,22,23,24,25,26,29,35,36,38,39,40],[0,1,3,4,5,7,13,14,15,16,18,21,22,23,24,25,26,29,32,35,38,39],[0,4,5,9,12,13,15,19,27,29,32,33,34,37],[0,3,4,6,8,10,11,16,17,19,21,27,29,31,32,34,36,37,39,40],[1,3,8,9,11,15,16,19,22,27,29,32,33,34,38,39],[0,2,3,6,8,12,13,14,15,17,19,20,21,22,27,29,31,33,34,36,38,40],[3,8,9,10,17,18,19,20,23,27,29,31,36,38,39],[1,3,4,5,6,8,16,19,21,23,27,29,35,38,40],[0,2,3,4,5,7,9,16,18,20,22,23,27,29,31,35,37],[5,6,7,8,12,13,16,17,20,21,22,23,27,29,32,33,36,37,39,40],[0,2,5,6,8,10,13,14,15,17,18,19,24,27,29,32,33,34,35,36,37,38,39],[1,2,4,5,6,10,11,12,13,16,18,19,20,21,24,27,29,31,32,35,38,40],[7,8,13,15,16,19,20,22,24,27,29,32,33,34,35,38],[2,3,4,5,7,8,10,11,14,15,17,21,22,24,27,29,31,33,35,36,37,38,39,40],[2,3,5,9,10,11,14,15,17,23,24,27,29,31,35,38,39],[0,2,5,9,10,11,19,20,21,23,24,27,29,34,36,37,38,40],[0,1,2,6,9,10,13,14,16,22,23,24,27,29,31,37,38],[0,5,6,8,9,13,14,19,20,21,22,23,24,27,29,32,33,34,35,36,38,39,40],[0,1,2,4,6,9,11,13,19,20,25,27,29,31,32,34,35,36,38],[0,1,2,3,4,9,11,12,14,17,20,21,25,27,29,32,33,34,38,40],[1,3,5,6,8,9,10,11,12,13,14,16,18,22,25,27,29,31,32,34,35,36,39,40],[0,2,3,9,11,14,15,16,17,18,19,20,21,22,25,27,29,34,39],[2,3,5,6,9,10,12,13,18,23,25,27,29,31,33,34,35,37],[1,2,3,4,5,8,9,10,11,12,14,15,16,20,21,23,25,27,29,33,34,35,36,37,40],[0,1,2,3,4,6,7,8,9,10,11,13,14,22,23,25,27,29,31,33,34,36,37,38,39,40],[1,5,7,8,9,18,19,21,22,23,25,27,29,32,34,37,38,39],[0,2,3,4,6,7,9,10,11,12,14,15,17,18,24,25,27,29,35,39],[1,2,3,5,6,7,11,12,13,14,16,17,20,21,24,25,27,29,31,33,34,36,37,39,40],[1,2,3,4,5,9,10,12,13,14,20,22,24,25,27,29,35,36,40],[1,5,8,10,12,13,14,18,19,20,21,22,24,25,27,29,31,32,34,37],[1,2,4,7,10,11,14,16,18,19,23,24,25,27,29,32,33,35,36,37],[0,1,2,3,4,5,7,8,9,12,17,19,20,21,23,24,25,27,29,31,32,33,34,35,40],[0,1,3,4,5,6,7,11,13,14,15,16,17,19,20,22,23,24,25,27,29,32,33,36,37,39,40],[0,2,3,4,5,6,7,9,12,15,16,17,20,21,22,23,24,25,27,29,31,34,39],[0,1,3,6,14,16,17,18,26,27,29,31,32,33,35,36,40],[0,1,2,3,7,8,10,12,14,19,21,26,27,29,31,32,34,35,36,39],[2,3,4,6,7,8,10,11,13,18,20,22,26,27,29,31,33,36,37,39,40],[0,1,2,4,5,8,10,11,12,14,15,18,21,22,26,27,29,31,32,33,34,36,37],[2,4,5,7,8,9,10,13,15,19,20,23,26,27,29,33,34,35,36,37,38,39],[1,3,5,6,8,9,11,16,18,21,23,26,27,29,33,36,37,38,40],[0,2,3,5,7,9,10,13,19,22,23,26,27,29,32,33,34,35,38],[2,3,4,6,8,9,10,11,13,14,16,18,21,22,23,26,27,29,38,39,40],[0,4,6,8,10,11,13,16,17,18,19,24,26,27,29,31,33,34,35,37,38,39,40],[1,2,3,5,6,7,9,10,11,14,18,20,21,24,26,27,29,31,34,35,38],[3,4,8,10,11,12,13,17,18,22,24,26,27,29,31,32,33,34,36,40],[3,7,8,9,11,12,13,16,18,21,22,24,26,27,29,31,33,34,36,37,39],[1,2,3,4,6,7,10,13,14,16,17,23,24,26,27,29,32,33,35,38,39],[0,1,3,4,5,6,9,10,11,12,13,14,18,20,21,23,24,26,27,29,32,33,37,38,40],[0,3,4,11,12,16,18,19,20,22,23,24,26,27,29,33,35,37],[0,1,4,7,8,9,10,14,21,22,23,24,26,27,29,32,39,40],[1,2,8,9,10,11,12,14,15,17,19,25,26,27,29,32,34,35,40],[1,5,6,7,8,10,12,13,14,15,17,18,20,21,25,26,27,29,32,33],[0,1,2,4,7,9,10,11,12,13,19,20,22,25,26,27,29,34,39],[2,3,4,6,8,12,14,16,18,21,22,25,26,27,29,32,35,39,40],[0,1,3,4,5,6,7,8,12,14,16,17,18,23,25,26,27,29,34,35,37,38],[0,2,9,13,15,16,18,21,23,25,26,27,29,35,37,38,40],[2,5,6,7,10,11,12,13,16,17,20,22,23,25,26,27,29,32,34,35,36,37,38,39,40],[0,2,4,5,9,11,14,15,16,21,22,23,25,26,27,29,33,35,36,37,38,39],[1,6,7,8,14,19,20,24,25,26,27,29,31,32,34,36,37,38,39,40],[0,2,3,4,6,8,10,11,12,13,15,17,21,24,25,26,27,29,31,32,33,34,35,36,38,39],[0,2,3,7,8,10,11,12,14,15,17,18,19,20,22,24,25,26,27,29,31,34,35,37],[0,2,3,4,5,10,13,15,17,20,21,22,24,25,26,27,29,31,32,34,40],[0,1,2,3,6,8,13,15,17,19,23,24,25,26,27,29,31,34,36,38],[1,3,6,7,10,14,16,17,20,21,23,24,25,26,27,29,31,34,36,37,38,40],[1,2,3,7,8,12,13,14,15,17,18,22,23,24,25,26,27,29,31,32,34,36,39,40],[2,5,8,14,20,21,22,23,24,25,26,27,29,31,33,34,36,37,39],[1,4,5,6,7,8,9,14,15,17,18,19,28,29,31,32,33,35,38,39,40],[0,1,4,7,8,9,11,13,15,17,18,21,28,29,32,33,37,38],[0,1,2,5,7,9,10,11,12,13,15,16,17,22,28,29,31,32,33,34,35,36],[0,3,5,6,7,8,9,12,15,17,18,20,21,22,28,29,34,36,37,39,40],[0,1,6,11,12,15,16,17,18,19,23,28,29,31,32,35,36,38],[3,4,5,8,11,13,14,15,18,19,21,23,28,29,32,33,35,36,37,38,39,40],[3,4,7,8,11,13,15,18,19,22,23,28,29,31,32,34,36,39,40],[2,3,6,7,8,10,11,12,15,16,19,21,22,23,28,29,34,36,37],[0,2,4,7,8,9,12,13,17,18,24,28,29,32,36,37,38,39,40],[0,1,2,3,7,8,10,11,15,17,21,24,28,29,31,32,34,35,36,37,38],[1,2,3,4,8,9,12,13,15,17,19,22,24,28,29,32,34,36,37,38],[0,1,3,5,11,15,16,18,19,21,22,24,28,29,31,33,35,36,37,38,39,40],[2,4,6,9,10,15,18,19,20,23,24,28,29,32,33,37,39],[2,4,6,8,13,19,20,21,23,24,28,29,31,32,34,37,40],[0,4,6,9,11,15,18,20,22,23,24,28,29,32,33,34,35,36,37,40],[1,2,3,4,5,6,11,13,14,16,19,20,21,22,23,24,28,29,31,33,35,36,37,39],[4,5,7,8,9,10,11,15,19,25,28,29,38,39],[0,4,5,6,7,11,12,13,14,15,16,19,20,21,25,28,29,31,37,38,39,40],[0,1,5,6,7,9,10,11,12,17,18,19,22,25,28,29,34,36,37],[0,2,3,7,10,11,13,15,17,18,19,21,22,25,28,29,31,32,33,34,36,40],[0,1,8,10,11,12,13,17,18,23,25,28,29,31,33,34,36,38,39,40],[3,4,6,8,9,12,15,18,19,21,23,25,28,29,34,35,36,37,38,39],[1,2,3,4,6,7,13,14,15,16,17,19,22,23,25,28,29,31,33,35,36,37,40],[1,3,5,7,8,9,11,16,18,21,22,23,25,28,29,32,33,36],[0,3,10,11,14,16,18,19,24,25,28,29,32,33,34,36,37,38,39],[0,1,4,5,8,10,11,13,14,16,17,21,24,25,28,29,31,32,33,36,37,38,39,40],[2,7,13,14,16,18,20,22,24,25,28,29,32,33,36,38],[0,4,7,10,15,19,21,22,24,25,28,29,31,34,36,38,40],[1,3,6,7,12,14,15,17,19,23,24,25,28,29,31,32,37,40],[1,3,5,6,7,11,13,21,23,24,25,28,29,32,33,34,35,37],[0,3,6,7,12,13,15,16,17,18,19,20,22,23,24,25,28,29,31,32,34,35,36,39,40],[1,2,6,7,8,10,11,19,21,22,23,24,25,28,29,36,39],[3,6,8,9,10,11,16,17,20,26,28,29,32,34,38,39],[0,2,7,8,10,11,12,19,20,21,26,28,29,32,35,36,37,38,40],[0,4,5,7,9,10,16,22,26,28,29,35,36,38,40],[0,1,4,6,8,12,14,16,17,18,19,20,21,22,26,28,29,32,33,34,37,38,39],[0,1,2,3,4,5,9,10,14,16,19,20,23,26,28,29,32,34,38],[3,5,6,7,8,10,11,18,19,20,21,23,26,28,29,32,33,36,37,38,39,40],[3,6,8,9,16,17,18,22,23,26,28,29,38,39,40],[4,5,7,8,10,11,16,17,19,21,22,23,26,28,29,32,34,36,37,38],[0,5,6,8,10,12,13,14,16,17,24,26,28,29,31,33,36,38,39],[0,1,2,4,6,7,8,12,13,15,17,21,24,26,28,29,31,33,35,38,40],[1,2,6,8,14,15,18,22,24,26,28,29,31,32,33,34,35,36,40],[0,1,2,3,4,6,7,14,20,21,22,24,26,28,29,31,34,39],[1,2,5,6,9,12,17,20,23,24,26,28,29,31,33,36,39],[1,3,6,7,8,9,10,11,18,19,20,21,23,24,26,28,29,31,40],[0,1,2,3,6,7,9,11,13,14,16,19,22,23,24,26,28,29,31,32,33,34,38,40],[2,3,6,9,12,13,15,16,20,21,22,23,24,26,28,29,31,33,34,36,38,39],[0,5,10,13,14,15,18,20,25,26,28,29,31,33,37,39,40],[2,3,6,7,8,11,13,18,20,21,25,26,28,29,31,33,34,36,39],[1,2,3,4,6,7,8,18,22,25,26,28,29,31,32,33,34,35,36,40],[2,3,4,8,11,15,16,17,18,19,21,22,25,26,28,29,31,35,37],[2,4,6,10,15,16,17,18,19,20,23,25,26,28,29,33,34,37,39,40],[0,1,5,7,12,16,17,21,23,25,26,28,29,35,36,39],[0,2,5,8,10,11,13,15,18,19,20,22,23,25,26,28,29,32,33,40],[0,2,3,4,5,6,7,10,11,12,13,14,15,17,19,20,21,22,23,25,26,28,29,33,34,35,36,37],[1,2,4,6,7,8,10,11,13,14,15,16,18,24,25,26,28,29,31,35,36,37,39,40],[6,9,10,12,13,14,15,16,17,20,21,24,25,26,28,29,31,35,37,39],[0,1,2,4,5,6,7,8,10,12,13,15,16,17,19,22,24,25,26,28,29,31,32,34,36,38,40],[1,2,3,6,8,9,11,13,14,19,20,21,22,24,25,26,28,29,31,33,34,38],[0,1,4,6,7,8,9,13,16,17,19,20,23,24,25,26,28,29,34,35,36,37,38,40],[0,1,2,3,4,6,8,13,14,16,17,18,19,21,23,24,25,26,28,29,33,34,37,38],[2,3,4,5,6,8,9,10,12,13,15,17,22,23,24,25,26,28,29,32,35,39,40],[0,1,2,6,7,8,9,11,12,16,17,19,21,22,23,24,25,26,28,29,36,39],[1,3,6,7,8,11,12,27,28,29,31,33,36,38,39],[0,1,3,5,6,8,9,10,11,15,16,18,19,21,27,28,29,35,38,40],[0,2,3,10,12,13,14,15,16,17,20,22,27,28,29,31,33,37,39,40],[0,1,7,8,9,10,13,15,17,18,19,20,21,22,27,28,29,32,33,35,36,37],[6,7,10,11,12,15,16,17,19,23,27,28,29,34,35,40],[0,1,3,4,5,6,8,9,12,14,18,19,21,23,27,28,29,31,34,35,36,39],[0,3,7,8,10,11,12,13,15,16,17,22,23,27,28,29,34,37,38],[0,2,3,4,8,9,10,12,13,15,16,19,21,22,23,27,28,29,31,32,33,34,36,37,38,39,40],[0,1,2,4,7,8,9,10,11,13,15,20,24,27,28,29,33,35,37,38],[0,2,3,6,8,9,10,11,13,14,15,16,17,18,19,21,24,27,28,29,31,34,36,38,39,40],[1,2,3,7,8,9,10,11,12,13,14,15,17,18,19,22,24,27,28,29,33,35,38,40],[0,1,3,4,5,6,9,11,12,13,14,17,21,22,24,27,28,29,31,32,33,34,36,37,38,39],[0,2,3,5,6,7,10,15,17,18,19,23,24,27,28,29,31,34,36,37,38,40],[0,2,3,5,8,10,11,12,15,16,17,18,19,20,21,23,24,27,28,29,38,39],[1,3,4,5,6,11,12,16,22,23,24,27,28,29,31,34,35,38],[0,2,4,7,10,14,15,18,21,22,23,24,27,28,29,32,33,35,36,37,38,39,40],[1,2,3,4,6,7,11,14,15,17,19,25,27,28,29,32,36,37,39],[0,1,2,3,4,6,8,15,16,17,18,21,25,27,28,29,31,32,33,37,39,40],[0,1,2,3,4,8,11,14,15,19,22,25,27,28,29,32,37,38,39],[0,4,5,7,8,10,14,16,17,18,21,22,25,27,28,29,31,36,37,38,39,40],[1,2,4,6,7,10,13,14,18,20,23,25,27,28,29,32,33,35,37,38,39,40],[0,2,3,6,10,12,13,14,16,17,18,21,23,25,27,28,29,31,32,33,36,37,38,39],[0,3,4,7,8,11,13,15,16,17,18,19,22,23,25,27,28,29,32,33,37,39,40],[0,2,3,5,10,11,12,13,14,18,21,22,23,25,27,28,29,31,35,36,37,39],[0,2,3,4,6,8,10,11,17,24,25,27,28,29,34],[0,1,2,5,7,9,12,15,21,24,25,27,28,29,31,33,36,37,40],[1,6,8,12,13,15,18,19,20,22,24,25,27,28,29,34],[1,5,7,9,13,14,17,19,21,22,24,25,27,28,29,31,32,36,37,40],[0,2,5,8,9,10,11,16,17,18,19,23,24,25,27,28,29,33,34,35,36,39,40],[0,2,6,7,8,11,14,15,16,19,21,23,24,25,27,28,29,31,33,37,39],[2,4,5,7,8,9,10,11,12,13,14,19,20,22,23,24,25,27,28,29,33,34,39,40],[1,6,7,10,11,13,15,16,17,19,20,21,22,23,24,25,27,28,29,31,32,35,36,37,39],[2,9,10,11,12,13,19,26,27,28,29,31,35,36,37,39],[0,3,9,12,15,17,21,26,27,28,29,31,33,34,36,37,40],[0,1,2,3,5,6,8,9,10,13,16,17,19,20,22,26,27,28,29,31,32,39,40],[0,2,3,6,9,10,11,14,17,18,21,22,26,27,28,29,31,34,35],[3,6,7,8,11,13,14,15,16,17,18,23,26,27,28,29,34,36,37,38],[0,1,2,3,4,6,7,10,11,12,16,18,21,23,26,27,28,29,36,37,38,39,40],[0,2,3,5,10,11,12,13,16,17,18,20,22,23,26,27,28,29,32,34,36,38,40],[0,2,4,6,7,9,12,14,15,16,18,19,21,22,23,26,27,28,29,33,36,38,39],[0,1,2,4,9,14,15,18,19,24,26,27,28,29,32,34,35,37],[0,5,6,11,12,13,15,17,20,21,24,26,27,28,29,32,33,34,39,40],[1,5,7,9,10,13,14,16,19,22,24,26,27,28,29,34,38,40],[3,6,7,10,12,13,15,16,17,18,19,21,22,24,26,27,28,29,32,34,35,37,38,39],[0,1,3,5,7,8,9,11,12,13,15,16,17,19,23,24,26,27,28,29,31,32,37],[0,1,3,6,9,10,12,13,17,18,20,21,23,24,26,27,28,29,31,32,39,40],[4,7,8,9,12,14,15,16,18,19,22,23,24,26,27,28,29,31,36,38,40],[4,5,6,8,17,18,20,21,22,23,24,26,27,28,29,31,32,33,36,37,38,39],[0,1,3,4,5,11,14,18,20,25,26,27,28,29,32,33,34,36,37,39],[1,2,4,8,9,11,12,13,16,18,19,21,25,26,27,28,29,32,36,37,39,40],[1,2,4,6,8,10,11,12,13,15,19,20,22,25,26,27,28,29,33,34,35,37,39],[0,4,5,7,8,9,10,11,16,18,21,22,25,26,27,28,29,32,33,35,37,39,40],[0,2,4,5,6,7,9,10,12,13,15,17,18,20,23,25,26,27,28,29,32,33,34,35,36,37,38,39],[0,2,5,6,8,9,10,13,14,17,21,23,25,26,27,28,29,32,33,36,37,38,39,40],[0,6,7,8,11,12,13,14,15,17,19,22,23,25,26,27,28,29,33,34,35,36,37,38,39],[0,4,5,10,11,13,15,16,17,19,20,21,22,23,25,26,27,28,29,32,36,37,38,39,40],[1,2,4,5,6,7,8,9,10,14,15,16,17,19,20,24,25,26,27,28,29,32,33,34,35,37],[1,2,3,4,6,8,11,17,20,21,24,25,26,27,28,29,32,34,35,40],[3,4,5,6,7,11,13,14,15,18,19,22,24,25,26,27,28,29,33,34,37,38],[2,3,6,7,9,10,11,12,13,17,20,21,22,24,25,26,27,28,29,32,33,34,38,40],[0,1,6,8,10,12,13,15,16,19,20,23,24,25,26,27,28,29,32,33,34,37,39],[5,7,9,12,16,17,18,19,21,23,24,25,26,27,28,29,32,33,34,35,39,40],[0,2,3,4,5,7,9,10,16,17,18,20,22,23,24,25,26,27,28,29,33,34,36,37,38,39],[5,8,9,14,15,16,17,19,21,22,23,24,25,26,27,28,29,32,34,35,36,38,39,40],[0,3,4,7,9,10,14,15,16,18,30,34,37,38],[4,6,14,19,21,30,31,32,34,35,37,38,39,40],[1,3,4,6,8,11,14,17,22,30,32,33,35,36,37,38,40],[2,3,4,5,7,9,11,17,21,22,30,31,32,36,37,38,39],[3,4,5,7,8,10,11,15,16,18,23,30,31,38],[0,1,3,5,6,9,12,14,19,20,21,23,30,32,33,38,39,40],[0,2,4,5,6,7,9,10,11,14,15,16,17,18,19,20,22,23,30,31,32,33,34,38,40],[0,3,10,12,14,15,16,21,22,23,30,32,33,34,38,39],[1,3,5,7,9,11,12,13,14,18,20,24,30,32,34,36,37,39,40],[3,4,9,11,13,16,18,21,24,30,31,35,36],[0,1,2,4,5,7,11,14,16,17,22,24,30,33,35,36,37,38,39],[1,3,5,8,10,11,12,14,15,16,19,21,22,24,30,31,34,36,38,40],[0,1,3,4,5,6,7,8,9,10,11,12,15,19,23,24,30,31,32,36,38,40],[0,1,4,6,9,10,12,15,16,18,19,20,21,23,24,30,33,34,36,37,38,39],[3,5,6,8,13,14,18,22,23,24,30,31,33,34],[0,1,2,3,5,6,7,8,10,11,13,15,21,22,23,24,30,33,37,39,40],[0,1,2,4,5,6,8,9,10,12,16,25,30,31,36,37,39],[1,2,3,4,7,9,10,11,14,16,21,25,30,32,36,37,39,40],[1,4,5,7,10,12,13,14,16,19,22,25,30,31,32,33,34,35,39],[2,4,5,6,11,13,14,15,17,18,19,21,22,25,30,32,34,35,39,40],[2,4,6,8,10,12,13,14,19,23,25,30,31,36],[0,1,2,5,7,8,10,12,13,14,18,19,20,21,23,25,30,32,33,35,36,40],[0,1,2,3,4,9,11,12,14,15,16,17,18,19,22,23,25,30,31,32,33,34,36,37],[0,1,6,7,8,9,10,11,12,19,20,21,22,23,25,30,32,33,34,35,36,37,40],[1,3,4,7,11,12,14,15,16,17,18,19,20,24,25,30,34,35,37,38,40],[3,8,9,10,12,14,16,18,20,21,24,25,30,31,32,35,38],[0,7,9,10,16,19,20,22,24,25,30,32,33,40],[2,3,4,5,10,11,14,21,22,24,25,30,31,32,34,37],[0,3,6,7,10,12,19,20,23,24,25,30,34,35,40],[0,6,9,14,15,17,18,19,21,23,24,25,30,31,32,33,37],[2,3,4,6,9,10,16,18,22,23,24,25,30,32,33,35,36,37,38,40],[0,1,3,4,5,6,7,8,10,12,21,22,23,24,25,30,31,32,33,34,36,38],[0,2,4,7,15,17,18,20,26,30,33,37,38,39],[4,5,6,7,10,11,12,13,17,20,21,26,30,32,33,34,35,36,37,38,40],[1,3,4,5,6,7,8,9,11,12,13,14,15,16,22,26,30,34,36,37,39,40],[4,5,7,9,15,17,18,21,22,26,30,33,35,37],[1,4,5,6,8,11,12,15,16,17,20,23,26,30,31,34,36,38,39,40],[0,2,3,10,11,12,13,14,16,17,18,19,20,21,23,26,30,31,32,33,38],[0,1,4,7,9,10,11,13,16,17,19,22,23,26,30,31,33,35,36,39],[0,1,6,7,9,10,11,18,19,20,21,22,23,26,30,31,33,34,35,40],[3,5,6,7,9,10,12,13,14,17,18,19,20,24,26,30,33,34,35,36,40],[1,2,4,5,6,7,10,11,12,18,21,24,26,30,32,33,34,37,39],[0,3,4,6,12,13,15,16,17,18,20,22,24,26,30,35,36],[3,5,6,8,9,10,11,12,17,19,21,22,24,26,30,33,37,39,40],[0,1,2,3,4,5,6,8,14,15,16,23,24,26,30,31,35,37,38,39],[0,1,3,4,5,6,9,12,13,14,15,16,17,19,21,23,24,26,30,31,32,33,35,36,38,40],[6,8,9,11,14,15,16,17,19,20,22,23,24,26,30,31,33,34,36,37,38,39,40],[0,1,3,5,6,8,10,11,12,13,17,18,21,22,23,24,26,30,31,33,34,38],[4,6,9,10,12,13,14,15,16,18,20,25,26,30,31,33,35,36,38],[0,2,4,8,10,12,15,17,21,25,26,30,31,32,33,34,35,38,40],[0,3,4,5,8,13,14,16,17,18,19,20,22,25,26,30,31,34,35,37],[0,1,4,6,8,9,10,14,15,16,17,18,19,20,21,22,25,26,30,31,33,35,36,37,40],[0,2,4,5,7,9,10,14,15,16,17,18,19,20,23,25,26,30,31,35,37,38,39,40],[1,3,5,6,7,10,11,12,13,14,15,18,20,21,23,25,26,30,31,32,33,34,36,37,38,39],[1,4,6,8,10,11,12,15,17,18,19,22,23,25,26,30,31,33,34,39,40],[1,5,9,13,14,17,20,21,22,23,25,26,30,31,33,35,36,39],[0,1,4,5,6,7,8,9,12,13,14,17,19,24,25,26,30,32,33,35,37,39,40],[0,2,3,6,7,9,10,14,15,16,17,19,21,24,25,26,30,33,35,36,39],[2,6,8,11,12,14,17,18,19,22,24,25,26,30,32,34,35,39,40],[0,2,4,6,8,11,13,19,21,22,24,25,26,30,32,33,34,35,36,37,39],[1,2,5,6,8,10,11,13,14,15,17,19,20,23,24,25,26,30,32,35,36,38,39],[1,6,8,16,17,18,19,20,21,23,24,25,26,30,33,37,38,39,40],[0,1,2,3,4,6,8,9,11,16,18,19,20,22,23,24,25,26,30,32,33,34,37,38,39],[2,4,6,9,13,16,17,18,20,21,22,23,24,25,26,30,32,33,34,35,36,38,39,40],[1,3,4,8,9,12,14,16,18,19,20,27,30,31,37,39],[0,1,4,8,9,11,13,14,20,21,27,30,32,33,35,36,40],[0,1,3,6,10,11,14,15,16,18,19,20,22,27,30,31,32,33,35,36,40],[0,2,3,5,6,8,12,13,16,17,18,21,22,27,30,32,33,37,39],[7,9,10,15,17,18,20,23,27,30,31,35,38,39],[0,1,4,7,8,9,10,13,14,15,16,17,18,19,20,21,23,27,30,32,35,36,37,38,40],[0,1,2,3,4,6,8,10,12,14,15,16,18,20,22,23,27,30,31,32,33,35,37,38,40],[0,1,5,6,8,12,13,14,16,17,21,22,23,27,30,32,35,36,38,39],[0,1,4,8,11,13,14,16,17,18,19,24,27,30,31,32,33,36,37,38,39,40],[0,5,6,8,9,10,15,18,19,20,21,24,27,30,34,35,37,38],[2,3,4,7,8,9,11,14,16,19,20,22,24,27,30,31,35,36],[0,6,7,13,14,16,18,21,22,24,27,30,34,39,40],[0,3,4,5,6,7,9,12,17,18,23,24,27,30,31,32,33,35,36,38,40],[0,4,7,8,10,13,15,16,19,21,23,24,27,30,33,34,35,38,39],[3,4,5,6,7,10,11,12,13,14,15,16,17,22,23,24,27,30,31,35,37,39],[0,1,2,3,4,5,7,9,10,11,15,16,17,19,20,21,22,23,24,27,30,33,34,35,36,37,40],[1,5,7,8,9,10,11,12,16,19,20,25,27,30,34,35,36,40],[0,1,3,7,11,12,13,14,15,16,17,19,21,25,27,30,31,32,33,34,35,37],[0,2,4,5,6,7,10,11,13,14,18,20,22,25,27,30,32,33,34,39,40],[0,1,4,5,6,7,9,10,11,14,16,20,21,22,25,27,30,31,32,33,34,36,37,39],[1,3,4,5,8,9,13,14,15,16,18,20,23,25,27,30,31,36,37,38,39,40],[0,3,8,10,11,12,14,16,17,19,20,21,23,25,27,30,32,35,38,39],[0,1,5,6,7,10,11,12,14,16,17,20,22,23,25,27,30,31,32,33,36,37,38,40],[0,1,2,3,4,5,6,7,8,9,10,13,17,19,20,21,22,23,25,27,30,32,35,38],[0,2,4,5,6,9,10,12,14,24,25,27,30,31,33,38],[0,1,2,5,8,9,10,13,14,18,21,24,25,27,30,32,34,36,38,40],[2,3,4,5,6,7,11,12,15,16,17,22,24,25,27,30,31,32,35,39],[0,7,10,11,13,14,20,21,22,24,25,27,30,32,34,35,36,39,40],[0,2,3,4,7,10,17,18,19,23,24,25,27,30,33,34,35,37,38],[0,2,4,6,7,10,11,13,14,17,18,21,23,24,25,27,30,31,32,33,36,37,38,40],[1,3,4,7,9,10,17,18,22,23,24,25,27,30,32,34,35,36,37,39],[0,2,3,4,5,6,7,8,9,11,13,15,16,19,21,22,23,24,25,27,30,31,32,33,37,39,40],[1,5,6,9,10,11,12,13,14,17,20,26,27,30,33,38,40],[0,1,2,6,7,10,11,12,13,14,18,19,21,26,27,30,32,34,35,37,38,39],[0,1,2,3,4,7,8,10,12,18,22,26,27,30,36,37,39],[0,2,4,9,12,14,15,16,18,19,20,21,22,26,27,30,34,35,36,40],[1,2,3,4,5,8,11,12,13,14,15,17,20,23,26,27,30,35,36,37],[0,7,9,13,15,20,21,23,26,27,30,32,34,35,36,39,40],[0,2,3,6,9,10,11,12,14,16,17,18,19,22,23,26,27,30,33,36,38,39,40],[0,2,3,4,6,7,14,15,17,19,21,22,23,26,27,30,34,36,37,38],[0,2,5,9,10,11,16,18,24,26,27,30,34,35,36,37],[0,1,3,4,5,6,7,9,11,12,14,15,16,18,19,20,21,24,26,27,30,32,33,34,36,37,39,40],[1,2,11,12,14,15,16,18,19,22,24,26,27,30,33,34,35,36,39,40],[0,1,2,4,5,6,7,8,11,14,15,17,21,22,24,26,27,30,33,34,36],[0,3,8,9,10,13,16,17,18,23,24,26,27,30,33,34,39,40],[0,2,3,6,7,9,11,13,15,16,17,20,21,23,24,26,27,30,32,33,34],[2,5,7,8,10,11,12,13,18,22,23,24,26,27,30,34,35,36,37],[0,1,2,3,6,8,10,12,13,14,16,17,18,21,22,23,24,26,27,30,33,34,35,36,37,39,40],[0,4,5,6,7,8,10,12,15,16,18,19,25,26,27,30,31,33,36,39],[2,4,5,6,11,14,18,21,25,26,27,30,31,32,34,36,37,39,40],[1,3,9,12,17,18,20,22,25,26,27,30,31,38],[5,7,9,11,19,20,21,22,25,26,27,30,31,34,37,38,40],[0,1,2,3,5,7,8,9,11,12,13,17,19,20,23,25,26,27,30,34,35,37,38,40],[4,5,8,9,10,11,12,13,15,16,17,18,19,20,21,23,25,26,27,30,32,38],[1,3,4,6,7,12,13,14,17,19,22,23,25,26,27,30,33,34,37,39,40],[1,3,5,6,8,12,13,19,21,22,23,25,26,27,30,35,39],[3,5,6,9,10,12,15,16,19,24,25,26,27,30,32,37,38,39,40],[1,2,4,7,8,10,11,12,15,17,18,20,21,24,25,26,27,30,33,37,38,39],[0,2,3,6,10,11,13,15,18,19,22,24,25,26,27,30,32,33,37,38,40],[2,3,4,7,9,13,14,18,20,21,22,24,25,26,27,30,32,33,37,38],[1,2,6,9,10,12,15,18,19,20,23,24,25,26,27,30,31,32,33,34,35,36,38,39],[1,5,7,10,14,15,16,17,18,19,21,23,24,25,26,27,30,31,33,34,36,38,39,40],[0,2,3,5,6,7,13,14,17,20,22,23,24,25,26,27,30,31,32,34,38],[1,2,5,8,9,12,14,17,18,21,22,23,24,25,26,27,30,31,32,33,34,35,38,40],[2,3,4,5,6,8,11,13,15,17,20,28,30,35,36,37,40],[2,3,4,5,6,9,10,12,13,16,19,20,21,28,30,31,32,35,36,37,39],[0,1,6,9,12,13,14,15,16,17,19,20,22,28,30,32,33,34,36,37,39,40],[2,3,5,6,11,13,15,16,17,18,20,21,22,28,30,31,32,34,36,37],[1,2,3,5,6,9,12,15,17,20,23,28,30,31,32,34,36,37],[2,4,5,6,10,12,14,16,18,20,21,23,28,30,33,34,35,36,37,39,40],[0,1,2,3,4,6,7,8,10,20,22,23,28,30,31,33,37,39],[1,3,5,6,7,9,10,20,21,22,23,28,30,33,35,37,40],[1,2,6,10,14,20,24,28,30,31,32,35,39],[0,2,3,4,5,8,10,11,16,18,19,21,24,28,30,34,35,37,40],[0,1,2,5,7,9,13,15,16,17,18,22,24,28,30,31,33,34,36,38],[0,1,4,5,6,7,9,10,11,13,16,18,19,20,21,22,24,28,30,36,37,38,39,40],[2,5,8,12,14,15,17,20,23,24,28,30,34,38,40],[0,2,6,8,14,15,16,17,21,23,24,28,30,31,32,33,35,37,38,39],[0,1,3,6,8,9,11,12,13,14,15,17,18,19,22,23,24,28,30,32,33,39,40],[0,2,9,10,11,13,19,20,21,22,23,24,28,30,31,32,33,34,35,37],[5,6,7,8,12,13,17,18,19,25,28,30,31,32,34,36,37,38,39,40],[6,7,8,12,13,14,17,20,21,25,28,30,34,35,36,37,38,39],[0,3,4,6,7,9,10,15,17,19,22,25,28,30,31,33,35,36,38],[1,2,4,6,7,8,9,16,20,21,22,25,28,30,36,38,40],[4,5,6,7,8,9,13,16,19,20,23,25,28,30,31,34,35,36,37,38],[1,3,6,7,9,11,12,13,16,19,21,23,25,28,30,32,33,34,35,36,37,38,40],[0,1,2,6,11,12,14,17,18,20,22,23,25,28,30,31,32,33,35,38,39,40],[1,4,6,10,15,16,21,22,23,25,28,30,32,33,35,38,39],[2,8,9,10,11,13,15,16,17,18,19,24,25,28,30,31,32,35,38],[0,1,2,3,4,6,8,11,12,13,16,18,21,24,25,28,30,34,37,38,40],[0,1,5,6,7,8,10,13,15,16,18,20,22,24,25,28,30,31,33,34,36,37,39,40],[0,1,2,4,7,9,10,12,13,14,15,19,20,21,22,24,25,28,30,35,36,39],[2,5,6,8,9,12,17,19,20,23,24,25,28,30,31,40],[0,2,5,10,11,12,14,15,18,19,20,21,23,24,25,28,30,32,33,34,37],[0,2,3,8,10,12,14,15,16,17,19,22,23,24,25,28,30,31,32,33,34,37,38,39],[0,1,5,6,8,9,10,11,12,14,15,17,19,21,22,23,24,25,28,30,32,33,38,39,40],[2,6,7,9,11,12,13,16,17,20,26,28,30,31,35,37,38,39],[3,5,6,8,9,10,11,12,15,16,17,20,21,26,28,30,31,32,34,35,36,37,38,40],[0,1,2,4,6,8,10,12,15,18,19,22,26,28,30,31,33,34,35,37],[2,4,6,7,8,10,12,13,14,15,16,17,19,21,22,26,28,30,31,35,36,37,39,40],[4,8,9,12,14,19,23,26,28,30,32,33,34,36,37,38,39],[1,2,5,7,8,9,10,11,13,15,18,21,23,26,28,30,35,37,38,40],[0,2,3,12,13,18,19,20,22,23,26,28,30,32,35,37],[2,4,7,8,11,16,17,18,20,21,22,23,26,28,30,32,34,36,37,39,40],[4,5,7,8,10,11,12,15,18,19,24,26,28,30,34,36,37,38,40],[0,1,2,5,6,9,10,11,13,14,15,17,19,20,21,24,26,28,30,32,34,38,39],[0,2,3,4,5,6,7,8,9,10,11,15,16,18,19,22,24,26,28,30,33,37,38,39,40],[0,2,8,11,12,13,18,19,20,21,22,24,26,28,30,36,38],[2,4,9,11,12,14,16,18,20,23,24,26,28,30,31,32,33,35,37,39,40],[0,3,4,6,7,12,13,14,16,17,18,19,21,23,24,26,28,30,31,36],[0,1,2,4,6,7,10,15,16,17,18,19,20,22,23,24,26,28,30,31,32,34,37,40],[0,2,4,5,8,9,11,13,14,17,21,22,23,24,26,28,30,31,32,34,35,36,39],[0,1,4,5,6,8,10,18,19,25,26,28,30,32,35,38],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,19,20,21,25,26,28,30,34,36,38,40],[1,2,5,6,7,9,10,14,17,18,19,20,22,25,26,28,30,32,33,34,35,37,39,40],[0,2,6,8,11,12,13,14,15,17,18,19,21,22,25,26,28,30,32,36,37,39],[0,2,5,7,8,10,14,23,25,26,28,30,33,36,38,39],[0,1,4,5,9,10,13,14,16,17,19,20,21,23,25,26,28,30,32,34,38,39,40],[1,2,3,4,5,7,9,11,14,15,16,19,20,22,23,25,26,28,30,34,35,37,40],[0,1,2,10,11,13,16,18,21,22,23,25,26,28,30,35,36,37],[0,3,4,6,7,8,12,14,15,20,24,25,26,28,30,35,36,38,39,40],[1,2,3,5,8,10,11,12,13,14,16,20,21,24,25,26,28,30,32,37,38,39],[1,4,7,8,9,10,11,13,18,19,20,22,24,25,26,28,30,33,34,35,37,38],[1,3,6,9,10,14,17,19,20,21,22,24,25,26,28,30,34,36,38,40],[0,1,2,3,4,5,6,8,9,10,11,12,13,17,18,19,20,23,24,25,26,28,30,32,33,39,40],[1,4,7,9,11,14,15,16,17,20,21,23,24,25,26,28,30,36,37,39],[1,3,4,5,7,8,10,11,16,19,20,22,23,24,25,26,28,30,32,34,35,37],[5,6,9,15,16,17,18,19,21,22,23,24,25,26,28,30,32,34,35,36,40],[0,3,5,7,8,9,10,12,14,16,17,18,27,28,30,33,34,35,38,39],[0,3,5,6,9,10,12,13,14,17,19,20,21,27,28,30,31,32,34,35,36,37,38,40],[2,10,11,12,16,17,18,22,27,28,30,32,34,37,38,39],[0,1,3,5,6,7,11,12,13,14,15,16,18,19,20,21,22,27,28,30,31,32,34,36,38,40],[9,12,13,14,15,17,19,20,23,27,28,30,32,33,34,35,39,40],[1,3,4,6,7,9,11,15,16,17,19,21,23,27,28,30,31,33,34,36,37],[0,1,5,8,10,12,13,14,16,20,22,23,27,28,30,34,35,36,37,39,40],[1,2,4,6,7,11,14,15,16,17,18,21,22,23,27,28,30,31,33,34],[0,3,5,7,10,11,12,13,17,18,19,20,24,27,28,30,31,32,34,35,36,37,38,39,40],[1,4,8,9,11,14,15,16,18,20,21,24,27,28,30,33,35,37,38],[1,3,4,6,7,9,11,14,15,22,24,27,28,30,31,33,34,39,40],[1,2,3,6,11,12,13,14,15,18,19,21,22,24,27,28,30,33,36],[4,5,6,8,9,10,12,13,16,23,24,27,28,30,31,34,35,36,37,38],[0,4,6,7,8,11,12,15,17,18,21,23,24,27,28,30,32,37,38,39,40],[0,2,3,7,8,10,11,18,20,22,23,24,27,28,30,31,32,33,34,35,36],[0,1,9,10,13,14,18,20,21,22,23,24,27,28,30,32,39,40],[0,1,5,6,9,12,14,16,17,25,27,28,30,31,32,33,35,37,38,40],[0,1,7,10,11,13,15,16,19,21,25,27,28,30,36,38],[3,6,7,8,10,12,13,14,15,17,18,19,22,25,27,28,30,31,37,38],[0,1,2,9,10,11,14,15,16,17,21,22,25,27,28,30,35,36,38,40],[3,6,7,9,10,11,12,14,15,16,19,23,25,27,28,30,33,34,35,37,39],[1,4,5,8,11,12,13,14,16,17,18,19,21,23,25,27,28,30,31,32,33,34,35,36,39,40],[0,2,3,5,6,7,8,10,12,13,15,16,17,18,19,22,23,25,27,28,30,32,34,35,36,37,39,40],[3,4,5,8,9,10,12,14,15,17,18,19,21,22,23,25,27,28,30,31,32,33,34,35,39],[0,2,3,4,5,7,9,11,14,16,19,20,24,25,27,28,30,31,32,34,36,38],[1,2,5,9,13,14,16,18,21,24,25,27,28,30,33,35,38,40],[3,6,7,12,14,17,19,22,24,25,27,28,30,31,33,34,35,40],[2,3,4,5,6,8,10,11,14,16,17,20,21,22,24,25,27,28,30,33,36],[1,2,5,6,11,13,14,16,20,23,24,25,27,28,30,36,38,40],[0,1,2,5,6,7,8,11,12,16,21,23,24,25,27,28,30,31,32,34,38],[0,2,3,4,7,9,10,11,12,13,15,16,19,22,23,24,25,27,28,30,32,33,36],[0,1,2,3,4,5,7,8,9,10,13,14,17,21,22,23,24,25,27,28,30,31,32,34,40],[0,2,5,6,8,9,10,11,13,15,17,18,19,20,26,27,28,30,33,35,36,37,38],[0,3,10,12,13,15,19,21,26,27,28,30,32,34,35,36,38,39,40],[2,5,6,12,19,22,26,27,28,30,35,36],[0,1,2,5,9,10,11,14,15,16,19,20,21,22,26,27,28,30,34,35,36,37,39,40],[1,3,11,12,14,19,20,23,26,27,28,30,32,35,37],[2,3,4,5,6,9,11,12,17,21,23,26,27,28,30,34,39,40],[0,2,7,8,9,11,13,16,18,22,23,26,27,28,30,32,33,36,38],[1,2,3,5,10,11,12,16,20,21,22,23,26,27,28,30,32,34,35,36,37,38,39,40],[0,1,3,5,9,10,11,15,17,19,20,24,26,27,28,30,31,34,37,38,40],[2,3,4,5,8,9,14,17,19,20,21,24,26,27,28,30,31,32,33,34,37,38,39],[2,4,5,6,7,10,11,15,17,20,22,24,26,27,28,30,31,33,34,36,38,40],[0,2,3,4,7,9,10,12,14,15,17,18,19,20,21,22,24,26,27,28,30,31,33,34,36,38,39],[2,4,5,8,9,10,12,14,15,17,18,19,20,23,24,26,27,28,30,31,32,33,34,36,37,38,39,40],[2,3,6,8,9,10,11,19,21,23,24,26,27,28,30,31,33,34,35,36,37,38],[0,2,5,6,8,11,12,16,18,19,20,22,23,24,26,27,28,30,31,32,34,35,36,38,39,40],[0,2,3,6,8,9,11,12,13,16,17,18,20,21,22,23,24,26,27,28,30,31,32,33,34,36,38],[2,7,8,10,11,16,19,20,25,26,27,28,30,31,32,33,36,37,39,40],[3,6,7,8,11,14,15,19,20,21,25,26,27,28,30,31,34,35,36,39],[0,1,7,9,10,11,12,14,17,22,25,26,27,28,30,31,32,36,37,38,39],[0,2,4,8,10,11,14,16,17,20,21,22,25,26,27,28,30,31,32,34,35,36,38,39,40],[0,3,5,6,7,8,9,12,14,15,19,23,25,26,27,28,30,34,37,38,40],[1,3,4,5,8,13,14,16,18,20,21,23,25,26,27,28,30,32,38],[0,1,2,3,4,5,6,7,8,10,11,14,15,17,18,19,22,23,25,26,27,28,30,33,34,35,36,37],[1,2,3,5,6,8,9,12,13,19,21,22,23,25,26,27,28,30,35,36,40],[2,4,8,9,10,11,12,14,17,18,19,20,24,25,26,27,28,30,31,37,39],[2,3,5,6,9,12,14,15,16,18,19,21,24,25,26,27,28,30,31,32,33,35,37,39,40],[1,2,3,7,8,9,12,13,14,15,16,17,18,22,24,25,26,27,28,30,31,33,36,37,39,40],[0,2,3,5,9,11,12,14,15,16,19,21,22,24,25,26,27,28,30,31,33,35,36,37,39],[0,6,7,8,10,12,14,17,19,23,24,25,26,27,28,30,32,33,34,36,37,39],[0,3,5,8,9,10,12,13,21,23,24,25,26,27,28,30,33,34,36,37,39,40],[0,1,5,6,7,9,10,16,17,18,20,22,23,24,25,26,27,28,30,32,34,35,36,37,39,40],[21,22,23,24,25,26,27,28,30,32,33,34,35,36,37,39],[2,4,5,6,9,12,14,15,18,19,29,30,31,32,33,38],[1,4,6,9,10,11,12,13,14,16,18,19,20,21,29,30,33,35,37,38],[1,2,3,5,8,10,12,13,19,20,22,29,30,31,34,35,36,40],[0,1,2,5,10,11,12,14,17,18,19,21,22,29,30,33,34,36,37,40],[0,2,3,4,9,10,12,14,16,19,20,23,29,30,34,35,36,37,38,39],[0,5,8,9,13,15,18,21,23,29,30,31,32,33,34,35,36,38,39],[0,3,6,7,8,10,11,12,13,14,17,18,22,23,29,30,32,33,35,36,37,39,40],[1,3,4,6,7,8,10,11,14,18,19,20,21,22,23,29,30,31,32,33,35,36,39,40],[0,4,6,7,8,10,11,14,16,17,24,29,30,31,35,38,39],[2,3,7,8,9,10,12,13,18,21,24,29,30,32,34,38,39],[0,2,4,6,8,9,10,12,16,19,22,24,29,30,31,32,33,34,38,39,40],[0,1,2,5,11,13,15,16,19,21,22,24,29,30,32,35,38,39,40],[3,6,7,8,9,10,13,14,18,20,23,24,29,30,32,33,34,36,37,39],[0,1,2,3,7,10,14,16,17,18,19,20,21,23,24,29,30,31,36,37,39],[1,6,7,8,12,13,14,15,16,18,20,22,23,24,29,30,37,39,40],[1,3,5,7,8,9,10,12,16,19,20,21,22,23,24,29,30,31,34,37,39,40],[2,3,9,10,12,14,15,16,17,19,25,29,30,31,32,33,34,36,39,40],[1,3,8,10,13,15,16,18,19,21,25,29,30,33,34,36,37,40],[4,6,8,10,11,12,14,15,17,20,22,25,29,30,31,35,37,38,39,40],[0,3,4,5,6,8,9,11,13,14,16,17,20,21,22,25,29,30,33,35,38,40],[0,1,2,5,6,8,9,11,12,13,14,16,19,23,25,29,30,31,34,35,37,39,40],[0,1,3,4,5,6,8,12,14,16,17,21,23,25,29,30,32,33,34,40],[0,2,4,5,7,10,11,12,13,15,16,17,19,20,22,23,25,29,30,31,32,33,35,38,39,40],[1,2,7,8,9,12,14,17,18,20,21,22,23,25,29,30,32,33,37,38,40],[0,1,2,4,5,6,9,11,12,13,16,17,18,24,25,29,30,32,36,40],[1,3,8,9,10,11,12,15,16,17,18,20,21,24,25,29,30,31,34,36,39,40],[0,2,4,5,6,7,10,11,15,22,24,25,29,30,33,34,35,36,37,40],[0,1,2,5,7,10,11,13,14,15,16,17,18,20,21,22,24,25,29,30,31,35,36,37,39,40],[2,3,5,6,8,11,12,13,16,17,18,23,24,25,29,30,33,35,37,38,39,40],[0,1,3,8,10,14,15,16,17,19,20,21,23,24,25,29,30,31,32,34,37,38,40],[5,6,8,9,14,16,17,19,22,23,24,25,29,30,32,34,35,36,38,39,40],[3,5,9,11,12,13,14,20,21,22,23,24,25,29,30,31,32,36,38,40],[0,6,7,8,9,13,16,19,26,29,30,31,32,34,35],[0,1,3,6,8,10,12,13,15,16,17,20,21,26,29,30,31,36,37],[0,1,2,4,5,12,13,16,17,19,22,26,29,30,31,32,33,35,36,40],[1,4,7,8,9,13,14,17,18,20,21,22,26,29,30,31,32,34,37,40],[1,2,3,5,6,8,10,12,13,14,15,16,17,18,23,26,29,30,37,39,40],[1,2,3,4,5,6,7,9,11,12,13,16,20,21,23,26,29,30,32,33,34,36,39,40],[1,2,4,9,11,13,17,18,19,22,23,26,29,30,33,34,35,37,39],[0,3,5,7,13,16,17,18,19,20,21,22,23,26,29,30,33,35,36,39],[1,3,5,9,10,12,13,14,15,16,17,19,20,24,26,29,30,31,32,33,35,37,39],[0,1,3,4,6,7,9,10,12,13,15,16,17,18,20,21,24,26,29,30,31,33,36,37,39],[1,11,12,14,16,17,18,22,24,26,29,30,31,32,34,35,37,38,39,40],[2,3,4,6,7,8,10,11,12,14,15,18,19,21,22,24,26,29,30,31,32,33,34,36,37,38,39,40],[0,2,4,5,6,7,9,10,11,15,16,17,18,20,23,24,26,29,30,33,34,38,39,40],[1,2,3,4,8,9,10,12,15,16,17,18,20,21,23,24,26,29,30,32,34,36,38,39,40],[0,1,4,6,10,11,13,14,15,22,23,24,26,29,30,35,36,39],[0,1,2,4,7,12,13,16,17,18,21,22,23,24,26,29,30,35,39],[1,4,7,15,16,18,19,25,26,29,30,31,32,34,36,37,39,40],[3,4,5,8,11,14,15,21,25,26,29,30,31,40],[1,5,6,8,9,10,11,12,13,14,17,22,25,26,29,30,31,32,33,39,40],[0,1,2,5,6,7,8,9,12,13,14,15,19,21,22,25,26,29,30,31,32,34,36,37,40],[0,1,2,3,4,5,8,9,10,11,12,13,14,18,20,23,25,26,29,30,31,34,35,36,39],[0,1,2,3,7,8,9,10,11,13,14,16,18,20,21,23,25,26,29,30,31,32,33,37],[0,6,10,11,14,20,22,23,25,26,29,30,31,33,36,37,39],[1,2,3,4,6,7,8,11,12,15,17,18,20,21,22,23,25,26,29,30,31,33,34,35],[0,1,2,5,7,9,10,13,18,19,20,24,25,26,29,30,33,34,35,36,40],[1,2,4,5,6,8,11,12,13,15,16,17,18,21,24,25,26,29,30,32,33,34,35,39,40],[0,3,7,10,13,14,16,18,19,22,24,25,26,29,30,35,36,37,38,40],[0,1,2,4,5,6,9,10,11,12,13,16,20,21,22,24,25,26,29,30,33,35,37,38,39,40],[1,3,4,5,6,8,9,10,12,13,14,16,17,18,23,24,25,26,29,30,32,33,34,36,37,38,39],[4,9,10,11,15,16,18,20,21,23,24,25,26,29,30,34,35,37,38],[1,3,4,6,7,8,11,12,13,14,15,16,18,19,20,22,23,24,25,26,29,30,32,35,39],[0,1,2,7,8,13,15,18,19,21,22,23,24,25,26,29,30,32,36],[0,2,3,4,6,11,12,13,14,15,16,19,20,27,29,30,31,32,34,37],[0,1,3,4,5,7,9,11,13,14,15,17,18,19,20,21,27,29,30,33,34,35,36,37],[0,2,4,7,8,9,10,11,18,22,27,29,30,31,33,34,35,36,38,39,40],[2,3,4,6,11,12,14,15,18,21,22,27,29,30,33,34,38,39,40],[0,1,2,3,7,9,13,14,15,16,20,23,27,29,30,31,33,34,36,38,39],[0,1,4,5,6,8,11,13,15,17,19,20,21,23,27,29,30,32,33,34,38,39],[0,3,6,7,8,11,12,14,15,16,17,18,22,23,27,29,30,31,32,34,36,37,40],[1,3,4,8,9,10,12,14,16,17,19,21,22,23,27,29,30,32,33,34,37,40],[1,6,7,8,13,14,15,16,18,19,24,27,29,30,31,34,35,37],[0,1,2,3,4,6,8,10,13,18,19,20,21,24,27,29,30,32,33,36],[2,4,6,7,8,9,11,13,15,17,18,19,22,24,27,29,30,31,32,33,34,39,40],[1,2,5,6,9,11,13,15,19,20,21,22,24,27,29,30,32,33,35,36,37,39,40],[5,6,8,10,12,14,16,17,18,23,24,27,29,30,31,32,33,34,35,36],[0,1,2,5,6,7,11,14,15,17,19,20,21,23,24,27,29,30,33,35,37],[3,4,5,6,7,8,9,12,14,15,16,17,18,19,22,23,24,27,29,30,31,34,35,37,39,40],[0,2,4,5,7,9,10,11,12,14,16,20,21,22,23,24,27,29,30,33,35,36,39,40],[0,1,4,5,6,8,13,14,17,18,25,27,29,30,31,32,35,36,39],[0,2,4,5,7,10,11,13,15,17,18,20,21,25,27,29,30,33,35],[0,2,3,4,5,7,9,11,12,13,14,17,18,20,22,25,27,29,30,31,33,38],[2,4,6,9,12,13,14,16,21,22,25,27,29,30,33,36,38,39],[0,1,5,7,9,12,14,16,19,20,23,25,27,29,30,33,34,35,37,38,39],[0,1,2,3,4,5,6,9,10,14,15,16,18,21,23,25,27,29,30,31,32,33,34,36,37,38],[0,1,5,6,7,8,10,15,17,22,23,25,27,29,30,32,34,35,37],[2,4,5,8,12,13,14,17,18,19,20,21,22,23,25,27,29,30,31,32,33,34,36,37,39],[1,4,5,8,9,11,16,20,24,25,27,29,30,32,34,35,36,39],[0,1,2,3,7,12,16,17,18,20,21,24,25,27,29,30,31,33,35,37],[1,5,8,10,11,13,15,16,17,18,19,20,22,24,25,27,29,30,33,34,36],[2,4,5,6,7,8,10,11,13,20,21,22,24,25,27,29,30,31,33,37,39],[1,4,7,9,10,12,15,18,19,23,24,25,27,29,30,31,33,35,37],[0,2,4,5,10,12,14,15,17,18,21,23,24,25,27,29,30,32,33,34,36,39],[1,3,4,6,7,8,9,11,13,14,17,18,19,22,23,24,25,27,29,30,31,32,35,36,37,39],[0,1,3,4,6,7,8,9,10,12,13,15,20,21,22,23,24,25,27,29,30,32,33,34],[2,3,4,7,9,13,14,18,26,27,29,30,32,33,34,35,40],[1,2,4,6,7,9,11,14,19,21,26,27,29,30,40],[3,4,5,6,7,8,13,14,16,17,18,19,22,26,27,29,30,32,34,35,36,37,39],[0,2,3,4,7,10,11,15,18,21,22,26,27,29,30,32,36,37,39],[3,7,9,11,13,16,17,18,20,23,26,27,29,30,33,34,35,37,38,39],[3,4,6,7,8,9,11,12,14,16,17,18,20,21,23,26,27,29,30,32,33,35,37,38,39],[1,5,6,8,10,13,14,15,16,17,18,20,22,23,26,27,29,30,34,38,40],[3,5,10,19,21,22,23,26,27,29,30,33,38,40],[0,2,3,6,8,12,13,16,18,19,24,26,27,29,30,32,33,35,37,40],[2,3,4,5,6,8,9,10,11,14,15,16,17,18,20,21,24,26,27,29,30,40],[0,1,2,4,5,6,7,8,9,10,11,15,19,20,22,24,26,27,29,30,32,35,38,39],[0,1,4,6,7,8,9,10,11,13,14,16,17,19,21,22,24,26,27,29,30,32,37,38,39],[0,3,5,8,9,10,12,14,15,18,19,20,23,24,26,27,29,30,33,35],[1,4,6,7,8,10,11,12,16,17,18,21,23,24,26,27,29,30,32,33,35,37],[0,1,3,9,12,13,17,18,19,20,22,23,24,26,27,29,30,36,37,38,39,40],[0,3,5,6,12,15,16,17,19,20,21,22,23,24,26,27,29,30,33,36,38,39,40],[0,3,4,7,10,11,12,14,19,20,25,26,27,29,30,32,33,34,35,36,38,39,40],[0,1,4,5,6,7,8,9,11,13,15,16,17,21,25,26,27,29,30,35,36,38,40],[0,1,3,4,5,6,7,8,9,12,13,15,17,18,19,20,22,25,26,27,29,30,32,34,35,38,40],[6,7,8,9,13,16,17,21,22,25,26,27,29,30,32,35,38,39,40],[0,2,3,5,6,8,12,16,18,19,20,23,25,26,27,29,30,31,33,35,36,37,39],[2,3,9,10,11,13,14,17,18,21,23,25,26,27,29,30,31,32,33,34,36,37],[3,7,10,12,14,16,17,18,22,23,25,26,27,29,30,31,36,37],[0,1,6,8,11,12,14,16,17,19,21,22,23,25,26,27,29,30,31,33,34,35,36,37,39],[1,2,4,7,10,11,12,13,14,17,20,24,25,26,27,29,30,31,33,34,36,37,38,39,40],[1,2,6,7,8,9,10,11,13,16,17,18,19,21,24,25,26,27,29,30,31,32,34,36,38,40],[2,5,6,7,9,15,17,22,24,25,26,27,29,30,31,34,36,37,40],[0,1,3,9,10,12,13,14,18,21,22,24,25,26,27,29,30,31,34,36,39,40],[0,2,5,7,11,12,13,14,15,18,19,20,23,24,25,26,27,29,30,32,33,36,38],[0,2,4,5,6,8,9,10,14,15,16,18,20,21,23,24,25,26,27,29,30,33,35,36,37,38,39],[0,3,4,5,8,9,11,12,17,18,22,23,24,25,26,27,29,30,32,35,39],[21,22,23,24,25,26,27,29,30,32,33,37],[1,2,4,6,7,8,16,17,19,20,28,29,30,31,32,35,36,39],[0,3,4,5,10,12,13,15,17,21,28,29,30,35,36,37,39],[4,5,6,9,12,13,16,17,18,19,22,28,29,30,31,33,34,36,38],[4,5,7,9,14,16,20,21,22,28,29,30,34,36,37,38],[2,3,7,8,10,12,13,14,15,19,23,28,29,30,32,33,34,35,40],[0,3,4,5,6,8,11,12,16,18,19,20,21,23,28,29,30,31,34,37,40],[2,5,7,9,11,16,17,18,20,22,23,28,29,30,35,36,38,39,40],[0,1,3,4,10,11,13,15,17,18,20,21,22,23,28,29,30,31,36,37,38,39,40],[1,3,4,5,6,8,9,10,11,14,15,16,17,18,20,24,28,29,30,33,36,37,38],[1,2,3,5,6,7,10,11,13,15,19,20,21,24,28,29,30,31,32,33,34,36,37,38],[1,8,14,16,18,19,20,22,24,28,29,30,32,34,35,37,38,39],[0,3,4,5,7,8,9,10,13,14,15,16,18,20,21,22,24,28,29,30,31,32,33,35,37,38,39],[4,6,8,10,12,15,17,18,23,24,28,29,30,31,34,37,40],[0,3,4,6,9,10,12,15,16,17,18,20,21,23,24,28,29,30,32,33,35,37,40],[0,2,3,5,6,7,9,10,13,14,15,16,19,22,23,24,28,29,30,31,32,33,37,39,40],[6,7,9,10,11,16,18,21,22,23,24,28,29,30,32,33,34,35,37,39,40],[2,3,4,6,7,10,11,14,18,20,25,28,29,30,31,34,36,38,40],[0,1,4,9,10,13,17,19,20,21,25,28,29,30,32,34,35,36,37,38,39,40],[2,3,4,5,6,8,9,12,15,16,18,19,22,25,28,29,30,31,32,33,35,36,37,39],[0,1,2,5,9,10,12,13,15,17,18,21,22,25,28,29,30,32,36],[2,7,8,12,15,20,23,25,28,29,30,31,33,34,38],[0,1,3,4,6,8,9,10,12,13,15,16,17,19,21,23,25,28,29,30,32,34,37,38,39],[2,3,7,8,9,12,13,15,17,18,19,22,23,25,28,29,30,31,32,36,37,39,40],[0,3,8,9,10,11,12,13,16,17,18,19,20,21,22,23,25,28,29,30,32,36,40],[1,2,3,5,7,8,12,13,14,15,16,17,19,20,24,25,28,29,30,31,33,36,37,39,40],[0,2,3,4,7,8,9,10,11,13,15,16,17,18,19,20,21,24,25,28,29,30,32,33,34,35,36,37,40],[0,2,3,4,5,7,13,18,19,20,22,24,25,28,29,30,31,32,34,35],[4,6,10,11,13,16,18,19,20,21,22,24,25,28,29,30,32,33,39],[3,6,7,13,14,16,18,20,23,24,25,28,29,30,31,37,38],[0,1,2,3,5,6,8,9,11,12,13,14,15,16,17,21,23,24,25,28,29,30,32,33,34,37,38,39],[1,2,3,4,5,8,11,12,13,19,22,23,24,25,28,29,30,31,32,33,34,38,39,40],[0,1,11,18,21,22,23,24,25,28,29,30,32,33,38,40],[0,1,2,4,6,7,8,10,13,20,26,28,29,30,32,39,40],[2,4,7,9,11,13,15,17,21,26,28,29,30,34,36,37,39,40],[0,2,3,4,6,7,9,13,14,15,17,20,22,26,28,29,30,32,33,34,40],[0,4,9,10,12,14,15,16,18,21,22,26,28,29,30,32,36,37,40],[0,1,3,6,8,9,15,19,20,23,26,28,29,30,31,32,34,40],[0,1,2,4,6,7,8,9,15,18,20,21,23,26,28,29,30,31,33,35,36,37,40],[0,1,2,4,5,10,11,12,13,17,18,20,22,23,26,28,29,30,31,32,33,35,36,39,40],[0,4,6,7,9,11,12,13,14,16,17,20,21,22,23,26,28,29,30,31,32,33,34,37,39,40],[0,2,4,5,8,13,15,16,24,26,28,29,30,31,32,33,34,38,40],[6,7,9,10,11,12,14,15,18,19,21,24,26,28,29,30,31,33,34,36,38,40],[0,1,2,4,5,9,13,14,16,20,22,24,26,28,29,30,31,32,36,39,40],[5,11,12,13,17,18,19,20,21,22,24,26,28,29,30,31,32,33,39,40],[0,2,8,10,11,13,14,18,20,23,24,26,28,29,30,32,33,40],[0,5,6,8,9,10,11,12,14,15,18,19,21,23,24,26,28,29,30,35,36,40],[2,5,6,7,9,13,15,16,17,20,22,23,24,26,28,29,30,32,34,35,38,39,40],[0,2,3,4,8,11,12,13,17,18,19,20,21,22,23,24,26,28,29,30,32,34,36,38,39,40],[1,2,4,5,6,7,8,9,10,11,14,15,18,19,20,25,26,28,29,30,37],[0,5,6,7,8,12,13,14,15,17,18,19,21,25,26,28,29,30,32,34,35,36,39],[0,3,5,8,11,12,14,15,22,25,26,28,29,30,33,34,39,40],[0,3,6,7,8,10,12,14,18,19,20,21,22,25,26,28,29,30,35,36,37,40],[0,2,5,6,8,10,12,13,15,18,20,23,25,26,28,29,30,37],[0,2,3,4,5,7,10,14,16,17,18,20,21,23,25,26,28,29,30,32,33,34,36,39],[1,2,4,5,6,8,11,14,15,20,22,23,25,26,28,29,30,33,34,35,36,39,40],[0,2,5,6,7,8,11,14,16,17,19,20,21,22,23,25,26,28,29,30,33,35,37,40],[1,2,4,5,8,10,13,15,18,24,25,26,28,29,30,32,33,35,37,38,39],[1,2,3,4,7,8,9,12,15,17,20,21,24,25,26,28,29,30,33,36,37,38],[1,2,3,5,7,13,15,18,19,22,24,25,26,28,29,30,32,34,35,36,40],[1,2,4,5,6,7,8,10,11,12,13,17,18,20,21,22,24,25,26,28,29,30,32,33,34,39,40],[0,2,3,4,13,14,15,19,23,24,25,26,28,29,30,32,33,35,37],[2,4,6,7,9,14,16,17,19,20,21,23,24,25,26,28,29,30,35,36,37,39],[0,1,3,5,6,7,10,11,12,14,16,17,22,23,24,25,26,28,29,30,32,34,38,39,40],[21,22,23,24,25,26,28,29,30,32,34,36,38,40],[0,3,5,7,14,16,17,19,27,28,29,30,32,34,35,38,39,40],[1,2,7,8,9,11,14,18,21,27,28,29,30,31,33,34,35,36,38,39,40],[0,2,3,4,7,8,9,13,14,17,18,20,22,27,28,29,30,33,34,37,39,40],[4,8,9,12,14,17,18,21,22,27,28,29,30,31,33,34,36,37,39,40],[3,6,9,11,13,16,18,23,27,28,29,30,32,33,34,36],[0,1,2,3,5,6,7,11,13,17,18,19,21,23,27,28,29,30,31,33,34,35],[1,3,6,8,12,16,18,19,20,22,23,27,28,29,30,34,37,38],[1,5,9,10,14,17,18,19,20,21,22,23,27,28,29,30,31,33,34,35,36,37,38],[0,1,2,3,4,5,11,18,19,20,24,27,28,29,30,31,34,37,39,40],[4,8,13,15,17,19,20,21,24,27,28,29,30,32,33,36,39,40],[1,6,7,8,15,17,18,22,24,27,28,29,30,31,32,33,34,35,36,39,40],[1,2,5,8,9,12,18,20,21,22,24,27,28,29,30,32,33,35,37,39,40],[1,4,9,14,16,17,19,20,23,24,27,28,29,30,31,33,34,35,36,37,39],[1,2,4,6,11,13,16,18,20,21,23,24,27,28,29,30,32,33,39],[0,1,2,3,5,8,11,12,13,19,22,23,24,27,28,29,30,31,32,34,35,36,39],[1,2,4,5,6,7,12,13,14,17,18,19,20,21,22,23,24,27,28,29,30,32,33,37,39],[0,2,4,5,6,7,12,15,18,19,20,25,27,28,29,30,35,37,38,40],[0,2,4,6,8,10,11,13,14,16,19,20,21,25,27,28,29,30,31,32,33,36,37,38,39,40],[0,2,4,5,7,10,14,15,16,17,18,22,25,27,28,29,30,32,33,37],[0,4,5,11,12,15,16,19,21,22,25,27,28,29,30,31,32,33,35,36,37,39],[0,2,7,11,17,20,23,25,27,28,29,30,31,33,34,36,37],[2,3,5,6,8,10,13,15,16,19,21,23,25,27,28,29,30,32,33,34,37,39],[0,1,2,5,8,11,14,15,16,17,19,22,23,25,27,28,29,30,31,32,34,37,38,40],[1,2,3,6,8,9,11,14,15,17,21,22,23,25,27,28,29,30,32,33,34,36,37,38,39,40],[0,1,2,3,4,5,8,9,11,15,16,18,19,20,24,25,27,28,29,30,34,35,40],[0,5,7,12,13,15,16,20,21,24,25,27,28,29,30,31,32,33,36,37,39,40],[3,5,6,9,10,14,16,18,22,24,25,27,28,29,30,32,33,34,36],[21,22,24,25,27,28,29,30,31,32,33,35,37,39],[1,2,4,5,6,7,8,13,17,19,23,24,25,27,28,29,30,31,33,36,39],[0,1,2,3,4,5,6,7,9,11,14,17,20,21,23,24,25,27,28,29,30,32,33,34,37],[2,9,11,12,13,17,19,20,22,23,24,25,27,28,29,30,31,32,36,39,40],[21,22,23,24,25,27,28,29,30,32,33,34,37,40],[2,3,4,6,7,8,9,10,11,19,20,26,27,28,29,30,32,36,37,39,40],[0,2,3,5,6,7,8,9,10,11,12,13,14,15,17,18,21,26,27,28,29,30,33,34,36,37,39,40],[0,1,4,5,7,8,11,12,18,20,22,26,27,28,29,30,32,33,36,39,40],[2,4,5,6,8,12,13,14,19,21,22,26,27,28,29,30,32,33,34,36,39,40],[1,2,6,15,16,18,19,20,23,26,27,28,29,30,32,35,36,37,38,40],[9,11,14,16,17,18,19,20,21,23,26,27,28,29,30,34,36,37,38,40],[4,5,6,7,8,12,13,15,16,20,22,23,26,27,28,29,30,32,33,38,40],[21,22,23,26,27,28,29,30,32,34,35,38,40],[0,1,4,5,6,7,8,12,14,16,19,20,24,26,27,28,29,30,31,32,34,36,37,38,39,40],[0,1,4,8,9,11,13,15,16,17,18,20,21,24,26,27,28,29,30,31,33,34,36,38,39,40],[2,3,4,7,8,10,13,15,18,22,24,26,27,28,29,30,31,32,33,34,39,40],[21,22,24,26,27,28,29,30,31,32,33,34,37,39,40],[2,3,6,7,8,12,14,15,16,17,18,19,20,23,24,26,27,28,29,30,31,32,34,35,36,37,38,39,40],[21,23,24,26,27,28,29,30,31,34,36,38,39,40],[0,1,2,3,5,7,13,14,16,17,22,23,24,26,27,28,29,30,31,32,33,34,36,39,40],[21,22,23,24,26,27,28,29,30,31,32,34,35,36,37,39,40],[0,4,6,9,10,12,17,19,25,26,27,28,29,30,35,36,37,38,40],[1,2,3,5,6,8,9,11,21,25,26,27,28,29,30,32,33,34,36,37,38,39,40],[1,2,3,4,5,8,9,10,12,13,22,25,26,27,28,29,30,33,35,36,37,38],[21,22,25,26,27,28,29,30,33,34,36,37,38,39],[1,3,5,6,7,8,9,12,13,16,18,23,25,26,27,28,29,30,31,34,36,37,40],[21,23,25,26,27,28,29,30,31,32,36,37,39,40],[22,23,25,26,27,28,29,30,31,33,34,35,37],[21,22,23,25,26,27,28,29,30,31,35,37,39],[4,6,7,8,9,10,11,12,13,16,19,24,25,26,27,28,29,30,32,36,37,40],[21,24,25,26,27,28,29,30,33,35,36,39,40],[22,24,25,26,27,28,29,30,32,33,37,38],[21,22,24,25,26,27,28,29,30,32,33,35,38,39],[23,24,25,26,27,28,29,30,31,32,34,35,36,37,39,40],[21,23,24,25,26,27,28,29,30,31,34,35,36,40],[22,23,24,25,26,27,28,29,30,31,32,33,34,36,37,38,39],[21,22,23,24,25,26,27,28,29,30,31,32,34,36,38]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[95,197,281,549,921],"A_d":8863695,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[2,1],[4,3],[6,1],[7,1],[8,3],[9,1],[10,2],[13,3],[14,3],[15,1],[16,2],[17,1],[18,1],[19,3],[20,2]],"CZ":[[0,1],[0,2],[0,7],[0,9],[0,12],[0,13],[0,14],[0,15],[0,16],[0,19],[0,20],[0,21],[0,23],[0,24],[0,25],[0,27],[0,28],[0,32],[0,35],[0,36],[0,38],[1,2],[1,4],[1,8],[1,10],[1,14],[1,15],[1,18],[1,19],[1,21],[1,25],[1,26],[1,28],[1,29],[1,31],[1,32],[1,35],[1,39],[2,4],[2,7],[2,10],[2,12],[2,13],[2,14],[2,15],[2,17],[2,18],[2,20],[2,21],[2,22],[2,23],[2,24],[2,25],[2,26],[2,27],[2,31],[2,32],[2,33],[2,34],[2,35],[2,37],[2,38],[3,4],[3,10],[3,11],[3,13],[3,14],[3,15],[3,21],[3,23],[3,25],[3,26],[3,27],[3,30],[3,35],[3,37],[3,39],[3,40],[4,6],[4,8],[4,13],[4,15],[4,16],[4,23],[4,25],[4,31],[4,32],[4,34],[4,35],[5,13],[5,15],[5,20],[5,22],[5,23],[5,25],[5,27],[5,30],[5,32],[5,33],[5,36],[5,37],[5,38],[5,39],[6,8],[6,9],[6,10],[6,11],[6,12],[6,15],[6,18],[6,20],[6,22],[6,29],[6,30],[6,31],[6,32],[6,33],[6,34],[6,39],[7,8],[7,9],[7,11],[7,12],[7,13],[7,14],[7,15],[7,16],[7,21],[7,22],[7,23],[7,24],[7,25],[7,28],[7,29],[7,30],[7,31],[7,32],[7,35],[7,37],[7,38],[7,40],[8,12],[8,22],[8,26],[8,27],[8,31],[8,32],[8,37],[8,38],[9,12],[9,15],[9,18],[9,19],[9,20],[9,21],[9,23],[9,25],[9,26],[9,27],[9,28],[9,31],[9,32],[9,33],[9,34],[9,35],[9,36],[9,38],[10,11],[10,17],[10,19],[10,20],[10,21],[10,23],[10,24],[10,26],[10,30],[10,31],[10,32],[10,33],[10,35],[10,37],[11,13],[11,14],[11,16],[11,17],[11,19],[11,20],[11,23],[11,24],[11,26],[11,27],[11,32],[11,33],[11,35],[11,38],[11,40],[12,14],[12,18],[12,19],[12,21],[12,23],[12,24],[12,27],[12,28],[12,29],[12,32],[12,34],[12,35],[12,38],[12,39],[12,40],[13,15],[13,16],[13,20],[13,25],[13,26],[13,27],[13,28],[13,29],[13,30],[13,32],[13,33],[13,35],[13,36],[13,38],[13,39],[13,40],[14,19],[14,20],[14,21],[14,22],[14,23],[14,27],[14,28],[14,29],[14,30],[14,31],[14,34],[14,35],[14,38],[14,39],[15,20],[15,22],[15,24],[15,25],[15,27],[15,34],[15,35],[15,38],[15,40],[16,17],[16,18],[16,20],[16,21],[16,22],[16,23],[16,24],[16,26],[16,27],[16,29],[16,33],[16,34],[16,35],[16,36],[16,39],[16,40],[17,18],[17,22],[17,23],[17,24],[17,26],[17,31],[17,34],[17,38],[17,39],[18,21],[18,22],[18,25],[18,26],[18,29],[18,32],[18,33],[18,34],[18,35],[18,37],[18,38],[19,21],[19,24],[19,25],[19,26],[19,29],[19,32],[19,36],[19,38],[19,39],[19,40],[20,21],[20,22],[20,23],[20,24],[20,25],[20,26],[20,27],[20,33],[20,39]]},"rotation_powers":null},"metrics":{"gamma":2.4144903622601332,"gamma_t":null,"gamma_rho":2.4144903622601332,"gamma_claim":2.4144903622601332,"gamma_t_claim":null,"gamma_rho_claim":2.4144903622601332,"v_ex":21,"rate":0.020527859237536656,"t_count":null,"poly_degree":null,"effective_width":21},"provenance":{"regimes":["AI search"],"discovery":"AI search","strongest_claim":"found by an AI search campaign; a verified witness, not a maximum","sources":[{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3.T4.T5.T6.T7.T8.T9.T10.T11.T12.T13.T14.T15.T16.T17.T18.T19.T20","N":41,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:403"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3.T4.T5.T6.T7.T8.T9.T10.T11.T12.T13.T14.T15.T16.T17.T18.T19.T20","N":41,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:404"}]},"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"}]}