{"id":"1023.25.5.a","row":1344,"stored":{"file":"master_catalog.json","row":1344,"construction":null,"columns_sha256":null},"parameters":{"n":1023,"k":25,"d":5,"N":45,"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","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","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]],"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]],"sk_fingerprint":"c136b8ab193e527e","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,2,4,5,8,9,11,16,19,20,22,23,24,25,35],[1,3,5,8,9,13,14,15,16,17,19,20,21,22,26,38],[1,3,6,7,10,12,13,14,16,17,20,21,24,25,26,35,36,37,38],[1,4,7,8,13,14,15,17,18,19,20,23,24,27,41],[1,2,5,6,7,8,9,11,15,17,18,19,20,21,22,23,24,25,27,35,37,39,41],[5,6,7,11,12,14,18,20,22,23,24,26,27,38,39,40,41],[0,6,9,10,11,13,15,16,18,21,24,25,26,27,35,36,38,40,41],[2,3,5,14,15,17,18,20,28,44],[0,1,2,3,5,6,7,11,12,14,18,19,20,22,25,28,35,38,41,44],[0,1,3,6,12,14,17,19,20,22,26,28,38,40,42,44],[0,2,3,4,6,10,12,14,16,23,25,26,28,35,36,37,40,41,42,44],[2,6,9,10,11,12,13,15,18,22,27,28,41,42,43,44],[1,2,6,7,8,9,10,14,16,17,18,20,21,23,24,25,27,28,35,37,38,39,42,43,44],[0,1,3,4,5,6,10,12,13,14,16,19,20,21,26,27,28,38,39,41,43,44],[2,3,5,8,12,16,17,19,20,22,24,25,26,27,28,35,36,43,44],[0,1,5,8,9,10,11,14,15,16,17,20,24,29,37,40],[0,3,4,5,6,7,9,12,13,14,24,25,29,35,37,39,40,43],[0,3,4,6,11,12,14,15,16,18,21,23,24,26,29,37,38,40,41,44],[1,2,4,6,8,11,12,13,14,15,16,17,18,21,24,25,26,29,35,36,38,39,40,41,43,44],[0,6,10,12,16,17,18,20,22,23,24,27,29,35,37,38,40,41,43],[1,3,4,6,7,11,14,15,16,18,19,20,21,22,25,27,29,38,40,41],[0,1,5,6,8,11,12,14,20,22,24,26,27,29,35,37,39,43,44],[0,2,3,5,8,11,12,16,17,19,21,22,25,26,27,29,36,37,39,44],[1,2,3,4,5,8,10,13,14,15,16,17,21,22,28,29,35,36,37,38,39,40,44],[1,4,8,9,11,14,15,16,17,21,22,23,24,25,28,29,36,37,40,41,43,44],[0,3,8,15,17,21,22,23,26,28,29,35,36,37,39,41,42],[4,5,6,7,8,9,12,13,16,17,20,21,22,23,24,25,26,28,29,38,42,43],[1,2,5,7,8,13,15,16,17,19,21,22,24,27,28,29,36,37,39,40,41,42,44],[0,1,3,6,7,9,10,11,13,14,15,17,20,22,24,25,27,28,29,35,36,38,39,40,42,43,44],[0,3,6,7,8,9,10,11,12,15,16,17,19,20,22,23,24,26,27,28,29,36,37,38,40],[0,4,5,6,10,11,14,16,17,20,21,22,24,25,26,27,28,29,35,37,40,41,43],[1,3,8,9,10,15,16,19,21,22,24,30,40,43],[3,4,5,6,9,11,12,14,16,20,25,30,38,43],[0,1,3,4,8,9,11,13,17,21,22,23,26,30,36,38,39,40,42,43],[2,3,4,5,7,9,11,13,14,16,17,19,24,25,26,30,37,39,42,43],[1,4,5,6,7,8,9,10,11,13,15,18,19,21,27,30,37,41,43,44],[0,6,7,8,9,12,16,18,19,21,22,23,25,27,30,38,39,40,41,43,44],[0,1,3,4,5,7,8,11,12,14,17,18,20,23,24,26,27,30,36,37,38,40,41,42,43,44],[0,2,3,4,6,8,11,12,13,14,17,18,22,23,24,25,26,27,30,37,39,41,42,43,44],[2,6,8,11,13,18,22,23,24,28,30,36,38,39,40,41,43,44],[6,7,8,9,10,13,14,16,17,18,19,21,24,25,28,30,36,38,39,43,44],[3,4,9,10,12,13,14,15,19,20,21,22,26,28,30,41,43,44],[0,3,6,10,13,17,25,26,28,30,36,37,40,43,44],[1,2,6,9,10,11,12,15,16,18,19,22,24,27,28,30,36,37,38,39,42],[0,1,7,8,12,13,15,16,17,18,19,20,25,27,28,30,36,38,40,41,42],[1,6,8,9,11,12,22,23,26,27,28,30,37,39,42],[1,4,6,11,13,15,16,17,24,25,26,27,28,30,36,37,40,41,42],[1,3,6,7,9,12,13,14,15,16,17,18,19,21,22,23,24,29,30,37,38,39,41,42,43],[0,1,2,4,6,8,11,12,15,16,18,19,20,22,24,25,29,30,37,40,41,42],[0,1,3,7,9,11,13,15,16,19,21,23,26,29,30,36,37,43,44],[0,1,6,7,8,10,11,12,14,17,19,23,25,26,29,30,38,39,40,44],[1,6,7,13,14,15,20,21,22,23,24,27,29,30,35,39,40,42,44],[1,2,3,4,9,11,13,14,15,16,17,19,20,21,22,23,25,27,29,30,35,37,38,39,42,43,44],[0,1,3,4,6,7,9,13,14,15,16,17,18,23,26,27,29,30,35,36,38,39,41],[1,4,6,7,10,12,13,14,16,18,19,20,24,25,26,27,29,30,35,39,40,41,43],[0,2,4,5,7,9,10,12,13,15,18,21,28,29,30,35,37,38,39,42,43,44],[1,2,3,4,6,7,9,10,11,14,16,18,24,25,28,29,30,35,37,38,40,41,42,44],[0,3,4,5,7,8,10,11,12,15,16,18,20,22,24,26,28,29,30,35,36,37,40,41,42,43],[0,1,2,8,11,12,13,14,15,16,18,21,22,23,25,26,28,29,30,35,39,42],[0,1,2,6,8,9,11,12,13,16,17,18,20,21,22,23,24,27,28,29,30,39,40,41,43],[0,2,3,5,6,9,13,15,16,17,18,19,21,22,24,25,27,28,29,30,37,39],[0,1,4,9,11,14,16,17,18,20,21,23,26,27,28,29,30,36,38,39,40,43,44],[2,3,5,6,7,8,9,10,11,14,17,18,19,20,21,23,24,25,26,27,28,29,30,38,39,41,44],[0,1,2,4,9,11,12,14,17,18,20,23,31,36,39,43],[3,4,10,11,13,14,16,19,20,22,24,25,31,35,36,37,39,40,41,43],[1,2,3,4,7,8,9,10,17,19,21,22,26,31,36,39,41],[2,6,8,10,11,13,15,18,20,21,24,25,26,31,35,39,40],[0,2,4,5,8,10,15,22,24,27,31,35,36,38,41,42,43],[0,1,3,4,5,6,9,12,14,15,17,18,20,21,24,25,27,31,36,38,39,40,42,43],[2,5,6,7,9,15,16,18,19,23,24,26,27,31,35,36,38,39,40,42],[0,1,2,3,4,5,6,8,11,14,17,19,21,22,24,25,26,27,31,37,38,41,42],[0,2,4,7,8,10,11,14,16,17,20,21,22,23,28,31,36,37,39,44],[2,3,5,6,11,13,14,15,16,17,18,19,21,23,25,28,31,35,36,38,39,40,44],[0,4,6,8,9,13,14,19,20,21,26,28,31,36,37,39,40,41,42,43,44],[0,2,3,4,5,6,9,11,12,14,16,18,20,21,22,23,25,26,28,31,35,37,38,39,41,42,43,44],[0,2,3,6,8,10,11,16,19,21,22,23,27,28,31,35,36,37,38,41,43,44],[0,2,4,5,6,7,8,11,14,15,18,19,24,25,27,28,31,36,37,39,40,41,43,44],[0,4,6,7,8,11,12,13,14,16,17,20,26,27,28,31,35,36,37,38,39,42,44],[2,3,4,5,7,8,13,16,17,18,21,22,24,25,26,27,28,31,40,42,44],[0,4,5,6,11,14,17,18,19,22,24,29,31,36,37,40,41,42,43,44],[0,4,7,11,14,15,16,17,19,22,24,25,29,31,35,36,39,42,44],[3,5,7,8,13,14,15,16,17,18,19,20,21,22,24,26,29,31,36,37,40,41,42],[0,2,3,4,7,8,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,29,31,35,37,39,42,43],[0,1,5,7,8,10,11,13,15,17,22,23,24,27,29,31,36,37,39,40,44],[1,10,11,14,17,18,19,20,21,22,25,27,29,31,35,36,37,39,41,43,44],[1,5,9,10,11,12,14,17,22,23,24,26,27,29,31,36,37,43],[1,2,4,6,8,9,13,16,17,18,19,21,22,23,25,26,27,29,31,35,40,41],[1,6,7,8,10,12,13,15,16,18,19,22,28,29,31,35,38,39,40,41,42],[2,4,6,7,9,10,13,15,16,17,19,20,22,23,24,25,28,29,31,37,41,42,43],[1,2,4,6,8,9,10,11,13,14,16,17,19,22,26,28,29,31,35,38,39,41,43,44],[0,2,4,7,13,14,15,18,19,22,24,25,26,28,29,31,36,40,41,44],[1,3,5,6,7,8,9,10,11,14,15,16,18,19,24,27,28,29,31,35,38,40,42],[0,2,3,4,5,7,8,10,11,12,13,15,17,21,24,25,27,28,29,31,42,43],[1,2,5,8,9,10,11,14,17,19,20,21,24,26,27,28,29,31,35,38,39,40,43,44],[2,5,7,8,13,15,18,23,24,25,26,27,28,29,31,36,37,39,44],[0,1,2,6,10,11,15,18,21,23,24,30,31,35,36,38,39,40,41,42,44],[0,1,2,3,10,11,13,14,17,19,22,23,25,30,31,35,36,37,39,40,42,44],[0,2,4,5,6,7,9,10,11,12,15,19,21,23,26,30,31,35,38,40,43,44],[3,5,6,9,13,14,15,16,17,18,20,22,24,25,26,30,31,35,36,40,41,43,44],[0,1,2,3,9,11,12,15,16,19,21,23,27,30,31,36,37],[1,2,8,9,11,12,17,18,19,20,21,22,25,27,30,31,36,37,38,39,41],[0,2,5,6,7,9,12,14,15,18,20,23,24,26,27,30,31,37,40,41,42,43],[0,3,4,5,8,9,10,11,14,15,17,20,22,23,24,25,26,27,30,31,36,38,39,40,42,43],[0,1,2,5,7,8,10,12,13,14,15,17,19,20,21,22,24,28,30,31,35,37,40,42,43],[0,3,4,9,10,15,16,17,18,23,24,25,28,30,31,35,40,42,43],[3,4,6,10,12,15,16,22,26,28,30,31,35,36,37,39,41,42],[0,1,4,5,8,9,11,12,13,14,16,18,19,21,25,26,28,30,31,35,37,39,41,42],[0,2,4,10,11,12,13,14,16,17,19,20,21,23,24,27,28,30,31,38,39,41,42,44],[1,3,5,6,7,9,10,11,13,14,16,17,18,19,20,21,22,23,25,27,28,30,31,38,41,42,44],[1,4,5,7,8,9,10,14,16,20,21,23,26,27,28,30,31,36,38,39,42,43,44],[3,4,7,8,11,14,15,18,21,22,24,25,26,27,28,30,31,37,38,42,43,44],[1,6,7,10,13,16,19,21,22,23,24,29,30,31,35,36,37,39,41,42],[0,2,5,6,9,12,13,14,16,18,19,22,24,25,29,30,31,35,36,38,42,43],[5,9,14,15,19,21,26,29,30,31,35,37,41,43,44],[1,4,6,11,16,18,19,20,25,26,29,30,31,35,36,37,38,39,44],[1,3,4,5,6,11,17,18,19,20,21,23,24,27,29,30,31,35,36,40,43,44],[2,3,4,7,8,9,10,11,12,13,16,17,21,23,25,27,29,30,31,35,36,38,40,41,44],[6,7,10,12,13,15,17,18,19,22,26,27,29,30,31,35,42],[0,1,4,5,6,7,8,9,10,11,12,17,22,23,24,25,26,27,29,30,31,35,36,37,38,41,42,43],[0,1,4,8,9,10,12,13,15,16,20,22,28,29,30,31,36,39,42,43,44],[1,6,9,12,13,14,17,18,21,22,24,25,28,29,30,31,36,37,42,44],[2,3,4,5,7,9,13,16,17,18,21,23,24,26,28,29,30,31,40,42],[3,4,5,8,9,11,12,13,14,16,25,26,28,29,30,31,36,39,40,42,43],[0,4,6,10,17,19,22,23,24,27,28,29,30,31,36,37,40,41,42,43],[0,6,13,15,18,22,24,25,27,28,29,30,31,36,37,40,41,42],[1,2,5,7,8,9,11,14,15,16,18,19,26,27,28,29,30,31,37,40,41,42,44],[0,1,5,6,8,9,12,13,14,15,17,20,25,26,27,28,29,30,31,36,40,41,42,43,44],[1,5,9,11,13,15,17,18,24,32,36,42],[0,2,3,5,7,9,11,12,13,16,25,32,35,36,39,42],[2,3,6,7,8,9,10,12,14,16,18,20,22,23,24,26,32,36,38,40,42,43,44],[1,2,4,7,8,9,11,12,14,16,17,22,25,26,32,35,37,38,39,40,42,43,44],[2,4,5,6,9,14,16,18,19,20,21,22,24,27,32,39,42,44],[1,3,4,5,7,8,9,12,13,15,16,17,22,23,24,25,27,32,35,37,39,42,44],[1,6,7,8,10,13,14,15,16,17,18,19,20,23,24,26,27,32,38,42,43],[0,3,4,6,7,11,15,20,21,23,24,25,26,27,32,35,36,38,42,43],[1,4,5,6,7,10,11,12,14,16,18,20,28,32,35,36,41,44],[0,1,3,7,8,9,10,11,12,14,16,23,25,28,32,36,38,39,44],[0,4,6,9,12,14,15,16,20,21,22,23,26,28,32,35,36,38,41,42,43],[0,2,3,4,5,6,7,8,10,11,14,18,20,21,22,23,25,26,28,32,37,39,42,43],[1,2,3,4,6,8,9,11,13,17,21,23,24,27,28,32,35,39,41,42,43],[1,2,5,6,8,11,14,16,17,18,19,23,25,27,28,32,37,38,39,42,43],[0,2,5,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,24,26,27,28,32,35,38,40,41,44],[3,6,8,16,17,19,22,23,25,26,27,28,32,36,40,44],[0,1,2,4,5,6,8,11,12,14,17,20,22,23,24,29,32,37,39,42],[0,1,2,4,8,9,10,11,12,13,14,16,17,18,19,20,24,25,29,32,35,37,39,42,43],[0,3,6,7,12,14,18,19,22,23,24,26,29,32,37,38,39,40,41,42,43],[2,3,4,5,6,9,11,13,14,15,20,23,24,25,26,29,32,35,36,38,39,40,41,42],[0,4,6,7,8,9,11,15,16,17,20,21,22,23,27,29,32,35,36,37,38,42,43,44],[4,5,6,7,10,11,14,15,16,17,18,23,24,25,27,29,32,36,38,39,42,44],[0,1,2,4,5,11,12,14,15,18,19,20,22,23,26,27,29,32,35,36,37,39,41,42,44],[0,1,6,7,8,9,16,19,20,21,24,25,26,27,29,32,37,41,42,43,44],[1,2,4,7,8,10,14,16,17,18,21,23,24,28,29,32,36,37,38,41,44],[12,13,14,15,16,19,20,21,22,23,25,28,29,32,35,36,37,43,44],[0,2,5,6,8,9,10,11,12,13,17,18,19,23,24,26,28,29,32,36,37,42,43,44],[1,2,5,9,10,12,16,22,24,25,26,28,29,32,35,38,41,42,44],[1,3,6,7,11,17,19,22,24,27,28,29,32,35,37,39,41,42],[0,2,3,4,10,11,12,14,15,16,18,19,21,23,24,25,27,28,29,32,38,42,43],[0,5,6,11,13,17,20,22,24,26,27,28,29,32,35,37,38,40,43],[0,1,5,6,13,14,18,21,24,25,26,27,28,29,32,36,37,39,40,41],[3,6,8,14,17,21,30,32,35,36,37,38,43,44],[7,8,9,10,18,23,25,30,32,35,36,37,39,40,43,44],[0,2,3,4,7,8,9,12,13,14,15,16,26,30,32,35,37,39,40,42],[7,8,11,13,17,18,20,21,24,25,26,30,32,35,36,38,42],[2,4,5,6,13,14,17,23,24,27,30,32,35,38,39,40,43,44],[0,2,3,4,5,6,7,8,9,10,14,16,18,19,20,23,24,25,27,30,32,35,37,39,43,44],[0,3,4,5,6,7,11,15,20,23,26,27,30,32,35,36,39,40,42],[0,2,5,7,8,9,12,13,17,18,19,20,24,25,26,27,30,32,35,38,39,42],[1,3,4,5,6,7,8,11,12,14,15,17,19,23,24,28,30,32,37,39,42,43],[2,6,7,10,11,16,17,18,19,20,21,23,24,25,28,30,32,37,40,41,42,43],[1,5,6,11,12,17,18,19,20,23,26,28,30,32,36,37,38,42,44],[0,3,7,8,12,14,17,19,20,21,25,26,28,30,32,38,39,40,41,42,44],[2,3,4,5,8,9,10,13,14,17,18,21,22,23,24,27,28,30,32,36,40],[0,1,6,8,9,12,14,15,17,19,21,22,24,25,27,28,30,32,36,37,41],[2,3,4,5,6,7,10,11,12,13,14,15,16,17,22,23,26,27,28,30,32,38,43,44],[1,2,4,6,10,12,14,15,17,18,19,20,22,23,24,25,26,27,28,30,32,36,38,40,41,43,44],[1,2,3,4,5,6,7,11,16,17,21,22,29,30,32,35,41,42,43,44],[0,3,4,6,7,11,12,13,14,15,16,17,18,19,24,25,29,30,32,35,38,40,41,42,44],[0,1,3,4,5,6,9,10,11,14,16,18,19,23,24,26,29,30,32,35,36,38,39,40,44],[0,3,7,9,13,20,21,22,24,25,26,29,30,32,35,37,39,43,44],[1,4,5,8,9,12,16,19,20,23,27,29,30,32,36,37,38,39,40,41,42,44],[2,4,6,9,15,18,19,22,24,25,27,29,30,32,36,41,42,43,44],[0,1,2,3,5,6,7,8,9,10,11,17,18,22,26,27,29,30,32,37,39,40,43,44],[2,3,4,6,9,17,24,25,26,27,29,30,32,36,37,38,44],[0,2,3,4,5,6,9,11,12,13,14,16,18,19,21,23,28,29,30,32,35,41,43],[2,3,5,7,8,11,12,17,20,22,24,25,28,29,30,32,35,40],[0,2,4,5,7,8,9,10,11,14,18,20,21,22,24,26,28,29,30,32,35,36,38,39],[0,4,5,7,12,13,15,17,19,20,25,26,28,29,30,32,35,37,38,39,40,41,43],[0,1,3,6,9,10,11,12,13,14,15,16,17,19,20,23,24,27,28,29,30,32,36,37,38,39,40,41,42,43],[0,1,3,4,6,7,10,11,12,13,14,15,16,18,19,20,22,23,24,25,27,28,29,30,32,36,38,42],[0,1,3,4,6,7,8,12,15,16,17,20,21,22,24,26,27,28,29,30,32,37,39,42],[1,2,3,4,7,8,9,10,11,18,21,23,25,26,27,28,29,30,32,36,37,40,41,42,43],[2,3,8,10,11,12,13,15,17,18,20,24,31,32,35,37,39,40,41,42,43,44],[0,3,4,5,7,12,16,17,18,25,31,32,42,43,44],[0,6,9,10,11,12,13,14,15,17,22,26,31,32,35,37,39,42,43],[0,5,8,9,10,11,14,15,17,22,23,25,26,31,32,36,37,40,41,42,43],[1,3,5,6,7,8,9,11,13,14,16,18,21,24,27,31,32,36,37,38,39,40,41,43],[1,2,3,4,8,9,10,13,15,16,18,19,23,25,27,31,32,35,36,37,38,39,43],[0,1,2,3,4,5,6,7,9,12,13,14,22,26,27,31,32,36,37,38,40,43,44],[1,2,3,4,6,7,9,13,16,19,20,21,22,25,26,27,31,32,35,38,41,43,44],[1,4,5,6,10,11,12,15,17,18,20,21,22,28,31,32,39,40],[0,4,5,9,13,15,18,20,21,22,23,24,25,28,31,32,35,37,38],[1,4,5,6,10,11,13,15,16,18,20,26,28,31,32,39,40,41,42,44],[2,5,6,7,9,10,11,17,18,22,23,24,25,26,28,31,32,35,36,38,41,42,44],[1,2,3,5,6,8,10,12,14,15,16,19,23,27,28,31,32,35,36,38,39,40,43,44],[2,3,5,6,9,11,15,17,20,21,23,24,25,27,28,31,32,36,39,43,44],[1,2,4,5,8,9,10,11,12,13,15,16,17,19,20,24,26,27,28,31,32,35,36,38,41,42,43],[0,5,6,7,10,11,12,13,14,16,20,21,22,24,25,26,27,28,31,32,37,40,41,42,43],[2,3,4,8,9,12,15,16,19,24,29,31,32,35,36,39,40,43],[1,2,6,11,15,17,20,24,25,29,31,32,36,37,39,41],[0,10,13,20,23,24,26,29,31,32,35,36,39,43],[1,2,3,7,8,9,13,15,17,19,20,22,23,24,25,26,29,31,32,39,40,41],[1,3,8,9,10,11,12,13,14,21,22,27,29,31,32,35,39,40,42,44],[0,4,8,10,17,24,25,27,29,31,32,41,42,43,44],[0,1,2,3,6,9,12,15,19,22,23,26,27,29,31,32,35,40,42,44],[0,7,10,12,13,14,16,17,19,20,21,24,25,26,27,29,31,32,36,37,39,41,42,43,44],[0,1,4,6,11,12,14,16,17,18,19,24,28,29,31,32,35,37,38,40,41,42,44],[0,1,2,3,4,5,6,7,12,14,15,16,17,18,23,24,25,28,29,31,32,41,42,43,44],[0,1,10,11,12,15,16,21,23,24,26,28,29,31,32,35,37,38,40,41,44],[1,3,4,5,6,11,15,19,20,21,23,25,26,28,29,31,32,36,37,41,43,44],[0,1,2,3,4,5,7,8,9,11,13,17,19,21,22,27,28,29,31,32,35,36,37,38,40,41,42],[1,4,6,9,14,15,16,17,19,20,23,25,27,28,29,31,32,36,37,39,41,42,43],[0,1,2,4,5,7,8,10,12,13,15,16,18,20,21,24,26,27,28,29,31,32,35,36,37,38,39,41],[0,1,2,3,7,14,15,16,18,20,22,24,25,26,27,28,29,31,32,40,41,43],[2,3,4,5,8,9,10,16,19,21,22,24,30,31,32,35,39,40,42,44],[1,2,3,6,7,10,11,12,13,14,16,19,20,22,23,24,25,30,31,32,35,37,38,40,41,42,44],[1,3,6,8,9,11,16,18,19,26,30,31,32,35,36,41],[0,2,3,5,6,10,11,13,14,15,18,19,21,22,23,24,25,26,30,31,32,35,38,39],[4,5,7,11,12,16,23,24,27,30,31,32,36,37,38,39,44],[0,1,9,19,22,24,25,27,30,31,32,36,37,39,41,44],[1,2,3,4,7,9,10,11,14,18,20,26,27,30,31,32,37,38,39,41,42],[3,4,5,6,7,11,14,15,18,19,23,25,26,27,30,31,32,36,39,42],[5,11,14,17,20,21,22,24,28,30,31,32,36,37,38,40,43],[2,5,13,15,16,20,23,25,28,30,31,32,36,38,39,40,43],[0,1,3,4,8,9,10,12,13,16,21,22,23,24,26,28,30,31,32,37,38,39,40,41,43,44],[1,3,6,7,8,9,14,16,17,20,21,22,23,25,26,28,30,31,32,36,37,38,40,41,43,44],[1,2,4,6,11,14,15,17,18,20,22,24,27,28,30,31,32,35],[0,1,4,8,14,18,19,25,27,28,30,31,32,35],[0,2,4,5,8,10,11,13,14,15,18,20,21,22,23,24,26,27,28,30,31,32,35,36,40,41,44],[0,2,5,7,11,12,13,14,15,16,17,18,19,20,23,25,26,27,28,30,31,32,35,37,40,41,44],[0,1,2,3,6,7,8,9,12,15,16,17,23,24,29,30,31,32,35,36,37,38,40,42],[1,4,6,7,9,10,11,12,14,16,19,20,21,24,25,29,30,31,32,35,36,40,41,42,43],[0,3,5,6,7,8,9,11,13,14,17,19,21,22,23,26,29,30,31,32,35,37,38,39],[0,5,9,11,12,13,16,24,25,26,29,30,31,32,35,36,37,39,41,43],[0,1,4,5,7,9,10,12,13,15,16,20,22,24,27,29,30,31,32,35,38,43],[0,1,2,3,5,6,7,9,11,12,17,20,23,25,27,29,30,31,32,35,39,41],[0,2,3,6,7,10,12,16,19,21,23,24,26,27,29,30,31,32,35,36,38,42,43],[2,6,10,13,16,17,19,20,21,25,26,27,29,30,31,32,35,37,39,41,42],[1,5,6,7,9,10,12,13,17,18,19,20,21,24,28,29,30,31,32,35,36,38,40,43,44],[0,3,11,13,14,16,17,18,20,24,25,28,29,30,31,32,35,36,37,38,40,44],[0,3,7,8,10,11,12,13,15,21,22,26,28,29,30,31,32,35,38,39,40,43,44],[0,1,2,4,5,7,8,9,10,11,12,13,14,19,20,21,22,25,26,28,29,30,31,32,35,36,38,39,40,44],[2,5,6,10,11,15,22,27,28,29,30,31,32,35,37,38,43,44],[1,2,3,6,7,8,9,12,13,15,23,25,27,28,29,30,31,32,35,37,38,39,44],[0,1,2,4,6,8,10,11,12,14,16,17,18,20,23,26,27,28,29,30,31,32,35,36,37,38,40,43,44],[0,1,2,4,6,7,8,16,19,20,23,25,26,27,28,29,30,31,32,35,38,39,40,44],[0,3,4,5,7,13,14,16,17,19,20,21,23,33,35,38,39],[0,3,7,9,12,13,15,16,17,19,20,24,25,33,38,39,41,43,44],[2,3,4,5,8,12,13,19,20,21,23,26,33,35,39,42],[0,3,4,6,7,8,9,10,11,12,13,14,16,19,22,24,25,26,33,36,37,39,41,42,43,44],[0,1,4,5,6,7,9,11,13,14,16,20,21,24,27,33,35,36,37,38,40,41,43],[1,7,8,11,12,14,15,19,21,24,25,27,33,36,38,39,40,44],[1,2,3,5,8,13,14,16,17,26,27,33,35,36,37,39,41,42,43],[1,3,7,9,10,11,14,16,17,19,21,25,26,27,33,37,42,44],[1,3,5,6,7,14,20,21,22,28,33,35,37,38,40,42],[2,3,5,8,16,17,21,25,28,33,37,40,42,43,44],[1,5,9,13,14,18,23,26,28,33,35,37,42],[0,4,5,8,9,10,11,12,13,15,17,18,23,24,25,26,28,33,36,38,42,43,44],[1,3,4,6,8,10,12,14,15,17,18,20,21,27,28,33,35,36,38,39,41],[0,2,3,4,6,7,8,10,12,13,14,15,18,19,21,22,23,24,25,27,28,33,36,37,41,43,44],[1,3,6,7,8,10,11,13,15,16,17,20,22,26,27,28,33,35,36,41],[3,4,7,8,12,19,20,21,22,24,25,26,27,28,33,38,39,41,43,44],[0,3,4,7,8,9,10,11,12,14,15,19,20,22,23,24,29,33,37,38,39,40,44],[1,2,6,8,9,11,12,13,15,17,21,25,29,33,35,37,38,40,41],[2,3,6,9,11,12,13,14,17,18,20,21,23,26,29,33,37,39,40,41,42],[1,2,6,9,15,16,18,19,21,25,26,29,33,35,36,40,42,44],[0,1,5,8,9,10,11,13,14,15,19,21,22,24,27,29,33,35,36,41,44],[0,2,3,4,5,7,9,11,13,14,15,16,17,19,21,22,23,24,25,27,29,33,36,37],[1,2,3,5,7,12,16,17,18,22,23,26,27,29,33,35,36,38,39,40,42],[0,2,5,6,7,8,11,15,16,18,20,22,23,25,26,27,29,33,38,39,40,41,42,44],[0,1,3,4,5,6,7,8,10,12,16,18,22,28,29,33,35,36,39,42,44],[1,4,6,7,9,13,14,15,18,19,20,24,25,28,29,33,36,38,42],[0,1,5,6,8,9,14,15,18,19,22,24,26,28,29,33,35,36,38,39,40,41,42],[0,1,2,3,4,7,11,13,15,18,20,21,22,24,25,26,28,29,33,37,40,41,42,44],[0,1,3,4,5,7,9,11,12,13,15,16,19,22,23,24,27,28,29,33,37,38,40,41,43,44],[0,1,4,6,7,10,11,13,16,19,21,25,27,28,29,33,35,40,41,43],[0,1,3,4,5,6,9,10,12,13,16,20,21,22,23,26,27,28,29,33,37,39,40,43],[1,2,6,7,10,11,12,13,22,25,26,27,28,29,33,35,36,37,38,39,40,43,44],[0,1,4,5,6,7,8,9,13,14,15,30,33,35,38,40,42],[2,7,8,9,10,13,14,15,16,20,21,22,23,24,25,30,33,35,41,42,43,44],[0,2,3,6,8,10,11,12,13,14,15,16,17,24,26,30,33,35,36,39,40,42],[0,1,2,3,5,6,7,8,10,13,14,16,17,20,23,24,25,26,30,33,35,37,38,39,41,42,43,44],[0,1,4,6,7,13,16,21,22,24,27,30,33,35,36,38,39,40,41,42,43,44],[0,2,5,6,7,8,10,14,16,20,21,24,25,27,30,33,35,36,37,42],[0,2,4,5,10,13,14,16,17,20,23,26,27,30,33,35,39,41,42,43,44],[1,2,4,6,7,8,10,11,12,15,17,20,21,25,26,27,30,33,35,36,38,40,42],[1,6,7,8,10,11,13,15,21,22,23,24,28,30,33,35,36,37,41],[0,1,6,9,11,12,13,17,19,20,21,22,23,25,28,30,33,35,36,37,40,41,43,44],[0,4,5,14,15,18,21,22,23,24,26,28,30,33,35,37,38,39,40,41,42],[0,2,5,6,8,9,11,14,15,16,17,18,23,24,25,26,28,30,33,35,36,38,39,41,42,43,44],[3,4,8,12,13,14,15,16,18,20,21,22,23,27,28,30,33,35,37,39,42,44],[3,4,6,7,8,9,10,17,18,19,23,24,25,27,28,30,33,35,40,42,43],[0,1,4,5,7,9,10,14,15,21,23,26,27,28,30,33,35,36,37,38,39,44],[1,2,5,7,10,11,13,15,17,19,22,24,25,26,27,28,30,33,35,37,38,40,43],[4,5,9,10,13,14,15,17,18,19,20,21,23,29,30,33,37,39,41,44],[3,5,7,10,12,14,16,18,20,21,22,24,25,29,30,33,37,38,40],[1,2,3,4,6,7,10,11,20,26,29,30,33,36,37,38],[0,1,4,7,9,13,17,19,20,25,26,29,30,33,39,40,41,44],[5,6,7,8,9,10,11,12,16,18,19,20,22,24,27,29,30,33,35,36,37,38],[0,3,4,5,10,11,14,15,16,17,18,19,20,25,27,29,30,33,35,36,40,41,44],[1,2,4,6,8,9,10,11,13,15,17,19,23,26,27,29,30,33,35,37,40,41,44],[1,3,4,6,13,14,15,16,19,21,23,25,26,27,29,30,33,35,36,37,38],[4,5,9,14,20,28,29,30,33,35,40,42,44],[1,2,3,4,6,8,9,13,14,19,23,24,25,28,29,30,33,35,39,42],[0,1,4,7,8,9,11,12,14,15,16,19,23,26,28,29,30,33,35,36,38,39,41],[3,5,9,10,13,14,20,21,22,24,25,26,28,29,30,33,35,37,38,40,41,44],[1,3,4,10,13,16,17,18,20,21,22,27,28,29,30,33,36,38,39,40,41,43],[0,2,4,5,10,13,14,17,18,19,20,25,27,28,29,30,33,36,37,38,39,41,43,44],[0,5,6,7,8,9,10,13,14,15,16,17,18,21,23,26,27,28,29,30,33,39,40,42,43,44],[0,1,3,4,8,9,11,12,13,16,17,21,22,25,26,27,28,29,30,33,36,39,42,43],[0,1,4,6,8,11,13,14,16,17,22,24,31,33,36,37,38,41],[0,3,4,6,9,10,15,16,18,19,20,22,23,24,25,31,33,35,36,38,40,41,43,44],[0,2,4,5,6,9,10,15,16,17,18,20,23,26,31,33,36,37,38,42,43],[1,3,5,7,8,10,12,13,14,15,19,21,23,24,25,26,31,33,35,37,38,40,42,44],[0,3,5,7,8,10,11,12,14,16,19,22,23,24,27,31,33,35,40,42,43],[1,5,6,7,8,9,12,14,15,17,22,25,27,31,33,39,42,44],[0,1,2,4,6,7,11,13,14,15,20,24,26,27,31,33,35,39,41],[0,3,6,9,11,12,13,14,15,17,19,20,23,24,25,26,27,31,33,36,37,40,41,43,44],[1,2,3,5,7,9,10,11,12,15,16,17,18,19,21,22,23,28,31,33,36,37,38,39,40,41,42,43],[1,4,6,9,13,14,15,17,18,20,22,24,25,28,31,33,35,36,39,42,44],[0,2,6,7,9,19,20,21,22,26,28,31,33,36,37,38,39,42],[2,3,5,6,7,9,13,14,15,18,19,21,22,25,26,28,31,33,35,37,39,40,41,42,43,44],[1,2,3,5,7,8,10,12,13,16,18,20,21,22,23,24,27,28,31,33,35,39,42,43],[0,1,4,11,13,16,19,20,21,22,23,24,25,27,28,31,33,38,40,41,42,44],[0,2,3,4,7,8,9,12,13,14,15,16,17,19,20,22,23,24,26,27,28,31,33,35,41,42],[0,2,4,5,6,7,9,12,13,14,17,21,23,25,26,27,28,31,33,36,37,38,39,40,42,43,44],[1,2,4,5,8,9,11,16,17,18,19,20,21,22,23,29,31,33,35,36,38,39,40,42],[0,1,4,6,7,9,12,14,16,17,21,24,25,29,31,33,36,37,38,42,44],[6,12,17,18,19,20,21,24,26,29,31,33,35,36,38,39,40,43,44],[4,5,6,8,10,12,14,15,16,17,19,20,21,22,23,24,25,26,29,31,33,38,43],[2,3,4,5,8,10,16,17,20,21,22,27,29,31,33,35,37,38,39,41],[3,4,7,8,10,11,12,13,17,19,20,21,23,24,25,27,29,31,33,37,38,39,40,41,44],[1,4,10,14,16,17,19,21,23,24,26,27,29,31,33,35,37,38,40,41,42,43,44],[0,1,5,6,13,14,15,16,17,18,19,20,21,22,23,25,26,27,29,31,33,36,38,41,42,43],[1,3,4,5,6,7,9,10,12,16,20,21,23,28,29,31,33,39,43],[0,3,5,6,7,10,11,12,14,15,17,21,22,25,28,29,31,33,35,37,38,40,41,43,44],[0,6,7,9,10,11,12,13,14,16,17,18,20,21,23,26,28,29,31,33,39,40,44],[0,1,2,11,13,16,18,20,21,25,26,28,29,31,33,35,36,38,41],[1,3,8,9,10,15,16,18,19,24,27,28,29,31,33,36,37,39,40,41],[3,4,6,10,11,13,16,17,19,20,22,24,25,27,28,29,31,33,35,36,37,38,39,44],[0,3,5,6,8,10,12,13,15,17,20,21,22,24,26,27,28,29,31,33,36,37,40,41,43,44],[1,2,3,5,6,7,9,15,16,18,22,24,25,26,27,28,29,31,33,35,38,43],[0,1,6,8,9,11,12,13,15,16,17,18,20,21,22,30,31,33,35,36,37,39,40,44],[1,2,3,9,15,17,18,19,23,25,30,31,33,35,36,38,39,40,43],[1,2,3,4,6,8,9,11,12,16,17,18,19,20,21,22,23,24,26,30,31,33,35,37,40,41,43,44],[1,2,6,7,9,10,11,12,13,15,16,18,19,20,21,24,25,26,30,31,33,35,36,37,38,40,41],[0,1,4,6,7,9,10,14,19,22,23,24,27,30,31,33,37,38,39,40,41,42,43],[0,1,2,3,4,6,7,9,10,11,12,17,18,19,20,21,23,24,25,27,30,31,33,37,40,41,42,44],[1,2,4,7,10,11,12,13,15,16,17,19,20,24,26,27,30,31,33,36,37,38,39,42],[0,1,2,3,6,11,12,13,14,19,20,24,25,26,27,30,31,33,42,43,44],[2,3,4,6,7,9,13,17,20,21,22,24,28,30,31,33,35,37,38,39,41,42,43,44],[0,1,2,5,6,11,15,17,18,19,20,21,23,24,25,28,30,31,33,35,38,39,42],[2,3,7,8,12,13,14,15,16,20,22,26,28,30,31,33,35,36,37,38,40,44],[1,5,6,7,8,9,10,14,15,18,19,20,22,25,26,28,30,31,33,35,37,38,40,41,43],[1,2,4,5,7,14,16,18,19,20,21,24,27,28,30,31,33,36,37,39,42,43],[2,3,6,8,9,11,15,18,20,21,22,24,25,27,28,30,31,33,36,37,41,42,44],[1,2,3,4,5,7,8,11,14,15,16,17,18,19,23,26,27,28,30,31,33,37,39,41],[0,4,7,9,10,11,12,15,16,17,19,21,22,25,26,27,28,30,31,33,36,43,44],[0,2,6,7,8,9,13,14,17,19,20,22,23,24,29,30,31,33,36,38,39,44],[0,1,2,5,6,10,11,13,14,15,16,19,20,21,23,25,29,30,31,33,36,37],[3,7,8,9,10,12,13,16,17,19,20,22,23,24,26,29,30,31,33,38,43],[0,1,2,3,4,5,6,7,10,13,16,17,19,21,23,24,25,26,29,30,31,33,36,39,43,44],[0,2,5,7,10,13,15,16,18,19,21,27,29,30,31,33,38,39,41,42],[1,2,6,9,11,14,16,18,21,22,23,24,25,27,29,30,31,33,39,41,42,44],[4,5,7,9,11,13,15,16,18,19,20,26,27,29,30,31,33,36,38,39,40,41,42,43,44],[1,2,7,11,12,14,15,17,19,20,21,22,23,24,25,26,27,29,30,31,33,37,39,40,41,42,43],[0,1,3,5,6,12,16,17,18,20,21,22,23,28,29,30,31,33,35,36,38,40,41,42,43,44],[0,1,2,3,4,5,10,11,16,17,21,24,25,28,29,30,31,33,35,36,37,38,39,40,42,43],[0,1,3,5,6,8,9,10,12,13,16,17,18,19,22,26,28,29,30,31,33,35,38,39,41],[1,3,5,6,7,8,9,10,12,13,15,17,19,20,21,25,26,28,29,30,31,33,35,36,38,44],[0,4,5,6,7,11,14,17,18,20,22,24,27,28,29,30,31,33,35,38,40,42],[2,5,6,7,8,10,12,13,16,19,20,21,22,24,25,27,28,29,30,31,33,35,38,40,41,42,44],[0,3,5,7,8,10,12,13,16,17,20,21,23,24,26,27,28,29,30,31,33,35,36,38,40,43,44],[1,2,4,7,8,9,11,13,18,25,26,27,28,29,30,31,33,35,37,38,40,41,43],[0,1,4,7,9,11,12,13,14,19,22,24,32,33,35,36,37,39,42,43,44],[0,3,4,8,9,12,13,17,18,19,22,25,32,33,36,37,41,42],[1,4,6,7,8,10,12,13,16,19,20,22,23,26,32,33,35,36,37,38,39,40],[0,2,3,7,13,14,15,17,21,22,23,25,26,32,33,38,40,41,43,44],[0,2,3,4,8,11,12,13,14,18,20,21,22,27,32,33,35,36,39,40,42],[1,2,4,6,7,8,12,14,17,25,27,32,33,36,37,39,40,41,42,43,44],[2,10,11,13,14,17,18,26,27,32,33,35,36,38,40,43,44],[1,3,4,11,12,14,15,16,19,20,21,22,23,25,26,27,32,33,38,40,41],[2,3,4,5,10,11,13,14,16,20,22,24,28,32,33,36,40,41,42,43,44],[6,9,10,12,13,15,16,18,19,20,21,25,28,32,33,35,36,38,39,40,41,42],[4,5,12,14,17,18,19,20,22,24,26,28,32,33,36,38,40,41,42],[0,3,4,7,9,10,12,16,17,18,20,22,23,25,26,28,32,33,35,37,39,40,41,42,43,44],[3,6,12,13,14,15,16,20,23,24,27,28,32,33,36,37,41,43],[0,2,4,5,6,8,9,11,14,16,17,18,19,20,23,24,25,27,28,32,33,35,36,38,41,44],[2,3,4,9,10,12,15,16,21,22,23,26,27,28,32,33,36,37,38,39,40,41,44],[2,4,5,6,7,8,12,13,15,16,17,19,23,25,26,27,28,32,33,35,37,39,40,41,43],[0,2,6,7,8,11,12,13,14,15,16,18,20,21,23,24,29,32,33,42,43],[5,7,9,10,16,17,18,25,29,32,33,35,41,42,43,44],[2,4,6,7,9,14,16,17,19,21,23,26,29,32,33,38,40,41],[2,5,6,8,13,16,18,19,20,21,23,24,25,26,29,32,33,35,36,37,38,40,44],[0,1,3,4,5,7,14,15,16,17,18,20,22,27,29,32,33,35,37,38,40,42,43,44],[0,1,2,3,4,7,9,10,11,12,14,18,22,25,27,29,32,33,38,39,40,41,42,43],[1,4,5,6,7,8,13,18,23,26,27,29,32,33,35,37,39,40,41,44],[0,1,8,9,13,16,21,22,23,24,25,26,27,29,32,33,36,37,40],[0,1,3,4,6,8,10,19,23,24,28,29,32,33,36,37,38,40,41,42,43],[3,6,7,8,11,13,14,16,19,20,22,24,25,28,29,32,33,35,36,37,40,41,42,43,44],[0,1,2,8,10,11,14,15,16,17,18,20,23,26,28,29,32,33,36,37,40,42],[0,6,8,10,11,12,13,17,19,21,22,24,25,26,28,29,32,33,35,38,40,42,44],[0,1,2,3,4,6,7,8,9,13,15,17,18,19,21,22,23,24,27,28,29,32,33,35,36,41,44],[0,2,3,9,10,11,13,15,16,18,19,21,22,25,27,28,29,32,33,36,37,38,39,41],[0,1,3,4,6,7,8,12,13,20,22,24,26,27,28,29,32,33,35,36,38,39,40,43,44],[2,3,4,6,7,13,15,18,23,25,26,27,28,29,32,33,40,43],[0,3,4,5,7,8,10,12,15,17,18,22,23,24,30,32,33,36,38,42,43],[2,4,5,6,9,11,16,17,18,19,20,21,23,24,25,30,32,33,36,39,40,41,42,44],[0,1,6,7,8,10,12,15,16,17,18,21,23,26,30,32,33,39,40,42,44],[0,1,3,4,6,7,9,10,12,15,17,18,22,25,26,30,32,33,36,37,38,41,42,43],[0,2,3,4,6,8,9,10,11,12,14,16,17,24,27,30,32,33,36,38,42],[0,4,6,7,8,13,15,16,18,19,20,21,23,24,25,27,30,32,33,36,37,40,41,42,43,44],[0,1,2,3,4,5,6,8,10,15,16,18,21,22,23,26,27,30,32,33,42,43,44],[1,2,5,8,9,10,13,14,16,19,20,22,23,25,26,27,30,32,33,36,38,40,41,42],[2,4,5,6,8,10,11,13,14,15,16,17,23,28,30,32,33,35,37,40,42,43],[0,1,2,3,6,8,13,14,15,16,18,19,22,25,28,30,32,33,35,37,39,42,44],[0,1,6,9,10,11,12,16,17,20,21,24,26,28,30,32,33,35,36,37,38,39,40,44],[0,2,3,5,7,9,10,11,16,17,21,22,23,24,25,26,28,30,32,33,35,38,43],[1,3,5,6,11,12,13,15,17,18,19,20,23,27,28,30,32,33,35,37,40,43],[4,8,10,12,14,16,17,18,20,21,22,24,25,27,28,30,32,33,35,44],[0,2,8,12,16,17,18,24,26,27,28,30,32,33,35,36,37,38,42,44],[1,3,5,7,13,14,15,16,17,18,21,22,23,25,26,27,28,30,32,33,35,37,38,40,42,43],[2,3,10,11,13,15,16,20,23,24,29,30,32,33,35,37,41,43,44],[1,2,3,5,8,10,15,16,17,18,19,20,21,24,25,29,30,32,33,35,37,38,40,43],[1,2,5,11,12,14,17,19,20,22,23,24,26,29,30,32,33,35,36,37,38,39,40,44],[0,4,6,7,8,10,11,13,14,17,18,21,23,24,25,26,29,30,32,33,35,39,41],[3,4,10,11,12,14,18,19,22,27,29,30,32,33,37,38,41,43,44],[0,1,3,4,5,6,10,12,16,17,19,21,22,24,25,27,29,30,32,33,39,40,43],[1,3,5,6,9,12,13,14,16,18,21,24,26,27,29,30,32,33,36,37,44],[2,3,4,6,7,9,10,13,17,19,23,25,26,27,29,30,32,33,37,38,39,40,41],[4,5,6,7,9,10,11,12,13,16,17,19,21,22,23,28,29,30,32,33,35,39,40,41,43,44],[2,5,10,15,16,18,22,25,28,29,30,32,33,35,39,41,43],[0,1,2,4,7,8,11,12,13,15,17,18,20,22,23,24,26,28,29,30,32,33,35,36,38,40,42,44],[1,2,4,7,8,9,10,11,12,15,16,18,19,20,22,24,25,26,28,29,30,32,33,35,37,38,42],[1,2,3,4,8,12,14,16,18,19,21,24,27,28,29,30,32,33,38,39,40,41,42,44],[0,1,3,7,9,11,16,17,18,20,21,22,23,25,27,28,29,30,32,33,37,38,41,42],[0,5,10,11,15,16,22,26,27,28,29,30,32,33,36,39,43,44],[1,2,3,4,7,10,12,13,17,18,19,20,23,25,26,27,28,29,30,32,33,40,43],[6,9,10,11,12,13,15,16,17,19,21,22,23,24,31,32,33,35,37,40,42,43],[4,5,6,7,9,11,14,15,16,19,20,22,23,24,25,31,32,33,39,42,44],[1,5,7,8,9,10,11,14,16,17,23,26,31,32,33,35,37,41,43,44],[0,1,2,6,7,8,9,10,13,17,18,20,21,22,23,24,25,26,31,32,33,36,37,39,40,41],[1,2,3,4,5,6,8,9,17,22,23,27,31,32,33,38,39,44],[0,1,2,3,7,9,10,12,16,18,20,21,23,25,27,31,32,33,35,38,39,40,43],[2,6,7,11,13,16,20,21,22,24,26,27,31,32,33,38,41,42],[5,6,7,8,13,18,19,21,22,25,26,27,31,32,33,35,36,37,38,40,41,42,43,44],[0,6,8,9,10,11,12,13,14,15,20,24,28,31,32,33,37,39,41,42],[0,1,2,11,12,15,16,17,19,22,23,24,25,28,31,32,33,35,38,40,42,43,44],[1,2,3,5,6,7,8,10,11,12,13,14,16,17,18,19,21,22,23,24,26,28,31,32,33,37,39,42,44],[0,2,3,4,5,6,9,10,14,15,23,24,25,26,28,31,32,33,35,36,37,38,40,41,42,43],[0,2,7,8,10,11,12,14,17,18,21,22,23,24,27,28,31,32,33,35,38,40,41,42,44],[1,7,8,9,11,12,14,16,17,18,19,20,21,25,27,28,31,32,33,42,43],[1,4,5,6,8,10,17,20,23,26,27,28,31,32,33,35,38,39,42],[5,7,8,9,10,11,12,14,15,19,20,25,26,27,28,31,32,33,36,37,39,40,41,42,43,44],[0,1,4,6,13,15,16,21,22,24,29,31,32,33,36,40,41,43],[2,3,9,13,18,20,22,24,25,29,31,32,33,35,36,37,41,43,44],[0,5,6,7,8,10,13,14,15,18,19,20,23,24,26,29,31,32,33,36,41,42,43],[0,1,3,5,6,8,9,11,12,13,18,21,22,24,25,26,29,31,32,33,35,40,41,42,43,44],[0,2,3,4,7,8,9,10,13,15,17,20,21,22,23,24,27,29,31,32,33,36,37,39,41,42,43,44],[0,1,7,10,12,13,14,16,17,25,27,29,31,32,33,35,36,37,40,41,42,43],[0,1,2,4,5,6,10,26,27,29,31,32,33,36,37,41,43,44],[2,3,6,10,12,13,14,16,17,18,19,20,23,25,26,27,29,31,32,33,35,39,40,41,43],[0,1,5,6,8,9,11,14,15,17,19,20,21,28,29,31,32,33,38],[1,3,6,7,9,11,12,14,16,18,20,24,25,28,29,31,32,33,35,37,40,41,44],[2,3,4,7,8,10,11,12,13,14,20,21,23,24,26,28,29,31,32,33,38],[5,6,7,12,13,14,17,21,22,24,25,26,28,29,31,32,33,35,36,40,41,44],[0,1,2,4,6,8,9,12,14,21,22,24,27,28,29,31,32,33,37,38,39,40,43,44],[0,1,6,10,11,13,14,15,16,17,19,20,23,25,27,28,29,31,32,33,35,37,41,43],[4,5,10,11,12,13,15,18,19,20,23,26,27,28,29,31,32,33,37,38,43,44],[1,2,3,4,5,6,7,8,9,10,11,12,15,18,19,20,23,25,26,27,28,29,31,32,33,35,36,39,40,41,43],[4,5,16,19,21,24,30,31,32,33,35,39,40,41,43],[0,1,2,6,7,9,13,15,17,19,20,24,25,30,31,32,33,35,37,38,40,41,44],[0,3,5,6,7,9,10,11,12,13,14,15,16,18,21,22,23,24,26,30,31,32,33,35,36,43,44],[0,1,3,6,7,15,18,19,21,22,23,24,25,26,30,31,32,33,35,38,39],[2,5,6,10,12,13,14,16,17,19,20,22,23,27,30,31,32,33,38,40,41,42],[1,4,6,7,8,9,10,12,13,15,16,19,20,24,25,27,30,31,32,33,40,41,42,43,44],[0,2,5,6,7,12,14,16,17,20,22,24,26,27,30,31,32,33,36,38,40,42,44],[0,2,7,8,9,10,11,14,17,18,19,20,23,25,26,27,30,31,32,33,37,40,42,43],[0,1,4,6,8,9,10,12,14,16,17,18,19,20,23,28,30,31,32,33,36,38,39,41],[1,4,6,10,11,12,15,17,18,25,28,30,31,32,33,36,37,38,43,44],[0,1,2,6,7,9,14,15,17,26,28,30,31,32,33,38,42,44],[4,6,7,9,11,13,15,18,19,20,23,25,26,28,30,31,32,33,36,38,39,41,42,43],[0,2,3,4,5,6,7,10,15,16,17,18,23,24,27,28,30,31,32,33,35,36,41],[0,2,3,4,5,7,9,10,11,13,16,18,19,20,23,25,27,28,30,31,32,33,35,36,43,44],[0,4,5,7,9,11,16,17,19,20,23,26,27,28,30,31,32,33,35,40,42,44],[0,1,3,4,10,11,12,13,14,18,19,20,23,25,26,27,28,30,31,32,33,35,36,37,40,41,42,43],[6,7,10,13,14,16,18,20,22,24,29,30,31,32,33,36,37,38,40,41,43],[3,4,6,7,8,9,13,16,19,20,23,25,29,30,31,32,33,36,40,41,43,44],[0,1,3,6,7,12,14,16,17,26,29,30,31,32,33,37,38,39,41,43],[1,3,4,5,7,9,11,18,19,20,23,25,26,29,30,31,32,33,36,37,39,41,43,44],[2,6,7,12,16,27,29,30,31,32,33,36,37,38,39,40,41,42,43],[0,2,3,4,6,7,11,12,13,14,15,25,27,29,30,31,32,33,36,37,40,41,42,43,44],[3,4,7,9,14,15,19,20,23,26,27,29,30,31,32,33,37,38,39,40,41,42,43],[2,5,6,7,8,9,10,12,13,15,17,18,19,20,23,25,26,27,29,30,31,32,33,36,40,41,42,43,44],[1,3,6,7,8,9,10,11,15,16,19,20,23,28,29,30,31,32,33,36,37,38,39,41],[0,1,3,4,6,8,9,10,11,12,17,18,19,20,23,25,28,29,30,31,32,33,36,38,39,44],[0,1,7,12,14,26,28,29,30,31,32,33,37,38,41,42],[0,1,2,6,8,10,11,12,14,25,26,28,29,30,31,32,33,36,37,38,42,44],[2,6,7,8,9,13,16,17,18,27,28,29,30,31,32,33,36,37,38,41,43],[0,1,2,4,6,10,11,12,15,16,19,20,23,25,27,28,29,30,31,32,33,36,37,38,39,43,44],[0,2,5,6,8,9,11,12,15,16,18,26,27,28,29,30,31,32,33,37,38,40,41,42,43],[0,1,2,3,5,7,8,11,12,13,15,18,19,20,23,25,26,27,28,29,30,31,32,33,36,38,39,40,42,43,44],[2,4,5,7,8,15,16,17,18,19,20,23,34,38,41,42],[0,1,4,5,11,13,14,16,17,19,20,21,24,25,34,35,36,38,39,41,42,43,44],[5,6,9,10,12,14,15,16,17,21,22,23,24,26,34,36,37,39,40,41,42,44],[1,4,5,8,9,13,16,19,22,23,25,26,34,35,36,40,41,42,43],[0,1,7,8,9,10,12,13,15,17,22,23,27,34,35,42],[0,2,6,8,9,10,11,12,13,14,16,17,19,21,22,23,25,27,34,36,37,42,43,44],[0,1,2,3,9,11,12,13,14,15,16,19,20,22,26,27,34,35,36,37,38,42,44],[2,3,4,9,10,11,13,14,15,16,17,18,19,21,22,23,25,26,27,34,36,37,38,42,43],[1,2,3,5,7,8,11,12,13,14,17,20,21,22,28,34,36,38,40,41,43,44],[0,1,2,3,4,6,7,8,9,14,22,23,24,25,28,34,35,39,40],[0,1,2,4,5,8,10,11,12,16,17,22,24,26,28,34,37,39,40,41,42,43],[0,1,4,7,8,9,11,12,13,16,18,19,20,21,22,23,25,26,28,34,35,38,40,42,44],[0,1,5,6,12,13,14,18,19,21,22,23,24,27,28,34,35,36,40,42,44],[0,1,4,6,8,9,11,14,15,17,18,20,21,22,25,27,28,34,37,38,40,41,42,43],[1,5,7,9,10,11,13,14,15,16,18,21,22,23,26,27,28,34,35,37,38],[0,1,2,6,8,11,15,16,18,20,25,26,27,28,34,37,41,43,44],[0,1,4,5,10,11,12,13,14,16,20,23,24,29,34,35,40,41,43],[0,1,3,4,6,8,9,13,15,17,18,19,20,22,24,25,29,34,36,40,41,43,44],[0,1,2,4,5,7,8,9,10,11,12,13,14,15,16,17,20,23,26,29,34,35,36,37,38,39,43],[1,3,10,11,12,13,15,21,24,25,26,29,34,36,38,39,43,44],[2,4,5,6,7,12,18,19,22,23,27,29,34,35,40],[0,2,3,4,6,7,9,10,11,13,14,16,17,18,19,20,24,25,27,29,34,36,37,39,40,44],[3,5,8,11,13,14,15,16,17,18,26,27,29,34,35,36,37,38,40,41],[2,4,6,7,8,9,11,13,15,23,24,25,26,27,29,34,36,37,38,39,40,41,44],[3,4,9,10,11,13,14,15,16,17,21,22,28,29,34,38,39,41,42,44],[1,2,7,9,15,17,25,28,29,34,35,36,39,42],[0,4,6,7,9,10,11,12,16,19,26,28,29,34,36,37,44],[1,3,4,7,9,10,11,13,16,17,18,20,21,22,24,25,26,28,29,34,35,36,38,41],[0,2,5,8,10,11,12,17,20,21,22,23,27,28,29,34,38,39,44],[1,3,4,5,6,7,12,14,15,16,17,18,19,20,24,25,27,28,29,34,35,36,37,41],[2,4,5,7,8,9,10,12,13,16,19,20,21,23,26,27,28,29,34,36,37,39,40,41,42,44],[1,2,3,4,5,7,9,10,13,15,17,20,21,23,24,25,26,27,28,29,34,35,36,37,38,40,42],[1,4,5,6,11,19,20,23,24,30,34,37,41,42,43],[1,4,5,7,8,9,10,12,13,17,18,20,22,23,24,25,30,34,36,37,38,39,40,41,42,44],[0,2,3,4,7,12,13,14,17,18,19,23,24,26,30,34,38,40,41,43,44],[3,7,8,9,12,13,14,15,17,18,21,22,24,25,26,30,34,37,39,41],[0,1,2,3,5,8,9,10,12,13,17,18,19,21,22,23,24,27,30,34,35,38,40,42,43,44],[1,2,3,5,7,8,11,14,15,16,19,20,21,23,25,27,30,34,35,36,37,42],[3,4,7,8,10,12,14,16,17,19,22,23,24,26,27,30,34,35,37,39,40,43],[2,3,6,7,8,9,10,12,13,16,17,18,19,20,22,23,25,26,27,30,34,35,37,38,39,44],[1,3,9,10,11,12,14,16,17,18,19,20,28,30,34,37,38,39,40,44],[2,3,4,5,9,12,18,23,25,28,30,34,36,37,38,41,43],[3,5,7,8,10,12,17,18,19,20,26,28,30,34,39,40],[0,1,3,6,8,10,16,18,19,20,21,23,24,25,26,28,30,34,37,41,43,44],[0,2,3,5,7,9,10,11,16,18,27,28,30,34,35,39,41,42,43],[1,3,4,6,7,8,9,12,13,16,24,25,27,28,30,34,35,36,37,39,40,42,44],[0,1,2,4,6,8,9,10,11,13,14,15,18,19,26,27,28,30,34,35,37,38,40,41,42,43,44],[0,2,4,5,6,7,9,10,11,12,14,15,18,19,21,23,24,25,26,27,28,30,34,35,37,38,42],[1,2,4,8,9,10,11,12,13,15,16,18,19,21,22,23,24,29,30,34,35,37,39,40,42],[0,3,4,5,9,10,17,18,20,22,24,25,29,30,34,35,36,37,38,39,42,44],[0,3,5,7,8,9,12,14,16,18,20,23,24,26,29,30,34,35,38,39,41],[0,1,4,6,9,10,12,13,14,15,16,17,20,21,24,25,26,29,30,34,35,37,39,40,41,44],[0,1,3,4,5,7,9,11,12,19,21,23,24,27,29,30,34,35,39,41,42,43,44],[0,2,4,6,7,9,13,14,15,16,17,21,22,23,25,27,29,30,34,35,36,37,38,40,41,42,43],[2,3,4,6,10,11,14,22,26,27,29,30,34,35,37,38,43,44],[0,1,2,5,6,7,11,12,15,17,18,19,22,23,24,25,26,27,29,30,34,35,37,39,40,43],[0,1,2,3,4,6,8,9,12,13,14,15,18,19,20,23,24,28,29,30,34,36,37,39,41,43,44],[1,2,7,8,11,12,18,23,25,28,29,30,34,37,39,40,43],[0,2,3,5,7,10,11,14,15,16,18,21,24,26,28,29,30,34,36,38,39,43,44],[0,5,7,9,11,12,13,14,15,16,17,18,19,22,24,25,26,28,29,30,34,36,37,38,39,40,41,43],[3,8,11,12,14,16,17,23,27,28,29,30,34,36,39,40,42,43],[4,7,9,12,14,16,17,18,22,23,25,27,28,29,30,34,37,41,42,43,44],[1,5,7,10,11,13,15,16,17,19,22,23,26,27,28,29,30,34,36,37,38,41,42,43],[0,1,2,3,5,6,7,8,9,11,12,13,16,20,24,25,26,27,28,29,30,34,36,37,38,39,40,42,43,44],[0,2,3,4,5,8,9,13,14,19,31,34,35,41,43],[7,8,9,10,12,13,16,18,19,21,24,25,31,34,36,37,39,40,44],[1,3,6,9,11,12,13,19,20,22,26,31,34,35,36,37,39,40,44],[1,5,9,12,13,18,19,22,24,25,26,31,34,36,37,41,43],[1,3,4,5,7,8,9,11,13,17,20,23,24,27,31,34,35,39,42,43],[1,2,6,9,10,11,14,16,18,21,22,23,25,27,31,34,36,39,40,41,42,44],[0,2,4,7,11,12,16,17,19,23,26,27,31,34,35,36,37,39,41,42,44],[2,3,4,5,7,8,17,18,19,23,24,25,26,27,31,34,36,39,40,42,43],[0,3,7,10,11,12,16,19,20,22,28,31,34,35,36,37,40,41,42,43,44],[1,6,7,8,9,11,12,13,16,17,19,23,24,25,28,31,34,38,39,41,42],[0,1,4,5,7,9,10,14,15,16,17,21,26,28,31,34,35,39,40],[0,2,3,5,8,10,12,15,16,19,20,23,25,26,28,31,34,38,43,44],[2,4,5,6,7,8,9,11,12,14,15,16,17,21,27,28,31,34,35,36,37,39,40,42,44],[1,2,3,4,5,6,7,8,10,11,12,13,14,17,19,20,21,23,24,25,27,28,31,34,37,38,39,42,43],[1,2,4,7,8,9,11,12,13,18,19,20,24,26,27,28,31,34,35,39,41,43],[0,3,6,8,12,13,15,19,20,21,25,26,27,28,31,34,37,38,39,40,41,44],[0,1,2,3,4,5,6,7,8,9,11,12,14,15,16,17,18,19,20,23,29,31,34,38,39,40,44],[0,2,3,5,7,8,14,16,17,20,21,23,24,25,29,31,34,35,36,37,38,39,41],[3,4,6,7,9,10,12,13,16,17,26,29,31,34,36,37,38,43,44],[0,1,2,3,4,6,12,16,17,18,19,22,24,25,26,29,31,34,35,36,37,38,40,41,43],[3,7,8,15,16,17,18,23,27,29,31,34,35,40,41,42,43,44],[0,1,3,4,7,9,11,12,13,14,25,27,29,31,34,36,39,42,43],[0,1,2,4,5,6,7,9,10,12,13,14,16,18,19,20,22,23,24,26,27,29,31,34,35,36,37,40,41,42,44],[0,4,5,8,12,13,14,15,16,17,25,26,27,29,31,34,36,39,42],[1,3,4,5,6,9,10,11,12,13,14,15,16,19,20,23,28,29,31,34,35,37,42],[1,2,3,4,6,7,8,9,10,11,12,17,18,19,20,23,25,28,29,31,34,36,38,40,42,44],[4,13,17,18,26,28,29,31,34,35,36,39,43],[0,5,6,8,10,11,13,14,16,18,25,26,28,29,31,34,36,38,39,40,43,44],[0,1,2,4,5,6,7,8,9,11,12,13,14,15,20,23,24,27,28,29,31,34,37,38,39,41,42],[1,4,8,9,11,12,16,18,19,22,25,27,28,29,31,34,35,36,37,40,41,42,44],[0,2,6,7,8,9,10,11,15,20,21,22,24,26,27,28,29,31,34,36,38,39,40,41,43],[0,2,4,5,6,7,8,9,12,15,17,18,20,23,24,25,26,27,28,29,31,34,35,36,37,41,43,44],[0,5,7,8,9,11,12,13,15,16,17,19,21,22,24,30,31,34,37,42,44],[0,1,3,4,6,8,11,12,13,14,15,16,19,20,21,22,24,25,30,31,34,36,38,39,41,42,43],[0,2,3,5,6,7,8,10,12,14,15,16,17,18,26,30,31,34,40,41,43],[1,6,7,8,9,12,13,15,17,18,19,21,24,25,26,30,31,34,38,39,40,44],[2,3,6,9,11,13,15,16,17,19,24,27,30,31,34,39,40,41],[0,1,2,4,5,6,7,8,11,12,14,15,16,17,18,21,22,23,24,25,27,30,31,34,36,38,39,40,43,44],[3,4,6,9,10,11,14,16,17,19,20,23,26,27,30,31,34,37,40,42,43,44],[1,2,4,5,8,12,14,15,16,18,25,26,27,30,31,34,38,40,41,42],[0,1,2,4,5,6,9,11,12,13,14,16,17,18,19,20,22,23,28,30,31,34,38,39,40,41],[0,1,3,4,5,6,8,9,13,14,15,18,25,28,30,31,34,36,37,38,40,41,43,44],[1,2,4,5,6,8,9,10,11,13,16,17,19,23,26,28,30,31,34,37,38,39,40,43,44],[0,1,2,3,5,7,9,10,11,12,14,15,16,17,25,26,28,30,31,34,37,38,40],[5,6,11,12,14,16,27,28,30,31,34,37,38,43,44],[0,2,3,5,11,13,14,16,25,27,28,30,31,34,36,37,38],[0,3,4,5,8,9,12,13,15,17,26,27,28,30,31,34,38,39,40,41],[0,5,7,8,9,11,12,14,25,26,27,28,30,31,34,37,38,39,40,41,43,44],[7,8,12,14,16,18,20,21,24,29,30,31,34,35,37,40,43],[0,2,4,7,8,10,11,15,16,19,20,23,25,29,30,31,34,35,36,38,40,41,43,44],[2,3,4,7,8,9,10,12,13,15,16,18,26,29,30,31,34,35,42],[2,3,4,6,8,9,11,12,13,15,18,19,20,21,22,23,24,25,26,29,30,31,34,35,38,41,42,44],[0,2,3,4,7,9,11,12,17,18,20,21,22,23,27,29,30,31,34,38,39,41,42,44],[0,3,6,7,8,9,10,14,15,17,18,19,20,23,25,27,29,30,31,34,36,42],[0,3,4,6,7,9,10,12,13,15,26,27,29,30,31,34,37,38,41,43,44],[3,4,6,8,9,10,11,12,14,16,17,19,20,23,25,26,27,29,30,31,34,39,43],[0,1,2,5,6,9,10,12,15,18,28,29,30,31,34,36,41,42,43,44],[2,7,8,10,11,14,16,18,19,21,24,25,28,29,30,31,34,37,41,42,43],[1,2,4,5,8,9,10,11,12,13,15,16,18,19,20,23,26,28,29,30,31,34,36,37,41,42,44],[15,18,19,23,24,25,26,28,29,30,31,34,36,37,41,42],[7,9,11,13,14,16,17,18,27,28,29,30,31,34,35,36,37,38,39,40,42,43],[1,5,12,13,17,18,25,27,28,29,30,31,34,35,37,38,40,42,43,44],[0,3,7,8,10,11,12,14,15,16,26,27,28,29,30,31,34,35,36,38,42],[0,11,14,17,25,26,27,28,29,30,31,34,35,36,37,38,39,42,44],[1,2,6,13,16,17,19,22,24,32,34,39,40,41,44],[0,1,3,4,5,6,9,13,14,15,16,19,20,22,24,25,32,34,35,36,39,40,41,43],[1,2,4,6,8,11,12,15,17,19,21,23,24,26,32,34,36,37,38,40,41,43,44],[1,2,3,4,5,7,8,9,11,12,14,15,18,19,20,23,25,26,32,34,35,36,38,40,41],[0,2,4,5,7,8,9,10,11,12,13,14,15,17,19,21,24,27,32,34,35,36,38,40,41],[0,3,6,7,12,14,15,16,17,19,20,23,25,27,32,34,37,38,39,40,41,43,44],[0,2,3,4,5,6,7,9,11,12,14,15,16,18,26,27,32,34,35,37,41,43],[2,4,6,8,9,10,13,16,17,19,20,23,25,26,27,32,34,37,39,41,44],[5,7,12,14,28,32,34,35,36,39,43],[0,1,3,5,6,8,9,10,11,12,13,16,17,18,22,23,24,25,28,32,34,38,39,41,44],[0,2,3,4,5,6,7,10,12,15,16,19,22,23,24,26,28,32,34,35,37,38,40,42],[0,1,5,6,7,8,9,11,13,15,16,17,18,19,20,23,25,26,28,32,34,40,41,42,43,44],[0,3,5,7,9,10,11,13,14,15,16,17,22,23,27,28,32,34,38,42,44],[0,1,5,9,10,11,17,19,20,21,22,23,25,27,28,32,34,35,36,37,39,41,42,43],[2,3,5,7,9,12,26,27,28,32,34,36,37,43,44],[0,1,4,5,6,7,10,13,14,16,25,26,27,28,32,34,35,36,37,38,39,41],[0,1,2,4,5,7,8,12,14,15,17,18,22,23,29,32,34,35,36,38,40,41,42,43,44],[0,2,5,6,8,10,11,15,25,29,32,34,38,39,40,41,42,43],[0,1,2,4,5,6,7,9,11,12,14,15,16,18,26,29,32,34,35,37,39,40,42],[4,5,6,7,9,10,11,13,15,16,18,19,20,23,25,26,29,32,34,40,42,44],[2,4,5,7,9,10,12,14,16,19,20,23,27,29,32,34,35,38,39,40,41,42],[0,1,2,5,8,9,10,13,14,17,18,19,20,23,25,27,29,32,34,36,37,38,39,40,41,42,44],[2,3,5,7,8,10,11,12,15,16,18,19,20,23,26,27,29,32,34,35,36,37,39,42,43,44],[1,3,5,6,7,9,10,12,14,17,25,26,27,29,32,34,36,37,39,42,43],[5,6,8,9,10,13,14,18,28,29,32,34,35,36,39,42],[2,6,9,11,12,15,17,19,20,23,25,28,29,32,34,38,41,42,44],[0,2,3,5,6,8,10,13,16,19,20,23,26,28,29,32,34,35,37,38,40,41,43,44],[2,3,4,7,14,17,20,23,24,25,26,28,29,32,34,39,40,43],[0,3,4,7,8,9,11,12,13,15,16,19,20,23,27,28,29,32,34,35,44],[2,3,4,5,6,7,8,12,13,17,25,27,28,29,32,34,36,37,38,41],[2,3,6,7,8,9,10,11,17,18,26,27,28,29,32,34,35,36,37,38,41,42,43],[2,3,4,5,6,8,9,10,13,15,17,18,25,26,27,28,29,32,34,36,37,42,43,44],[5,6,7,8,9,10,13,17,30,32,34,35,39,41,42,43],[1,3,4,7,8,9,13,17,25,30,32,34,35,36,38,39,40,41,42,44],[0,1,3,6,7,8,9,10,13,14,15,16,18,19,20,23,26,30,32,34,35,37,38,39,41],[2,5,6,8,14,15,17,18,25,26,30,32,34,35,39,40,41,43,44],[0,3,4,5,6,8,9,10,13,16,18,19,20,23,27,30,32,34,36,37,38,40,41,42,43],[1,6,8,9,10,11,13,14,15,17,18,19,20,23,25,27,30,32,34,39,41,42,44],[1,3,8,10,16,19,20,23,26,27,30,32,34,36,39,41],[2,5,6,7,8,13,15,17,18,19,20,23,25,26,27,30,32,34,36,38,40,41,43,44],[2,5,6,10,12,15,16,19,20,23,28,30,32,34,38,40,41,42,44],[3,5,6,7,8,10,11,15,16,17,18,19,20,23,25,28,30,32,34,36,38,42,43],[1,21,22,23,24,26,28,30,32,34,37,41,42,43,44],[0,1,3,4,6,8,10,13,17,19,20,23,25,26,28,30,32,34,40,42],[0,1,2,9,12,13,14,18,27,28,30,32,34,35,36,37,39,41,43,44],[1,3,6,7,8,10,13,14,16,17,25,27,28,30,32,34,35,40],[0,3,4,5,8,10,11,12,13,17,18,19,20,23,26,27,28,30,32,34,35,36,38,41,44],[0,5,11,13,14,15,16,17,18,19,20,23,25,26,27,28,30,32,34,35,36,38,39,40,43],[1,4,5,6,7,9,12,13,14,16,17,19,20,23,29,30,32,34,36,39,42],[0,1,2,5,6,8,11,12,14,15,17,18,25,29,30,32,34,38,40,42,44],[0,3,7,8,11,12,13,14,16,17,18,19,20,23,26,29,30,32,34,36,37,38,39,41,43,44],[0,3,6,7,8,9,11,12,15,16,25,26,29,30,32,34,36,40,41,43],[0,1,3,4,7,12,14,15,16,19,20,23,27,29,30,32,34,37,40,42,43],[0,1,2,3,6,9,10,13,15,16,17,19,20,23,25,27,29,30,32,34,36,38,42,43,44],[3,4,5,7,13,16,17,19,20,23,26,27,29,30,32,34,38,39,41,44],[0,3,4,5,7,8,9,11,12,18,25,26,27,29,30,32,34,39,40,41],[0,1,2,6,9,11,12,13,14,16,28,29,30,32,34,39,40,42,43,44],[2,5,11,14,17,18,25,28,29,30,32,34,36,41,42,43],[0,4,5,6,9,12,16,17,26,28,29,30,32,34,37,38,39,41,42],[0,1,2,6,7,8,9,10,11,12,16,19,20,23,25,26,28,29,30,32,34,38,40,42,44],[2,4,6,7,9,11,13,18,27,28,29,30,32,34,36,37,43,44],[1,2,4,5,6,7,9,11,12,13,14,15,18,19,20,23,25,27,28,29,30,32,34,40,41,43],[1,3,4,5,8,9,11,13,16,17,26,27,28,29,30,32,34,36,38,39,41],[1,4,5,8,9,12,14,15,16,17,25,26,27,28,29,30,32,34,36,38,39,40,44],[1,2,4,5,6,7,9,11,14,15,16,18,31,32,34,37,38,39,42,43],[0,4,5,6,8,9,10,11,12,14,16,17,18,19,20,23,25,31,32,34,35,36,38,39,40,41,42,44],[0,2,6,7,10,11,12,13,16,19,20,23,26,31,32,34,36,38,41,42,43],[0,1,2,4,7,8,11,14,16,17,25,26,31,32,34,35,36,38,40,42,44],[0,2,4,5,12,13,14,15,16,17,27,31,32,34,36,37,38,39,43,44],[0,1,4,5,6,10,17,19,20,23,25,27,31,32,34,35,37,38,40,41],[1,2,3,4,6,8,9,12,13,16,18,19,20,21,22,23,24,26,27,31,32,34,38,39,40,41,43,44],[0,2,3,6,9,10,16,18,25,26,27,31,32,34,35,37,38],[1,2,3,4,5,9,12,13,15,16,18,19,20,23,28,31,32,34,35,36,38,39,40,41,42,43,44],[0,1,2,3,6,9,13,14,16,18,25,28,31,32,34,37,39,41,42],[6,7,12,15,16,17,26,28,31,32,34,35,37,38,43,44],[2,5,6,7,10,11,14,19,20,23,25,26,28,31,32,34,37,40],[0,1,2,10,12,13,15,16,17,18,27,28,31,32,34,35,38,39,40,41,42],[0,1,2,4,5,9,13,17,18,19,20,23,25,27,28,31,32,34,36,41,42,43,44],[0,5,7,9,11,12,13,14,16,17,26,27,28,31,32,34,35,36,37,38,39,40],[2,6,7,10,11,13,16,18,25,26,27,28,31,32,34,36,43,44],[1,6,7,9,15,16,18,19,20,23,29,31,32,34,35,36,37,39,41,42,44],[1,3,5,6,13,14,16,17,25,29,31,32,34,40,42],[0,5,7,8,12,14,15,16,26,29,31,32,34,35,41,42],[2,3,4,7,8,9,12,14,15,17,18,19,20,23,25,26,29,31,32,34,39,40,42,44],[0,4,5,6,7,12,14,15,17,18,27,29,31,32,34,37,38,39,41,43],[3,4,6,8,12,13,15,19,20,23,25,27,29,31,32,34,35,36,37,38,39,40,43,44],[1,3,6,11,12,15,16,17,26,27,29,31,32,34,36,38,39,40,41,43,44],[1,2,4,5,8,9,10,11,12,13,14,15,17,19,20,23,25,26,27,29,31,32,34,35,36,37,38,39,43],[0,1,3,4,5,7,8,10,11,14,17,18,28,29,31,32,34,35,36,38,40,42],[0,2,5,8,12,13,25,28,29,31,32,34,37,39,42,44],[0,2,4,13,14,15,17,18,26,28,29,31,32,34,35,37,38,39,44],[1,2,3,4,8,13,18,19,20,23,25,26,28,29,31,32,34,37,40],[1,4,5,6,7,9,10,14,27,28,29,31,32,34,40,42,44],[0,2,3,5,7,9,10,12,13,14,15,16,25,27,28,29,31,32,34,35,36,38,42],[2,4,5,6,10,17,18,19,20,23,26,27,28,29,31,32,34,36,37,40],[0,7,8,11,14,16,17,19,20,23,25,26,27,28,29,31,32,34,35,36,38,44],[1,3,6,9,13,17,18,19,20,23,30,31,32,34,37,39,40,41,42],[1,3,6,9,10,14,25,30,31,32,34,36,38,39,40,42,43,44],[1,6,7,8,9,10,11,12,14,15,16,19,20,23,26,30,31,32,34,39,40],[0,1,2,4,6,7,8,9,11,12,13,14,15,16,25,26,30,31,32,34,38,39,40,41,43,44],[0,1,5,7,10,11,12,14,17,19,20,23,27,30,31,32,34,36,39,41],[1,5,6,9,10,12,25,27,30,31,32,34,38,43,44],[0,1,4,5,8,12,13,15,18,19,20,23,26,27,30,31,32,34,36,37,40,42],[0,1,2,5,8,9,13,14,25,26,27,30,31,32,34,36,38,39,40,41,42,43,44],[5,8,9,11,12,16,18,19,20,23,28,30,31,32,34,35,38,41,42,44],[1,2,4,8,10,12,13,14,15,18,25,28,30,31,32,34,35,36,37,38,41,42,43],[0,2,5,6,7,8,9,10,11,12,14,15,26,28,30,31,32,34,35,37,38,40,42,44],[0,3,9,11,12,13,18,19,20,23,25,26,28,30,31,32,34,35,37,38,40,42,43],[0,1,4,5,6,8,11,12,13,16,18,19,20,23,27,28,30,31,32,34,35,36,37,38,40,41,42,43,44],[0,1,3,4,5,6,11,13,15,16,17,18,25,27,28,30,31,32,34,35,37,38,39,40,41,42],[1,5,7,8,9,11,13,18,26,27,28,30,31,32,34,35,36,38,39,40,42,43,44],[0,1,2,3,6,7,8,9,10,11,13,17,18,19,20,23,25,26,27,28,30,31,32,34,35,36,37,38,40,42],[0,2,4,11,13,14,15,16,29,30,31,32,34,35,36,37,40,41,43,44],[6,10,12,19,20,23,25,29,30,31,32,34,35,38,39,40,43],[0,2,6,7,8,9,11,14,15,16,26,29,30,31,32,34,35,36,40,41,42,43],[0,3,4,5,6,8,9,12,14,15,16,17,25,26,29,30,31,32,34,35,36,38,39,40,42,43,44],[2,5,6,9,12,13,14,17,18,19,20,23,27,29,30,31,32,34,38,41,42,44],[2,3,6,8,10,12,15,16,17,18,25,27,29,30,31,32,34,36,42],[2,3,5,6,8,10,12,13,15,16,26,27,29,30,31,32,34,37,38,39,40,41],[1,4,6,13,17,18,25,26,27,29,30,31,32,34,39,40,44],[1,2,6,12,19,23,24,28,29,30,31,32,34,35,41,43],[1,2,4,7,8,9,10,12,17,19,20,23,25,28,29,30,31,32,34,35,36,37,39,41,43,44],[2,5,6,7,13,14,16,17,26,28,29,30,31,32,34,35,37,40,41,43,44],[0,2,3,5,6,9,10,11,13,16,17,18,25,26,28,29,30,31,32,34,35,37,39,40,41,43],[1,4,5,10,11,13,14,16,18,19,20,23,27,28,29,30,31,32,34,36,37,38,40,41,43],[0,1,2,3,4,6,7,8,9,11,14,16,17,18,25,27,28,29,30,31,32,34,37,38,40,41,43,44],[0,1,3,6,7,8,10,12,14,18,26,27,28,29,30,31,32,34,36,38,39,40,41,43,44],[25,26,27,28,29,30,31,32,34,36,37,38,39,40,41,43],[0,6,7,8,9,12,14,16,33,34,35,36,37,42],[0,1,7,8,10,11,12,13,25,33,34,37,39,41,42],[1,3,4,5,10,11,13,14,15,16,17,19,20,23,26,33,34,35,38,39,40,44],[0,2,3,5,8,10,13,14,25,26,33,34,37,38,40,41,44],[1,2,3,5,6,7,8,10,11,13,14,15,17,18,27,33,34,38,39,40,41,42,43],[0,2,3,5,7,8,10,11,13,14,16,17,25,27,33,34,35,36,37,38,39,40,42,43],[0,2,3,6,7,11,12,13,14,15,26,27,33,34,36,37,39,40,41,43,44],[0,1,3,4,6,9,10,11,14,16,17,18,25,26,27,33,34,35,36,37,39,40,43,44],[2,5,6,7,8,11,12,13,14,15,16,19,20,23,28,33,34,35,39,42,43],[4,6,7,9,10,13,15,16,25,28,33,34,36,38,42,43],[1,4,6,8,11,13,15,17,18,19,20,23,26,28,33,34,35,36,37,38,42,43,44],[0,1,4,6,10,12,14,16,18,19,20,23,25,26,28,33,34,36,39,42,43,44],[0,4,5,6,8,11,13,15,16,19,20,23,27,28,33,34,36,37,38,40,41,43],[2,7,9,11,14,15,18,19,20,23,25,27,28,33,34,35,40,41,43],[0,1,2,3,4,5,8,12,13,14,18,19,20,23,26,27,28,33,34,41,43,44],[0,1,2,3,4,9,11,12,14,16,17,19,20,23,25,26,27,28,33,34,35,38,41,43,44],[0,2,8,11,17,19,20,23,29,33,34,35,36,37,38,40,43,44],[3,5,8,9,11,14,25,29,33,34,37,38,40,41,44],[1,2,3,6,8,9,11,12,13,14,16,17,26,29,33,34,35,39,41,42,43,44],[1,2,4,5,6,7,9,10,12,13,14,16,17,18,25,26,29,33,34,37,39,42,44],[1,3,4,6,7,11,12,13,15,16,18,19,20,23,27,29,33,34,35,38,39,41,43,44],[1,2,4,8,15,16,17,19,20,23,25,27,29,33,34,36,37,38,44],[0,3,6,7,10,11,13,19,20,23,26,27,29,33,34,35,36,37,39,42,43,44],[4,6,7,8,10,13,17,18,25,26,27,29,33,34,36,37,41,42,44],[0,4,6,7,10,11,12,14,15,19,20,23,28,29,33,34,36,40,44],[1,3,8,10,11,12,16,17,18,19,20,23,25,28,29,33,34,35,38,40,43,44],[0,1,2,4,5,6,7,8,9,10,11,12,14,15,26,28,29,33,34,37,38,39,40,41,44],[0,3,4,7,9,11,12,15,18,19,20,23,25,26,28,29,33,34,35,39,40,41,43,44],[2,4,7,9,10,14,15,17,27,28,29,33,34,37,39,41,42,43,44],[1,2,3,6,9,14,15,16,17,19,20,23,25,27,28,29,33,34,35,36,38,41,42,44],[1,3,5,7,10,12,16,17,18,19,20,23,26,27,28,29,33,34,36,38,39,40,42,43,44],[0,2,5,8,9,11,13,14,16,18,25,26,27,28,29,33,34,35,36,40,42,44],[0,1,2,5,8,9,15,18,30,33,34,35,36,38,39],[1,8,9,10,18,19,20,23,25,30,33,34,35,40,41],[0,1,2,4,5,6,7,9,11,12,13,14,15,19,20,23,26,30,33,34,35,36,37,39,40,44],[0,1,2,4,5,7,8,11,12,13,14,15,17,19,20,23,25,26,30,33,34,35,36,38,41,44],[1,4,5,6,7,10,11,13,18,19,20,23,27,30,33,34,41,43,44],[1,2,4,6,7,8,9,10,12,13,14,15,18,19,20,23,25,27,30,33,34,36,37,38,40,43,44],[1,3,4,7,12,15,16,17,26,27,30,33,34,37,38,39,41,43],[0,1,3,4,5,6,8,12,15,16,18,19,20,23,25,26,27,30,33,34,37,39,40,43],[5,6,8,9,10,11,13,15,18,19,20,23,28,30,33,34,35,36,37,39,41,43],[0,1,4,5,6,10,12,14,15,16,17,19,20,23,25,28,30,33,34,35,37,40,41,43],[0,2,3,6,8,9,10,11,12,13,14,15,18,19,20,23,26,28,30,33,34,35,36,38,39,41,42,43,44],[0,1,3,4,5,6,7,8,12,14,17,19,20,23,25,26,28,30,33,34,35,36,37,38,40,41,42,43,44],[0,1,2,3,4,7,9,10,11,13,14,16,27,28,30,33,34,37,38,42,43,44],[0,2,3,5,7,8,11,12,13,15,16,17,18,19,20,23,25,27,28,30,33,34,36,38,40,42,43,44],[1,3,4,6,9,10,11,14,16,17,26,27,28,30,33,34,39,40,43],[0,2,3,4,5,7,12,14,15,16,25,26,27,28,30,33,34,39,43],[4,6,10,14,15,16,18,19,20,23,29,30,33,34,35,36,38,40,41,43,44],[1,3,4,5,9,10,12,13,15,18,25,29,30,33,34,35,44],[4,5,6,8,9,10,11,12,13,14,15,16,17,19,20,23,26,29,30,33,34,35,36,37,43,44],[0,1,2,3,5,6,7,10,11,15,18,19,20,23,25,26,29,30,33,34,35,36,38,40,41,44],[0,2,4,7,8,10,12,13,16,17,27,29,30,33,34,35,38,39,40,43],[1,2,3,6,8,13,16,17,18,19,20,23,25,27,29,30,33,34,35,36,37,41],[0,2,4,6,7,8,12,13,15,19,20,23,26,27,29,30,33,34,35,37,40,41,43],[0,1,3,4,5,6,7,9,10,11,14,15,16,18,25,26,27,29,30,33,34,35,37,38,39],[1,2,4,5,6,7,8,11,12,13,16,19,20,23,28,29,30,33,34,37,38,39,40,44],[1,6,8,11,12,13,14,15,17,19,20,23,25,28,29,30,33,34,36,37,38,39,43,44],[0,1,6,8,10,12,15,16,17,18,26,28,29,30,33,34,39,40,41,42,44],[1,3,5,6,8,14,15,17,18,19,20,23,25,26,28,29,30,33,34,37,39,41,42,43,44],[0,3,8,10,11,12,13,15,16,18,27,28,29,30,33,34,36,37,38,40,41,42,43],[3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,23,25,27,28,29,30,33,34,38,39,41,42],[2,3,4,7,8,9,10,16,17,19,20,23,26,27,28,29,30,33,34,36,39,43],[0,1,2,3,4,7,9,10,11,12,15,17,25,26,27,28,29,30,33,34,36,40],[0,2,3,4,5,7,8,10,31,33,34,35,36,38,41],[0,2,5,7,9,10,11,13,15,16,25,31,33,34,37,38,39,40,41],[0,2,3,4,5,6,7,8,10,12,14,18,26,31,33,34,35,37,38,39,40,42,43,44],[3,8,14,15,17,19,20,23,25,26,31,33,34,37,38,42,43,44],[1,3,6,7,8,9,10,13,14,16,17,19,20,23,27,31,33,34,35,37,38,40,42,43],[0,1,7,8,10,12,13,16,17,18,25,27,31,33,34,36,37,38,42,43],[1,5,9,12,14,19,20,23,26,27,31,33,34,35,36,38,40,41,44],[1,2,5,6,7,9,11,12,14,19,20,23,25,26,27,31,33,34,36,37,38,41,44],[1,2,3,4,5,6,9,11,15,17,18,19,20,23,28,31,33,34,35,38,39,41],[3,4,7,8,13,14,17,19,20,23,25,28,31,33,34,36,37,40],[0,1,4,6,7,11,14,15,16,17,26,28,31,33,34,35,36,37,38,43,44],[3,4,6,8,9,11,14,16,17,18,25,26,28,31,33,34,36,37,39,40,41,43,44],[0,1,3,4,7,9,11,12,13,14,16,19,20,23,27,28,31,33,34,35,36,37,38,39,40],[2,3,4,6,10,13,14,17,18,19,20,23,25,27,28,31,33,34,37,39,41],[1,4,5,6,7,9,10,13,16,17,26,27,28,31,33,34,35,38,39,41,43,44],[0,1,2,4,5,7,8,9,10,11,12,13,18,19,20,23,25,26,27,28,31,33,34,37,39,40,43,44],[3,4,5,6,8,11,13,15,16,19,20,23,29,31,33,34,35,36,39,40,43],[0,1,4,5,8,11,12,14,17,19,20,23,25,29,31,33,34,37,39],[3,5,8,11,14,15,16,19,20,23,26,29,31,33,34,35,37,42],[1,2,4,8,9,11,13,14,15,18,25,26,29,31,33,34,37,40,42,43],[0,1,3,4,5,6,9,11,14,16,18,19,20,23,27,29,31,33,34,37,38,39,41,42,43],[0,7,9,10,11,13,14,15,16,17,25,27,29,31,33,34,35,36,37,38,40,41,42],[0,1,2,4,9,10,12,15,16,18,26,27,29,31,33,34,36,38,39,41],[0,1,2,5,9,11,15,16,18,19,20,23,25,26,27,29,31,33,34,35,36,37,38,40,41,43],[1,2,4,5,7,8,10,11,14,17,28,29,31,33,34,36,38,39,40,43],[0,1,4,5,7,9,12,13,16,17,18,19,20,23,25,28,29,31,33,34,35,37,39,41],[0,1,4,6,7,9,10,11,13,16,17,18,26,28,29,31,33,34,37,38,40],[2,3,5,6,7,11,13,14,16,17,25,26,28,29,31,33,34,35,37,41,43],[0,1,2,3,5,8,10,12,13,15,16,18,27,28,29,31,33,34,35,37,39,41],[0,1,10,11,14,15,16,19,20,23,25,27,28,29,31,33,34,36,37,38,40,43],[1,3,7,11,12,13,14,17,26,27,28,29,31,33,34,35,36,39,40,41,43],[0,1,4,7,10,12,14,17,18,19,20,23,25,26,27,28,29,31,33,34,36,37,38],[0,2,4,5,6,7,8,10,12,13,15,16,30,31,33,34,36,37,38,39,44],[1,5,7,8,9,10,13,16,18,19,20,23,25,30,31,33,34,44],[1,2,3,4,7,9,10,13,14,17,26,30,31,33,34,36,38,39,40,41,43],[2,4,5,10,11,12,14,15,16,17,18,19,20,23,25,26,30,31,33,34,36,40,41,43],[3,4,11,12,13,15,17,18,27,30,31,33,34,37,38,39,41,42,43],[1,5,12,14,15,16,25,27,30,31,33,34,36,37,39,41,42,43],[0,7,9,10,13,16,17,18,26,27,30,31,33,34,38,42,44],[0,2,3,5,7,11,12,15,25,26,27,30,31,33,34,37,42,44],[3,4,8,11,12,14,17,19,20,23,28,30,31,33,34,36,37,39,41,44],[0,1,3,5,7,9,12,15,16,17,18,19,20,23,25,28,30,31,33,34,44],[4,5,6,7,10,11,14,15,17,19,20,23,26,28,30,31,33,34,36,39,42,43],[0,2,3,5,6,7,9,11,14,17,18,19,20,23,25,26,28,30,31,33,34,36,41,42,43],[0,4,5,6,8,12,16,17,18,19,20,23,27,28,30,31,33,34,37,39],[0,1,2,3,4,5,8,10,11,12,14,15,16,18,25,27,28,30,31,33,34,36,37,39,41],[5,7,9,10,12,13,14,15,16,18,26,27,28,30,31,33,34,40,41,42,43,44],[0,1,3,5,6,9,10,12,13,14,15,16,25,26,27,28,30,31,33,34,37,40,42,43,44],[0,2,3,4,11,12,13,16,17,18,29,30,31,33,34,36,37,38,39,40,42,43,44],[0,1,2,5,8,9,10,11,16,17,18,19,20,23,25,29,30,31,33,34,39,40,42,44],[1,2,6,8,9,10,11,14,15,19,20,23,26,29,30,31,33,34,36,38,39,42,44],[0,3,4,5,6,7,8,9,11,15,16,17,25,26,29,30,31,33,34,36,39,42,43,44],[0,3,6,7,8,9,10,12,15,16,17,19,20,23,27,29,30,31,33,34,35,37,39,40,41,43],[1,2,3,4,6,7,8,9,10,12,14,15,17,19,20,23,25,27,29,30,31,33,34,35,36,37,38,40,41],[0,1,2,4,6,7,9,10,11,12,13,16,26,27,29,30,31,33,34,35,40,41],[1,2,3,5,6,7,9,10,13,18,25,26,27,29,30,31,33,34,35,37,38,39,40,41,43],[0,1,4,6,10,11,13,14,16,18,21,22,28,29,30,31,33,34,35,37,38,40,41,42,43,44],[1,3,5,7,8,11,14,15,17,19,20,23,25,28,29,30,31,33,34,35,36,38,40,42,44],[3,4,5,6,7,9,14,15,16,17,18,19,20,23,26,28,29,30,31,33,34,35,38,40,41,44],[0,1,2,3,8,9,11,12,14,15,16,17,25,26,28,29,30,31,33,34,35,38,40,43,44],[0,1,2,6,8,11,12,16,17,19,20,23,27,28,29,30,31,33,34,36,37,40,42],[5,6,10,12,15,17,18,19,20,23,25,27,28,29,30,31,33,34,37,39,40,41,42,43],[0,2,3,4,5,6,8,11,14,15,17,19,20,23,26,27,28,29,30,31,33,34,36,39,43],[25,26,27,28,29,30,31,33,34,36,37,41],[0,1,3,4,6,7,8,10,12,14,15,16,32,33,34,35,36,39,40,43],[0,1,2,3,4,6,10,16,18,19,20,23,25,32,33,34,39,40,41,43],[3,5,11,13,14,15,16,18,26,32,33,34,35,37,38,40,42],[0,2,3,6,7,10,11,13,18,19,20,23,25,26,32,33,34,38,40,41,42],[2,6,9,11,18,19,20,23,27,32,33,34,36,37,38,39,44],[0,1,2,3,5,6,7,9,11,13,14,15,16,19,20,23,25,27,32,33,34,35,38,41,44],[0,1,3,5,9,11,12,13,18,19,20,23,26,27,32,33,34,39,40,42,43,44],[0,1,2,3,4,6,7,8,9,11,13,14,15,16,17,18,25,26,27,32,33,34,35,40,41,42,43,44],[1,3,4,6,7,12,13,15,17,18,28,32,33,34,37,40,41,42],[1,2,3,5,8,9,11,14,25,28,32,33,34,35,36,37,38,40,41,42],[2,3,4,5,7,11,12,13,14,17,26,28,32,33,34,36,38,39,41,42,43],[0,2,3,7,9,10,11,17,25,26,28,32,33,34,35,36,37,39,41,42,43],[0,2,4,6,7,10,12,13,16,19,20,23,27,28,32,33,34,35,38,41,44],[0,1,3,4,5,8,10,11,13,14,15,16,25,27,28,32,33,34,36,37,39,41,44],[3,7,8,9,10,11,12,16,18,19,20,23,26,27,28,32,33,34,35,36,37,41,43,44],[0,3,4,8,9,10,13,14,16,17,18,19,20,23,25,26,27,28,32,33,34,36,37,38,39,41,43,44],[0,3,6,12,16,18,19,20,22,23,29,32,33,34,35,38,40,42,44],[1,2,3,4,7,8,10,11,14,15,17,18,21,23,25,29,32,33,34,36,38,39,40,41,42,43,44],[1,2,5,7,8,9,10,11,12,15,19,21,22,23,24,26,29,32,33,34,35,36,37,39,40,41,43],[0,6,7,8,11,12,14,17,18,19,20,23,25,26,29,32,33,34,36,40],[1,4,7,9,10,11,12,13,17,18,27,29,32,33,34,35,37,38,42],[0,2,3,4,6,7,8,10,12,13,14,16,25,27,29,32,33,34,36,38,41,42,43],[0,1,4,5,7,8,9,11,17,18,26,27,29,32,33,34,35,36,40,41,43,44],[0,2,4,5,6,11,15,17,25,26,27,29,32,33,34,36,40,44],[0,5,6,7,10,12,14,15,21,23,28,29,32,33,34,35,37,40,41,43,44],[2,3,4,6,7,9,10,14,16,17,25,28,29,32,33,34,36,37,38,39,40,41,44],[0,1,3,4,5,6,9,10,12,14,15,16,17,18,26,28,29,32,33,34,35,36,38,39],[1,2,5,7,8,9,15,18,25,26,28,29,32,33,34,36,37,43],[3,5,8,9,13,18,27,28,29,32,33,34,35,41,42],[0,1,4,7,8,10,13,14,15,16,25,27,28,29,32,33,34,36,37,38,41,42,43],[4,5,7,8,9,12,16,17,26,27,28,29,32,33,34,35,36,37,38,42,43,44],[0,3,5,6,8,12,14,15,16,17,18,19,20,23,25,26,27,28,29,32,33,34,36,37,42,44],[0,2,3,4,6,13,15,16,17,18,19,22,30,32,33,34,36,43,44],[1,5,8,10,11,12,16,17,18,19,20,22,24,25,30,32,33,34,38,40,41,43,44],[0,3,4,6,7,10,12,15,16,17,18,22,26,30,32,33,34,36,37,38,44],[0,1,2,4,6,9,12,13,14,15,16,17,18,19,20,23,25,26,30,32,33,34,36,40,41,44],[2,3,4,8,10,11,12,13,14,16,18,20,24,27,30,32,33,34,35,36,38,44],[1,2,3,6,8,9,11,17,25,27,30,32,33,34,35,37,39,40,41,44],[0,5,6,7,9,10,11,16,26,27,30,32,33,34,35,36,37,39,40,43,44],[3,5,6,7,9,15,17,19,20,23,25,26,27,30,32,33,34,35,36,37,38,41,43,44],[1,2,5,7,13,14,15,16,17,18,19,21,22,23,24,28,30,32,33,34,35,36,37,38,42,44],[2,3,4,5,8,10,11,13,14,18,25,28,30,32,33,34,35,37,38,40,42,44],[0,4,6,7,9,10,11,13,14,15,16,17,26,28,30,32,33,34,35,36,40,43,44],[0,5,7,8,9,11,13,14,15,18,25,26,28,30,32,33,34,35,36,37,43,44],[0,1,3,4,8,11,17,19,20,23,27,28,30,32,33,34,36,37,44],[0,4,8,11,13,15,16,19,20,23,25,27,28,30,32,33,34,39,40,44],[0,3,4,6,10,12,13,15,18,19,20,23,26,27,28,30,32,33,34,36,38,39,42,43,44],[3,4,6,7,10,13,14,17,18,19,20,23,25,26,27,28,30,32,33,34,36,38,40,42,43,44],[2,3,6,8,9,11,13,14,15,16,17,19,20,21,22,23,29,30,32,33,34,41],[0,4,6,7,8,9,10,12,13,15,16,19,20,23,25,29,30,32,33,34,36,38,39,40,43],[3,4,5,10,11,12,15,17,18,19,20,23,26,29,30,32,33,34,37,38,43,44],[1,3,4,6,8,9,12,13,14,18,25,26,29,30,32,33,34,39,40,41,44],[0,1,5,6,7,12,13,14,15,18,27,29,30,32,33,34,41],[0,1,3,7,9,11,14,15,18,19,20,23,25,27,29,30,32,33,34,36,37,38,40,43],[0,1,2,5,7,8,9,10,14,15,18,19,20,23,26,27,29,30,32,33,34,37,38,39,40,43,44],[1,10,14,15,16,19,20,23,25,26,27,29,30,32,33,34,37,39,41,44],[0,2,7,9,10,11,17,18,28,29,30,32,33,34,36,37,39,41,42,43],[2,4,5,6,8,9,11,12,13,15,25,28,29,30,32,33,34,37,40,41,42],[0,9,10,13,15,16,26,28,29,30,32,33,34,36,38,39,40,44],[0,1,2,4,5,6,7,8,11,13,14,15,16,17,18,19,20,23,25,26,28,29,30,32,33,34,36,37,38,43,44],[2,6,8,12,13,14,16,17,18,19,20,23,27,28,29,30,32,33,34,36,37,39,41],[0,2,3,4,6,10,13,19,20,23,25,27,28,29,30,32,33,34,39,40,41,43],[3,4,6,7,10,14,18,19,20,23,26,27,28,29,30,32,33,34,36,38,42,43,44],[25,26,27,28,29,30,32,33,34,36,38,40,42,44],[1,2,4,5,6,7,8,10,11,12,13,14,15,18,19,20,21,22,31,32,33,34,36,38,39,42,43,44],[2,4,5,6,7,8,9,11,13,15,16,17,19,20,22,23,24,25,31,32,33,34,35,37,38,39,40,42,43,44],[1,3,5,6,7,11,12,13,16,17,24,26,31,32,33,34,37,38,41,43,44],[0,1,5,7,11,13,14,16,17,18,25,26,31,32,33,34,35,37,38,40,41,43,44],[0,2,3,5,6,8,9,10,12,14,15,16,18,20,21,23,24,27,31,32,33,34,36,37,38,40],[1,2,3,5,6,8,11,12,16,17,18,19,20,23,25,27,31,32,33,34,35,37,38,39],[1,5,6,7,8,9,12,14,17,18,26,27,31,32,33,34,38,41,42],[0,1,3,4,9,12,14,16,17,19,20,23,25,26,27,31,32,33,34,35,37,38,39,40,41,42],[0,6,7,10,18,20,24,28,31,32,33,34,35,38,41,43,44],[0,1,3,4,9,11,14,16,18,19,20,23,25,28,31,32,33,34,36,37,40,43,44],[1,2,3,4,5,7,8,10,13,15,16,17,26,28,31,32,33,34,35,36,37,38,39,40,43,44],[0,1,2,3,5,6,7,10,12,13,14,16,17,19,20,23,25,26,28,31,32,33,34,36,37,39,41,43,44],[2,5,6,16,17,18,27,28,31,32,33,34,35,37,38,39,40,41,43],[0,2,4,6,8,9,11,13,25,27,28,31,32,33,34,36,37,43],[4,6,8,9,10,15,16,19,20,23,26,27,28,31,32,33,34,35,36,38,39,40,43],[0,1,2,3,6,8,10,11,12,13,25,26,27,28,31,32,33,34,36,37,41,43],[0,6,8,12,14,15,17,18,20,23,24,29,31,32,33,34,39,41,42,44],[2,6,7,11,13,14,16,17,25,29,31,32,33,34,35,36,37,40,41,42,43,44],[2,3,6,8,11,13,14,15,18,19,20,23,26,29,31,32,33,34,36,37,41],[0,1,2,6,7,10,11,14,18,19,20,23,25,26,29,31,32,33,34,35,36,37,39,40,41,43],[1,2,5,9,12,13,18,19,20,23,27,29,31,32,33,34,35,37,38,40,41],[1,2,5,6,8,9,13,14,17,18,25,27,29,31,32,33,34,36,37,38,41,43],[1,3,5,8,10,11,12,13,14,16,26,27,29,31,32,33,34,35,36,38,41,42,44],[1,11,13,14,25,26,27,29,31,32,33,34,36,37,38,40,41,42,43,44],[0,1,3,5,6,7,8,10,11,15,16,18,28,29,31,32,33,34,38,39,44],[4,5,9,10,14,15,17,18,25,28,29,31,32,33,34,35,36,37,40,41,43,44],[0,4,9,10,11,13,14,17,26,28,29,31,32,33,34,36,37,38,40],[25,26,28,29,31,32,33,34,35,36,37,39,41,43],[2,5,7,8,17,19,20,23,27,28,29,31,32,33,34,35,37,40,43],[4,5,6,7,10,11,12,14,16,19,20,23,25,27,28,29,31,32,33,34,36,37,38,41],[0,1,4,6,7,8,9,10,12,13,15,16,18,19,20,23,26,27,28,29,31,32,33,34,35,36,40,43,44],[25,26,27,28,29,31,32,33,34,36,37,38,41,44],[1,3,6,8,10,11,13,14,15,18,20,23,24,30,31,32,33,34,36,40,41,43,44],[2,4,5,6,13,15,16,17,25,30,31,32,33,34,37,38,40,41,43,44],[2,3,4,7,13,15,26,30,31,32,33,34,36,37,40,43,44],[1,3,4,5,6,7,8,12,13,14,15,17,18,19,20,23,25,26,30,31,32,33,34,36,37,38,40,43,44],[0,2,3,4,6,8,14,16,17,19,20,23,27,30,31,32,33,34,36,39,40,41,42,44],[0,1,4,6,7,8,9,10,11,19,20,23,25,27,30,31,32,33,34,38,40,41,42,44],[2,5,6,7,8,9,11,12,16,17,26,27,30,31,32,33,34,36,37,42,44],[25,26,27,30,31,32,33,34,36,38,39,42,44],[3,8,9,10,13,14,18,19,20,23,28,30,31,32,33,34,35,36,38,40,41,42,43,44],[0,4,7,9,10,11,12,15,17,18,25,28,30,31,32,33,34,35,37,38,40,42,43,44],[1,2,3,4,5,7,8,9,10,11,12,13,15,16,18,19,20,23,26,28,30,31,32,33,34,35,36,37,38,43,44],[25,26,28,30,31,32,33,34,35,36,37,38,41,43,44],[0,1,3,6,7,8,9,12,13,15,27,28,30,31,32,33,34,35,36,38,39,40,41,42,43,44],[25,27,28,30,31,32,33,34,35,38,40,42,43,44],[0,2,7,9,11,12,14,15,16,19,20,23,26,27,28,30,31,32,33,34,35,36,37,38,40,43,44],[25,26,27,28,30,31,32,33,34,35,36,38,39,40,41,43,44],[3,7,9,11,12,13,14,15,18,19,20,23,29,30,31,32,33,34,39,40,41,42,44],[0,1,2,4,6,8,10,14,16,18,25,29,30,31,32,33,34,36,37,38,40,41,42,43,44],[1,4,6,9,11,13,14,15,17,19,20,23,26,29,30,31,32,33,34,37,39,40,41,42],[25,26,29,30,31,32,33,34,37,38,40,41,42,43],[0,1,2,4,5,6,7,8,10,11,13,14,16,17,27,29,30,31,32,33,34,35,38,40,41,44],[25,27,29,30,31,32,33,34,35,36,40,41,43,44],[26,27,29,30,31,32,33,34,35,37,38,39,41],[25,26,27,29,30,31,32,33,34,35,39,41,43],[0,5,6,7,8,12,14,16,18,19,20,23,28,29,30,31,32,33,34,36,40,41,44],[25,28,29,30,31,32,33,34,37,39,40,43,44],[26,28,29,30,31,32,33,34,36,37,41,42],[25,26,28,29,30,31,32,33,34,36,37,39,42,43],[27,28,29,30,31,32,33,34,35,36,38,39,40,41,43,44],[25,27,28,29,30,31,32,33,34,35,38,39,40,44],[26,27,28,29,30,31,32,33,34,35,36,37,38,40,41,42,43],[25,26,27,28,29,30,31,32,33,34,35,36,38,40,42]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[95,197,281,549,921],"A_d":8860380,"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]],"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],[0,27],[0,28],[0,29],[0,31],[0,32],[0,35],[0,37],[0,38],[0,39],[0,40],[0,41],[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],[1,29],[1,33],[1,34],[1,35],[1,36],[1,37],[1,41],[1,42],[1,44],[2,4],[2,9],[2,14],[2,15],[2,16],[2,18],[2,19],[2,20],[2,21],[2,24],[2,26],[2,28],[2,30],[2,33],[2,34],[2,35],[2,36],[2,37],[2,41],[2,43],[2,44],[3,4],[3,5],[3,8],[3,9],[3,12],[3,14],[3,18],[3,19],[3,20],[3,25],[3,28],[3,29],[3,30],[3,31],[3,36],[3,37],[3,38],[3,39],[3,41],[4,5],[4,6],[4,8],[4,13],[4,14],[4,15],[4,16],[4,25],[4,28],[4,31],[4,33],[4,34],[4,35],[4,38],[4,39],[4,40],[4,43],[4,44],[5,7],[5,9],[5,11],[5,13],[5,14],[5,17],[5,19],[5,20],[5,21],[5,24],[5,25],[5,27],[5,28],[5,29],[5,31],[5,32],[5,33],[5,34],[5,35],[5,38],[5,39],[5,40],[5,42],[6,8],[6,10],[6,13],[6,14],[6,16],[6,17],[6,20],[6,21],[6,22],[6,25],[6,29],[6,30],[6,32],[6,34],[6,35],[6,41],[6,44],[7,8],[7,10],[7,11],[7,14],[7,17],[7,19],[7,20],[7,22],[7,23],[7,25],[7,27],[7,28],[7,29],[7,31],[7,32],[7,34],[7,36],[7,40],[7,42],[8,9],[8,10],[8,11],[8,12],[8,17],[8,18],[8,22],[8,24],[8,26],[8,27],[8,28],[8,30],[8,33],[8,35],[8,36],[8,37],[8,38],[8,39],[8,41],[8,43],[9,13],[9,14],[9,15],[9,16],[9,17],[9,20],[9,21],[9,22],[9,23],[9,26],[9,29],[9,30],[9,32],[9,39],[9,40],[9,41],[10,12],[10,13],[10,15],[10,16],[10,17],[10,18],[10,19],[10,24],[10,26],[10,27],[10,28],[10,32],[10,33],[10,35],[10,36],[10,40],[10,43],[11,12],[11,13],[11,14],[11,16],[11,22],[11,24],[11,25],[11,26],[11,27],[11,32],[11,33],[11,34],[11,35],[11,37],[11,42],[12,13],[12,14],[12,19],[12,21],[12,26],[12,29],[12,32],[12,33],[12,34],[12,35],[12,38],[12,39],[12,42],[13,16],[13,20],[13,22],[13,23],[13,24],[13,25],[13,26],[13,27],[13,28],[13,29],[13,34],[13,35],[13,36],[13,39],[13,40],[13,42],[13,43],[13,44],[14,15],[14,18],[14,19],[14,20],[14,22],[14,24],[14,26],[14,27],[14,29],[14,30],[14,31],[14,33],[14,34],[14,35],[14,36],[14,40],[14,41],[14,43],[14,44],[15,16],[15,18],[15,20],[15,27],[15,29],[15,30],[15,32],[15,35],[15,37],[15,38],[15,43],[15,44],[16,17],[16,19],[16,20],[16,21],[16,22],[16,23],[16,27],[16,28],[16,31],[16,32],[16,35],[16,36],[16,37],[16,39],[16,40],[16,42],[16,43],[16,44],[17,18],[17,19],[17,21],[17,23],[17,25],[17,26],[17,27],[17,31],[17,32],[17,34],[17,38],[17,40],[17,42],[18,20],[18,22],[18,25],[18,27],[18,31],[18,32],[18,36],[18,41],[18,42],[18,43],[18,44],[19,20],[19,23],[19,24],[19,25],[19,26],[19,28],[19,29],[19,32],[19,36],[19,41],[20,23],[20,24],[20,25],[20,31],[20,32],[20,36],[20,38],[20,42],[20,43],[21,22],[21,29],[21,31],[21,32],[21,33],[21,34],[21,36],[21,38],[21,39],[21,41],[22,23],[22,24],[22,29],[22,30],[22,35],[22,36],[22,37],[22,38],[22,39],[22,41],[22,42],[23,24],[23,26],[23,27],[23,28],[23,31],[23,32],[23,35],[23,37],[23,38],[23,39],[23,42],[23,44],[24,25],[24,27],[24,29],[24,32],[24,34],[24,35],[24,37],[24,39],[24,40],[24,41],[24,43]]},"rotation_powers":null},"metrics":{"gamma":2.3061585118682864,"gamma_t":null,"gamma_rho":2.3061585118682864,"gamma_claim":2.3061585118682864,"gamma_t_claim":null,"gamma_rho_claim":2.3061585118682864,"v_ex":25,"rate":0.024437927663734114,"t_count":null,"poly_degree":null,"effective_width":25},"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","N":45,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:399"}]},"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"}]}