{"id":"1023.26.5.a","row":1345,"stored":{"file":"master_catalog.json","row":1345,"construction":null,"columns_sha256":null},"parameters":{"n":1023,"k":26,"d":5,"N":46,"r":20,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25","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","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]],"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]],"sk_fingerprint":"f3bfadac5cccd0be","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,2,4,5,8,9,11,16,19,20,22,23,24,26,36],[1,3,5,8,9,13,14,15,16,17,19,20,21,22,25,27,39],[1,3,6,7,10,12,13,14,16,17,20,21,24,25,26,27,36,37,38,39],[1,4,7,8,13,14,15,17,18,19,20,23,24,28,42],[1,2,5,6,7,8,9,11,15,17,18,19,20,21,22,23,24,26,28,36,38,40,42],[5,6,7,11,12,14,18,20,22,23,24,25,27,28,39,40,41,42],[0,6,9,10,11,13,15,16,18,21,24,25,26,27,28,36,37,39,41,42],[2,3,5,14,15,17,18,20,25,29,45],[0,1,2,3,5,6,7,11,12,14,18,19,20,22,25,26,29,36,39,42,45],[0,1,3,6,12,14,17,19,20,22,25,27,29,39,41,43,45],[0,2,3,4,6,10,12,14,16,23,25,26,27,29,36,37,38,41,42,43,45],[2,6,9,10,11,12,13,15,18,22,25,28,29,42,43,44,45],[1,2,6,7,8,9,10,14,16,17,18,20,21,23,24,25,26,28,29,36,38,39,40,43,44,45],[0,1,3,4,5,6,10,12,13,14,16,19,20,21,25,27,28,29,39,40,42,44,45],[2,3,5,8,12,16,17,19,20,22,24,25,26,27,28,29,36,37,44,45],[0,1,5,8,9,10,11,14,15,16,17,20,24,25,30,38,41],[0,3,4,5,6,7,9,12,13,14,24,26,30,36,38,40,41,44],[0,3,4,6,11,12,14,15,16,18,21,23,24,27,30,38,39,41,42,45],[1,2,4,6,8,11,12,13,14,15,16,17,18,21,24,25,26,27,30,36,37,39,40,41,42,44,45],[0,6,10,12,16,17,18,20,22,23,24,28,30,36,38,39,41,42,44],[1,3,4,6,7,11,14,15,16,18,19,20,21,22,25,26,28,30,39,41,42],[0,1,5,6,8,11,12,14,20,22,24,25,27,28,30,36,38,40,44,45],[0,2,3,5,8,11,12,16,17,19,21,22,26,27,28,30,37,38,40,45],[1,2,3,4,5,8,10,13,14,15,16,17,21,22,25,29,30,36,37,38,39,40,41,45],[1,4,8,9,11,14,15,16,17,21,22,23,24,26,29,30,37,38,41,42,44,45],[0,3,8,15,17,21,22,23,25,27,29,30,36,37,38,40,42,43],[4,5,6,7,8,9,12,13,16,17,20,21,22,23,24,26,27,29,30,39,43,44],[1,2,5,7,8,13,15,16,17,19,21,22,24,28,29,30,37,38,40,41,42,43,45],[0,1,3,6,7,9,10,11,13,14,15,17,20,22,24,25,26,28,29,30,36,37,39,40,41,43,44,45],[0,3,6,7,8,9,10,11,12,15,16,17,19,20,22,23,24,27,28,29,30,37,38,39,41],[0,4,5,6,10,11,14,16,17,20,21,22,24,25,26,27,28,29,30,36,38,41,42,44],[1,3,8,9,10,15,16,19,21,22,24,31,41,44],[3,4,5,6,9,11,12,14,16,20,26,31,39,44],[0,1,3,4,8,9,11,13,17,21,22,23,25,27,31,37,39,40,41,43,44],[2,3,4,5,7,9,11,13,14,16,17,19,24,25,26,27,31,38,40,43,44],[1,4,5,6,7,8,9,10,11,13,15,18,19,21,28,31,38,42,44,45],[0,6,7,8,9,12,16,18,19,21,22,23,26,28,31,39,40,41,42,44,45],[0,1,3,4,5,7,8,11,12,14,17,18,20,23,24,25,27,28,31,37,38,39,41,42,43,44,45],[0,2,3,4,6,8,11,12,13,14,17,18,22,23,24,25,26,27,28,31,38,40,42,43,44,45],[2,6,8,11,13,18,22,23,24,25,29,31,37,39,40,41,42,44,45],[6,7,8,9,10,13,14,16,17,18,19,21,24,25,26,29,31,37,39,40,44,45],[3,4,9,10,12,13,14,15,19,20,21,22,25,27,29,31,42,44,45],[0,3,6,10,13,17,25,26,27,29,31,37,38,41,44,45],[1,2,6,9,10,11,12,15,16,18,19,22,24,25,28,29,31,37,38,39,40,43],[0,1,7,8,12,13,15,16,17,18,19,20,25,26,28,29,31,37,39,41,42,43],[1,6,8,9,11,12,22,23,25,27,28,29,31,38,40,43],[1,4,6,11,13,15,16,17,24,25,26,27,28,29,31,37,38,41,42,43],[1,3,6,7,9,12,13,14,15,16,17,18,19,21,22,23,24,30,31,38,39,40,42,43,44],[0,1,2,4,6,8,11,12,15,16,18,19,20,22,24,25,26,30,31,38,41,42,43],[0,1,3,7,9,11,13,15,16,19,21,23,25,27,30,31,37,38,44,45],[0,1,6,7,8,10,11,12,14,17,19,23,26,27,30,31,39,40,41,45],[1,6,7,13,14,15,20,21,22,23,24,25,28,30,31,36,40,41,43,45],[1,2,3,4,9,11,13,14,15,16,17,19,20,21,22,23,26,28,30,31,36,38,39,40,43,44,45],[0,1,3,4,6,7,9,13,14,15,16,17,18,23,27,28,30,31,36,37,39,40,42],[1,4,6,7,10,12,13,14,16,18,19,20,24,25,26,27,28,30,31,36,40,41,42,44],[0,2,4,5,7,9,10,12,13,15,18,21,29,30,31,36,38,39,40,43,44,45],[1,2,3,4,6,7,9,10,11,14,16,18,24,25,26,29,30,31,36,38,39,41,42,43,45],[0,3,4,5,7,8,10,11,12,15,16,18,20,22,24,27,29,30,31,36,37,38,41,42,43,44],[0,1,2,8,11,12,13,14,15,16,18,21,22,23,25,26,27,29,30,31,36,40,43],[0,1,2,6,8,9,11,12,13,16,17,18,20,21,22,23,24,25,28,29,30,31,40,41,42,44],[0,2,3,5,6,9,13,15,16,17,18,19,21,22,24,26,28,29,30,31,38,40],[0,1,4,9,11,14,16,17,18,20,21,23,25,27,28,29,30,31,37,39,40,41,44,45],[2,3,5,6,7,8,9,10,11,14,17,18,19,20,21,23,24,25,26,27,28,29,30,31,39,40,42,45],[0,1,2,4,9,11,12,14,17,18,20,23,25,32,37,40,44],[3,4,10,11,13,14,16,19,20,22,24,25,26,32,36,37,38,40,41,42,44],[1,2,3,4,7,8,9,10,17,19,21,22,27,32,37,40,42],[2,6,8,10,11,13,15,18,20,21,24,26,27,32,36,40,41],[0,2,4,5,8,10,15,22,24,25,28,32,36,37,39,42,43,44],[0,1,3,4,5,6,9,12,14,15,17,18,20,21,24,25,26,28,32,37,39,40,41,43,44],[2,5,6,7,9,15,16,18,19,23,24,27,28,32,36,37,39,40,41,43],[0,1,2,3,4,5,6,8,11,14,17,19,21,22,24,26,27,28,32,38,39,42,43],[0,2,4,7,8,10,11,14,16,17,20,21,22,23,25,29,32,37,38,40,45],[2,3,5,6,11,13,14,15,16,17,18,19,21,23,25,26,29,32,36,37,39,40,41,45],[0,4,6,8,9,13,14,19,20,21,25,27,29,32,37,38,40,41,42,43,44,45],[0,2,3,4,5,6,9,11,12,14,16,18,20,21,22,23,25,26,27,29,32,36,38,39,40,42,43,44,45],[0,2,3,6,8,10,11,16,19,21,22,23,25,28,29,32,36,37,38,39,42,44,45],[0,2,4,5,6,7,8,11,14,15,18,19,24,25,26,28,29,32,37,38,40,41,42,44,45],[0,4,6,7,8,11,12,13,14,16,17,20,25,27,28,29,32,36,37,38,39,40,43,45],[2,3,4,5,7,8,13,16,17,18,21,22,24,25,26,27,28,29,32,41,43,45],[0,4,5,6,11,14,17,18,19,22,24,25,30,32,37,38,41,42,43,44,45],[0,4,7,11,14,15,16,17,19,22,24,26,30,32,36,37,40,43,45],[3,5,7,8,13,14,15,16,17,18,19,20,21,22,24,27,30,32,37,38,41,42,43],[0,2,3,4,7,8,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,30,32,36,38,40,43,44],[0,1,5,7,8,10,11,13,15,17,22,23,24,28,30,32,37,38,40,41,45],[1,10,11,14,17,18,19,20,21,22,25,26,28,30,32,36,37,38,40,42,44,45],[1,5,9,10,11,12,14,17,22,23,24,25,27,28,30,32,37,38,44],[1,2,4,6,8,9,13,16,17,18,19,21,22,23,26,27,28,30,32,36,41,42],[1,6,7,8,10,12,13,15,16,18,19,22,29,30,32,36,39,40,41,42,43],[2,4,6,7,9,10,13,15,16,17,19,20,22,23,24,25,26,29,30,32,38,42,43,44],[1,2,4,6,8,9,10,11,13,14,16,17,19,22,27,29,30,32,36,39,40,42,44,45],[0,2,4,7,13,14,15,18,19,22,24,25,26,27,29,30,32,37,41,42,45],[1,3,5,6,7,8,9,10,11,14,15,16,18,19,24,25,28,29,30,32,36,39,41,43],[0,2,3,4,5,7,8,10,11,12,13,15,17,21,24,26,28,29,30,32,43,44],[1,2,5,8,9,10,11,14,17,19,20,21,24,25,27,28,29,30,32,36,39,40,41,44,45],[2,5,7,8,13,15,18,23,24,26,27,28,29,30,32,37,38,40,45],[0,1,2,6,10,11,15,18,21,23,24,31,32,36,37,39,40,41,42,43,45],[0,1,2,3,10,11,13,14,17,19,22,23,26,31,32,36,37,38,40,41,43,45],[0,2,4,5,6,7,9,10,11,12,15,19,21,23,25,27,31,32,36,39,41,44,45],[3,5,6,9,13,14,15,16,17,18,20,22,24,25,26,27,31,32,36,37,41,42,44,45],[0,1,2,3,9,11,12,15,16,19,21,23,28,31,32,37,38],[1,2,8,9,11,12,17,18,19,20,21,22,26,28,31,32,37,38,39,40,42],[0,2,5,6,7,9,12,14,15,18,20,23,24,25,27,28,31,32,38,41,42,43,44],[0,3,4,5,8,9,10,11,14,15,17,20,22,23,24,25,26,27,28,31,32,37,39,40,41,43,44],[0,1,2,5,7,8,10,12,13,14,15,17,19,20,21,22,24,29,31,32,36,38,41,43,44],[0,3,4,9,10,15,16,17,18,23,24,26,29,31,32,36,41,43,44],[3,4,6,10,12,15,16,22,27,29,31,32,36,37,38,40,42,43],[0,1,4,5,8,9,11,12,13,14,16,18,19,21,26,27,29,31,32,36,38,40,42,43],[0,2,4,10,11,12,13,14,16,17,19,20,21,23,24,28,29,31,32,39,40,42,43,45],[1,3,5,6,7,9,10,11,13,14,16,17,18,19,20,21,22,23,26,28,29,31,32,39,42,43,45],[1,4,5,7,8,9,10,14,16,20,21,23,27,28,29,31,32,37,39,40,43,44,45],[3,4,7,8,11,14,15,18,21,22,24,26,27,28,29,31,32,38,39,43,44,45],[1,6,7,10,13,16,19,21,22,23,24,25,30,31,32,36,37,38,40,42,43],[0,2,5,6,9,12,13,14,16,18,19,22,24,26,30,31,32,36,37,39,43,44],[5,9,14,15,19,21,27,30,31,32,36,38,42,44,45],[1,4,6,11,16,18,19,20,25,26,27,30,31,32,36,37,38,39,40,45],[1,3,4,5,6,11,17,18,19,20,21,23,24,28,30,31,32,36,37,41,44,45],[2,3,4,7,8,9,10,11,12,13,16,17,21,23,25,26,28,30,31,32,36,37,39,41,42,45],[6,7,10,12,13,15,17,18,19,22,25,27,28,30,31,32,36,43],[0,1,4,5,6,7,8,9,10,11,12,17,22,23,24,26,27,28,30,31,32,36,37,38,39,42,43,44],[0,1,4,8,9,10,12,13,15,16,20,22,29,30,31,32,37,40,43,44,45],[1,6,9,12,13,14,17,18,21,22,24,25,26,29,30,31,32,37,38,43,45],[2,3,4,5,7,9,13,16,17,18,21,23,24,27,29,30,31,32,41,43],[3,4,5,8,9,11,12,13,14,16,25,26,27,29,30,31,32,37,40,41,43,44],[0,4,6,10,17,19,22,23,24,25,28,29,30,31,32,37,38,41,42,43,44],[0,6,13,15,18,22,24,25,26,28,29,30,31,32,37,38,41,42,43],[1,2,5,7,8,9,11,14,15,16,18,19,25,27,28,29,30,31,32,38,41,42,43,45],[0,1,5,6,8,9,12,13,14,15,17,20,25,26,27,28,29,30,31,32,37,41,42,43,44,45],[1,5,9,11,13,15,17,18,24,25,33,37,43],[0,2,3,5,7,9,11,12,13,16,26,33,36,37,40,43],[2,3,6,7,8,9,10,12,14,16,18,20,22,23,24,25,27,33,37,39,41,43,44,45],[1,2,4,7,8,9,11,12,14,16,17,22,25,26,27,33,36,38,39,40,41,43,44,45],[2,4,5,6,9,14,16,18,19,20,21,22,24,25,28,33,40,43,45],[1,3,4,5,7,8,9,12,13,15,16,17,22,23,24,25,26,28,33,36,38,40,43,45],[1,6,7,8,10,13,14,15,16,17,18,19,20,23,24,27,28,33,39,43,44],[0,3,4,6,7,11,15,20,21,23,24,26,27,28,33,36,37,39,43,44],[1,4,5,6,7,10,11,12,14,16,18,20,25,29,33,36,37,42,45],[0,1,3,7,8,9,10,11,12,14,16,23,25,26,29,33,37,39,40,45],[0,4,6,9,12,14,15,16,20,21,22,23,25,27,29,33,36,37,39,42,43,44],[0,2,3,4,5,6,7,8,10,11,14,18,20,21,22,23,25,26,27,29,33,38,40,43,44],[1,2,3,4,6,8,9,11,13,17,21,23,24,25,28,29,33,36,40,42,43,44],[1,2,5,6,8,11,14,16,17,18,19,23,26,28,29,33,38,39,40,43,44],[0,2,5,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,24,25,27,28,29,33,36,39,41,42,45],[3,6,8,16,17,19,22,23,25,26,27,28,29,33,37,41,45],[0,1,2,4,5,6,8,11,12,14,17,20,22,23,24,30,33,38,40,43],[0,1,2,4,8,9,10,11,12,13,14,16,17,18,19,20,24,25,26,30,33,36,38,40,43,44],[0,3,6,7,12,14,18,19,22,23,24,25,27,30,33,38,39,40,41,42,43,44],[2,3,4,5,6,9,11,13,14,15,20,23,24,25,26,27,30,33,36,37,39,40,41,42,43],[0,4,6,7,8,9,11,15,16,17,20,21,22,23,28,30,33,36,37,38,39,43,44,45],[4,5,6,7,10,11,14,15,16,17,18,23,24,26,28,30,33,37,39,40,43,45],[0,1,2,4,5,11,12,14,15,18,19,20,22,23,25,27,28,30,33,36,37,38,40,42,43,45],[0,1,6,7,8,9,16,19,20,21,24,26,27,28,30,33,38,42,43,44,45],[1,2,4,7,8,10,14,16,17,18,21,23,24,25,29,30,33,37,38,39,42,45],[12,13,14,15,16,19,20,21,22,23,25,26,29,30,33,36,37,38,44,45],[0,2,5,6,8,9,10,11,12,13,17,18,19,23,24,25,27,29,30,33,37,38,43,44,45],[1,2,5,9,10,12,16,22,24,25,26,27,29,30,33,36,39,42,43,45],[1,3,6,7,11,17,19,22,24,25,28,29,30,33,36,38,40,42,43],[0,2,3,4,10,11,12,14,15,16,18,19,21,23,24,26,28,29,30,33,39,43,44],[0,5,6,11,13,17,20,22,24,27,28,29,30,33,36,38,39,41,44],[0,1,5,6,13,14,18,21,24,26,27,28,29,30,33,37,38,40,41,42],[3,6,8,14,17,21,31,33,36,37,38,39,44,45],[7,8,9,10,18,23,25,26,31,33,36,37,38,40,41,44,45],[0,2,3,4,7,8,9,12,13,14,15,16,27,31,33,36,38,40,41,43],[7,8,11,13,17,18,20,21,24,25,26,27,31,33,36,37,39,43],[2,4,5,6,13,14,17,23,24,28,31,33,36,39,40,41,44,45],[0,2,3,4,5,6,7,8,9,10,14,16,18,19,20,23,24,25,26,28,31,33,36,38,40,44,45],[0,3,4,5,6,7,11,15,20,23,27,28,31,33,36,37,40,41,43],[0,2,5,7,8,9,12,13,17,18,19,20,24,25,26,27,28,31,33,36,39,40,43],[1,3,4,5,6,7,8,11,12,14,15,17,19,23,24,25,29,31,33,38,40,43,44],[2,6,7,10,11,16,17,18,19,20,21,23,24,26,29,31,33,38,41,42,43,44],[1,5,6,11,12,17,18,19,20,23,25,27,29,31,33,37,38,39,43,45],[0,3,7,8,12,14,17,19,20,21,25,26,27,29,31,33,39,40,41,42,43,45],[2,3,4,5,8,9,10,13,14,17,18,21,22,23,24,25,28,29,31,33,37,41],[0,1,6,8,9,12,14,15,17,19,21,22,24,26,28,29,31,33,37,38,42],[2,3,4,5,6,7,10,11,12,13,14,15,16,17,22,23,27,28,29,31,33,39,44,45],[1,2,4,6,10,12,14,15,17,18,19,20,22,23,24,25,26,27,28,29,31,33,37,39,41,42,44,45],[1,2,3,4,5,6,7,11,16,17,21,22,25,30,31,33,36,42,43,44,45],[0,3,4,6,7,11,12,13,14,15,16,17,18,19,24,26,30,31,33,36,39,41,42,43,45],[0,1,3,4,5,6,9,10,11,14,16,18,19,23,24,25,27,30,31,33,36,37,39,40,41,45],[0,3,7,9,13,20,21,22,24,26,27,30,31,33,36,38,40,44,45],[1,4,5,8,9,12,16,19,20,23,28,30,31,33,37,38,39,40,41,42,43,45],[2,4,6,9,15,18,19,22,24,25,26,28,30,31,33,37,42,43,44,45],[0,1,2,3,5,6,7,8,9,10,11,17,18,22,25,27,28,30,31,33,38,40,41,44,45],[2,3,4,6,9,17,24,26,27,28,30,31,33,37,38,39,45],[0,2,3,4,5,6,9,11,12,13,14,16,18,19,21,23,25,29,30,31,33,36,42,44],[2,3,5,7,8,11,12,17,20,22,24,26,29,30,31,33,36,41],[0,2,4,5,7,8,9,10,11,14,18,20,21,22,24,27,29,30,31,33,36,37,39,40],[0,4,5,7,12,13,15,17,19,20,25,26,27,29,30,31,33,36,38,39,40,41,42,44],[0,1,3,6,9,10,11,12,13,14,15,16,17,19,20,23,24,28,29,30,31,33,37,38,39,40,41,42,43,44],[0,1,3,4,6,7,10,11,12,13,14,15,16,18,19,20,22,23,24,25,26,28,29,30,31,33,37,39,43],[0,1,3,4,6,7,8,12,15,16,17,20,21,22,24,27,28,29,30,31,33,38,40,43],[1,2,3,4,7,8,9,10,11,18,21,23,25,26,27,28,29,30,31,33,37,38,41,42,43,44],[2,3,8,10,11,12,13,15,17,18,20,24,32,33,36,38,40,41,42,43,44,45],[0,3,4,5,7,12,16,17,18,25,26,32,33,43,44,45],[0,6,9,10,11,12,13,14,15,17,22,27,32,33,36,38,40,43,44],[0,5,8,9,10,11,14,15,17,22,23,25,26,27,32,33,37,38,41,42,43,44],[1,3,5,6,7,8,9,11,13,14,16,18,21,24,25,28,32,33,37,38,39,40,41,42,44],[1,2,3,4,8,9,10,13,15,16,18,19,23,25,26,28,32,33,36,37,38,39,40,44],[0,1,2,3,4,5,6,7,9,12,13,14,22,25,27,28,32,33,37,38,39,41,44,45],[1,2,3,4,6,7,9,13,16,19,20,21,22,25,26,27,28,32,33,36,39,42,44,45],[1,4,5,6,10,11,12,15,17,18,20,21,22,29,32,33,40,41],[0,4,5,9,13,15,18,20,21,22,23,24,25,26,29,32,33,36,38,39],[1,4,5,6,10,11,13,15,16,18,20,27,29,32,33,40,41,42,43,45],[2,5,6,7,9,10,11,17,18,22,23,24,26,27,29,32,33,36,37,39,42,43,45],[1,2,3,5,6,8,10,12,14,15,16,19,23,28,29,32,33,36,37,39,40,41,44,45],[2,3,5,6,9,11,15,17,20,21,23,24,25,26,28,29,32,33,37,40,44,45],[1,2,4,5,8,9,10,11,12,13,15,16,17,19,20,24,25,27,28,29,32,33,36,37,39,42,43,44],[0,5,6,7,10,11,12,13,14,16,20,21,22,24,26,27,28,29,32,33,38,41,42,43,44],[2,3,4,8,9,12,15,16,19,24,25,30,32,33,36,37,40,41,44],[1,2,6,11,15,17,20,24,26,30,32,33,37,38,40,42],[0,10,13,20,23,24,27,30,32,33,36,37,40,44],[1,2,3,7,8,9,13,15,17,19,20,22,23,24,26,27,30,32,33,40,41,42],[1,3,8,9,10,11,12,13,14,21,22,25,28,30,32,33,36,40,41,43,45],[0,4,8,10,17,24,26,28,30,32,33,42,43,44,45],[0,1,2,3,6,9,12,15,19,22,23,27,28,30,32,33,36,41,43,45],[0,7,10,12,13,14,16,17,19,20,21,24,25,26,27,28,30,32,33,37,38,40,42,43,44,45],[0,1,4,6,11,12,14,16,17,18,19,24,29,30,32,33,36,38,39,41,42,43,45],[0,1,2,3,4,5,6,7,12,14,15,16,17,18,23,24,25,26,29,30,32,33,42,43,44,45],[0,1,10,11,12,15,16,21,23,24,27,29,30,32,33,36,38,39,41,42,45],[1,3,4,5,6,11,15,19,20,21,23,25,26,27,29,30,32,33,37,38,42,44,45],[0,1,2,3,4,5,7,8,9,11,13,17,19,21,22,28,29,30,32,33,36,37,38,39,41,42,43],[1,4,6,9,14,15,16,17,19,20,23,26,28,29,30,32,33,37,38,40,42,43,44],[0,1,2,4,5,7,8,10,12,13,15,16,18,20,21,24,27,28,29,30,32,33,36,37,38,39,40,42],[0,1,2,3,7,14,15,16,18,20,22,24,25,26,27,28,29,30,32,33,41,42,44],[2,3,4,5,8,9,10,16,19,21,22,24,31,32,33,36,40,41,43,45],[1,2,3,6,7,10,11,12,13,14,16,19,20,22,23,24,25,26,31,32,33,36,38,39,41,42,43,45],[1,3,6,8,9,11,16,18,19,25,27,31,32,33,36,37,42],[0,2,3,5,6,10,11,13,14,15,18,19,21,22,23,24,26,27,31,32,33,36,39,40],[4,5,7,11,12,16,23,24,28,31,32,33,37,38,39,40,45],[0,1,9,19,22,24,25,26,28,31,32,33,37,38,40,42,45],[1,2,3,4,7,9,10,11,14,18,20,27,28,31,32,33,38,39,40,42,43],[3,4,5,6,7,11,14,15,18,19,23,26,27,28,31,32,33,37,40,43],[5,11,14,17,20,21,22,24,29,31,32,33,37,38,39,41,44],[2,5,13,15,16,20,23,26,29,31,32,33,37,39,40,41,44],[0,1,3,4,8,9,10,12,13,16,21,22,23,24,27,29,31,32,33,38,39,40,41,42,44,45],[1,3,6,7,8,9,14,16,17,20,21,22,23,25,26,27,29,31,32,33,37,38,39,41,42,44,45],[1,2,4,6,11,14,15,17,18,20,22,24,25,28,29,31,32,33,36],[0,1,4,8,14,18,19,26,28,29,31,32,33,36],[0,2,4,5,8,10,11,13,14,15,18,20,21,22,23,24,25,27,28,29,31,32,33,36,37,41,42,45],[0,2,5,7,11,12,13,14,15,16,17,18,19,20,23,25,26,27,28,29,31,32,33,36,38,41,42,45],[0,1,2,3,6,7,8,9,12,15,16,17,23,24,25,30,31,32,33,36,37,38,39,41,43],[1,4,6,7,9,10,11,12,14,16,19,20,21,24,26,30,31,32,33,36,37,41,42,43,44],[0,3,5,6,7,8,9,11,13,14,17,19,21,22,23,25,27,30,31,32,33,36,38,39,40],[0,5,9,11,12,13,16,24,25,26,27,30,31,32,33,36,37,38,40,42,44],[0,1,4,5,7,9,10,12,13,15,16,20,22,24,25,28,30,31,32,33,36,39,44],[0,1,2,3,5,6,7,9,11,12,17,20,23,25,26,28,30,31,32,33,36,40,42],[0,2,3,6,7,10,12,16,19,21,23,24,25,27,28,30,31,32,33,36,37,39,43,44],[2,6,10,13,16,17,19,20,21,25,26,27,28,30,31,32,33,36,38,40,42,43],[1,5,6,7,9,10,12,13,17,18,19,20,21,24,29,30,31,32,33,36,37,39,41,44,45],[0,3,11,13,14,16,17,18,20,24,25,26,29,30,31,32,33,36,37,38,39,41,45],[0,3,7,8,10,11,12,13,15,21,22,25,27,29,30,31,32,33,36,39,40,41,44,45],[0,1,2,4,5,7,8,9,10,11,12,13,14,19,20,21,22,26,27,29,30,31,32,33,36,37,39,40,41,45],[2,5,6,10,11,15,22,25,28,29,30,31,32,33,36,38,39,44,45],[1,2,3,6,7,8,9,12,13,15,23,26,28,29,30,31,32,33,36,38,39,40,45],[0,1,2,4,6,8,10,11,12,14,16,17,18,20,23,27,28,29,30,31,32,33,36,37,38,39,41,44,45],[0,1,2,4,6,7,8,16,19,20,23,26,27,28,29,30,31,32,33,36,39,40,41,45],[0,3,4,5,7,13,14,16,17,19,20,21,23,25,34,36,39,40],[0,3,7,9,12,13,15,16,17,19,20,24,25,26,34,39,40,42,44,45],[2,3,4,5,8,12,13,19,20,21,23,27,34,36,40,43],[0,3,4,6,7,8,9,10,11,12,13,14,16,19,22,24,25,26,27,34,37,38,40,42,43,44,45],[0,1,4,5,6,7,9,11,13,14,16,20,21,24,28,34,36,37,38,39,41,42,44],[1,7,8,11,12,14,15,19,21,24,26,28,34,37,39,40,41,45],[1,2,3,5,8,13,14,16,17,27,28,34,36,37,38,40,42,43,44],[1,3,7,9,10,11,14,16,17,19,21,26,27,28,34,38,43,45],[1,3,5,6,7,14,20,21,22,29,34,36,38,39,41,43],[2,3,5,8,16,17,21,25,26,29,34,38,41,43,44,45],[1,5,9,13,14,18,23,27,29,34,36,38,43],[0,4,5,8,9,10,11,12,13,15,17,18,23,24,26,27,29,34,37,39,43,44,45],[1,3,4,6,8,10,12,14,15,17,18,20,21,28,29,34,36,37,39,40,42],[0,2,3,4,6,7,8,10,12,13,14,15,18,19,21,22,23,24,25,26,28,29,34,37,38,42,44,45],[1,3,6,7,8,10,11,13,15,16,17,20,22,27,28,29,34,36,37,42],[3,4,7,8,12,19,20,21,22,24,26,27,28,29,34,39,40,42,44,45],[0,3,4,7,8,9,10,11,12,14,15,19,20,22,23,24,25,30,34,38,39,40,41,45],[1,2,6,8,9,11,12,13,15,17,21,26,30,34,36,38,39,41,42],[2,3,6,9,11,12,13,14,17,18,20,21,23,27,30,34,38,40,41,42,43],[1,2,6,9,15,16,18,19,21,26,27,30,34,36,37,41,43,45],[0,1,5,8,9,10,11,13,14,15,19,21,22,24,28,30,34,36,37,42,45],[0,2,3,4,5,7,9,11,13,14,15,16,17,19,21,22,23,24,25,26,28,30,34,37,38],[1,2,3,5,7,12,16,17,18,22,23,25,27,28,30,34,36,37,39,40,41,43],[0,2,5,6,7,8,11,15,16,18,20,22,23,25,26,27,28,30,34,39,40,41,42,43,45],[0,1,3,4,5,6,7,8,10,12,16,18,22,29,30,34,36,37,40,43,45],[1,4,6,7,9,13,14,15,18,19,20,24,26,29,30,34,37,39,43],[0,1,5,6,8,9,14,15,18,19,22,24,25,27,29,30,34,36,37,39,40,41,42,43],[0,1,2,3,4,7,11,13,15,18,20,21,22,24,26,27,29,30,34,38,41,42,43,45],[0,1,3,4,5,7,9,11,12,13,15,16,19,22,23,24,25,28,29,30,34,38,39,41,42,44,45],[0,1,4,6,7,10,11,13,16,19,21,25,26,28,29,30,34,36,41,42,44],[0,1,3,4,5,6,9,10,12,13,16,20,21,22,23,25,27,28,29,30,34,38,40,41,44],[1,2,6,7,10,11,12,13,22,25,26,27,28,29,30,34,36,37,38,39,40,41,44,45],[0,1,4,5,6,7,8,9,13,14,15,31,34,36,39,41,43],[2,7,8,9,10,13,14,15,16,20,21,22,23,24,25,26,31,34,36,42,43,44,45],[0,2,3,6,8,10,11,12,13,14,15,16,17,24,25,27,31,34,36,37,40,41,43],[0,1,2,3,5,6,7,8,10,13,14,16,17,20,23,24,25,26,27,31,34,36,38,39,40,42,43,44,45],[0,1,4,6,7,13,16,21,22,24,28,31,34,36,37,39,40,41,42,43,44,45],[0,2,5,6,7,8,10,14,16,20,21,24,26,28,31,34,36,37,38,43],[0,2,4,5,10,13,14,16,17,20,23,27,28,31,34,36,40,42,43,44,45],[1,2,4,6,7,8,10,11,12,15,17,20,21,25,26,27,28,31,34,36,37,39,41,43],[1,6,7,8,10,11,13,15,21,22,23,24,29,31,34,36,37,38,42],[0,1,6,9,11,12,13,17,19,20,21,22,23,25,26,29,31,34,36,37,38,41,42,44,45],[0,4,5,14,15,18,21,22,23,24,25,27,29,31,34,36,38,39,40,41,42,43],[0,2,5,6,8,9,11,14,15,16,17,18,23,24,26,27,29,31,34,36,37,39,40,42,43,44,45],[3,4,8,12,13,14,15,16,18,20,21,22,23,28,29,31,34,36,38,40,43,45],[3,4,6,7,8,9,10,17,18,19,23,24,25,26,28,29,31,34,36,41,43,44],[0,1,4,5,7,9,10,14,15,21,23,25,27,28,29,31,34,36,37,38,39,40,45],[1,2,5,7,10,11,13,15,17,19,22,24,26,27,28,29,31,34,36,38,39,41,44],[4,5,9,10,13,14,15,17,18,19,20,21,23,25,30,31,34,38,40,42,45],[3,5,7,10,12,14,16,18,20,21,22,24,26,30,31,34,38,39,41],[1,2,3,4,6,7,10,11,20,25,27,30,31,34,37,38,39],[0,1,4,7,9,13,17,19,20,26,27,30,31,34,40,41,42,45],[5,6,7,8,9,10,11,12,16,18,19,20,22,24,25,28,30,31,34,36,37,38,39],[0,3,4,5,10,11,14,15,16,17,18,19,20,25,26,28,30,31,34,36,37,41,42,45],[1,2,4,6,8,9,10,11,13,15,17,19,23,27,28,30,31,34,36,38,41,42,45],[1,3,4,6,13,14,15,16,19,21,23,26,27,28,30,31,34,36,37,38,39],[4,5,9,14,20,25,29,30,31,34,36,41,43,45],[1,2,3,4,6,8,9,13,14,19,23,24,26,29,30,31,34,36,40,43],[0,1,4,7,8,9,11,12,14,15,16,19,23,27,29,30,31,34,36,37,39,40,42],[3,5,9,10,13,14,20,21,22,24,26,27,29,30,31,34,36,38,39,41,42,45],[1,3,4,10,13,16,17,18,20,21,22,28,29,30,31,34,37,39,40,41,42,44],[0,2,4,5,10,13,14,17,18,19,20,25,26,28,29,30,31,34,37,38,39,40,42,44,45],[0,5,6,7,8,9,10,13,14,15,16,17,18,21,23,27,28,29,30,31,34,40,41,43,44,45],[0,1,3,4,8,9,11,12,13,16,17,21,22,26,27,28,29,30,31,34,37,40,43,44],[0,1,4,6,8,11,13,14,16,17,22,24,25,32,34,37,38,39,42],[0,3,4,6,9,10,15,16,18,19,20,22,23,24,25,26,32,34,36,37,39,41,42,44,45],[0,2,4,5,6,9,10,15,16,17,18,20,23,25,27,32,34,37,38,39,43,44],[1,3,5,7,8,10,12,13,14,15,19,21,23,24,25,26,27,32,34,36,38,39,41,43,45],[0,3,5,7,8,10,11,12,14,16,19,22,23,24,28,32,34,36,41,43,44],[1,5,6,7,8,9,12,14,15,17,22,25,26,28,32,34,40,43,45],[0,1,2,4,6,7,11,13,14,15,20,24,27,28,32,34,36,40,42],[0,3,6,9,11,12,13,14,15,17,19,20,23,24,25,26,27,28,32,34,37,38,41,42,44,45],[1,2,3,5,7,9,10,11,12,15,16,17,18,19,21,22,23,25,29,32,34,37,38,39,40,41,42,43,44],[1,4,6,9,13,14,15,17,18,20,22,24,26,29,32,34,36,37,40,43,45],[0,2,6,7,9,19,20,21,22,27,29,32,34,37,38,39,40,43],[2,3,5,6,7,9,13,14,15,18,19,21,22,26,27,29,32,34,36,38,40,41,42,43,44,45],[1,2,3,5,7,8,10,12,13,16,18,20,21,22,23,24,28,29,32,34,36,40,43,44],[0,1,4,11,13,16,19,20,21,22,23,24,26,28,29,32,34,39,41,42,43,45],[0,2,3,4,7,8,9,12,13,14,15,16,17,19,20,22,23,24,25,27,28,29,32,34,36,42,43],[0,2,4,5,6,7,9,12,13,14,17,21,23,26,27,28,29,32,34,37,38,39,40,41,43,44,45],[1,2,4,5,8,9,11,16,17,18,19,20,21,22,23,30,32,34,36,37,39,40,41,43],[0,1,4,6,7,9,12,14,16,17,21,24,25,26,30,32,34,37,38,39,43,45],[6,12,17,18,19,20,21,24,25,27,30,32,34,36,37,39,40,41,44,45],[4,5,6,8,10,12,14,15,16,17,19,20,21,22,23,24,26,27,30,32,34,39,44],[2,3,4,5,8,10,16,17,20,21,22,28,30,32,34,36,38,39,40,42],[3,4,7,8,10,11,12,13,17,19,20,21,23,24,25,26,28,30,32,34,38,39,40,41,42,45],[1,4,10,14,16,17,19,21,23,24,27,28,30,32,34,36,38,39,41,42,43,44,45],[0,1,5,6,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,30,32,34,37,39,42,43,44],[1,3,4,5,6,7,9,10,12,16,20,21,23,29,30,32,34,40,44],[0,3,5,6,7,10,11,12,14,15,17,21,22,25,26,29,30,32,34,36,38,39,41,42,44,45],[0,6,7,9,10,11,12,13,14,16,17,18,20,21,23,25,27,29,30,32,34,40,41,45],[0,1,2,11,13,16,18,20,21,25,26,27,29,30,32,34,36,37,39,42],[1,3,8,9,10,15,16,18,19,24,28,29,30,32,34,37,38,40,41,42],[3,4,6,10,11,13,16,17,19,20,22,24,26,28,29,30,32,34,36,37,38,39,40,45],[0,3,5,6,8,10,12,13,15,17,20,21,22,24,25,27,28,29,30,32,34,37,38,41,42,44,45],[1,2,3,5,6,7,9,15,16,18,22,24,25,26,27,28,29,30,32,34,36,39,44],[0,1,6,8,9,11,12,13,15,16,17,18,20,21,22,25,31,32,34,36,37,38,40,41,45],[1,2,3,9,15,17,18,19,23,26,31,32,34,36,37,39,40,41,44],[1,2,3,4,6,8,9,11,12,16,17,18,19,20,21,22,23,24,25,27,31,32,34,36,38,41,42,44,45],[1,2,6,7,9,10,11,12,13,15,16,18,19,20,21,24,26,27,31,32,34,36,37,38,39,41,42],[0,1,4,6,7,9,10,14,19,22,23,24,25,28,31,32,34,38,39,40,41,42,43,44],[0,1,2,3,4,6,7,9,10,11,12,17,18,19,20,21,23,24,26,28,31,32,34,38,41,42,43,45],[1,2,4,7,10,11,12,13,15,16,17,19,20,24,25,27,28,31,32,34,37,38,39,40,43],[0,1,2,3,6,11,12,13,14,19,20,24,26,27,28,31,32,34,43,44,45],[2,3,4,6,7,9,13,17,20,21,22,24,29,31,32,34,36,38,39,40,42,43,44,45],[0,1,2,5,6,11,15,17,18,19,20,21,23,24,26,29,31,32,34,36,39,40,43],[2,3,7,8,12,13,14,15,16,20,22,25,27,29,31,32,34,36,37,38,39,41,45],[1,5,6,7,8,9,10,14,15,18,19,20,22,25,26,27,29,31,32,34,36,38,39,41,42,44],[1,2,4,5,7,14,16,18,19,20,21,24,28,29,31,32,34,37,38,40,43,44],[2,3,6,8,9,11,15,18,20,21,22,24,26,28,29,31,32,34,37,38,42,43,45],[1,2,3,4,5,7,8,11,14,15,16,17,18,19,23,27,28,29,31,32,34,38,40,42],[0,4,7,9,10,11,12,15,16,17,19,21,22,26,27,28,29,31,32,34,37,44,45],[0,2,6,7,8,9,13,14,17,19,20,22,23,24,25,30,31,32,34,37,39,40,45],[0,1,2,5,6,10,11,13,14,15,16,19,20,21,23,26,30,31,32,34,37,38],[3,7,8,9,10,12,13,16,17,19,20,22,23,24,27,30,31,32,34,39,44],[0,1,2,3,4,5,6,7,10,13,16,17,19,21,23,24,25,26,27,30,31,32,34,37,40,44,45],[0,2,5,7,10,13,15,16,18,19,21,28,30,31,32,34,39,40,42,43],[1,2,6,9,11,14,16,18,21,22,23,24,25,26,28,30,31,32,34,40,42,43,45],[4,5,7,9,11,13,15,16,18,19,20,25,27,28,30,31,32,34,37,39,40,41,42,43,44,45],[1,2,7,11,12,14,15,17,19,20,21,22,23,24,25,26,27,28,30,31,32,34,38,40,41,42,43,44],[0,1,3,5,6,12,16,17,18,20,21,22,23,25,29,30,31,32,34,36,37,39,41,42,43,44,45],[0,1,2,3,4,5,10,11,16,17,21,24,26,29,30,31,32,34,36,37,38,39,40,41,43,44],[0,1,3,5,6,8,9,10,12,13,16,17,18,19,22,27,29,30,31,32,34,36,39,40,42],[1,3,5,6,7,8,9,10,12,13,15,17,19,20,21,25,26,27,29,30,31,32,34,36,37,39,45],[0,4,5,6,7,11,14,17,18,20,22,24,28,29,30,31,32,34,36,39,41,43],[2,5,6,7,8,10,12,13,16,19,20,21,22,24,25,26,28,29,30,31,32,34,36,39,41,42,43,45],[0,3,5,7,8,10,12,13,16,17,20,21,23,24,25,27,28,29,30,31,32,34,36,37,39,41,44,45],[1,2,4,7,8,9,11,13,18,26,27,28,29,30,31,32,34,36,38,39,41,42,44],[0,1,4,7,9,11,12,13,14,19,22,24,25,33,34,36,37,38,40,43,44,45],[0,3,4,8,9,12,13,17,18,19,22,25,26,33,34,37,38,42,43],[1,4,6,7,8,10,12,13,16,19,20,22,23,25,27,33,34,36,37,38,39,40,41],[0,2,3,7,13,14,15,17,21,22,23,26,27,33,34,39,41,42,44,45],[0,2,3,4,8,11,12,13,14,18,20,21,22,25,28,33,34,36,37,40,41,43],[1,2,4,6,7,8,12,14,17,26,28,33,34,37,38,40,41,42,43,44,45],[2,10,11,13,14,17,18,27,28,33,34,36,37,39,41,44,45],[1,3,4,11,12,14,15,16,19,20,21,22,23,25,26,27,28,33,34,39,41,42],[2,3,4,5,10,11,13,14,16,20,22,24,25,29,33,34,37,41,42,43,44,45],[6,9,10,12,13,15,16,18,19,20,21,26,29,33,34,36,37,39,40,41,42,43],[4,5,12,14,17,18,19,20,22,24,27,29,33,34,37,39,41,42,43],[0,3,4,7,9,10,12,16,17,18,20,22,23,26,27,29,33,34,36,38,40,41,42,43,44,45],[3,6,12,13,14,15,16,20,23,24,28,29,33,34,37,38,42,44],[0,2,4,5,6,8,9,11,14,16,17,18,19,20,23,24,26,28,29,33,34,36,37,39,42,45],[2,3,4,9,10,12,15,16,21,22,23,27,28,29,33,34,37,38,39,40,41,42,45],[2,4,5,6,7,8,12,13,15,16,17,19,23,26,27,28,29,33,34,36,38,40,41,42,44],[0,2,6,7,8,11,12,13,14,15,16,18,20,21,23,24,30,33,34,43,44],[5,7,9,10,16,17,18,25,26,30,33,34,36,42,43,44,45],[2,4,6,7,9,14,16,17,19,21,23,25,27,30,33,34,39,41,42],[2,5,6,8,13,16,18,19,20,21,23,24,26,27,30,33,34,36,37,38,39,41,45],[0,1,3,4,5,7,14,15,16,17,18,20,22,28,30,33,34,36,38,39,41,43,44,45],[0,1,2,3,4,7,9,10,11,12,14,18,22,25,26,28,30,33,34,39,40,41,42,43,44],[1,4,5,6,7,8,13,18,23,25,27,28,30,33,34,36,38,40,41,42,45],[0,1,8,9,13,16,21,22,23,24,25,26,27,28,30,33,34,37,38,41],[0,1,3,4,6,8,10,19,23,24,29,30,33,34,37,38,39,41,42,43,44],[3,6,7,8,11,13,14,16,19,20,22,24,26,29,30,33,34,36,37,38,41,42,43,44,45],[0,1,2,8,10,11,14,15,16,17,18,20,23,27,29,30,33,34,37,38,41,43],[0,6,8,10,11,12,13,17,19,21,22,24,25,26,27,29,30,33,34,36,39,41,43,45],[0,1,2,3,4,6,7,8,9,13,15,17,18,19,21,22,23,24,25,28,29,30,33,34,36,37,42,45],[0,2,3,9,10,11,13,15,16,18,19,21,22,25,26,28,29,30,33,34,37,38,39,40,42],[0,1,3,4,6,7,8,12,13,20,22,24,27,28,29,30,33,34,36,37,39,40,41,44,45],[2,3,4,6,7,13,15,18,23,25,26,27,28,29,30,33,34,41,44],[0,3,4,5,7,8,10,12,15,17,18,22,23,24,25,31,33,34,37,39,43,44],[2,4,5,6,9,11,16,17,18,19,20,21,23,24,25,26,31,33,34,37,40,41,42,43,45],[0,1,6,7,8,10,12,15,16,17,18,21,23,25,27,31,33,34,40,41,43,45],[0,1,3,4,6,7,9,10,12,15,17,18,22,26,27,31,33,34,37,38,39,42,43,44],[0,2,3,4,6,8,9,10,11,12,14,16,17,24,28,31,33,34,37,39,43],[0,4,6,7,8,13,15,16,18,19,20,21,23,24,26,28,31,33,34,37,38,41,42,43,44,45],[0,1,2,3,4,5,6,8,10,15,16,18,21,22,23,25,27,28,31,33,34,43,44,45],[1,2,5,8,9,10,13,14,16,19,20,22,23,25,26,27,28,31,33,34,37,39,41,42,43],[2,4,5,6,8,10,11,13,14,15,16,17,23,25,29,31,33,34,36,38,41,43,44],[0,1,2,3,6,8,13,14,15,16,18,19,22,26,29,31,33,34,36,38,40,43,45],[0,1,6,9,10,11,12,16,17,20,21,24,25,27,29,31,33,34,36,37,38,39,40,41,45],[0,2,3,5,7,9,10,11,16,17,21,22,23,24,26,27,29,31,33,34,36,39,44],[1,3,5,6,11,12,13,15,17,18,19,20,23,28,29,31,33,34,36,38,41,44],[4,8,10,12,14,16,17,18,20,21,22,24,26,28,29,31,33,34,36,45],[0,2,8,12,16,17,18,24,25,27,28,29,31,33,34,36,37,38,39,43,45],[1,3,5,7,13,14,15,16,17,18,21,22,23,25,26,27,28,29,31,33,34,36,38,39,41,43,44],[2,3,10,11,13,15,16,20,23,24,30,31,33,34,36,38,42,44,45],[1,2,3,5,8,10,15,16,17,18,19,20,21,24,26,30,31,33,34,36,38,39,41,44],[1,2,5,11,12,14,17,19,20,22,23,24,25,27,30,31,33,34,36,37,38,39,40,41,45],[0,4,6,7,8,10,11,13,14,17,18,21,23,24,26,27,30,31,33,34,36,40,42],[3,4,10,11,12,14,18,19,22,25,28,30,31,33,34,38,39,42,44,45],[0,1,3,4,5,6,10,12,16,17,19,21,22,24,25,26,28,30,31,33,34,40,41,44],[1,3,5,6,9,12,13,14,16,18,21,24,27,28,30,31,33,34,37,38,45],[2,3,4,6,7,9,10,13,17,19,23,26,27,28,30,31,33,34,38,39,40,41,42],[4,5,6,7,9,10,11,12,13,16,17,19,21,22,23,29,30,31,33,34,36,40,41,42,44,45],[2,5,10,15,16,18,22,26,29,30,31,33,34,36,40,42,44],[0,1,2,4,7,8,11,12,13,15,17,18,20,22,23,24,25,27,29,30,31,33,34,36,37,39,41,43,45],[1,2,4,7,8,9,10,11,12,15,16,18,19,20,22,24,26,27,29,30,31,33,34,36,38,39,43],[1,2,3,4,8,12,14,16,18,19,21,24,25,28,29,30,31,33,34,39,40,41,42,43,45],[0,1,3,7,9,11,16,17,18,20,21,22,23,26,28,29,30,31,33,34,38,39,42,43],[0,5,10,11,15,16,22,25,27,28,29,30,31,33,34,37,40,44,45],[1,2,3,4,7,10,12,13,17,18,19,20,23,26,27,28,29,30,31,33,34,41,44],[6,9,10,11,12,13,15,16,17,19,21,22,23,24,32,33,34,36,38,41,43,44],[4,5,6,7,9,11,14,15,16,19,20,22,23,24,26,32,33,34,40,43,45],[1,5,7,8,9,10,11,14,16,17,23,25,27,32,33,34,36,38,42,44,45],[0,1,2,6,7,8,9,10,13,17,18,20,21,22,23,24,25,26,27,32,33,34,37,38,40,41,42],[1,2,3,4,5,6,8,9,17,22,23,28,32,33,34,39,40,45],[0,1,2,3,7,9,10,12,16,18,20,21,23,25,26,28,32,33,34,36,39,40,41,44],[2,6,7,11,13,16,20,21,22,24,27,28,32,33,34,39,42,43],[5,6,7,8,13,18,19,21,22,26,27,28,32,33,34,36,37,38,39,41,42,43,44,45],[0,6,8,9,10,11,12,13,14,15,20,24,25,29,32,33,34,38,40,42,43],[0,1,2,11,12,15,16,17,19,22,23,24,26,29,32,33,34,36,39,41,43,44,45],[1,2,3,5,6,7,8,10,11,12,13,14,16,17,18,19,21,22,23,24,25,27,29,32,33,34,38,40,43,45],[0,2,3,4,5,6,9,10,14,15,23,24,26,27,29,32,33,34,36,37,38,39,41,42,43,44],[0,2,7,8,10,11,12,14,17,18,21,22,23,24,25,28,29,32,33,34,36,39,41,42,43,45],[1,7,8,9,11,12,14,16,17,18,19,20,21,25,26,28,29,32,33,34,43,44],[1,4,5,6,8,10,17,20,23,27,28,29,32,33,34,36,39,40,43],[5,7,8,9,10,11,12,14,15,19,20,26,27,28,29,32,33,34,37,38,40,41,42,43,44,45],[0,1,4,6,13,15,16,21,22,24,30,32,33,34,37,41,42,44],[2,3,9,13,18,20,22,24,26,30,32,33,34,36,37,38,42,44,45],[0,5,6,7,8,10,13,14,15,18,19,20,23,24,27,30,32,33,34,37,42,43,44],[0,1,3,5,6,8,9,11,12,13,18,21,22,24,26,27,30,32,33,34,36,41,42,43,44,45],[0,2,3,4,7,8,9,10,13,15,17,20,21,22,23,24,28,30,32,33,34,37,38,40,42,43,44,45],[0,1,7,10,12,13,14,16,17,26,28,30,32,33,34,36,37,38,41,42,43,44],[0,1,2,4,5,6,10,27,28,30,32,33,34,37,38,42,44,45],[2,3,6,10,12,13,14,16,17,18,19,20,23,26,27,28,30,32,33,34,36,40,41,42,44],[0,1,5,6,8,9,11,14,15,17,19,20,21,29,30,32,33,34,39],[1,3,6,7,9,11,12,14,16,18,20,24,26,29,30,32,33,34,36,38,41,42,45],[2,3,4,7,8,10,11,12,13,14,20,21,23,24,25,27,29,30,32,33,34,39],[5,6,7,12,13,14,17,21,22,24,26,27,29,30,32,33,34,36,37,41,42,45],[0,1,2,4,6,8,9,12,14,21,22,24,25,28,29,30,32,33,34,38,39,40,41,44,45],[0,1,6,10,11,13,14,15,16,17,19,20,23,26,28,29,30,32,33,34,36,38,42,44],[4,5,10,11,12,13,15,18,19,20,23,27,28,29,30,32,33,34,38,39,44,45],[1,2,3,4,5,6,7,8,9,10,11,12,15,18,19,20,23,26,27,28,29,30,32,33,34,36,37,40,41,42,44],[4,5,16,19,21,24,25,31,32,33,34,36,40,41,42,44],[0,1,2,6,7,9,13,15,17,19,20,24,26,31,32,33,34,36,38,39,41,42,45],[0,3,5,6,7,9,10,11,12,13,14,15,16,18,21,22,23,24,25,27,31,32,33,34,36,37,44,45],[0,1,3,6,7,15,18,19,21,22,23,24,25,26,27,31,32,33,34,36,39,40],[2,5,6,10,12,13,14,16,17,19,20,22,23,25,28,31,32,33,34,39,41,42,43],[1,4,6,7,8,9,10,12,13,15,16,19,20,24,25,26,28,31,32,33,34,41,42,43,44,45],[0,2,5,6,7,12,14,16,17,20,22,24,25,27,28,31,32,33,34,37,39,41,43,45],[0,2,7,8,9,10,11,14,17,18,19,20,23,26,27,28,31,32,33,34,38,41,43,44],[0,1,4,6,8,9,10,12,14,16,17,18,19,20,23,29,31,32,33,34,37,39,40,42],[1,4,6,10,11,12,15,17,18,26,29,31,32,33,34,37,38,39,44,45],[0,1,2,6,7,9,14,15,17,27,29,31,32,33,34,39,43,45],[4,6,7,9,11,13,15,18,19,20,23,26,27,29,31,32,33,34,37,39,40,42,43,44],[0,2,3,4,5,6,7,10,15,16,17,18,23,24,25,28,29,31,32,33,34,36,37,42],[0,2,3,4,5,7,9,10,11,13,16,18,19,20,23,26,28,29,31,32,33,34,36,37,44,45],[0,4,5,7,9,11,16,17,19,20,23,27,28,29,31,32,33,34,36,41,43,45],[0,1,3,4,10,11,12,13,14,18,19,20,23,26,27,28,29,31,32,33,34,36,37,38,41,42,43,44],[6,7,10,13,14,16,18,20,22,24,30,31,32,33,34,37,38,39,41,42,44],[3,4,6,7,8,9,13,16,19,20,23,26,30,31,32,33,34,37,41,42,44,45],[0,1,3,6,7,12,14,16,17,27,30,31,32,33,34,38,39,40,42,44],[1,3,4,5,7,9,11,18,19,20,23,26,27,30,31,32,33,34,37,38,40,42,44,45],[2,6,7,12,16,28,30,31,32,33,34,37,38,39,40,41,42,43,44],[0,2,3,4,6,7,11,12,13,14,15,26,28,30,31,32,33,34,37,38,41,42,43,44,45],[3,4,7,9,14,15,19,20,23,27,28,30,31,32,33,34,38,39,40,41,42,43,44],[2,5,6,7,8,9,10,12,13,15,17,18,19,20,23,26,27,28,30,31,32,33,34,37,41,42,43,44,45],[1,3,6,7,8,9,10,11,15,16,19,20,23,29,30,31,32,33,34,37,38,39,40,42],[0,1,3,4,6,8,9,10,11,12,17,18,19,20,23,26,29,30,31,32,33,34,37,39,40,45],[0,1,7,12,14,27,29,30,31,32,33,34,38,39,42,43],[0,1,2,6,8,10,11,12,14,26,27,29,30,31,32,33,34,37,38,39,43,45],[2,6,7,8,9,13,16,17,18,28,29,30,31,32,33,34,37,38,39,42,44],[0,1,2,4,6,10,11,12,15,16,19,20,23,26,28,29,30,31,32,33,34,37,38,39,40,44,45],[0,2,5,6,8,9,11,12,15,16,18,27,28,29,30,31,32,33,34,38,39,41,42,43,44],[0,1,2,3,5,7,8,11,12,13,15,18,19,20,23,26,27,28,29,30,31,32,33,34,37,39,40,41,43,44,45],[2,4,5,7,8,15,16,17,18,19,20,23,35,39,42,43],[0,1,4,5,11,13,14,16,17,19,20,21,24,25,26,35,36,37,39,40,42,43,44,45],[5,6,9,10,12,14,15,16,17,21,22,23,24,27,35,37,38,40,41,42,43,45],[1,4,5,8,9,13,16,19,22,23,26,27,35,36,37,41,42,43,44],[0,1,7,8,9,10,12,13,15,17,22,23,28,35,36,43],[0,2,6,8,9,10,11,12,13,14,16,17,19,21,22,23,26,28,35,37,38,43,44,45],[0,1,2,3,9,11,12,13,14,15,16,19,20,22,27,28,35,36,37,38,39,43,45],[2,3,4,9,10,11,13,14,15,16,17,18,19,21,22,23,26,27,28,35,37,38,39,43,44],[1,2,3,5,7,8,11,12,13,14,17,20,21,22,25,29,35,37,39,41,42,44,45],[0,1,2,3,4,6,7,8,9,14,22,23,24,26,29,35,36,40,41],[0,1,2,4,5,8,10,11,12,16,17,22,24,25,27,29,35,38,40,41,42,43,44],[0,1,4,7,8,9,11,12,13,16,18,19,20,21,22,23,25,26,27,29,35,36,39,41,43,45],[0,1,5,6,12,13,14,18,19,21,22,23,24,28,29,35,36,37,41,43,45],[0,1,4,6,8,9,11,14,15,17,18,20,21,22,25,26,28,29,35,38,39,41,42,43,44],[1,5,7,9,10,11,13,14,15,16,18,21,22,23,27,28,29,35,36,38,39],[0,1,2,6,8,11,15,16,18,20,25,26,27,28,29,35,38,42,44,45],[0,1,4,5,10,11,12,13,14,16,20,23,24,30,35,36,41,42,44],[0,1,3,4,6,8,9,13,15,17,18,19,20,22,24,26,30,35,37,41,42,44,45],[0,1,2,4,5,7,8,9,10,11,12,13,14,15,16,17,20,23,27,30,35,36,37,38,39,40,44],[1,3,10,11,12,13,15,21,24,26,27,30,35,37,39,40,44,45],[2,4,5,6,7,12,18,19,22,23,25,28,30,35,36,41],[0,2,3,4,6,7,9,10,11,13,14,16,17,18,19,20,24,25,26,28,30,35,37,38,40,41,45],[3,5,8,11,13,14,15,16,17,18,27,28,30,35,36,37,38,39,41,42],[2,4,6,7,8,9,11,13,15,23,24,26,27,28,30,35,37,38,39,40,41,42,45],[3,4,9,10,11,13,14,15,16,17,21,22,29,30,35,39,40,42,43,45],[1,2,7,9,15,17,25,26,29,30,35,36,37,40,43],[0,4,6,7,9,10,11,12,16,19,25,27,29,30,35,37,38,45],[1,3,4,7,9,10,11,13,16,17,18,20,21,22,24,26,27,29,30,35,36,37,39,42],[0,2,5,8,10,11,12,17,20,21,22,23,28,29,30,35,39,40,45],[1,3,4,5,6,7,12,14,15,16,17,18,19,20,24,26,28,29,30,35,36,37,38,42],[2,4,5,7,8,9,10,12,13,16,19,20,21,23,27,28,29,30,35,37,38,40,41,42,43,45],[1,2,3,4,5,7,9,10,13,15,17,20,21,23,24,26,27,28,29,30,35,36,37,38,39,41,43],[1,4,5,6,11,19,20,23,24,31,35,38,42,43,44],[1,4,5,7,8,9,10,12,13,17,18,20,22,23,24,26,31,35,37,38,39,40,41,42,43,45],[0,2,3,4,7,12,13,14,17,18,19,23,24,27,31,35,39,41,42,44,45],[3,7,8,9,12,13,14,15,17,18,21,22,24,25,26,27,31,35,38,40,42],[0,1,2,3,5,8,9,10,12,13,17,18,19,21,22,23,24,28,31,35,36,39,41,43,44,45],[1,2,3,5,7,8,11,14,15,16,19,20,21,23,26,28,31,35,36,37,38,43],[3,4,7,8,10,12,14,16,17,19,22,23,24,25,27,28,31,35,36,38,40,41,44],[2,3,6,7,8,9,10,12,13,16,17,18,19,20,22,23,25,26,27,28,31,35,36,38,39,40,45],[1,3,9,10,11,12,14,16,17,18,19,20,25,29,31,35,38,39,40,41,45],[2,3,4,5,9,12,18,23,25,26,29,31,35,37,38,39,42,44],[3,5,7,8,10,12,17,18,19,20,25,27,29,31,35,40,41],[0,1,3,6,8,10,16,18,19,20,21,23,24,26,27,29,31,35,38,42,44,45],[0,2,3,5,7,9,10,11,16,18,28,29,31,35,36,40,42,43,44],[1,3,4,6,7,8,9,12,13,16,24,25,26,28,29,31,35,36,37,38,40,41,43,45],[0,1,2,4,6,8,9,10,11,13,14,15,18,19,25,27,28,29,31,35,36,38,39,41,42,43,44,45],[0,2,4,5,6,7,9,10,11,12,14,15,18,19,21,23,24,26,27,28,29,31,35,36,38,39,43],[1,2,4,8,9,10,11,12,13,15,16,18,19,21,22,23,24,25,30,31,35,36,38,40,41,43],[0,3,4,5,9,10,17,18,20,22,24,25,26,30,31,35,36,37,38,39,40,43,45],[0,3,5,7,8,9,12,14,16,18,20,23,24,25,27,30,31,35,36,39,40,42],[0,1,4,6,9,10,12,13,14,15,16,17,20,21,24,25,26,27,30,31,35,36,38,40,41,42,45],[0,1,3,4,5,7,9,11,12,19,21,23,24,28,30,31,35,36,40,42,43,44,45],[0,2,4,6,7,9,13,14,15,16,17,21,22,23,26,28,30,31,35,36,37,38,39,41,42,43,44],[2,3,4,6,10,11,14,22,25,27,28,30,31,35,36,38,39,44,45],[0,1,2,5,6,7,11,12,15,17,18,19,22,23,24,25,26,27,28,30,31,35,36,38,40,41,44],[0,1,2,3,4,6,8,9,12,13,14,15,18,19,20,23,24,29,30,31,35,37,38,40,42,44,45],[1,2,7,8,11,12,18,23,25,26,29,30,31,35,38,40,41,44],[0,2,3,5,7,10,11,14,15,16,18,21,24,25,27,29,30,31,35,37,39,40,44,45],[0,5,7,9,11,12,13,14,15,16,17,18,19,22,24,26,27,29,30,31,35,37,38,39,40,41,42,44],[3,8,11,12,14,16,17,23,25,28,29,30,31,35,37,40,41,43,44],[4,7,9,12,14,16,17,18,22,23,25,26,28,29,30,31,35,38,42,43,44,45],[1,5,7,10,11,13,15,16,17,19,22,23,27,28,29,30,31,35,37,38,39,42,43,44],[0,1,2,3,5,6,7,8,9,11,12,13,16,20,24,26,27,28,29,30,31,35,37,38,39,40,41,43,44,45],[0,2,3,4,5,8,9,13,14,19,25,32,35,36,42,44],[7,8,9,10,12,13,16,18,19,21,24,25,26,32,35,37,38,40,41,45],[1,3,6,9,11,12,13,19,20,22,27,32,35,36,37,38,40,41,45],[1,5,9,12,13,18,19,22,24,26,27,32,35,37,38,42,44],[1,3,4,5,7,8,9,11,13,17,20,23,24,28,32,35,36,40,43,44],[1,2,6,9,10,11,14,16,18,21,22,23,26,28,32,35,37,40,41,42,43,45],[0,2,4,7,11,12,16,17,19,23,27,28,32,35,36,37,38,40,42,43,45],[2,3,4,5,7,8,17,18,19,23,24,26,27,28,32,35,37,40,41,43,44],[0,3,7,10,11,12,16,19,20,22,29,32,35,36,37,38,41,42,43,44,45],[1,6,7,8,9,11,12,13,16,17,19,23,24,26,29,32,35,39,40,42,43],[0,1,4,5,7,9,10,14,15,16,17,21,27,29,32,35,36,40,41],[0,2,3,5,8,10,12,15,16,19,20,23,26,27,29,32,35,39,44,45],[2,4,5,6,7,8,9,11,12,14,15,16,17,21,25,28,29,32,35,36,37,38,40,41,43,45],[1,2,3,4,5,6,7,8,10,11,12,13,14,17,19,20,21,23,24,26,28,29,32,35,38,39,40,43,44],[1,2,4,7,8,9,11,12,13,18,19,20,24,25,27,28,29,32,35,36,40,42,44],[0,3,6,8,12,13,15,19,20,21,25,26,27,28,29,32,35,38,39,40,41,42,45],[0,1,2,3,4,5,6,7,8,9,11,12,14,15,16,17,18,19,20,23,30,32,35,39,40,41,45],[0,2,3,5,7,8,14,16,17,20,21,23,24,25,26,30,32,35,36,37,38,39,40,42],[3,4,6,7,9,10,12,13,16,17,27,30,32,35,37,38,39,44,45],[0,1,2,3,4,6,12,16,17,18,19,22,24,26,27,30,32,35,36,37,38,39,41,42,44],[3,7,8,15,16,17,18,23,25,28,30,32,35,36,41,42,43,44,45],[0,1,3,4,7,9,11,12,13,14,26,28,30,32,35,37,40,43,44],[0,1,2,4,5,6,7,9,10,12,13,14,16,18,19,20,22,23,24,25,27,28,30,32,35,36,37,38,41,42,43,45],[0,4,5,8,12,13,14,15,16,17,26,27,28,30,32,35,37,40,43],[1,3,4,5,6,9,10,11,12,13,14,15,16,19,20,23,29,30,32,35,36,38,43],[1,2,3,4,6,7,8,9,10,11,12,17,18,19,20,23,26,29,30,32,35,37,39,41,43,45],[4,13,17,18,27,29,30,32,35,36,37,40,44],[0,5,6,8,10,11,13,14,16,18,26,27,29,30,32,35,37,39,40,41,44,45],[0,1,2,4,5,6,7,8,9,11,12,13,14,15,20,23,24,25,28,29,30,32,35,38,39,40,42,43],[1,4,8,9,11,12,16,18,19,22,26,28,29,30,32,35,36,37,38,41,42,43,45],[0,2,6,7,8,9,10,11,15,20,21,22,24,25,27,28,29,30,32,35,37,39,40,41,42,44],[0,2,4,5,6,7,8,9,12,15,17,18,20,23,24,26,27,28,29,30,32,35,36,37,38,42,44,45],[0,5,7,8,9,11,12,13,15,16,17,19,21,22,24,25,31,32,35,38,43,45],[0,1,3,4,6,8,11,12,13,14,15,16,19,20,21,22,24,25,26,31,32,35,37,39,40,42,43,44],[0,2,3,5,6,7,8,10,12,14,15,16,17,18,27,31,32,35,41,42,44],[1,6,7,8,9,12,13,15,17,18,19,21,24,25,26,27,31,32,35,39,40,41,45],[2,3,6,9,11,13,15,16,17,19,24,25,28,31,32,35,40,41,42],[0,1,2,4,5,6,7,8,11,12,14,15,16,17,18,21,22,23,24,25,26,28,31,32,35,37,39,40,41,44,45],[3,4,6,9,10,11,14,16,17,19,20,23,27,28,31,32,35,38,41,43,44,45],[1,2,4,5,8,12,14,15,16,18,26,27,28,31,32,35,39,41,42,43],[0,1,2,4,5,6,9,11,12,13,14,16,17,18,19,20,22,23,25,29,31,32,35,39,40,41,42],[0,1,3,4,5,6,8,9,13,14,15,18,26,29,31,32,35,37,38,39,41,42,44,45],[1,2,4,5,6,8,9,10,11,13,16,17,19,23,25,27,29,31,32,35,38,39,40,41,44,45],[0,1,2,3,5,7,9,10,11,12,14,15,16,17,26,27,29,31,32,35,38,39,41],[5,6,11,12,14,16,28,29,31,32,35,38,39,44,45],[0,2,3,5,11,13,14,16,26,28,29,31,32,35,37,38,39],[0,3,4,5,8,9,12,13,15,17,27,28,29,31,32,35,39,40,41,42],[0,5,7,8,9,11,12,14,26,27,28,29,31,32,35,38,39,40,41,42,44,45],[7,8,12,14,16,18,20,21,24,30,31,32,35,36,38,41,44],[0,2,4,7,8,10,11,15,16,19,20,23,26,30,31,32,35,36,37,39,41,42,44,45],[2,3,4,7,8,9,10,12,13,15,16,18,27,30,31,32,35,36,43],[2,3,4,6,8,9,11,12,13,15,18,19,20,21,22,23,24,25,26,27,30,31,32,35,36,39,42,43,45],[0,2,3,4,7,9,11,12,17,18,20,21,22,23,28,30,31,32,35,39,40,42,43,45],[0,3,6,7,8,9,10,14,15,17,18,19,20,23,26,28,30,31,32,35,37,43],[0,3,4,6,7,9,10,12,13,15,27,28,30,31,32,35,38,39,42,44,45],[3,4,6,8,9,10,11,12,14,16,17,19,20,23,26,27,28,30,31,32,35,40,44],[0,1,2,5,6,9,10,12,15,18,29,30,31,32,35,37,42,43,44,45],[2,7,8,10,11,14,16,18,19,21,24,26,29,30,31,32,35,38,42,43,44],[1,2,4,5,8,9,10,11,12,13,15,16,18,19,20,23,27,29,30,31,32,35,37,38,42,43,45],[15,18,19,23,24,26,27,29,30,31,32,35,37,38,42,43],[7,9,11,13,14,16,17,18,28,29,30,31,32,35,36,37,38,39,40,41,43,44],[1,5,12,13,17,18,26,28,29,30,31,32,35,36,38,39,41,43,44,45],[0,3,7,8,10,11,12,14,15,16,27,28,29,30,31,32,35,36,37,39,43],[0,11,14,17,26,27,28,29,30,31,32,35,36,37,38,39,40,43,45],[1,2,6,13,16,17,19,22,24,33,35,40,41,42,45],[0,1,3,4,5,6,9,13,14,15,16,19,20,22,24,26,33,35,36,37,40,41,42,44],[1,2,4,6,8,11,12,15,17,19,21,23,24,27,33,35,37,38,39,41,42,44,45],[1,2,3,4,5,7,8,9,11,12,14,15,18,19,20,23,26,27,33,35,36,37,39,41,42],[0,2,4,5,7,8,9,10,11,12,13,14,15,17,19,21,24,25,28,33,35,36,37,39,41,42],[0,3,6,7,12,14,15,16,17,19,20,23,26,28,33,35,38,39,40,41,42,44,45],[0,2,3,4,5,6,7,9,11,12,14,15,16,18,27,28,33,35,36,38,42,44],[2,4,6,8,9,10,13,16,17,19,20,23,26,27,28,33,35,38,40,42,45],[5,7,12,14,29,33,35,36,37,40,44],[0,1,3,5,6,8,9,10,11,12,13,16,17,18,22,23,24,26,29,33,35,39,40,42,45],[0,2,3,4,5,6,7,10,12,15,16,19,22,23,24,25,27,29,33,35,36,38,39,41,43],[0,1,5,6,7,8,9,11,13,15,16,17,18,19,20,23,26,27,29,33,35,41,42,43,44,45],[0,3,5,7,9,10,11,13,14,15,16,17,22,23,28,29,33,35,39,43,45],[0,1,5,9,10,11,17,19,20,21,22,23,25,26,28,29,33,35,36,37,38,40,42,43,44],[2,3,5,7,9,12,27,28,29,33,35,37,38,44,45],[0,1,4,5,6,7,10,13,14,16,26,27,28,29,33,35,36,37,38,39,40,42],[0,1,2,4,5,7,8,12,14,15,17,18,22,23,30,33,35,36,37,39,41,42,43,44,45],[0,2,5,6,8,10,11,15,26,30,33,35,39,40,41,42,43,44],[0,1,2,4,5,6,7,9,11,12,14,15,16,18,27,30,33,35,36,38,40,41,43],[4,5,6,7,9,10,11,13,15,16,18,19,20,23,26,27,30,33,35,41,43,45],[2,4,5,7,9,10,12,14,16,19,20,23,28,30,33,35,36,39,40,41,42,43],[0,1,2,5,8,9,10,13,14,17,18,19,20,23,26,28,30,33,35,37,38,39,40,41,42,43,45],[2,3,5,7,8,10,11,12,15,16,18,19,20,23,27,28,30,33,35,36,37,38,40,43,44,45],[1,3,5,6,7,9,10,12,14,17,26,27,28,30,33,35,37,38,40,43,44],[5,6,8,9,10,13,14,18,29,30,33,35,36,37,40,43],[2,6,9,11,12,15,17,19,20,23,26,29,30,33,35,39,42,43,45],[0,2,3,5,6,8,10,13,16,19,20,23,27,29,30,33,35,36,38,39,41,42,44,45],[2,3,4,7,14,17,20,23,24,25,26,27,29,30,33,35,40,41,44],[0,3,4,7,8,9,11,12,13,15,16,19,20,23,28,29,30,33,35,36,45],[2,3,4,5,6,7,8,12,13,17,26,28,29,30,33,35,37,38,39,42],[2,3,6,7,8,9,10,11,17,18,27,28,29,30,33,35,36,37,38,39,42,43,44],[2,3,4,5,6,8,9,10,13,15,17,18,26,27,28,29,30,33,35,37,38,43,44,45],[5,6,7,8,9,10,13,17,31,33,35,36,40,42,43,44],[1,3,4,7,8,9,13,17,26,31,33,35,36,37,39,40,41,42,43,45],[0,1,3,6,7,8,9,10,13,14,15,16,18,19,20,23,27,31,33,35,36,38,39,40,42],[2,5,6,8,14,15,17,18,26,27,31,33,35,36,40,41,42,44,45],[0,3,4,5,6,8,9,10,13,16,18,19,20,23,28,31,33,35,37,38,39,41,42,43,44],[1,6,8,9,10,11,13,14,15,17,18,19,20,23,26,28,31,33,35,40,42,43,45],[1,3,8,10,16,19,20,23,27,28,31,33,35,37,40,42],[2,5,6,7,8,13,15,17,18,19,20,23,26,27,28,31,33,35,37,39,41,42,44,45],[2,5,6,10,12,15,16,19,20,23,29,31,33,35,39,41,42,43,45],[3,5,6,7,8,10,11,15,16,17,18,19,20,23,26,29,31,33,35,37,39,43,44],[1,21,22,23,24,27,29,31,33,35,38,42,43,44,45],[0,1,3,4,6,8,10,13,17,19,20,23,26,27,29,31,33,35,41,43],[0,1,2,9,12,13,14,18,28,29,31,33,35,36,37,38,40,42,44,45],[1,3,6,7,8,10,13,14,16,17,26,28,29,31,33,35,36,41],[0,3,4,5,8,10,11,12,13,17,18,19,20,23,27,28,29,31,33,35,36,37,39,42,45],[0,5,11,13,14,15,16,17,18,19,20,23,26,27,28,29,31,33,35,36,37,39,40,41,44],[1,4,5,6,7,9,12,13,14,16,17,19,20,23,30,31,33,35,37,40,43],[0,1,2,5,6,8,11,12,14,15,17,18,26,30,31,33,35,39,41,43,45],[0,3,7,8,11,12,13,14,16,17,18,19,20,23,27,30,31,33,35,37,38,39,40,42,44,45],[0,3,6,7,8,9,11,12,15,16,26,27,30,31,33,35,37,41,42,44],[0,1,3,4,7,12,14,15,16,19,20,23,28,30,31,33,35,38,41,43,44],[0,1,2,3,6,9,10,13,15,16,17,19,20,23,26,28,30,31,33,35,37,39,43,44,45],[3,4,5,7,13,16,17,19,20,23,27,28,30,31,33,35,39,40,42,45],[0,3,4,5,7,8,9,11,12,18,26,27,28,30,31,33,35,40,41,42],[0,1,2,6,9,11,12,13,14,16,29,30,31,33,35,40,41,43,44,45],[2,5,11,14,17,18,26,29,30,31,33,35,37,42,43,44],[0,4,5,6,9,12,16,17,27,29,30,31,33,35,38,39,40,42,43],[0,1,2,6,7,8,9,10,11,12,16,19,20,23,26,27,29,30,31,33,35,39,41,43,45],[2,4,6,7,9,11,13,18,28,29,30,31,33,35,37,38,44,45],[1,2,4,5,6,7,9,11,12,13,14,15,18,19,20,23,26,28,29,30,31,33,35,41,42,44],[1,3,4,5,8,9,11,13,16,17,27,28,29,30,31,33,35,37,39,40,42],[1,4,5,8,9,12,14,15,16,17,26,27,28,29,30,31,33,35,37,39,40,41,45],[1,2,4,5,6,7,9,11,14,15,16,18,32,33,35,38,39,40,43,44],[0,4,5,6,8,9,10,11,12,14,16,17,18,19,20,23,26,32,33,35,36,37,39,40,41,42,43,45],[0,2,6,7,10,11,12,13,16,19,20,23,27,32,33,35,37,39,42,43,44],[0,1,2,4,7,8,11,14,16,17,26,27,32,33,35,36,37,39,41,43,45],[0,2,4,5,12,13,14,15,16,17,28,32,33,35,37,38,39,40,44,45],[0,1,4,5,6,10,17,19,20,23,26,28,32,33,35,36,38,39,41,42],[1,2,3,4,6,8,9,12,13,16,18,19,20,21,22,23,24,25,27,28,32,33,35,39,40,41,42,44,45],[0,2,3,6,9,10,16,18,26,27,28,32,33,35,36,38,39],[1,2,3,4,5,9,12,13,15,16,18,19,20,23,29,32,33,35,36,37,39,40,41,42,43,44,45],[0,1,2,3,6,9,13,14,16,18,26,29,32,33,35,38,40,42,43],[6,7,12,15,16,17,27,29,32,33,35,36,38,39,44,45],[2,5,6,7,10,11,14,19,20,23,26,27,29,32,33,35,38,41],[0,1,2,10,12,13,15,16,17,18,28,29,32,33,35,36,39,40,41,42,43],[0,1,2,4,5,9,13,17,18,19,20,23,26,28,29,32,33,35,37,42,43,44,45],[0,5,7,9,11,12,13,14,16,17,27,28,29,32,33,35,36,37,38,39,40,41],[2,6,7,10,11,13,16,18,26,27,28,29,32,33,35,37,44,45],[1,6,7,9,15,16,18,19,20,23,30,32,33,35,36,37,38,40,42,43,45],[1,3,5,6,13,14,16,17,26,30,32,33,35,41,43],[0,5,7,8,12,14,15,16,27,30,32,33,35,36,42,43],[2,3,4,7,8,9,12,14,15,17,18,19,20,23,26,27,30,32,33,35,40,41,43,45],[0,4,5,6,7,12,14,15,17,18,28,30,32,33,35,38,39,40,42,44],[3,4,6,8,12,13,15,19,20,23,26,28,30,32,33,35,36,37,38,39,40,41,44,45],[1,3,6,11,12,15,16,17,27,28,30,32,33,35,37,39,40,41,42,44,45],[1,2,4,5,8,9,10,11,12,13,14,15,17,19,20,23,26,27,28,30,32,33,35,36,37,38,39,40,44],[0,1,3,4,5,7,8,10,11,14,17,18,29,30,32,33,35,36,37,39,41,43],[0,2,5,8,12,13,26,29,30,32,33,35,38,40,43,45],[0,2,4,13,14,15,17,18,27,29,30,32,33,35,36,38,39,40,45],[1,2,3,4,8,13,18,19,20,23,26,27,29,30,32,33,35,38,41],[1,4,5,6,7,9,10,14,28,29,30,32,33,35,41,43,45],[0,2,3,5,7,9,10,12,13,14,15,16,26,28,29,30,32,33,35,36,37,39,43],[2,4,5,6,10,17,18,19,20,23,27,28,29,30,32,33,35,37,38,41],[0,7,8,11,14,16,17,19,20,23,26,27,28,29,30,32,33,35,36,37,39,45],[1,3,6,9,13,17,18,19,20,23,31,32,33,35,38,40,41,42,43],[1,3,6,9,10,14,26,31,32,33,35,37,39,40,41,43,44,45],[1,6,7,8,9,10,11,12,14,15,16,19,20,23,27,31,32,33,35,40,41],[0,1,2,4,6,7,8,9,11,12,13,14,15,16,26,27,31,32,33,35,39,40,41,42,44,45],[0,1,5,7,10,11,12,14,17,19,20,23,28,31,32,33,35,37,40,42],[1,5,6,9,10,12,26,28,31,32,33,35,39,44,45],[0,1,4,5,8,12,13,15,18,19,20,23,27,28,31,32,33,35,37,38,41,43],[0,1,2,5,8,9,13,14,26,27,28,31,32,33,35,37,39,40,41,42,43,44,45],[5,8,9,11,12,16,18,19,20,23,29,31,32,33,35,36,39,42,43,45],[1,2,4,8,10,12,13,14,15,18,26,29,31,32,33,35,36,37,38,39,42,43,44],[0,2,5,6,7,8,9,10,11,12,14,15,27,29,31,32,33,35,36,38,39,41,43,45],[0,3,9,11,12,13,18,19,20,23,26,27,29,31,32,33,35,36,38,39,41,43,44],[0,1,4,5,6,8,11,12,13,16,18,19,20,23,28,29,31,32,33,35,36,37,38,39,41,42,43,44,45],[0,1,3,4,5,6,11,13,15,16,17,18,26,28,29,31,32,33,35,36,38,39,40,41,42,43],[1,5,7,8,9,11,13,18,27,28,29,31,32,33,35,36,37,39,40,41,43,44,45],[0,1,2,3,6,7,8,9,10,11,13,17,18,19,20,23,26,27,28,29,31,32,33,35,36,37,38,39,41,43],[0,2,4,11,13,14,15,16,30,31,32,33,35,36,37,38,41,42,44,45],[6,10,12,19,20,23,26,30,31,32,33,35,36,39,40,41,44],[0,2,6,7,8,9,11,14,15,16,27,30,31,32,33,35,36,37,41,42,43,44],[0,3,4,5,6,8,9,12,14,15,16,17,26,27,30,31,32,33,35,36,37,39,40,41,43,44,45],[2,5,6,9,12,13,14,17,18,19,20,23,28,30,31,32,33,35,39,42,43,45],[2,3,6,8,10,12,15,16,17,18,26,28,30,31,32,33,35,37,43],[2,3,5,6,8,10,12,13,15,16,27,28,30,31,32,33,35,38,39,40,41,42],[1,4,6,13,17,18,26,27,28,30,31,32,33,35,40,41,45],[1,2,6,12,19,23,24,25,29,30,31,32,33,35,36,42,44],[1,2,4,7,8,9,10,12,17,19,20,23,26,29,30,31,32,33,35,36,37,38,40,42,44,45],[2,5,6,7,13,14,16,17,27,29,30,31,32,33,35,36,38,41,42,44,45],[0,2,3,5,6,9,10,11,13,16,17,18,26,27,29,30,31,32,33,35,36,38,40,41,42,44],[1,4,5,10,11,13,14,16,18,19,20,23,28,29,30,31,32,33,35,37,38,39,41,42,44],[0,1,2,3,4,6,7,8,9,11,14,16,17,18,26,28,29,30,31,32,33,35,38,39,41,42,44,45],[0,1,3,6,7,8,10,12,14,18,27,28,29,30,31,32,33,35,37,39,40,41,42,44,45],[26,27,28,29,30,31,32,33,35,37,38,39,40,41,42,44],[0,6,7,8,9,12,14,16,34,35,36,37,38,43],[0,1,7,8,10,11,12,13,26,34,35,38,40,42,43],[1,3,4,5,10,11,13,14,15,16,17,19,20,23,27,34,35,36,39,40,41,45],[0,2,3,5,8,10,13,14,26,27,34,35,38,39,41,42,45],[1,2,3,5,6,7,8,10,11,13,14,15,17,18,28,34,35,39,40,41,42,43,44],[0,2,3,5,7,8,10,11,13,14,16,17,26,28,34,35,36,37,38,39,40,41,43,44],[0,2,3,6,7,11,12,13,14,15,27,28,34,35,37,38,40,41,42,44,45],[0,1,3,4,6,9,10,11,14,16,17,18,26,27,28,34,35,36,37,38,40,41,44,45],[2,5,6,7,8,11,12,13,14,15,16,19,20,23,29,34,35,36,40,43,44],[4,6,7,9,10,13,15,16,26,29,34,35,37,39,43,44],[1,4,6,8,11,13,15,17,18,19,20,23,27,29,34,35,36,37,38,39,43,44,45],[0,1,4,6,10,12,14,16,18,19,20,23,26,27,29,34,35,37,40,43,44,45],[0,4,5,6,8,11,13,15,16,19,20,23,28,29,34,35,37,38,39,41,42,44],[2,7,9,11,14,15,18,19,20,23,26,28,29,34,35,36,41,42,44],[0,1,2,3,4,5,8,12,13,14,18,19,20,23,27,28,29,34,35,42,44,45],[0,1,2,3,4,9,11,12,14,16,17,19,20,23,26,27,28,29,34,35,36,39,42,44,45],[0,2,8,11,17,19,20,23,30,34,35,36,37,38,39,41,44,45],[3,5,8,9,11,14,26,30,34,35,38,39,41,42,45],[1,2,3,6,8,9,11,12,13,14,16,17,27,30,34,35,36,40,42,43,44,45],[1,2,4,5,6,7,9,10,12,13,14,16,17,18,26,27,30,34,35,38,40,43,45],[1,3,4,6,7,11,12,13,15,16,18,19,20,23,28,30,34,35,36,39,40,42,44,45],[1,2,4,8,15,16,17,19,20,23,26,28,30,34,35,37,38,39,45],[0,3,6,7,10,11,13,19,20,23,27,28,30,34,35,36,37,38,40,43,44,45],[4,6,7,8,10,13,17,18,26,27,28,30,34,35,37,38,42,43,45],[0,4,6,7,10,11,12,14,15,19,20,23,29,30,34,35,37,41,45],[1,3,8,10,11,12,16,17,18,19,20,23,26,29,30,34,35,36,39,41,44,45],[0,1,2,4,5,6,7,8,9,10,11,12,14,15,27,29,30,34,35,38,39,40,41,42,45],[0,3,4,7,9,11,12,15,18,19,20,23,26,27,29,30,34,35,36,40,41,42,44,45],[2,4,7,9,10,14,15,17,28,29,30,34,35,38,40,42,43,44,45],[1,2,3,6,9,14,15,16,17,19,20,23,26,28,29,30,34,35,36,37,39,42,43,45],[1,3,5,7,10,12,16,17,18,19,20,23,27,28,29,30,34,35,37,39,40,41,43,44,45],[0,2,5,8,9,11,13,14,16,18,26,27,28,29,30,34,35,36,37,41,43,45],[0,1,2,5,8,9,15,18,31,34,35,36,37,39,40],[1,8,9,10,18,19,20,23,26,31,34,35,36,41,42],[0,1,2,4,5,6,7,9,11,12,13,14,15,19,20,23,27,31,34,35,36,37,38,40,41,45],[0,1,2,4,5,7,8,11,12,13,14,15,17,19,20,23,26,27,31,34,35,36,37,39,42,45],[1,4,5,6,7,10,11,13,18,19,20,23,28,31,34,35,42,44,45],[1,2,4,6,7,8,9,10,12,13,14,15,18,19,20,23,26,28,31,34,35,37,38,39,41,44,45],[1,3,4,7,12,15,16,17,27,28,31,34,35,38,39,40,42,44],[0,1,3,4,5,6,8,12,15,16,18,19,20,23,26,27,28,31,34,35,38,40,41,44],[5,6,8,9,10,11,13,15,18,19,20,23,29,31,34,35,36,37,38,40,42,44],[0,1,4,5,6,10,12,14,15,16,17,19,20,23,26,29,31,34,35,36,38,41,42,44],[0,2,3,6,8,9,10,11,12,13,14,15,18,19,20,23,27,29,31,34,35,36,37,39,40,42,43,44,45],[0,1,3,4,5,6,7,8,12,14,17,19,20,23,26,27,29,31,34,35,36,37,38,39,41,42,43,44,45],[0,1,2,3,4,7,9,10,11,13,14,16,28,29,31,34,35,38,39,43,44,45],[0,2,3,5,7,8,11,12,13,15,16,17,18,19,20,23,26,28,29,31,34,35,37,39,41,43,44,45],[1,3,4,6,9,10,11,14,16,17,27,28,29,31,34,35,40,41,44],[0,2,3,4,5,7,12,14,15,16,26,27,28,29,31,34,35,40,44],[4,6,10,14,15,16,18,19,20,23,30,31,34,35,36,37,39,41,42,44,45],[1,3,4,5,9,10,12,13,15,18,26,30,31,34,35,36,45],[4,5,6,8,9,10,11,12,13,14,15,16,17,19,20,23,27,30,31,34,35,36,37,38,44,45],[0,1,2,3,5,6,7,10,11,15,18,19,20,23,26,27,30,31,34,35,36,37,39,41,42,45],[0,2,4,7,8,10,12,13,16,17,28,30,31,34,35,36,39,40,41,44],[1,2,3,6,8,13,16,17,18,19,20,23,26,28,30,31,34,35,36,37,38,42],[0,2,4,6,7,8,12,13,15,19,20,23,27,28,30,31,34,35,36,38,41,42,44],[0,1,3,4,5,6,7,9,10,11,14,15,16,18,26,27,28,30,31,34,35,36,38,39,40],[1,2,4,5,6,7,8,11,12,13,16,19,20,23,29,30,31,34,35,38,39,40,41,45],[1,6,8,11,12,13,14,15,17,19,20,23,26,29,30,31,34,35,37,38,39,40,44,45],[0,1,6,8,10,12,15,16,17,18,27,29,30,31,34,35,40,41,42,43,45],[1,3,5,6,8,14,15,17,18,19,20,23,26,27,29,30,31,34,35,38,40,42,43,44,45],[0,3,8,10,11,12,13,15,16,18,28,29,30,31,34,35,37,38,39,41,42,43,44],[3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,23,26,28,29,30,31,34,35,39,40,42,43],[2,3,4,7,8,9,10,16,17,19,20,23,27,28,29,30,31,34,35,37,40,44],[0,1,2,3,4,7,9,10,11,12,15,17,26,27,28,29,30,31,34,35,37,41],[0,2,3,4,5,7,8,10,32,34,35,36,37,39,42],[0,2,5,7,9,10,11,13,15,16,26,32,34,35,38,39,40,41,42],[0,2,3,4,5,6,7,8,10,12,14,18,27,32,34,35,36,38,39,40,41,43,44,45],[3,8,14,15,17,19,20,23,26,27,32,34,35,38,39,43,44,45],[1,3,6,7,8,9,10,13,14,16,17,19,20,23,28,32,34,35,36,38,39,41,43,44],[0,1,7,8,10,12,13,16,17,18,26,28,32,34,35,37,38,39,43,44],[1,5,9,12,14,19,20,23,27,28,32,34,35,36,37,39,41,42,45],[1,2,5,6,7,9,11,12,14,19,20,23,26,27,28,32,34,35,37,38,39,42,45],[1,2,3,4,5,6,9,11,15,17,18,19,20,23,29,32,34,35,36,39,40,42],[3,4,7,8,13,14,17,19,20,23,26,29,32,34,35,37,38,41],[0,1,4,6,7,11,14,15,16,17,27,29,32,34,35,36,37,38,39,44,45],[3,4,6,8,9,11,14,16,17,18,26,27,29,32,34,35,37,38,40,41,42,44,45],[0,1,3,4,7,9,11,12,13,14,16,19,20,23,28,29,32,34,35,36,37,38,39,40,41],[2,3,4,6,10,13,14,17,18,19,20,23,26,28,29,32,34,35,38,40,42],[1,4,5,6,7,9,10,13,16,17,27,28,29,32,34,35,36,39,40,42,44,45],[0,1,2,4,5,7,8,9,10,11,12,13,18,19,20,23,26,27,28,29,32,34,35,38,40,41,44,45],[3,4,5,6,8,11,13,15,16,19,20,23,30,32,34,35,36,37,40,41,44],[0,1,4,5,8,11,12,14,17,19,20,23,26,30,32,34,35,38,40],[3,5,8,11,14,15,16,19,20,23,27,30,32,34,35,36,38,43],[1,2,4,8,9,11,13,14,15,18,26,27,30,32,34,35,38,41,43,44],[0,1,3,4,5,6,9,11,14,16,18,19,20,23,28,30,32,34,35,38,39,40,42,43,44],[0,7,9,10,11,13,14,15,16,17,26,28,30,32,34,35,36,37,38,39,41,42,43],[0,1,2,4,9,10,12,15,16,18,27,28,30,32,34,35,37,39,40,42],[0,1,2,5,9,11,15,16,18,19,20,23,26,27,28,30,32,34,35,36,37,38,39,41,42,44],[1,2,4,5,7,8,10,11,14,17,29,30,32,34,35,37,39,40,41,44],[0,1,4,5,7,9,12,13,16,17,18,19,20,23,26,29,30,32,34,35,36,38,40,42],[0,1,4,6,7,9,10,11,13,16,17,18,27,29,30,32,34,35,38,39,41],[2,3,5,6,7,11,13,14,16,17,26,27,29,30,32,34,35,36,38,42,44],[0,1,2,3,5,8,10,12,13,15,16,18,28,29,30,32,34,35,36,38,40,42],[0,1,10,11,14,15,16,19,20,23,26,28,29,30,32,34,35,37,38,39,41,44],[1,3,7,11,12,13,14,17,27,28,29,30,32,34,35,36,37,40,41,42,44],[0,1,4,7,10,12,14,17,18,19,20,23,26,27,28,29,30,32,34,35,37,38,39],[0,2,4,5,6,7,8,10,12,13,15,16,31,32,34,35,37,38,39,40,45],[1,5,7,8,9,10,13,16,18,19,20,23,26,31,32,34,35,45],[1,2,3,4,7,9,10,13,14,17,27,31,32,34,35,37,39,40,41,42,44],[2,4,5,10,11,12,14,15,16,17,18,19,20,23,26,27,31,32,34,35,37,41,42,44],[3,4,11,12,13,15,17,18,28,31,32,34,35,38,39,40,42,43,44],[1,5,12,14,15,16,26,28,31,32,34,35,37,38,40,42,43,44],[0,7,9,10,13,16,17,18,27,28,31,32,34,35,39,43,45],[0,2,3,5,7,11,12,15,26,27,28,31,32,34,35,38,43,45],[3,4,8,11,12,14,17,19,20,23,29,31,32,34,35,37,38,40,42,45],[0,1,3,5,7,9,12,15,16,17,18,19,20,23,26,29,31,32,34,35,45],[4,5,6,7,10,11,14,15,17,19,20,23,27,29,31,32,34,35,37,40,43,44],[0,2,3,5,6,7,9,11,14,17,18,19,20,23,26,27,29,31,32,34,35,37,42,43,44],[0,4,5,6,8,12,16,17,18,19,20,23,28,29,31,32,34,35,38,40],[0,1,2,3,4,5,8,10,11,12,14,15,16,18,26,28,29,31,32,34,35,37,38,40,42],[5,7,9,10,12,13,14,15,16,18,27,28,29,31,32,34,35,41,42,43,44,45],[0,1,3,5,6,9,10,12,13,14,15,16,26,27,28,29,31,32,34,35,38,41,43,44,45],[0,2,3,4,11,12,13,16,17,18,30,31,32,34,35,37,38,39,40,41,43,44,45],[0,1,2,5,8,9,10,11,16,17,18,19,20,23,26,30,31,32,34,35,40,41,43,45],[1,2,6,8,9,10,11,14,15,19,20,23,27,30,31,32,34,35,37,39,40,43,45],[0,3,4,5,6,7,8,9,11,15,16,17,26,27,30,31,32,34,35,37,40,43,44,45],[0,3,6,7,8,9,10,12,15,16,17,19,20,23,28,30,31,32,34,35,36,38,40,41,42,44],[1,2,3,4,6,7,8,9,10,12,14,15,17,19,20,23,26,28,30,31,32,34,35,36,37,38,39,41,42],[0,1,2,4,6,7,9,10,11,12,13,16,27,28,30,31,32,34,35,36,41,42],[1,2,3,5,6,7,9,10,13,18,26,27,28,30,31,32,34,35,36,38,39,40,41,42,44],[0,1,4,6,10,11,13,14,16,18,21,22,29,30,31,32,34,35,36,38,39,41,42,43,44,45],[1,3,5,7,8,11,14,15,17,19,20,23,26,29,30,31,32,34,35,36,37,39,41,43,45],[3,4,5,6,7,9,14,15,16,17,18,19,20,23,27,29,30,31,32,34,35,36,39,41,42,45],[0,1,2,3,8,9,11,12,14,15,16,17,26,27,29,30,31,32,34,35,36,39,41,44,45],[0,1,2,6,8,11,12,16,17,19,20,23,28,29,30,31,32,34,35,37,38,41,43],[5,6,10,12,15,17,18,19,20,23,26,28,29,30,31,32,34,35,38,40,41,42,43,44],[0,2,3,4,5,6,8,11,14,15,17,19,20,23,27,28,29,30,31,32,34,35,37,40,44],[26,27,28,29,30,31,32,34,35,37,38,42],[0,1,3,4,6,7,8,10,12,14,15,16,33,34,35,36,37,40,41,44],[0,1,2,3,4,6,10,16,18,19,20,23,26,33,34,35,40,41,42,44],[3,5,11,13,14,15,16,18,27,33,34,35,36,38,39,41,43],[0,2,3,6,7,10,11,13,18,19,20,23,26,27,33,34,35,39,41,42,43],[2,6,9,11,18,19,20,23,28,33,34,35,37,38,39,40,45],[0,1,2,3,5,6,7,9,11,13,14,15,16,19,20,23,26,28,33,34,35,36,39,42,45],[0,1,3,5,9,11,12,13,18,19,20,23,27,28,33,34,35,40,41,43,44,45],[0,1,2,3,4,6,7,8,9,11,13,14,15,16,17,18,26,27,28,33,34,35,36,41,42,43,44,45],[1,3,4,6,7,12,13,15,17,18,29,33,34,35,38,41,42,43],[1,2,3,5,8,9,11,14,26,29,33,34,35,36,37,38,39,41,42,43],[2,3,4,5,7,11,12,13,14,17,27,29,33,34,35,37,39,40,42,43,44],[0,2,3,7,9,10,11,17,26,27,29,33,34,35,36,37,38,40,42,43,44],[0,2,4,6,7,10,12,13,16,19,20,23,28,29,33,34,35,36,39,42,45],[0,1,3,4,5,8,10,11,13,14,15,16,26,28,29,33,34,35,37,38,40,42,45],[3,7,8,9,10,11,12,16,18,19,20,23,27,28,29,33,34,35,36,37,38,42,44,45],[0,3,4,8,9,10,13,14,16,17,18,19,20,23,26,27,28,29,33,34,35,37,38,39,40,42,44,45],[0,3,6,12,16,18,19,20,22,23,25,30,33,34,35,36,39,41,43,45],[1,2,3,4,7,8,10,11,14,15,17,18,21,23,25,26,30,33,34,35,37,39,40,41,42,43,44,45],[1,2,5,7,8,9,10,11,12,15,19,21,22,23,24,25,27,30,33,34,35,36,37,38,40,41,42,44],[0,6,7,8,11,12,14,17,18,19,20,23,26,27,30,33,34,35,37,41],[1,4,7,9,10,11,12,13,17,18,25,28,30,33,34,35,36,38,39,43],[0,2,3,4,6,7,8,10,12,13,14,16,26,28,30,33,34,35,37,39,42,43,44],[0,1,4,5,7,8,9,11,17,18,27,28,30,33,34,35,36,37,41,42,44,45],[0,2,4,5,6,11,15,17,26,27,28,30,33,34,35,37,41,45],[0,5,6,7,10,12,14,15,21,23,25,29,30,33,34,35,36,38,41,42,44,45],[2,3,4,6,7,9,10,14,16,17,26,29,30,33,34,35,37,38,39,40,41,42,45],[0,1,3,4,5,6,9,10,12,14,15,16,17,18,27,29,30,33,34,35,36,37,39,40],[1,2,5,7,8,9,15,18,26,27,29,30,33,34,35,37,38,44],[3,5,8,9,13,18,28,29,30,33,34,35,36,42,43],[0,1,4,7,8,10,13,14,15,16,26,28,29,30,33,34,35,37,38,39,42,43,44],[4,5,7,8,9,12,16,17,27,28,29,30,33,34,35,36,37,38,39,43,44,45],[0,3,5,6,8,12,14,15,16,17,18,19,20,23,26,27,28,29,30,33,34,35,37,38,43,45],[0,2,3,4,6,13,15,16,17,18,19,22,31,33,34,35,37,44,45],[1,5,8,10,11,12,16,17,18,19,20,22,24,25,26,31,33,34,35,39,41,42,44,45],[0,3,4,6,7,10,12,15,16,17,18,22,27,31,33,34,35,37,38,39,45],[0,1,2,4,6,9,12,13,14,15,16,17,18,19,20,23,26,27,31,33,34,35,37,41,42,45],[2,3,4,8,10,11,12,13,14,16,18,20,24,25,28,31,33,34,35,36,37,39,45],[1,2,3,6,8,9,11,17,26,28,31,33,34,35,36,38,40,41,42,45],[0,5,6,7,9,10,11,16,27,28,31,33,34,35,36,37,38,40,41,44,45],[3,5,6,7,9,15,17,19,20,23,26,27,28,31,33,34,35,36,37,38,39,42,44,45],[1,2,5,7,13,14,15,16,17,18,19,21,22,23,24,25,29,31,33,34,35,36,37,38,39,43,45],[2,3,4,5,8,10,11,13,14,18,26,29,31,33,34,35,36,38,39,41,43,45],[0,4,6,7,9,10,11,13,14,15,16,17,27,29,31,33,34,35,36,37,41,44,45],[0,5,7,8,9,11,13,14,15,18,26,27,29,31,33,34,35,36,37,38,44,45],[0,1,3,4,8,11,17,19,20,23,28,29,31,33,34,35,37,38,45],[0,4,8,11,13,15,16,19,20,23,26,28,29,31,33,34,35,40,41,45],[0,3,4,6,10,12,13,15,18,19,20,23,27,28,29,31,33,34,35,37,39,40,43,44,45],[3,4,6,7,10,13,14,17,18,19,20,23,26,27,28,29,31,33,34,35,37,39,41,43,44,45],[2,3,6,8,9,11,13,14,15,16,17,19,20,21,22,23,30,31,33,34,35,42],[0,4,6,7,8,9,10,12,13,15,16,19,20,23,26,30,31,33,34,35,37,39,40,41,44],[3,4,5,10,11,12,15,17,18,19,20,23,27,30,31,33,34,35,38,39,44,45],[1,3,4,6,8,9,12,13,14,18,26,27,30,31,33,34,35,40,41,42,45],[0,1,5,6,7,12,13,14,15,18,28,30,31,33,34,35,42],[0,1,3,7,9,11,14,15,18,19,20,23,26,28,30,31,33,34,35,37,38,39,41,44],[0,1,2,5,7,8,9,10,14,15,18,19,20,23,27,28,30,31,33,34,35,38,39,40,41,44,45],[1,10,14,15,16,19,20,23,26,27,28,30,31,33,34,35,38,40,42,45],[0,2,7,9,10,11,17,18,29,30,31,33,34,35,37,38,40,42,43,44],[2,4,5,6,8,9,11,12,13,15,26,29,30,31,33,34,35,38,41,42,43],[0,9,10,13,15,16,27,29,30,31,33,34,35,37,39,40,41,45],[0,1,2,4,5,6,7,8,11,13,14,15,16,17,18,19,20,23,26,27,29,30,31,33,34,35,37,38,39,44,45],[2,6,8,12,13,14,16,17,18,19,20,23,28,29,30,31,33,34,35,37,38,40,42],[0,2,3,4,6,10,13,19,20,23,26,28,29,30,31,33,34,35,40,41,42,44],[3,4,6,7,10,14,18,19,20,23,27,28,29,30,31,33,34,35,37,39,43,44,45],[26,27,28,29,30,31,33,34,35,37,39,41,43,45],[1,2,4,5,6,7,8,10,11,12,13,14,15,18,19,20,21,22,25,32,33,34,35,37,39,40,43,44,45],[2,4,5,6,7,8,9,11,13,15,16,17,19,20,22,23,24,26,32,33,34,35,36,38,39,40,41,43,44,45],[1,3,5,6,7,11,12,13,16,17,24,25,27,32,33,34,35,38,39,42,44,45],[0,1,5,7,11,13,14,16,17,18,26,27,32,33,34,35,36,38,39,41,42,44,45],[0,2,3,5,6,8,9,10,12,14,15,16,18,20,21,23,24,28,32,33,34,35,37,38,39,41],[1,2,3,5,6,8,11,12,16,17,18,19,20,23,26,28,32,33,34,35,36,38,39,40],[1,5,6,7,8,9,12,14,17,18,27,28,32,33,34,35,39,42,43],[0,1,3,4,9,12,14,16,17,19,20,23,26,27,28,32,33,34,35,36,38,39,40,41,42,43],[0,6,7,10,18,20,24,25,29,32,33,34,35,36,39,42,44,45],[0,1,3,4,9,11,14,16,18,19,20,23,26,29,32,33,34,35,37,38,41,44,45],[1,2,3,4,5,7,8,10,13,15,16,17,27,29,32,33,34,35,36,37,38,39,40,41,44,45],[0,1,2,3,5,6,7,10,12,13,14,16,17,19,20,23,26,27,29,32,33,34,35,37,38,40,42,44,45],[2,5,6,16,17,18,28,29,32,33,34,35,36,38,39,40,41,42,44],[0,2,4,6,8,9,11,13,26,28,29,32,33,34,35,37,38,44],[4,6,8,9,10,15,16,19,20,23,27,28,29,32,33,34,35,36,37,39,40,41,44],[0,1,2,3,6,8,10,11,12,13,26,27,28,29,32,33,34,35,37,38,42,44],[0,6,8,12,14,15,17,18,20,23,24,25,30,32,33,34,35,40,42,43,45],[2,6,7,11,13,14,16,17,26,30,32,33,34,35,36,37,38,41,42,43,44,45],[2,3,6,8,11,13,14,15,18,19,20,23,27,30,32,33,34,35,37,38,42],[0,1,2,6,7,10,11,14,18,19,20,23,26,27,30,32,33,34,35,36,37,38,40,41,42,44],[1,2,5,9,12,13,18,19,20,23,28,30,32,33,34,35,36,38,39,41,42],[1,2,5,6,8,9,13,14,17,18,26,28,30,32,33,34,35,37,38,39,42,44],[1,3,5,8,10,11,12,13,14,16,27,28,30,32,33,34,35,36,37,39,42,43,45],[1,11,13,14,26,27,28,30,32,33,34,35,37,38,39,41,42,43,44,45],[0,1,3,5,6,7,8,10,11,15,16,18,29,30,32,33,34,35,39,40,45],[4,5,9,10,14,15,17,18,26,29,30,32,33,34,35,36,37,38,41,42,44,45],[0,4,9,10,11,13,14,17,27,29,30,32,33,34,35,37,38,39,41],[26,27,29,30,32,33,34,35,36,37,38,40,42,44],[2,5,7,8,17,19,20,23,28,29,30,32,33,34,35,36,38,41,44],[4,5,6,7,10,11,12,14,16,19,20,23,26,28,29,30,32,33,34,35,37,38,39,42],[0,1,4,6,7,8,9,10,12,13,15,16,18,19,20,23,27,28,29,30,32,33,34,35,36,37,41,44,45],[26,27,28,29,30,32,33,34,35,37,38,39,42,45],[1,3,6,8,10,11,13,14,15,18,20,23,24,31,32,33,34,35,37,41,42,44,45],[2,4,5,6,13,15,16,17,26,31,32,33,34,35,38,39,41,42,44,45],[2,3,4,7,13,15,27,31,32,33,34,35,37,38,41,44,45],[1,3,4,5,6,7,8,12,13,14,15,17,18,19,20,23,26,27,31,32,33,34,35,37,38,39,41,44,45],[0,2,3,4,6,8,14,16,17,19,20,23,28,31,32,33,34,35,37,40,41,42,43,45],[0,1,4,6,7,8,9,10,11,19,20,23,26,28,31,32,33,34,35,39,41,42,43,45],[2,5,6,7,8,9,11,12,16,17,27,28,31,32,33,34,35,37,38,43,45],[26,27,28,31,32,33,34,35,37,39,40,43,45],[3,8,9,10,13,14,18,19,20,23,29,31,32,33,34,35,36,37,39,41,42,43,44,45],[0,4,7,9,10,11,12,15,17,18,26,29,31,32,33,34,35,36,38,39,41,43,44,45],[1,2,3,4,5,7,8,9,10,11,12,13,15,16,18,19,20,23,27,29,31,32,33,34,35,36,37,38,39,44,45],[26,27,29,31,32,33,34,35,36,37,38,39,42,44,45],[0,1,3,6,7,8,9,12,13,15,28,29,31,32,33,34,35,36,37,39,40,41,42,43,44,45],[26,28,29,31,32,33,34,35,36,39,41,43,44,45],[0,2,7,9,11,12,14,15,16,19,20,23,27,28,29,31,32,33,34,35,36,37,38,39,41,44,45],[26,27,28,29,31,32,33,34,35,36,37,39,40,41,42,44,45],[3,7,9,11,12,13,14,15,18,19,20,23,30,31,32,33,34,35,40,41,42,43,45],[0,1,2,4,6,8,10,14,16,18,26,30,31,32,33,34,35,37,38,39,41,42,43,44,45],[1,4,6,9,11,13,14,15,17,19,20,23,27,30,31,32,33,34,35,38,40,41,42,43],[26,27,30,31,32,33,34,35,38,39,41,42,43,44],[0,1,2,4,5,6,7,8,10,11,13,14,16,17,28,30,31,32,33,34,35,36,39,41,42,45],[26,28,30,31,32,33,34,35,36,37,41,42,44,45],[27,28,30,31,32,33,34,35,36,38,39,40,42],[26,27,28,30,31,32,33,34,35,36,40,42,44],[0,5,6,7,8,12,14,16,18,19,20,23,29,30,31,32,33,34,35,37,41,42,45],[26,29,30,31,32,33,34,35,38,40,41,44,45],[27,29,30,31,32,33,34,35,37,38,42,43],[26,27,29,30,31,32,33,34,35,37,38,40,43,44],[28,29,30,31,32,33,34,35,36,37,39,40,41,42,44,45],[26,28,29,30,31,32,33,34,35,36,39,40,41,45],[27,28,29,30,31,32,33,34,35,36,37,38,39,41,42,43,44],[26,27,28,29,30,31,32,33,34,35,36,37,39,41,43]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[95,197,281,549,921],"A_d":8863902,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,2],[2,1],[3,3],[4,1],[8,2],[11,2],[12,3],[13,2],[14,2],[16,3],[17,3],[18,3],[19,1],[20,1],[21,2],[22,2],[23,1],[24,1],[25,3]],"CZ":[[0,1],[0,3],[0,4],[0,5],[0,6],[0,7],[0,10],[0,11],[0,12],[0,13],[0,14],[0,15],[0,17],[0,19],[0,20],[0,22],[0,24],[0,25],[0,28],[0,29],[0,30],[0,32],[0,33],[0,36],[0,38],[0,39],[0,40],[0,41],[0,42],[1,4],[1,5],[1,8],[1,9],[1,10],[1,13],[1,15],[1,17],[1,18],[1,21],[1,25],[1,26],[1,27],[1,28],[1,30],[1,34],[1,35],[1,36],[1,37],[1,38],[1,42],[1,43],[1,45],[2,4],[2,9],[2,14],[2,15],[2,16],[2,18],[2,19],[2,20],[2,21],[2,24],[2,27],[2,29],[2,31],[2,34],[2,35],[2,36],[2,37],[2,38],[2,42],[2,44],[2,45],[3,4],[3,5],[3,8],[3,9],[3,12],[3,14],[3,18],[3,19],[3,20],[3,25],[3,26],[3,29],[3,30],[3,31],[3,32],[3,37],[3,38],[3,39],[3,40],[3,42],[4,5],[4,6],[4,8],[4,13],[4,14],[4,15],[4,16],[4,26],[4,29],[4,32],[4,34],[4,35],[4,36],[4,39],[4,40],[4,41],[4,44],[4,45],[5,7],[5,9],[5,11],[5,13],[5,14],[5,17],[5,19],[5,20],[5,21],[5,24],[5,26],[5,28],[5,29],[5,30],[5,32],[5,33],[5,34],[5,35],[5,36],[5,39],[5,40],[5,41],[5,43],[6,8],[6,10],[6,13],[6,14],[6,16],[6,17],[6,20],[6,21],[6,22],[6,25],[6,26],[6,30],[6,31],[6,33],[6,35],[6,36],[6,42],[6,45],[7,8],[7,10],[7,11],[7,14],[7,17],[7,19],[7,20],[7,22],[7,23],[7,25],[7,26],[7,28],[7,29],[7,30],[7,32],[7,33],[7,35],[7,37],[7,41],[7,43],[8,9],[8,10],[8,11],[8,12],[8,17],[8,18],[8,22],[8,24],[8,25],[8,27],[8,28],[8,29],[8,31],[8,34],[8,36],[8,37],[8,38],[8,39],[8,40],[8,42],[8,44],[9,13],[9,14],[9,15],[9,16],[9,17],[9,20],[9,21],[9,22],[9,23],[9,25],[9,27],[9,30],[9,31],[9,33],[9,40],[9,41],[9,42],[10,12],[10,13],[10,15],[10,16],[10,17],[10,18],[10,19],[10,24],[10,27],[10,28],[10,29],[10,33],[10,34],[10,36],[10,37],[10,41],[10,44],[11,12],[11,13],[11,14],[11,16],[11,22],[11,24],[11,25],[11,26],[11,27],[11,28],[11,33],[11,34],[11,35],[11,36],[11,38],[11,43],[12,13],[12,14],[12,19],[12,21],[12,27],[12,30],[12,33],[12,34],[12,35],[12,36],[12,39],[12,40],[12,43],[13,16],[13,20],[13,22],[13,23],[13,24],[13,25],[13,26],[13,27],[13,28],[13,29],[13,30],[13,35],[13,36],[13,37],[13,40],[13,41],[13,43],[13,44],[13,45],[14,15],[14,18],[14,19],[14,20],[14,22],[14,24],[14,27],[14,28],[14,30],[14,31],[14,32],[14,34],[14,35],[14,36],[14,37],[14,41],[14,42],[14,44],[14,45],[15,16],[15,18],[15,20],[15,25],[15,28],[15,30],[15,31],[15,33],[15,36],[15,38],[15,39],[15,44],[15,45],[16,17],[16,19],[16,20],[16,21],[16,22],[16,23],[16,25],[16,28],[16,29],[16,32],[16,33],[16,36],[16,37],[16,38],[16,40],[16,41],[16,43],[16,44],[16,45],[17,18],[17,19],[17,21],[17,23],[17,26],[17,27],[17,28],[17,32],[17,33],[17,35],[17,39],[17,41],[17,43],[18,20],[18,22],[18,25],[18,26],[18,28],[18,32],[18,33],[18,37],[18,42],[18,43],[18,44],[18,45],[19,20],[19,23],[19,24],[19,26],[19,27],[19,29],[19,30],[19,33],[19,37],[19,42],[20,23],[20,24],[20,26],[20,32],[20,33],[20,37],[20,39],[20,43],[20,44],[21,22],[21,30],[21,32],[21,33],[21,34],[21,35],[21,37],[21,39],[21,40],[21,42],[22,23],[22,24],[22,30],[22,31],[22,36],[22,37],[22,38],[22,39],[22,40],[22,42],[22,43],[23,24],[23,25],[23,27],[23,28],[23,29],[23,32],[23,33],[23,36],[23,38],[23,39],[23,40],[23,43],[23,45],[24,25],[24,26],[24,28],[24,30],[24,33],[24,35],[24,36],[24,38],[24,40],[24,41],[24,42],[24,44],[25,26],[25,27],[25,28],[25,30],[25,31],[25,32],[25,33],[25,34],[25,38],[25,39],[25,40]]},"rotation_powers":null},"metrics":{"gamma":2.2817893126278106,"gamma_t":null,"gamma_rho":2.2817893126278106,"gamma_claim":2.2817893126278106,"gamma_t_claim":null,"gamma_rho_claim":2.2817893126278106,"v_ex":26,"rate":0.02541544477028348,"t_count":null,"poly_degree":null,"effective_width":26},"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.T21.T22.T23.T24.T25","N":46,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:398"}]},"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"}]}