{"id":"2526.10.2.a","row":80,"stored":{"file":"master_catalog_large.json","row":80,"construction":{"family":"two-group","k":10,"N":15,"s_total":4,"s_O":3},"columns_sha256":"42d25cefe9f4a603a6e7b398137638cb70699a5971cd06312b787fbcf6e0ab90"},"parameters":{"n":2526,"k":10,"d":2,"N":15,"r":5,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9]],"sk_fingerprint":"97115137a69484d8","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,13],[0,1,2,3,4,5,6,7,8,9,10,11,14],[0,1,2,3,4,5,6,7,8,9,10,12,13],[0,1,2,3,4,5,6,7,8,9,10,12,14],[0,1,2,3,4,5,6,7,8,9,10,13,14],[0,1,2,3,4,5,6,7,8,9,11,12,13],[0,1,2,3,4,5,6,7,8,9,11,12,14],[0,1,2,3,4,5,6,7,8,9,11,13,14],[0,1,2,3,4,5,6,7,8,9,12,13,14],[0,1,2,3,4,5,6,10,11],[0,1,2,3,4,5,6,10,12],[0,1,2,3,4,5,6,10,13],[0,1,2,3,4,5,6,10,14],[0,1,2,3,4,5,6,11,12],[0,1,2,3,4,5,6,11,13],[0,1,2,3,4,5,6,11,14],[0,1,2,3,4,5,6,12,13],[0,1,2,3,4,5,6,12,14],[0,1,2,3,4,5,6,13,14],[0,1,2,3,4,5,7,10,11],[0,1,2,3,4,5,7,10,12],[0,1,2,3,4,5,7,10,13],[0,1,2,3,4,5,7,10,14],[0,1,2,3,4,5,7,11,12],[0,1,2,3,4,5,7,11,13],[0,1,2,3,4,5,7,11,14],[0,1,2,3,4,5,7,12,13],[0,1,2,3,4,5,7,12,14],[0,1,2,3,4,5,7,13,14],[0,1,2,3,4,5,8,10,11],[0,1,2,3,4,5,8,10,12],[0,1,2,3,4,5,8,10,13],[0,1,2,3,4,5,8,10,14],[0,1,2,3,4,5,8,11,12],[0,1,2,3,4,5,8,11,13],[0,1,2,3,4,5,8,11,14],[0,1,2,3,4,5,8,12,13],[0,1,2,3,4,5,8,12,14],[0,1,2,3,4,5,8,13,14],[0,1,2,3,4,5,9,10,11],[0,1,2,3,4,5,9,10,12],[0,1,2,3,4,5,9,10,13],[0,1,2,3,4,5,9,10,14],[0,1,2,3,4,5,9,11,12],[0,1,2,3,4,5,9,11,13],[0,1,2,3,4,5,9,11,14],[0,1,2,3,4,5,9,12,13],[0,1,2,3,4,5,9,12,14],[0,1,2,3,4,5,9,13,14],[0,1,2,3,4,6,7,10,11],[0,1,2,3,4,6,7,10,12],[0,1,2,3,4,6,7,10,13],[0,1,2,3,4,6,7,10,14],[0,1,2,3,4,6,7,11,12],[0,1,2,3,4,6,7,11,13],[0,1,2,3,4,6,7,11,14],[0,1,2,3,4,6,7,12,13],[0,1,2,3,4,6,7,12,14],[0,1,2,3,4,6,7,13,14],[0,1,2,3,4,6,8,10,11],[0,1,2,3,4,6,8,10,12],[0,1,2,3,4,6,8,10,13],[0,1,2,3,4,6,8,10,14],[0,1,2,3,4,6,8,11,12],[0,1,2,3,4,6,8,11,13],[0,1,2,3,4,6,8,11,14],[0,1,2,3,4,6,8,12,13],[0,1,2,3,4,6,8,12,14],[0,1,2,3,4,6,8,13,14],[0,1,2,3,4,6,9,10,11],[0,1,2,3,4,6,9,10,12],[0,1,2,3,4,6,9,10,13],[0,1,2,3,4,6,9,10,14],[0,1,2,3,4,6,9,11,12],[0,1,2,3,4,6,9,11,13],[0,1,2,3,4,6,9,11,14],[0,1,2,3,4,6,9,12,13],[0,1,2,3,4,6,9,12,14],[0,1,2,3,4,6,9,13,14],[0,1,2,3,4,7,8,10,11],[0,1,2,3,4,7,8,10,12],[0,1,2,3,4,7,8,10,13],[0,1,2,3,4,7,8,10,14],[0,1,2,3,4,7,8,11,12],[0,1,2,3,4,7,8,11,13],[0,1,2,3,4,7,8,11,14],[0,1,2,3,4,7,8,12,13],[0,1,2,3,4,7,8,12,14],[0,1,2,3,4,7,8,13,14],[0,1,2,3,4,7,9,10,11],[0,1,2,3,4,7,9,10,12],[0,1,2,3,4,7,9,10,13],[0,1,2,3,4,7,9,10,14],[0,1,2,3,4,7,9,11,12],[0,1,2,3,4,7,9,11,13],[0,1,2,3,4,7,9,11,14],[0,1,2,3,4,7,9,12,13],[0,1,2,3,4,7,9,12,14],[0,1,2,3,4,7,9,13,14],[0,1,2,3,4,8,9,10,11],[0,1,2,3,4,8,9,10,12],[0,1,2,3,4,8,9,10,13],[0,1,2,3,4,8,9,10,14],[0,1,2,3,4,8,9,11,12],[0,1,2,3,4,8,9,11,13],[0,1,2,3,4,8,9,11,14],[0,1,2,3,4,8,9,12,13],[0,1,2,3,4,8,9,12,14],[0,1,2,3,4,8,9,13,14],[0,1,2,3,5,6,7,10,11],[0,1,2,3,5,6,7,10,12],[0,1,2,3,5,6,7,10,13],[0,1,2,3,5,6,7,10,14],[0,1,2,3,5,6,7,11,12],[0,1,2,3,5,6,7,11,13],[0,1,2,3,5,6,7,11,14],[0,1,2,3,5,6,7,12,13],[0,1,2,3,5,6,7,12,14],[0,1,2,3,5,6,7,13,14],[0,1,2,3,5,6,8,10,11],[0,1,2,3,5,6,8,10,12],[0,1,2,3,5,6,8,10,13],[0,1,2,3,5,6,8,10,14],[0,1,2,3,5,6,8,11,12],[0,1,2,3,5,6,8,11,13],[0,1,2,3,5,6,8,11,14],[0,1,2,3,5,6,8,12,13],[0,1,2,3,5,6,8,12,14],[0,1,2,3,5,6,8,13,14],[0,1,2,3,5,6,9,10,11],[0,1,2,3,5,6,9,10,12],[0,1,2,3,5,6,9,10,13],[0,1,2,3,5,6,9,10,14],[0,1,2,3,5,6,9,11,12],[0,1,2,3,5,6,9,11,13],[0,1,2,3,5,6,9,11,14],[0,1,2,3,5,6,9,12,13],[0,1,2,3,5,6,9,12,14],[0,1,2,3,5,6,9,13,14],[0,1,2,3,5,7,8,10,11],[0,1,2,3,5,7,8,10,12],[0,1,2,3,5,7,8,10,13],[0,1,2,3,5,7,8,10,14],[0,1,2,3,5,7,8,11,12],[0,1,2,3,5,7,8,11,13],[0,1,2,3,5,7,8,11,14],[0,1,2,3,5,7,8,12,13],[0,1,2,3,5,7,8,12,14],[0,1,2,3,5,7,8,13,14],[0,1,2,3,5,7,9,10,11],[0,1,2,3,5,7,9,10,12],[0,1,2,3,5,7,9,10,13],[0,1,2,3,5,7,9,10,14],[0,1,2,3,5,7,9,11,12],[0,1,2,3,5,7,9,11,13],[0,1,2,3,5,7,9,11,14],[0,1,2,3,5,7,9,12,13],[0,1,2,3,5,7,9,12,14],[0,1,2,3,5,7,9,13,14],[0,1,2,3,5,8,9,10,11],[0,1,2,3,5,8,9,10,12],[0,1,2,3,5,8,9,10,13],[0,1,2,3,5,8,9,10,14],[0,1,2,3,5,8,9,11,12],[0,1,2,3,5,8,9,11,13],[0,1,2,3,5,8,9,11,14],[0,1,2,3,5,8,9,12,13],[0,1,2,3,5,8,9,12,14],[0,1,2,3,5,8,9,13,14],[0,1,2,3,6,7,8,10,11],[0,1,2,3,6,7,8,10,12],[0,1,2,3,6,7,8,10,13],[0,1,2,3,6,7,8,10,14],[0,1,2,3,6,7,8,11,12],[0,1,2,3,6,7,8,11,13],[0,1,2,3,6,7,8,11,14],[0,1,2,3,6,7,8,12,13],[0,1,2,3,6,7,8,12,14],[0,1,2,3,6,7,8,13,14],[0,1,2,3,6,7,9,10,11],[0,1,2,3,6,7,9,10,12],[0,1,2,3,6,7,9,10,13],[0,1,2,3,6,7,9,10,14],[0,1,2,3,6,7,9,11,12],[0,1,2,3,6,7,9,11,13],[0,1,2,3,6,7,9,11,14],[0,1,2,3,6,7,9,12,13],[0,1,2,3,6,7,9,12,14],[0,1,2,3,6,7,9,13,14],[0,1,2,3,6,8,9,10,11],[0,1,2,3,6,8,9,10,12],[0,1,2,3,6,8,9,10,13],[0,1,2,3,6,8,9,10,14],[0,1,2,3,6,8,9,11,12],[0,1,2,3,6,8,9,11,13],[0,1,2,3,6,8,9,11,14],[0,1,2,3,6,8,9,12,13],[0,1,2,3,6,8,9,12,14],[0,1,2,3,6,8,9,13,14],[0,1,2,3,7,8,9,10,11],[0,1,2,3,7,8,9,10,12],[0,1,2,3,7,8,9,10,13],[0,1,2,3,7,8,9,10,14],[0,1,2,3,7,8,9,11,12],[0,1,2,3,7,8,9,11,13],[0,1,2,3,7,8,9,11,14],[0,1,2,3,7,8,9,12,13],[0,1,2,3,7,8,9,12,14],[0,1,2,3,7,8,9,13,14],[0,1,2,3,10],[0,1,2,3,10,11,12,13,14],[0,1,2,3,11],[0,1,2,3,12],[0,1,2,3,13],[0,1,2,3,14],[0,1,2,4,5,6,7,10,11],[0,1,2,4,5,6,7,10,12],[0,1,2,4,5,6,7,10,13],[0,1,2,4,5,6,7,10,14],[0,1,2,4,5,6,7,11,12],[0,1,2,4,5,6,7,11,13],[0,1,2,4,5,6,7,11,14],[0,1,2,4,5,6,7,12,13],[0,1,2,4,5,6,7,12,14],[0,1,2,4,5,6,7,13,14],[0,1,2,4,5,6,8,10,11],[0,1,2,4,5,6,8,10,12],[0,1,2,4,5,6,8,10,13],[0,1,2,4,5,6,8,10,14],[0,1,2,4,5,6,8,11,12],[0,1,2,4,5,6,8,11,13],[0,1,2,4,5,6,8,11,14],[0,1,2,4,5,6,8,12,13],[0,1,2,4,5,6,8,12,14],[0,1,2,4,5,6,8,13,14],[0,1,2,4,5,6,9,10,11],[0,1,2,4,5,6,9,10,12],[0,1,2,4,5,6,9,10,13],[0,1,2,4,5,6,9,10,14],[0,1,2,4,5,6,9,11,12],[0,1,2,4,5,6,9,11,13],[0,1,2,4,5,6,9,11,14],[0,1,2,4,5,6,9,12,13],[0,1,2,4,5,6,9,12,14],[0,1,2,4,5,6,9,13,14],[0,1,2,4,5,7,8,10,11],[0,1,2,4,5,7,8,10,12],[0,1,2,4,5,7,8,10,13],[0,1,2,4,5,7,8,10,14],[0,1,2,4,5,7,8,11,12],[0,1,2,4,5,7,8,11,13],[0,1,2,4,5,7,8,11,14],[0,1,2,4,5,7,8,12,13],[0,1,2,4,5,7,8,12,14],[0,1,2,4,5,7,8,13,14],[0,1,2,4,5,7,9,10,11],[0,1,2,4,5,7,9,10,12],[0,1,2,4,5,7,9,10,13],[0,1,2,4,5,7,9,10,14],[0,1,2,4,5,7,9,11,12],[0,1,2,4,5,7,9,11,13],[0,1,2,4,5,7,9,11,14],[0,1,2,4,5,7,9,12,13],[0,1,2,4,5,7,9,12,14],[0,1,2,4,5,7,9,13,14],[0,1,2,4,5,8,9,10,11],[0,1,2,4,5,8,9,10,12],[0,1,2,4,5,8,9,10,13],[0,1,2,4,5,8,9,10,14],[0,1,2,4,5,8,9,11,12],[0,1,2,4,5,8,9,11,13],[0,1,2,4,5,8,9,11,14],[0,1,2,4,5,8,9,12,13],[0,1,2,4,5,8,9,12,14],[0,1,2,4,5,8,9,13,14],[0,1,2,4,6,7,8,10,11],[0,1,2,4,6,7,8,10,12],[0,1,2,4,6,7,8,10,13],[0,1,2,4,6,7,8,10,14],[0,1,2,4,6,7,8,11,12],[0,1,2,4,6,7,8,11,13],[0,1,2,4,6,7,8,11,14],[0,1,2,4,6,7,8,12,13],[0,1,2,4,6,7,8,12,14],[0,1,2,4,6,7,8,13,14],[0,1,2,4,6,7,9,10,11],[0,1,2,4,6,7,9,10,12],[0,1,2,4,6,7,9,10,13],[0,1,2,4,6,7,9,10,14],[0,1,2,4,6,7,9,11,12],[0,1,2,4,6,7,9,11,13],[0,1,2,4,6,7,9,11,14],[0,1,2,4,6,7,9,12,13],[0,1,2,4,6,7,9,12,14],[0,1,2,4,6,7,9,13,14],[0,1,2,4,6,8,9,10,11],[0,1,2,4,6,8,9,10,12],[0,1,2,4,6,8,9,10,13],[0,1,2,4,6,8,9,10,14],[0,1,2,4,6,8,9,11,12],[0,1,2,4,6,8,9,11,13],[0,1,2,4,6,8,9,11,14],[0,1,2,4,6,8,9,12,13],[0,1,2,4,6,8,9,12,14],[0,1,2,4,6,8,9,13,14],[0,1,2,4,7,8,9,10,11],[0,1,2,4,7,8,9,10,12],[0,1,2,4,7,8,9,10,13],[0,1,2,4,7,8,9,10,14],[0,1,2,4,7,8,9,11,12],[0,1,2,4,7,8,9,11,13],[0,1,2,4,7,8,9,11,14],[0,1,2,4,7,8,9,12,13],[0,1,2,4,7,8,9,12,14],[0,1,2,4,7,8,9,13,14],[0,1,2,4,10],[0,1,2,4,10,11,12,13,14],[0,1,2,4,11],[0,1,2,4,12],[0,1,2,4,13],[0,1,2,4,14],[0,1,2,5,6,7,8,10,11],[0,1,2,5,6,7,8,10,12],[0,1,2,5,6,7,8,10,13],[0,1,2,5,6,7,8,10,14],[0,1,2,5,6,7,8,11,12],[0,1,2,5,6,7,8,11,13],[0,1,2,5,6,7,8,11,14],[0,1,2,5,6,7,8,12,13],[0,1,2,5,6,7,8,12,14],[0,1,2,5,6,7,8,13,14],[0,1,2,5,6,7,9,10,11],[0,1,2,5,6,7,9,10,12],[0,1,2,5,6,7,9,10,13],[0,1,2,5,6,7,9,10,14],[0,1,2,5,6,7,9,11,12],[0,1,2,5,6,7,9,11,13],[0,1,2,5,6,7,9,11,14],[0,1,2,5,6,7,9,12,13],[0,1,2,5,6,7,9,12,14],[0,1,2,5,6,7,9,13,14],[0,1,2,5,6,8,9,10,11],[0,1,2,5,6,8,9,10,12],[0,1,2,5,6,8,9,10,13],[0,1,2,5,6,8,9,10,14],[0,1,2,5,6,8,9,11,12],[0,1,2,5,6,8,9,11,13],[0,1,2,5,6,8,9,11,14],[0,1,2,5,6,8,9,12,13],[0,1,2,5,6,8,9,12,14],[0,1,2,5,6,8,9,13,14],[0,1,2,5,7,8,9,10,11],[0,1,2,5,7,8,9,10,12],[0,1,2,5,7,8,9,10,13],[0,1,2,5,7,8,9,10,14],[0,1,2,5,7,8,9,11,12],[0,1,2,5,7,8,9,11,13],[0,1,2,5,7,8,9,11,14],[0,1,2,5,7,8,9,12,13],[0,1,2,5,7,8,9,12,14],[0,1,2,5,7,8,9,13,14],[0,1,2,5,10],[0,1,2,5,10,11,12,13,14],[0,1,2,5,11],[0,1,2,5,12],[0,1,2,5,13],[0,1,2,5,14],[0,1,2,6,7,8,9,10,11],[0,1,2,6,7,8,9,10,12],[0,1,2,6,7,8,9,10,13],[0,1,2,6,7,8,9,10,14],[0,1,2,6,7,8,9,11,12],[0,1,2,6,7,8,9,11,13],[0,1,2,6,7,8,9,11,14],[0,1,2,6,7,8,9,12,13],[0,1,2,6,7,8,9,12,14],[0,1,2,6,7,8,9,13,14],[0,1,2,6,10],[0,1,2,6,10,11,12,13,14],[0,1,2,6,11],[0,1,2,6,12],[0,1,2,6,13],[0,1,2,6,14],[0,1,2,7,10],[0,1,2,7,10,11,12,13,14],[0,1,2,7,11],[0,1,2,7,12],[0,1,2,7,13],[0,1,2,7,14],[0,1,2,8,10],[0,1,2,8,10,11,12,13,14],[0,1,2,8,11],[0,1,2,8,12],[0,1,2,8,13],[0,1,2,8,14],[0,1,2,9,10],[0,1,2,9,10,11,12,13,14],[0,1,2,9,11],[0,1,2,9,12],[0,1,2,9,13],[0,1,2,9,14],[0,1,3,4,5,6,7,10,11],[0,1,3,4,5,6,7,10,12],[0,1,3,4,5,6,7,10,13],[0,1,3,4,5,6,7,10,14],[0,1,3,4,5,6,7,11,12],[0,1,3,4,5,6,7,11,13],[0,1,3,4,5,6,7,11,14],[0,1,3,4,5,6,7,12,13],[0,1,3,4,5,6,7,12,14],[0,1,3,4,5,6,7,13,14],[0,1,3,4,5,6,8,10,11],[0,1,3,4,5,6,8,10,12],[0,1,3,4,5,6,8,10,13],[0,1,3,4,5,6,8,10,14],[0,1,3,4,5,6,8,11,12],[0,1,3,4,5,6,8,11,13],[0,1,3,4,5,6,8,11,14],[0,1,3,4,5,6,8,12,13],[0,1,3,4,5,6,8,12,14],[0,1,3,4,5,6,8,13,14],[0,1,3,4,5,6,9,10,11],[0,1,3,4,5,6,9,10,12],[0,1,3,4,5,6,9,10,13],[0,1,3,4,5,6,9,10,14],[0,1,3,4,5,6,9,11,12],[0,1,3,4,5,6,9,11,13],[0,1,3,4,5,6,9,11,14],[0,1,3,4,5,6,9,12,13],[0,1,3,4,5,6,9,12,14],[0,1,3,4,5,6,9,13,14],[0,1,3,4,5,7,8,10,11],[0,1,3,4,5,7,8,10,12],[0,1,3,4,5,7,8,10,13],[0,1,3,4,5,7,8,10,14],[0,1,3,4,5,7,8,11,12],[0,1,3,4,5,7,8,11,13],[0,1,3,4,5,7,8,11,14],[0,1,3,4,5,7,8,12,13],[0,1,3,4,5,7,8,12,14],[0,1,3,4,5,7,8,13,14],[0,1,3,4,5,7,9,10,11],[0,1,3,4,5,7,9,10,12],[0,1,3,4,5,7,9,10,13],[0,1,3,4,5,7,9,10,14],[0,1,3,4,5,7,9,11,12],[0,1,3,4,5,7,9,11,13],[0,1,3,4,5,7,9,11,14],[0,1,3,4,5,7,9,12,13],[0,1,3,4,5,7,9,12,14],[0,1,3,4,5,7,9,13,14],[0,1,3,4,5,8,9,10,11],[0,1,3,4,5,8,9,10,12],[0,1,3,4,5,8,9,10,13],[0,1,3,4,5,8,9,10,14],[0,1,3,4,5,8,9,11,12],[0,1,3,4,5,8,9,11,13],[0,1,3,4,5,8,9,11,14],[0,1,3,4,5,8,9,12,13],[0,1,3,4,5,8,9,12,14],[0,1,3,4,5,8,9,13,14],[0,1,3,4,6,7,8,10,11],[0,1,3,4,6,7,8,10,12],[0,1,3,4,6,7,8,10,13],[0,1,3,4,6,7,8,10,14],[0,1,3,4,6,7,8,11,12],[0,1,3,4,6,7,8,11,13],[0,1,3,4,6,7,8,11,14],[0,1,3,4,6,7,8,12,13],[0,1,3,4,6,7,8,12,14],[0,1,3,4,6,7,8,13,14],[0,1,3,4,6,7,9,10,11],[0,1,3,4,6,7,9,10,12],[0,1,3,4,6,7,9,10,13],[0,1,3,4,6,7,9,10,14],[0,1,3,4,6,7,9,11,12],[0,1,3,4,6,7,9,11,13],[0,1,3,4,6,7,9,11,14],[0,1,3,4,6,7,9,12,13],[0,1,3,4,6,7,9,12,14],[0,1,3,4,6,7,9,13,14],[0,1,3,4,6,8,9,10,11],[0,1,3,4,6,8,9,10,12],[0,1,3,4,6,8,9,10,13],[0,1,3,4,6,8,9,10,14],[0,1,3,4,6,8,9,11,12],[0,1,3,4,6,8,9,11,13],[0,1,3,4,6,8,9,11,14],[0,1,3,4,6,8,9,12,13],[0,1,3,4,6,8,9,12,14],[0,1,3,4,6,8,9,13,14],[0,1,3,4,7,8,9,10,11],[0,1,3,4,7,8,9,10,12],[0,1,3,4,7,8,9,10,13],[0,1,3,4,7,8,9,10,14],[0,1,3,4,7,8,9,11,12],[0,1,3,4,7,8,9,11,13],[0,1,3,4,7,8,9,11,14],[0,1,3,4,7,8,9,12,13],[0,1,3,4,7,8,9,12,14],[0,1,3,4,7,8,9,13,14],[0,1,3,4,10],[0,1,3,4,10,11,12,13,14],[0,1,3,4,11],[0,1,3,4,12],[0,1,3,4,13],[0,1,3,4,14],[0,1,3,5,6,7,8,10,11],[0,1,3,5,6,7,8,10,12],[0,1,3,5,6,7,8,10,13],[0,1,3,5,6,7,8,10,14],[0,1,3,5,6,7,8,11,12],[0,1,3,5,6,7,8,11,13],[0,1,3,5,6,7,8,11,14],[0,1,3,5,6,7,8,12,13],[0,1,3,5,6,7,8,12,14],[0,1,3,5,6,7,8,13,14],[0,1,3,5,6,7,9,10,11],[0,1,3,5,6,7,9,10,12],[0,1,3,5,6,7,9,10,13],[0,1,3,5,6,7,9,10,14],[0,1,3,5,6,7,9,11,12],[0,1,3,5,6,7,9,11,13],[0,1,3,5,6,7,9,11,14],[0,1,3,5,6,7,9,12,13],[0,1,3,5,6,7,9,12,14],[0,1,3,5,6,7,9,13,14],[0,1,3,5,6,8,9,10,11],[0,1,3,5,6,8,9,10,12],[0,1,3,5,6,8,9,10,13],[0,1,3,5,6,8,9,10,14],[0,1,3,5,6,8,9,11,12],[0,1,3,5,6,8,9,11,13],[0,1,3,5,6,8,9,11,14],[0,1,3,5,6,8,9,12,13],[0,1,3,5,6,8,9,12,14],[0,1,3,5,6,8,9,13,14],[0,1,3,5,7,8,9,10,11],[0,1,3,5,7,8,9,10,12],[0,1,3,5,7,8,9,10,13],[0,1,3,5,7,8,9,10,14],[0,1,3,5,7,8,9,11,12],[0,1,3,5,7,8,9,11,13],[0,1,3,5,7,8,9,11,14],[0,1,3,5,7,8,9,12,13],[0,1,3,5,7,8,9,12,14],[0,1,3,5,7,8,9,13,14],[0,1,3,5,10],[0,1,3,5,10,11,12,13,14],[0,1,3,5,11],[0,1,3,5,12],[0,1,3,5,13],[0,1,3,5,14],[0,1,3,6,7,8,9,10,11],[0,1,3,6,7,8,9,10,12],[0,1,3,6,7,8,9,10,13],[0,1,3,6,7,8,9,10,14],[0,1,3,6,7,8,9,11,12],[0,1,3,6,7,8,9,11,13],[0,1,3,6,7,8,9,11,14],[0,1,3,6,7,8,9,12,13],[0,1,3,6,7,8,9,12,14],[0,1,3,6,7,8,9,13,14],[0,1,3,6,10],[0,1,3,6,10,11,12,13,14],[0,1,3,6,11],[0,1,3,6,12],[0,1,3,6,13],[0,1,3,6,14],[0,1,3,7,10],[0,1,3,7,10,11,12,13,14],[0,1,3,7,11],[0,1,3,7,12],[0,1,3,7,13],[0,1,3,7,14],[0,1,3,8,10],[0,1,3,8,10,11,12,13,14],[0,1,3,8,11],[0,1,3,8,12],[0,1,3,8,13],[0,1,3,8,14],[0,1,3,9,10],[0,1,3,9,10,11,12,13,14],[0,1,3,9,11],[0,1,3,9,12],[0,1,3,9,13],[0,1,3,9,14],[0,1,4,5,6,7,8,10,11],[0,1,4,5,6,7,8,10,12],[0,1,4,5,6,7,8,10,13],[0,1,4,5,6,7,8,10,14],[0,1,4,5,6,7,8,11,12],[0,1,4,5,6,7,8,11,13],[0,1,4,5,6,7,8,11,14],[0,1,4,5,6,7,8,12,13],[0,1,4,5,6,7,8,12,14],[0,1,4,5,6,7,8,13,14],[0,1,4,5,6,7,9,10,11],[0,1,4,5,6,7,9,10,12],[0,1,4,5,6,7,9,10,13],[0,1,4,5,6,7,9,10,14],[0,1,4,5,6,7,9,11,12],[0,1,4,5,6,7,9,11,13],[0,1,4,5,6,7,9,11,14],[0,1,4,5,6,7,9,12,13],[0,1,4,5,6,7,9,12,14],[0,1,4,5,6,7,9,13,14],[0,1,4,5,6,8,9,10,11],[0,1,4,5,6,8,9,10,12],[0,1,4,5,6,8,9,10,13],[0,1,4,5,6,8,9,10,14],[0,1,4,5,6,8,9,11,12],[0,1,4,5,6,8,9,11,13],[0,1,4,5,6,8,9,11,14],[0,1,4,5,6,8,9,12,13],[0,1,4,5,6,8,9,12,14],[0,1,4,5,6,8,9,13,14],[0,1,4,5,7,8,9,10,11],[0,1,4,5,7,8,9,10,12],[0,1,4,5,7,8,9,10,13],[0,1,4,5,7,8,9,10,14],[0,1,4,5,7,8,9,11,12],[0,1,4,5,7,8,9,11,13],[0,1,4,5,7,8,9,11,14],[0,1,4,5,7,8,9,12,13],[0,1,4,5,7,8,9,12,14],[0,1,4,5,7,8,9,13,14],[0,1,4,5,10],[0,1,4,5,10,11,12,13,14],[0,1,4,5,11],[0,1,4,5,12],[0,1,4,5,13],[0,1,4,5,14],[0,1,4,6,7,8,9,10,11],[0,1,4,6,7,8,9,10,12],[0,1,4,6,7,8,9,10,13],[0,1,4,6,7,8,9,10,14],[0,1,4,6,7,8,9,11,12],[0,1,4,6,7,8,9,11,13],[0,1,4,6,7,8,9,11,14],[0,1,4,6,7,8,9,12,13],[0,1,4,6,7,8,9,12,14],[0,1,4,6,7,8,9,13,14],[0,1,4,6,10],[0,1,4,6,10,11,12,13,14],[0,1,4,6,11],[0,1,4,6,12],[0,1,4,6,13],[0,1,4,6,14],[0,1,4,7,10],[0,1,4,7,10,11,12,13,14],[0,1,4,7,11],[0,1,4,7,12],[0,1,4,7,13],[0,1,4,7,14],[0,1,4,8,10],[0,1,4,8,10,11,12,13,14],[0,1,4,8,11],[0,1,4,8,12],[0,1,4,8,13],[0,1,4,8,14],[0,1,4,9,10],[0,1,4,9,10,11,12,13,14],[0,1,4,9,11],[0,1,4,9,12],[0,1,4,9,13],[0,1,4,9,14],[0,1,5,6,7,8,9,10,11],[0,1,5,6,7,8,9,10,12],[0,1,5,6,7,8,9,10,13],[0,1,5,6,7,8,9,10,14],[0,1,5,6,7,8,9,11,12],[0,1,5,6,7,8,9,11,13],[0,1,5,6,7,8,9,11,14],[0,1,5,6,7,8,9,12,13],[0,1,5,6,7,8,9,12,14],[0,1,5,6,7,8,9,13,14],[0,1,5,6,10],[0,1,5,6,10,11,12,13,14],[0,1,5,6,11],[0,1,5,6,12],[0,1,5,6,13],[0,1,5,6,14],[0,1,5,7,10],[0,1,5,7,10,11,12,13,14],[0,1,5,7,11],[0,1,5,7,12],[0,1,5,7,13],[0,1,5,7,14],[0,1,5,8,10],[0,1,5,8,10,11,12,13,14],[0,1,5,8,11],[0,1,5,8,12],[0,1,5,8,13],[0,1,5,8,14],[0,1,5,9,10],[0,1,5,9,10,11,12,13,14],[0,1,5,9,11],[0,1,5,9,12],[0,1,5,9,13],[0,1,5,9,14],[0,1,6,7,10],[0,1,6,7,10,11,12,13,14],[0,1,6,7,11],[0,1,6,7,12],[0,1,6,7,13],[0,1,6,7,14],[0,1,6,8,10],[0,1,6,8,10,11,12,13,14],[0,1,6,8,11],[0,1,6,8,12],[0,1,6,8,13],[0,1,6,8,14],[0,1,6,9,10],[0,1,6,9,10,11,12,13,14],[0,1,6,9,11],[0,1,6,9,12],[0,1,6,9,13],[0,1,6,9,14],[0,1,7,8,10],[0,1,7,8,10,11,12,13,14],[0,1,7,8,11],[0,1,7,8,12],[0,1,7,8,13],[0,1,7,8,14],[0,1,7,9,10],[0,1,7,9,10,11,12,13,14],[0,1,7,9,11],[0,1,7,9,12],[0,1,7,9,13],[0,1,7,9,14],[0,1,8,9,10],[0,1,8,9,10,11,12,13,14],[0,1,8,9,11],[0,1,8,9,12],[0,1,8,9,13],[0,1,8,9,14],[0,2,3,4,5,6,7,10,11],[0,2,3,4,5,6,7,10,12],[0,2,3,4,5,6,7,10,13],[0,2,3,4,5,6,7,10,14],[0,2,3,4,5,6,7,11,12],[0,2,3,4,5,6,7,11,13],[0,2,3,4,5,6,7,11,14],[0,2,3,4,5,6,7,12,13],[0,2,3,4,5,6,7,12,14],[0,2,3,4,5,6,7,13,14],[0,2,3,4,5,6,8,10,11],[0,2,3,4,5,6,8,10,12],[0,2,3,4,5,6,8,10,13],[0,2,3,4,5,6,8,10,14],[0,2,3,4,5,6,8,11,12],[0,2,3,4,5,6,8,11,13],[0,2,3,4,5,6,8,11,14],[0,2,3,4,5,6,8,12,13],[0,2,3,4,5,6,8,12,14],[0,2,3,4,5,6,8,13,14],[0,2,3,4,5,6,9,10,11],[0,2,3,4,5,6,9,10,12],[0,2,3,4,5,6,9,10,13],[0,2,3,4,5,6,9,10,14],[0,2,3,4,5,6,9,11,12],[0,2,3,4,5,6,9,11,13],[0,2,3,4,5,6,9,11,14],[0,2,3,4,5,6,9,12,13],[0,2,3,4,5,6,9,12,14],[0,2,3,4,5,6,9,13,14],[0,2,3,4,5,7,8,10,11],[0,2,3,4,5,7,8,10,12],[0,2,3,4,5,7,8,10,13],[0,2,3,4,5,7,8,10,14],[0,2,3,4,5,7,8,11,12],[0,2,3,4,5,7,8,11,13],[0,2,3,4,5,7,8,11,14],[0,2,3,4,5,7,8,12,13],[0,2,3,4,5,7,8,12,14],[0,2,3,4,5,7,8,13,14],[0,2,3,4,5,7,9,10,11],[0,2,3,4,5,7,9,10,12],[0,2,3,4,5,7,9,10,13],[0,2,3,4,5,7,9,10,14],[0,2,3,4,5,7,9,11,12],[0,2,3,4,5,7,9,11,13],[0,2,3,4,5,7,9,11,14],[0,2,3,4,5,7,9,12,13],[0,2,3,4,5,7,9,12,14],[0,2,3,4,5,7,9,13,14],[0,2,3,4,5,8,9,10,11],[0,2,3,4,5,8,9,10,12],[0,2,3,4,5,8,9,10,13],[0,2,3,4,5,8,9,10,14],[0,2,3,4,5,8,9,11,12],[0,2,3,4,5,8,9,11,13],[0,2,3,4,5,8,9,11,14],[0,2,3,4,5,8,9,12,13],[0,2,3,4,5,8,9,12,14],[0,2,3,4,5,8,9,13,14],[0,2,3,4,6,7,8,10,11],[0,2,3,4,6,7,8,10,12],[0,2,3,4,6,7,8,10,13],[0,2,3,4,6,7,8,10,14],[0,2,3,4,6,7,8,11,12],[0,2,3,4,6,7,8,11,13],[0,2,3,4,6,7,8,11,14],[0,2,3,4,6,7,8,12,13],[0,2,3,4,6,7,8,12,14],[0,2,3,4,6,7,8,13,14],[0,2,3,4,6,7,9,10,11],[0,2,3,4,6,7,9,10,12],[0,2,3,4,6,7,9,10,13],[0,2,3,4,6,7,9,10,14],[0,2,3,4,6,7,9,11,12],[0,2,3,4,6,7,9,11,13],[0,2,3,4,6,7,9,11,14],[0,2,3,4,6,7,9,12,13],[0,2,3,4,6,7,9,12,14],[0,2,3,4,6,7,9,13,14],[0,2,3,4,6,8,9,10,11],[0,2,3,4,6,8,9,10,12],[0,2,3,4,6,8,9,10,13],[0,2,3,4,6,8,9,10,14],[0,2,3,4,6,8,9,11,12],[0,2,3,4,6,8,9,11,13],[0,2,3,4,6,8,9,11,14],[0,2,3,4,6,8,9,12,13],[0,2,3,4,6,8,9,12,14],[0,2,3,4,6,8,9,13,14],[0,2,3,4,7,8,9,10,11],[0,2,3,4,7,8,9,10,12],[0,2,3,4,7,8,9,10,13],[0,2,3,4,7,8,9,10,14],[0,2,3,4,7,8,9,11,12],[0,2,3,4,7,8,9,11,13],[0,2,3,4,7,8,9,11,14],[0,2,3,4,7,8,9,12,13],[0,2,3,4,7,8,9,12,14],[0,2,3,4,7,8,9,13,14],[0,2,3,4,10],[0,2,3,4,10,11,12,13,14],[0,2,3,4,11],[0,2,3,4,12],[0,2,3,4,13],[0,2,3,4,14],[0,2,3,5,6,7,8,10,11],[0,2,3,5,6,7,8,10,12],[0,2,3,5,6,7,8,10,13],[0,2,3,5,6,7,8,10,14],[0,2,3,5,6,7,8,11,12],[0,2,3,5,6,7,8,11,13],[0,2,3,5,6,7,8,11,14],[0,2,3,5,6,7,8,12,13],[0,2,3,5,6,7,8,12,14],[0,2,3,5,6,7,8,13,14],[0,2,3,5,6,7,9,10,11],[0,2,3,5,6,7,9,10,12],[0,2,3,5,6,7,9,10,13],[0,2,3,5,6,7,9,10,14],[0,2,3,5,6,7,9,11,12],[0,2,3,5,6,7,9,11,13],[0,2,3,5,6,7,9,11,14],[0,2,3,5,6,7,9,12,13],[0,2,3,5,6,7,9,12,14],[0,2,3,5,6,7,9,13,14],[0,2,3,5,6,8,9,10,11],[0,2,3,5,6,8,9,10,12],[0,2,3,5,6,8,9,10,13],[0,2,3,5,6,8,9,10,14],[0,2,3,5,6,8,9,11,12],[0,2,3,5,6,8,9,11,13],[0,2,3,5,6,8,9,11,14],[0,2,3,5,6,8,9,12,13],[0,2,3,5,6,8,9,12,14],[0,2,3,5,6,8,9,13,14],[0,2,3,5,7,8,9,10,11],[0,2,3,5,7,8,9,10,12],[0,2,3,5,7,8,9,10,13],[0,2,3,5,7,8,9,10,14],[0,2,3,5,7,8,9,11,12],[0,2,3,5,7,8,9,11,13],[0,2,3,5,7,8,9,11,14],[0,2,3,5,7,8,9,12,13],[0,2,3,5,7,8,9,12,14],[0,2,3,5,7,8,9,13,14],[0,2,3,5,10],[0,2,3,5,10,11,12,13,14],[0,2,3,5,11],[0,2,3,5,12],[0,2,3,5,13],[0,2,3,5,14],[0,2,3,6,7,8,9,10,11],[0,2,3,6,7,8,9,10,12],[0,2,3,6,7,8,9,10,13],[0,2,3,6,7,8,9,10,14],[0,2,3,6,7,8,9,11,12],[0,2,3,6,7,8,9,11,13],[0,2,3,6,7,8,9,11,14],[0,2,3,6,7,8,9,12,13],[0,2,3,6,7,8,9,12,14],[0,2,3,6,7,8,9,13,14],[0,2,3,6,10],[0,2,3,6,10,11,12,13,14],[0,2,3,6,11],[0,2,3,6,12],[0,2,3,6,13],[0,2,3,6,14],[0,2,3,7,10],[0,2,3,7,10,11,12,13,14],[0,2,3,7,11],[0,2,3,7,12],[0,2,3,7,13],[0,2,3,7,14],[0,2,3,8,10],[0,2,3,8,10,11,12,13,14],[0,2,3,8,11],[0,2,3,8,12],[0,2,3,8,13],[0,2,3,8,14],[0,2,3,9,10],[0,2,3,9,10,11,12,13,14],[0,2,3,9,11],[0,2,3,9,12],[0,2,3,9,13],[0,2,3,9,14],[0,2,4,5,6,7,8,10,11],[0,2,4,5,6,7,8,10,12],[0,2,4,5,6,7,8,10,13],[0,2,4,5,6,7,8,10,14],[0,2,4,5,6,7,8,11,12],[0,2,4,5,6,7,8,11,13],[0,2,4,5,6,7,8,11,14],[0,2,4,5,6,7,8,12,13],[0,2,4,5,6,7,8,12,14],[0,2,4,5,6,7,8,13,14],[0,2,4,5,6,7,9,10,11],[0,2,4,5,6,7,9,10,12],[0,2,4,5,6,7,9,10,13],[0,2,4,5,6,7,9,10,14],[0,2,4,5,6,7,9,11,12],[0,2,4,5,6,7,9,11,13],[0,2,4,5,6,7,9,11,14],[0,2,4,5,6,7,9,12,13],[0,2,4,5,6,7,9,12,14],[0,2,4,5,6,7,9,13,14],[0,2,4,5,6,8,9,10,11],[0,2,4,5,6,8,9,10,12],[0,2,4,5,6,8,9,10,13],[0,2,4,5,6,8,9,10,14],[0,2,4,5,6,8,9,11,12],[0,2,4,5,6,8,9,11,13],[0,2,4,5,6,8,9,11,14],[0,2,4,5,6,8,9,12,13],[0,2,4,5,6,8,9,12,14],[0,2,4,5,6,8,9,13,14],[0,2,4,5,7,8,9,10,11],[0,2,4,5,7,8,9,10,12],[0,2,4,5,7,8,9,10,13],[0,2,4,5,7,8,9,10,14],[0,2,4,5,7,8,9,11,12],[0,2,4,5,7,8,9,11,13],[0,2,4,5,7,8,9,11,14],[0,2,4,5,7,8,9,12,13],[0,2,4,5,7,8,9,12,14],[0,2,4,5,7,8,9,13,14],[0,2,4,5,10],[0,2,4,5,10,11,12,13,14],[0,2,4,5,11],[0,2,4,5,12],[0,2,4,5,13],[0,2,4,5,14],[0,2,4,6,7,8,9,10,11],[0,2,4,6,7,8,9,10,12],[0,2,4,6,7,8,9,10,13],[0,2,4,6,7,8,9,10,14],[0,2,4,6,7,8,9,11,12],[0,2,4,6,7,8,9,11,13],[0,2,4,6,7,8,9,11,14],[0,2,4,6,7,8,9,12,13],[0,2,4,6,7,8,9,12,14],[0,2,4,6,7,8,9,13,14],[0,2,4,6,10],[0,2,4,6,10,11,12,13,14],[0,2,4,6,11],[0,2,4,6,12],[0,2,4,6,13],[0,2,4,6,14],[0,2,4,7,10],[0,2,4,7,10,11,12,13,14],[0,2,4,7,11],[0,2,4,7,12],[0,2,4,7,13],[0,2,4,7,14],[0,2,4,8,10],[0,2,4,8,10,11,12,13,14],[0,2,4,8,11],[0,2,4,8,12],[0,2,4,8,13],[0,2,4,8,14],[0,2,4,9,10],[0,2,4,9,10,11,12,13,14],[0,2,4,9,11],[0,2,4,9,12],[0,2,4,9,13],[0,2,4,9,14],[0,2,5,6,7,8,9,10,11],[0,2,5,6,7,8,9,10,12],[0,2,5,6,7,8,9,10,13],[0,2,5,6,7,8,9,10,14],[0,2,5,6,7,8,9,11,12],[0,2,5,6,7,8,9,11,13],[0,2,5,6,7,8,9,11,14],[0,2,5,6,7,8,9,12,13],[0,2,5,6,7,8,9,12,14],[0,2,5,6,7,8,9,13,14],[0,2,5,6,10],[0,2,5,6,10,11,12,13,14],[0,2,5,6,11],[0,2,5,6,12],[0,2,5,6,13],[0,2,5,6,14],[0,2,5,7,10],[0,2,5,7,10,11,12,13,14],[0,2,5,7,11],[0,2,5,7,12],[0,2,5,7,13],[0,2,5,7,14],[0,2,5,8,10],[0,2,5,8,10,11,12,13,14],[0,2,5,8,11],[0,2,5,8,12],[0,2,5,8,13],[0,2,5,8,14],[0,2,5,9,10],[0,2,5,9,10,11,12,13,14],[0,2,5,9,11],[0,2,5,9,12],[0,2,5,9,13],[0,2,5,9,14],[0,2,6,7,10],[0,2,6,7,10,11,12,13,14],[0,2,6,7,11],[0,2,6,7,12],[0,2,6,7,13],[0,2,6,7,14],[0,2,6,8,10],[0,2,6,8,10,11,12,13,14],[0,2,6,8,11],[0,2,6,8,12],[0,2,6,8,13],[0,2,6,8,14],[0,2,6,9,10],[0,2,6,9,10,11,12,13,14],[0,2,6,9,11],[0,2,6,9,12],[0,2,6,9,13],[0,2,6,9,14],[0,2,7,8,10],[0,2,7,8,10,11,12,13,14],[0,2,7,8,11],[0,2,7,8,12],[0,2,7,8,13],[0,2,7,8,14],[0,2,7,9,10],[0,2,7,9,10,11,12,13,14],[0,2,7,9,11],[0,2,7,9,12],[0,2,7,9,13],[0,2,7,9,14],[0,2,8,9,10],[0,2,8,9,10,11,12,13,14],[0,2,8,9,11],[0,2,8,9,12],[0,2,8,9,13],[0,2,8,9,14],[0,3,4,5,6,7,8,10,11],[0,3,4,5,6,7,8,10,12],[0,3,4,5,6,7,8,10,13],[0,3,4,5,6,7,8,10,14],[0,3,4,5,6,7,8,11,12],[0,3,4,5,6,7,8,11,13],[0,3,4,5,6,7,8,11,14],[0,3,4,5,6,7,8,12,13],[0,3,4,5,6,7,8,12,14],[0,3,4,5,6,7,8,13,14],[0,3,4,5,6,7,9,10,11],[0,3,4,5,6,7,9,10,12],[0,3,4,5,6,7,9,10,13],[0,3,4,5,6,7,9,10,14],[0,3,4,5,6,7,9,11,12],[0,3,4,5,6,7,9,11,13],[0,3,4,5,6,7,9,11,14],[0,3,4,5,6,7,9,12,13],[0,3,4,5,6,7,9,12,14],[0,3,4,5,6,7,9,13,14],[0,3,4,5,6,8,9,10,11],[0,3,4,5,6,8,9,10,12],[0,3,4,5,6,8,9,10,13],[0,3,4,5,6,8,9,10,14],[0,3,4,5,6,8,9,11,12],[0,3,4,5,6,8,9,11,13],[0,3,4,5,6,8,9,11,14],[0,3,4,5,6,8,9,12,13],[0,3,4,5,6,8,9,12,14],[0,3,4,5,6,8,9,13,14],[0,3,4,5,7,8,9,10,11],[0,3,4,5,7,8,9,10,12],[0,3,4,5,7,8,9,10,13],[0,3,4,5,7,8,9,10,14],[0,3,4,5,7,8,9,11,12],[0,3,4,5,7,8,9,11,13],[0,3,4,5,7,8,9,11,14],[0,3,4,5,7,8,9,12,13],[0,3,4,5,7,8,9,12,14],[0,3,4,5,7,8,9,13,14],[0,3,4,5,10],[0,3,4,5,10,11,12,13,14],[0,3,4,5,11],[0,3,4,5,12],[0,3,4,5,13],[0,3,4,5,14],[0,3,4,6,7,8,9,10,11],[0,3,4,6,7,8,9,10,12],[0,3,4,6,7,8,9,10,13],[0,3,4,6,7,8,9,10,14],[0,3,4,6,7,8,9,11,12],[0,3,4,6,7,8,9,11,13],[0,3,4,6,7,8,9,11,14],[0,3,4,6,7,8,9,12,13],[0,3,4,6,7,8,9,12,14],[0,3,4,6,7,8,9,13,14],[0,3,4,6,10],[0,3,4,6,10,11,12,13,14],[0,3,4,6,11],[0,3,4,6,12],[0,3,4,6,13],[0,3,4,6,14],[0,3,4,7,10],[0,3,4,7,10,11,12,13,14],[0,3,4,7,11],[0,3,4,7,12],[0,3,4,7,13],[0,3,4,7,14],[0,3,4,8,10],[0,3,4,8,10,11,12,13,14],[0,3,4,8,11],[0,3,4,8,12],[0,3,4,8,13],[0,3,4,8,14],[0,3,4,9,10],[0,3,4,9,10,11,12,13,14],[0,3,4,9,11],[0,3,4,9,12],[0,3,4,9,13],[0,3,4,9,14],[0,3,5,6,7,8,9,10,11],[0,3,5,6,7,8,9,10,12],[0,3,5,6,7,8,9,10,13],[0,3,5,6,7,8,9,10,14],[0,3,5,6,7,8,9,11,12],[0,3,5,6,7,8,9,11,13],[0,3,5,6,7,8,9,11,14],[0,3,5,6,7,8,9,12,13],[0,3,5,6,7,8,9,12,14],[0,3,5,6,7,8,9,13,14],[0,3,5,6,10],[0,3,5,6,10,11,12,13,14],[0,3,5,6,11],[0,3,5,6,12],[0,3,5,6,13],[0,3,5,6,14],[0,3,5,7,10],[0,3,5,7,10,11,12,13,14],[0,3,5,7,11],[0,3,5,7,12],[0,3,5,7,13],[0,3,5,7,14],[0,3,5,8,10],[0,3,5,8,10,11,12,13,14],[0,3,5,8,11],[0,3,5,8,12],[0,3,5,8,13],[0,3,5,8,14],[0,3,5,9,10],[0,3,5,9,10,11,12,13,14],[0,3,5,9,11],[0,3,5,9,12],[0,3,5,9,13],[0,3,5,9,14],[0,3,6,7,10],[0,3,6,7,10,11,12,13,14],[0,3,6,7,11],[0,3,6,7,12],[0,3,6,7,13],[0,3,6,7,14],[0,3,6,8,10],[0,3,6,8,10,11,12,13,14],[0,3,6,8,11],[0,3,6,8,12],[0,3,6,8,13],[0,3,6,8,14],[0,3,6,9,10],[0,3,6,9,10,11,12,13,14],[0,3,6,9,11],[0,3,6,9,12],[0,3,6,9,13],[0,3,6,9,14],[0,3,7,8,10],[0,3,7,8,10,11,12,13,14],[0,3,7,8,11],[0,3,7,8,12],[0,3,7,8,13],[0,3,7,8,14],[0,3,7,9,10],[0,3,7,9,10,11,12,13,14],[0,3,7,9,11],[0,3,7,9,12],[0,3,7,9,13],[0,3,7,9,14],[0,3,8,9,10],[0,3,8,9,10,11,12,13,14],[0,3,8,9,11],[0,3,8,9,12],[0,3,8,9,13],[0,3,8,9,14],[0,4,5,6,7,8,9,10,11],[0,4,5,6,7,8,9,10,12],[0,4,5,6,7,8,9,10,13],[0,4,5,6,7,8,9,10,14],[0,4,5,6,7,8,9,11,12],[0,4,5,6,7,8,9,11,13],[0,4,5,6,7,8,9,11,14],[0,4,5,6,7,8,9,12,13],[0,4,5,6,7,8,9,12,14],[0,4,5,6,7,8,9,13,14],[0,4,5,6,10],[0,4,5,6,10,11,12,13,14],[0,4,5,6,11],[0,4,5,6,12],[0,4,5,6,13],[0,4,5,6,14],[0,4,5,7,10],[0,4,5,7,10,11,12,13,14],[0,4,5,7,11],[0,4,5,7,12],[0,4,5,7,13],[0,4,5,7,14],[0,4,5,8,10],[0,4,5,8,10,11,12,13,14],[0,4,5,8,11],[0,4,5,8,12],[0,4,5,8,13],[0,4,5,8,14],[0,4,5,9,10],[0,4,5,9,10,11,12,13,14],[0,4,5,9,11],[0,4,5,9,12],[0,4,5,9,13],[0,4,5,9,14],[0,4,6,7,10],[0,4,6,7,10,11,12,13,14],[0,4,6,7,11],[0,4,6,7,12],[0,4,6,7,13],[0,4,6,7,14],[0,4,6,8,10],[0,4,6,8,10,11,12,13,14],[0,4,6,8,11],[0,4,6,8,12],[0,4,6,8,13],[0,4,6,8,14],[0,4,6,9,10],[0,4,6,9,10,11,12,13,14],[0,4,6,9,11],[0,4,6,9,12],[0,4,6,9,13],[0,4,6,9,14],[0,4,7,8,10],[0,4,7,8,10,11,12,13,14],[0,4,7,8,11],[0,4,7,8,12],[0,4,7,8,13],[0,4,7,8,14],[0,4,7,9,10],[0,4,7,9,10,11,12,13,14],[0,4,7,9,11],[0,4,7,9,12],[0,4,7,9,13],[0,4,7,9,14],[0,4,8,9,10],[0,4,8,9,10,11,12,13,14],[0,4,8,9,11],[0,4,8,9,12],[0,4,8,9,13],[0,4,8,9,14],[0,5,6,7,10],[0,5,6,7,10,11,12,13,14],[0,5,6,7,11],[0,5,6,7,12],[0,5,6,7,13],[0,5,6,7,14],[0,5,6,8,10],[0,5,6,8,10,11,12,13,14],[0,5,6,8,11],[0,5,6,8,12],[0,5,6,8,13],[0,5,6,8,14],[0,5,6,9,10],[0,5,6,9,10,11,12,13,14],[0,5,6,9,11],[0,5,6,9,12],[0,5,6,9,13],[0,5,6,9,14],[0,5,7,8,10],[0,5,7,8,10,11,12,13,14],[0,5,7,8,11],[0,5,7,8,12],[0,5,7,8,13],[0,5,7,8,14],[0,5,7,9,10],[0,5,7,9,10,11,12,13,14],[0,5,7,9,11],[0,5,7,9,12],[0,5,7,9,13],[0,5,7,9,14],[0,5,8,9,10],[0,5,8,9,10,11,12,13,14],[0,5,8,9,11],[0,5,8,9,12],[0,5,8,9,13],[0,5,8,9,14],[0,6,7,8,10],[0,6,7,8,10,11,12,13,14],[0,6,7,8,11],[0,6,7,8,12],[0,6,7,8,13],[0,6,7,8,14],[0,6,7,9,10],[0,6,7,9,10,11,12,13,14],[0,6,7,9,11],[0,6,7,9,12],[0,6,7,9,13],[0,6,7,9,14],[0,6,8,9,10],[0,6,8,9,10,11,12,13,14],[0,6,8,9,11],[0,6,8,9,12],[0,6,8,9,13],[0,6,8,9,14],[0,7,8,9,10],[0,7,8,9,10,11,12,13,14],[0,7,8,9,11],[0,7,8,9,12],[0,7,8,9,13],[0,7,8,9,14],[0,10,11,12,13],[0,10,11,12,14],[0,10,11,13,14],[0,10,12,13,14],[0,11,12,13,14],[1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,10,12],[1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,10,14],[1,2,3,4,5,6,7,11,12],[1,2,3,4,5,6,7,11,13],[1,2,3,4,5,6,7,11,14],[1,2,3,4,5,6,7,12,13],[1,2,3,4,5,6,7,12,14],[1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,10,11],[1,2,3,4,5,6,8,10,12],[1,2,3,4,5,6,8,10,13],[1,2,3,4,5,6,8,10,14],[1,2,3,4,5,6,8,11,12],[1,2,3,4,5,6,8,11,13],[1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,8,12,13],[1,2,3,4,5,6,8,12,14],[1,2,3,4,5,6,8,13,14],[1,2,3,4,5,6,9,10,11],[1,2,3,4,5,6,9,10,12],[1,2,3,4,5,6,9,10,13],[1,2,3,4,5,6,9,10,14],[1,2,3,4,5,6,9,11,12],[1,2,3,4,5,6,9,11,13],[1,2,3,4,5,6,9,11,14],[1,2,3,4,5,6,9,12,13],[1,2,3,4,5,6,9,12,14],[1,2,3,4,5,6,9,13,14],[1,2,3,4,5,7,8,10,11],[1,2,3,4,5,7,8,10,12],[1,2,3,4,5,7,8,10,13],[1,2,3,4,5,7,8,10,14],[1,2,3,4,5,7,8,11,12],[1,2,3,4,5,7,8,11,13],[1,2,3,4,5,7,8,11,14],[1,2,3,4,5,7,8,12,13],[1,2,3,4,5,7,8,12,14],[1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,11],[1,2,3,4,5,7,9,10,12],[1,2,3,4,5,7,9,10,13],[1,2,3,4,5,7,9,10,14],[1,2,3,4,5,7,9,11,12],[1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,9,11,14],[1,2,3,4,5,7,9,12,13],[1,2,3,4,5,7,9,12,14],[1,2,3,4,5,7,9,13,14],[1,2,3,4,5,8,9,10,11],[1,2,3,4,5,8,9,10,12],[1,2,3,4,5,8,9,10,13],[1,2,3,4,5,8,9,10,14],[1,2,3,4,5,8,9,11,12],[1,2,3,4,5,8,9,11,13],[1,2,3,4,5,8,9,11,14],[1,2,3,4,5,8,9,12,13],[1,2,3,4,5,8,9,12,14],[1,2,3,4,5,8,9,13,14],[1,2,3,4,6,7,8,10,11],[1,2,3,4,6,7,8,10,12],[1,2,3,4,6,7,8,10,13],[1,2,3,4,6,7,8,10,14],[1,2,3,4,6,7,8,11,12],[1,2,3,4,6,7,8,11,13],[1,2,3,4,6,7,8,11,14],[1,2,3,4,6,7,8,12,13],[1,2,3,4,6,7,8,12,14],[1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,9,10,11],[1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,9,10,13],[1,2,3,4,6,7,9,10,14],[1,2,3,4,6,7,9,11,12],[1,2,3,4,6,7,9,11,13],[1,2,3,4,6,7,9,11,14],[1,2,3,4,6,7,9,12,13],[1,2,3,4,6,7,9,12,14],[1,2,3,4,6,7,9,13,14],[1,2,3,4,6,8,9,10,11],[1,2,3,4,6,8,9,10,12],[1,2,3,4,6,8,9,10,13],[1,2,3,4,6,8,9,10,14],[1,2,3,4,6,8,9,11,12],[1,2,3,4,6,8,9,11,13],[1,2,3,4,6,8,9,11,14],[1,2,3,4,6,8,9,12,13],[1,2,3,4,6,8,9,12,14],[1,2,3,4,6,8,9,13,14],[1,2,3,4,7,8,9,10,11],[1,2,3,4,7,8,9,10,12],[1,2,3,4,7,8,9,10,13],[1,2,3,4,7,8,9,10,14],[1,2,3,4,7,8,9,11,12],[1,2,3,4,7,8,9,11,13],[1,2,3,4,7,8,9,11,14],[1,2,3,4,7,8,9,12,13],[1,2,3,4,7,8,9,12,14],[1,2,3,4,7,8,9,13,14],[1,2,3,4,10],[1,2,3,4,10,11,12,13,14],[1,2,3,4,11],[1,2,3,4,12],[1,2,3,4,13],[1,2,3,4,14],[1,2,3,5,6,7,8,10,11],[1,2,3,5,6,7,8,10,12],[1,2,3,5,6,7,8,10,13],[1,2,3,5,6,7,8,10,14],[1,2,3,5,6,7,8,11,12],[1,2,3,5,6,7,8,11,13],[1,2,3,5,6,7,8,11,14],[1,2,3,5,6,7,8,12,13],[1,2,3,5,6,7,8,12,14],[1,2,3,5,6,7,8,13,14],[1,2,3,5,6,7,9,10,11],[1,2,3,5,6,7,9,10,12],[1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,10,14],[1,2,3,5,6,7,9,11,12],[1,2,3,5,6,7,9,11,13],[1,2,3,5,6,7,9,11,14],[1,2,3,5,6,7,9,12,13],[1,2,3,5,6,7,9,12,14],[1,2,3,5,6,7,9,13,14],[1,2,3,5,6,8,9,10,11],[1,2,3,5,6,8,9,10,12],[1,2,3,5,6,8,9,10,13],[1,2,3,5,6,8,9,10,14],[1,2,3,5,6,8,9,11,12],[1,2,3,5,6,8,9,11,13],[1,2,3,5,6,8,9,11,14],[1,2,3,5,6,8,9,12,13],[1,2,3,5,6,8,9,12,14],[1,2,3,5,6,8,9,13,14],[1,2,3,5,7,8,9,10,11],[1,2,3,5,7,8,9,10,12],[1,2,3,5,7,8,9,10,13],[1,2,3,5,7,8,9,10,14],[1,2,3,5,7,8,9,11,12],[1,2,3,5,7,8,9,11,13],[1,2,3,5,7,8,9,11,14],[1,2,3,5,7,8,9,12,13],[1,2,3,5,7,8,9,12,14],[1,2,3,5,7,8,9,13,14],[1,2,3,5,10],[1,2,3,5,10,11,12,13,14],[1,2,3,5,11],[1,2,3,5,12],[1,2,3,5,13],[1,2,3,5,14],[1,2,3,6,7,8,9,10,11],[1,2,3,6,7,8,9,10,12],[1,2,3,6,7,8,9,10,13],[1,2,3,6,7,8,9,10,14],[1,2,3,6,7,8,9,11,12],[1,2,3,6,7,8,9,11,13],[1,2,3,6,7,8,9,11,14],[1,2,3,6,7,8,9,12,13],[1,2,3,6,7,8,9,12,14],[1,2,3,6,7,8,9,13,14],[1,2,3,6,10],[1,2,3,6,10,11,12,13,14],[1,2,3,6,11],[1,2,3,6,12],[1,2,3,6,13],[1,2,3,6,14],[1,2,3,7,10],[1,2,3,7,10,11,12,13,14],[1,2,3,7,11],[1,2,3,7,12],[1,2,3,7,13],[1,2,3,7,14],[1,2,3,8,10],[1,2,3,8,10,11,12,13,14],[1,2,3,8,11],[1,2,3,8,12],[1,2,3,8,13],[1,2,3,8,14],[1,2,3,9,10],[1,2,3,9,10,11,12,13,14],[1,2,3,9,11],[1,2,3,9,12],[1,2,3,9,13],[1,2,3,9,14],[1,2,4,5,6,7,8,10,11],[1,2,4,5,6,7,8,10,12],[1,2,4,5,6,7,8,10,13],[1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,8,11,12],[1,2,4,5,6,7,8,11,13],[1,2,4,5,6,7,8,11,14],[1,2,4,5,6,7,8,12,13],[1,2,4,5,6,7,8,12,14],[1,2,4,5,6,7,8,13,14],[1,2,4,5,6,7,9,10,11],[1,2,4,5,6,7,9,10,12],[1,2,4,5,6,7,9,10,13],[1,2,4,5,6,7,9,10,14],[1,2,4,5,6,7,9,11,12],[1,2,4,5,6,7,9,11,13],[1,2,4,5,6,7,9,11,14],[1,2,4,5,6,7,9,12,13],[1,2,4,5,6,7,9,12,14],[1,2,4,5,6,7,9,13,14],[1,2,4,5,6,8,9,10,11],[1,2,4,5,6,8,9,10,12],[1,2,4,5,6,8,9,10,13],[1,2,4,5,6,8,9,10,14],[1,2,4,5,6,8,9,11,12],[1,2,4,5,6,8,9,11,13],[1,2,4,5,6,8,9,11,14],[1,2,4,5,6,8,9,12,13],[1,2,4,5,6,8,9,12,14],[1,2,4,5,6,8,9,13,14],[1,2,4,5,7,8,9,10,11],[1,2,4,5,7,8,9,10,12],[1,2,4,5,7,8,9,10,13],[1,2,4,5,7,8,9,10,14],[1,2,4,5,7,8,9,11,12],[1,2,4,5,7,8,9,11,13],[1,2,4,5,7,8,9,11,14],[1,2,4,5,7,8,9,12,13],[1,2,4,5,7,8,9,12,14],[1,2,4,5,7,8,9,13,14],[1,2,4,5,10],[1,2,4,5,10,11,12,13,14],[1,2,4,5,11],[1,2,4,5,12],[1,2,4,5,13],[1,2,4,5,14],[1,2,4,6,7,8,9,10,11],[1,2,4,6,7,8,9,10,12],[1,2,4,6,7,8,9,10,13],[1,2,4,6,7,8,9,10,14],[1,2,4,6,7,8,9,11,12],[1,2,4,6,7,8,9,11,13],[1,2,4,6,7,8,9,11,14],[1,2,4,6,7,8,9,12,13],[1,2,4,6,7,8,9,12,14],[1,2,4,6,7,8,9,13,14],[1,2,4,6,10],[1,2,4,6,10,11,12,13,14],[1,2,4,6,11],[1,2,4,6,12],[1,2,4,6,13],[1,2,4,6,14],[1,2,4,7,10],[1,2,4,7,10,11,12,13,14],[1,2,4,7,11],[1,2,4,7,12],[1,2,4,7,13],[1,2,4,7,14],[1,2,4,8,10],[1,2,4,8,10,11,12,13,14],[1,2,4,8,11],[1,2,4,8,12],[1,2,4,8,13],[1,2,4,8,14],[1,2,4,9,10],[1,2,4,9,10,11,12,13,14],[1,2,4,9,11],[1,2,4,9,12],[1,2,4,9,13],[1,2,4,9,14],[1,2,5,6,7,8,9,10,11],[1,2,5,6,7,8,9,10,12],[1,2,5,6,7,8,9,10,13],[1,2,5,6,7,8,9,10,14],[1,2,5,6,7,8,9,11,12],[1,2,5,6,7,8,9,11,13],[1,2,5,6,7,8,9,11,14],[1,2,5,6,7,8,9,12,13],[1,2,5,6,7,8,9,12,14],[1,2,5,6,7,8,9,13,14],[1,2,5,6,10],[1,2,5,6,10,11,12,13,14],[1,2,5,6,11],[1,2,5,6,12],[1,2,5,6,13],[1,2,5,6,14],[1,2,5,7,10],[1,2,5,7,10,11,12,13,14],[1,2,5,7,11],[1,2,5,7,12],[1,2,5,7,13],[1,2,5,7,14],[1,2,5,8,10],[1,2,5,8,10,11,12,13,14],[1,2,5,8,11],[1,2,5,8,12],[1,2,5,8,13],[1,2,5,8,14],[1,2,5,9,10],[1,2,5,9,10,11,12,13,14],[1,2,5,9,11],[1,2,5,9,12],[1,2,5,9,13],[1,2,5,9,14],[1,2,6,7,10],[1,2,6,7,10,11,12,13,14],[1,2,6,7,11],[1,2,6,7,12],[1,2,6,7,13],[1,2,6,7,14],[1,2,6,8,10],[1,2,6,8,10,11,12,13,14],[1,2,6,8,11],[1,2,6,8,12],[1,2,6,8,13],[1,2,6,8,14],[1,2,6,9,10],[1,2,6,9,10,11,12,13,14],[1,2,6,9,11],[1,2,6,9,12],[1,2,6,9,13],[1,2,6,9,14],[1,2,7,8,10],[1,2,7,8,10,11,12,13,14],[1,2,7,8,11],[1,2,7,8,12],[1,2,7,8,13],[1,2,7,8,14],[1,2,7,9,10],[1,2,7,9,10,11,12,13,14],[1,2,7,9,11],[1,2,7,9,12],[1,2,7,9,13],[1,2,7,9,14],[1,2,8,9,10],[1,2,8,9,10,11,12,13,14],[1,2,8,9,11],[1,2,8,9,12],[1,2,8,9,13],[1,2,8,9,14],[1,3,4,5,6,7,8,10,11],[1,3,4,5,6,7,8,10,12],[1,3,4,5,6,7,8,10,13],[1,3,4,5,6,7,8,10,14],[1,3,4,5,6,7,8,11,12],[1,3,4,5,6,7,8,11,13],[1,3,4,5,6,7,8,11,14],[1,3,4,5,6,7,8,12,13],[1,3,4,5,6,7,8,12,14],[1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,10,12],[1,3,4,5,6,7,9,10,13],[1,3,4,5,6,7,9,10,14],[1,3,4,5,6,7,9,11,12],[1,3,4,5,6,7,9,11,13],[1,3,4,5,6,7,9,11,14],[1,3,4,5,6,7,9,12,13],[1,3,4,5,6,7,9,12,14],[1,3,4,5,6,7,9,13,14],[1,3,4,5,6,8,9,10,11],[1,3,4,5,6,8,9,10,12],[1,3,4,5,6,8,9,10,13],[1,3,4,5,6,8,9,10,14],[1,3,4,5,6,8,9,11,12],[1,3,4,5,6,8,9,11,13],[1,3,4,5,6,8,9,11,14],[1,3,4,5,6,8,9,12,13],[1,3,4,5,6,8,9,12,14],[1,3,4,5,6,8,9,13,14],[1,3,4,5,7,8,9,10,11],[1,3,4,5,7,8,9,10,12],[1,3,4,5,7,8,9,10,13],[1,3,4,5,7,8,9,10,14],[1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,9,11,13],[1,3,4,5,7,8,9,11,14],[1,3,4,5,7,8,9,12,13],[1,3,4,5,7,8,9,12,14],[1,3,4,5,7,8,9,13,14],[1,3,4,5,10],[1,3,4,5,10,11,12,13,14],[1,3,4,5,11],[1,3,4,5,12],[1,3,4,5,13],[1,3,4,5,14],[1,3,4,6,7,8,9,10,11],[1,3,4,6,7,8,9,10,12],[1,3,4,6,7,8,9,10,13],[1,3,4,6,7,8,9,10,14],[1,3,4,6,7,8,9,11,12],[1,3,4,6,7,8,9,11,13],[1,3,4,6,7,8,9,11,14],[1,3,4,6,7,8,9,12,13],[1,3,4,6,7,8,9,12,14],[1,3,4,6,7,8,9,13,14],[1,3,4,6,10],[1,3,4,6,10,11,12,13,14],[1,3,4,6,11],[1,3,4,6,12],[1,3,4,6,13],[1,3,4,6,14],[1,3,4,7,10],[1,3,4,7,10,11,12,13,14],[1,3,4,7,11],[1,3,4,7,12],[1,3,4,7,13],[1,3,4,7,14],[1,3,4,8,10],[1,3,4,8,10,11,12,13,14],[1,3,4,8,11],[1,3,4,8,12],[1,3,4,8,13],[1,3,4,8,14],[1,3,4,9,10],[1,3,4,9,10,11,12,13,14],[1,3,4,9,11],[1,3,4,9,12],[1,3,4,9,13],[1,3,4,9,14],[1,3,5,6,7,8,9,10,11],[1,3,5,6,7,8,9,10,12],[1,3,5,6,7,8,9,10,13],[1,3,5,6,7,8,9,10,14],[1,3,5,6,7,8,9,11,12],[1,3,5,6,7,8,9,11,13],[1,3,5,6,7,8,9,11,14],[1,3,5,6,7,8,9,12,13],[1,3,5,6,7,8,9,12,14],[1,3,5,6,7,8,9,13,14],[1,3,5,6,10],[1,3,5,6,10,11,12,13,14],[1,3,5,6,11],[1,3,5,6,12],[1,3,5,6,13],[1,3,5,6,14],[1,3,5,7,10],[1,3,5,7,10,11,12,13,14],[1,3,5,7,11],[1,3,5,7,12],[1,3,5,7,13],[1,3,5,7,14],[1,3,5,8,10],[1,3,5,8,10,11,12,13,14],[1,3,5,8,11],[1,3,5,8,12],[1,3,5,8,13],[1,3,5,8,14],[1,3,5,9,10],[1,3,5,9,10,11,12,13,14],[1,3,5,9,11],[1,3,5,9,12],[1,3,5,9,13],[1,3,5,9,14],[1,3,6,7,10],[1,3,6,7,10,11,12,13,14],[1,3,6,7,11],[1,3,6,7,12],[1,3,6,7,13],[1,3,6,7,14],[1,3,6,8,10],[1,3,6,8,10,11,12,13,14],[1,3,6,8,11],[1,3,6,8,12],[1,3,6,8,13],[1,3,6,8,14],[1,3,6,9,10],[1,3,6,9,10,11,12,13,14],[1,3,6,9,11],[1,3,6,9,12],[1,3,6,9,13],[1,3,6,9,14],[1,3,7,8,10],[1,3,7,8,10,11,12,13,14],[1,3,7,8,11],[1,3,7,8,12],[1,3,7,8,13],[1,3,7,8,14],[1,3,7,9,10],[1,3,7,9,10,11,12,13,14],[1,3,7,9,11],[1,3,7,9,12],[1,3,7,9,13],[1,3,7,9,14],[1,3,8,9,10],[1,3,8,9,10,11,12,13,14],[1,3,8,9,11],[1,3,8,9,12],[1,3,8,9,13],[1,3,8,9,14],[1,4,5,6,7,8,9,10,11],[1,4,5,6,7,8,9,10,12],[1,4,5,6,7,8,9,10,13],[1,4,5,6,7,8,9,10,14],[1,4,5,6,7,8,9,11,12],[1,4,5,6,7,8,9,11,13],[1,4,5,6,7,8,9,11,14],[1,4,5,6,7,8,9,12,13],[1,4,5,6,7,8,9,12,14],[1,4,5,6,7,8,9,13,14],[1,4,5,6,10],[1,4,5,6,10,11,12,13,14],[1,4,5,6,11],[1,4,5,6,12],[1,4,5,6,13],[1,4,5,6,14],[1,4,5,7,10],[1,4,5,7,10,11,12,13,14],[1,4,5,7,11],[1,4,5,7,12],[1,4,5,7,13],[1,4,5,7,14],[1,4,5,8,10],[1,4,5,8,10,11,12,13,14],[1,4,5,8,11],[1,4,5,8,12],[1,4,5,8,13],[1,4,5,8,14],[1,4,5,9,10],[1,4,5,9,10,11,12,13,14],[1,4,5,9,11],[1,4,5,9,12],[1,4,5,9,13],[1,4,5,9,14],[1,4,6,7,10],[1,4,6,7,10,11,12,13,14],[1,4,6,7,11],[1,4,6,7,12],[1,4,6,7,13],[1,4,6,7,14],[1,4,6,8,10],[1,4,6,8,10,11,12,13,14],[1,4,6,8,11],[1,4,6,8,12],[1,4,6,8,13],[1,4,6,8,14],[1,4,6,9,10],[1,4,6,9,10,11,12,13,14],[1,4,6,9,11],[1,4,6,9,12],[1,4,6,9,13],[1,4,6,9,14],[1,4,7,8,10],[1,4,7,8,10,11,12,13,14],[1,4,7,8,11],[1,4,7,8,12],[1,4,7,8,13],[1,4,7,8,14],[1,4,7,9,10],[1,4,7,9,10,11,12,13,14],[1,4,7,9,11],[1,4,7,9,12],[1,4,7,9,13],[1,4,7,9,14],[1,4,8,9,10],[1,4,8,9,10,11,12,13,14],[1,4,8,9,11],[1,4,8,9,12],[1,4,8,9,13],[1,4,8,9,14],[1,5,6,7,10],[1,5,6,7,10,11,12,13,14],[1,5,6,7,11],[1,5,6,7,12],[1,5,6,7,13],[1,5,6,7,14],[1,5,6,8,10],[1,5,6,8,10,11,12,13,14],[1,5,6,8,11],[1,5,6,8,12],[1,5,6,8,13],[1,5,6,8,14],[1,5,6,9,10],[1,5,6,9,10,11,12,13,14],[1,5,6,9,11],[1,5,6,9,12],[1,5,6,9,13],[1,5,6,9,14],[1,5,7,8,10],[1,5,7,8,10,11,12,13,14],[1,5,7,8,11],[1,5,7,8,12],[1,5,7,8,13],[1,5,7,8,14],[1,5,7,9,10],[1,5,7,9,10,11,12,13,14],[1,5,7,9,11],[1,5,7,9,12],[1,5,7,9,13],[1,5,7,9,14],[1,5,8,9,10],[1,5,8,9,10,11,12,13,14],[1,5,8,9,11],[1,5,8,9,12],[1,5,8,9,13],[1,5,8,9,14],[1,6,7,8,10],[1,6,7,8,10,11,12,13,14],[1,6,7,8,11],[1,6,7,8,12],[1,6,7,8,13],[1,6,7,8,14],[1,6,7,9,10],[1,6,7,9,10,11,12,13,14],[1,6,7,9,11],[1,6,7,9,12],[1,6,7,9,13],[1,6,7,9,14],[1,6,8,9,10],[1,6,8,9,10,11,12,13,14],[1,6,8,9,11],[1,6,8,9,12],[1,6,8,9,13],[1,6,8,9,14],[1,7,8,9,10],[1,7,8,9,10,11,12,13,14],[1,7,8,9,11],[1,7,8,9,12],[1,7,8,9,13],[1,7,8,9,14],[1,10,11,12,13],[1,10,11,12,14],[1,10,11,13,14],[1,10,12,13,14],[1,11,12,13,14],[2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,10,13],[2,3,4,5,6,7,8,10,14],[2,3,4,5,6,7,8,11,12],[2,3,4,5,6,7,8,11,13],[2,3,4,5,6,7,8,11,14],[2,3,4,5,6,7,8,12,13],[2,3,4,5,6,7,8,12,14],[2,3,4,5,6,7,8,13,14],[2,3,4,5,6,7,9,10,11],[2,3,4,5,6,7,9,10,12],[2,3,4,5,6,7,9,10,13],[2,3,4,5,6,7,9,10,14],[2,3,4,5,6,7,9,11,12],[2,3,4,5,6,7,9,11,13],[2,3,4,5,6,7,9,11,14],[2,3,4,5,6,7,9,12,13],[2,3,4,5,6,7,9,12,14],[2,3,4,5,6,7,9,13,14],[2,3,4,5,6,8,9,10,11],[2,3,4,5,6,8,9,10,12],[2,3,4,5,6,8,9,10,13],[2,3,4,5,6,8,9,10,14],[2,3,4,5,6,8,9,11,12],[2,3,4,5,6,8,9,11,13],[2,3,4,5,6,8,9,11,14],[2,3,4,5,6,8,9,12,13],[2,3,4,5,6,8,9,12,14],[2,3,4,5,6,8,9,13,14],[2,3,4,5,7,8,9,10,11],[2,3,4,5,7,8,9,10,12],[2,3,4,5,7,8,9,10,13],[2,3,4,5,7,8,9,10,14],[2,3,4,5,7,8,9,11,12],[2,3,4,5,7,8,9,11,13],[2,3,4,5,7,8,9,11,14],[2,3,4,5,7,8,9,12,13],[2,3,4,5,7,8,9,12,14],[2,3,4,5,7,8,9,13,14],[2,3,4,5,10],[2,3,4,5,10,11,12,13,14],[2,3,4,5,11],[2,3,4,5,12],[2,3,4,5,13],[2,3,4,5,14],[2,3,4,6,7,8,9,10,11],[2,3,4,6,7,8,9,10,12],[2,3,4,6,7,8,9,10,13],[2,3,4,6,7,8,9,10,14],[2,3,4,6,7,8,9,11,12],[2,3,4,6,7,8,9,11,13],[2,3,4,6,7,8,9,11,14],[2,3,4,6,7,8,9,12,13],[2,3,4,6,7,8,9,12,14],[2,3,4,6,7,8,9,13,14],[2,3,4,6,10],[2,3,4,6,10,11,12,13,14],[2,3,4,6,11],[2,3,4,6,12],[2,3,4,6,13],[2,3,4,6,14],[2,3,4,7,10],[2,3,4,7,10,11,12,13,14],[2,3,4,7,11],[2,3,4,7,12],[2,3,4,7,13],[2,3,4,7,14],[2,3,4,8,10],[2,3,4,8,10,11,12,13,14],[2,3,4,8,11],[2,3,4,8,12],[2,3,4,8,13],[2,3,4,8,14],[2,3,4,9,10],[2,3,4,9,10,11,12,13,14],[2,3,4,9,11],[2,3,4,9,12],[2,3,4,9,13],[2,3,4,9,14],[2,3,5,6,7,8,9,10,11],[2,3,5,6,7,8,9,10,12],[2,3,5,6,7,8,9,10,13],[2,3,5,6,7,8,9,10,14],[2,3,5,6,7,8,9,11,12],[2,3,5,6,7,8,9,11,13],[2,3,5,6,7,8,9,11,14],[2,3,5,6,7,8,9,12,13],[2,3,5,6,7,8,9,12,14],[2,3,5,6,7,8,9,13,14],[2,3,5,6,10],[2,3,5,6,10,11,12,13,14],[2,3,5,6,11],[2,3,5,6,12],[2,3,5,6,13],[2,3,5,6,14],[2,3,5,7,10],[2,3,5,7,10,11,12,13,14],[2,3,5,7,11],[2,3,5,7,12],[2,3,5,7,13],[2,3,5,7,14],[2,3,5,8,10],[2,3,5,8,10,11,12,13,14],[2,3,5,8,11],[2,3,5,8,12],[2,3,5,8,13],[2,3,5,8,14],[2,3,5,9,10],[2,3,5,9,10,11,12,13,14],[2,3,5,9,11],[2,3,5,9,12],[2,3,5,9,13],[2,3,5,9,14],[2,3,6,7,10],[2,3,6,7,10,11,12,13,14],[2,3,6,7,11],[2,3,6,7,12],[2,3,6,7,13],[2,3,6,7,14],[2,3,6,8,10],[2,3,6,8,10,11,12,13,14],[2,3,6,8,11],[2,3,6,8,12],[2,3,6,8,13],[2,3,6,8,14],[2,3,6,9,10],[2,3,6,9,10,11,12,13,14],[2,3,6,9,11],[2,3,6,9,12],[2,3,6,9,13],[2,3,6,9,14],[2,3,7,8,10],[2,3,7,8,10,11,12,13,14],[2,3,7,8,11],[2,3,7,8,12],[2,3,7,8,13],[2,3,7,8,14],[2,3,7,9,10],[2,3,7,9,10,11,12,13,14],[2,3,7,9,11],[2,3,7,9,12],[2,3,7,9,13],[2,3,7,9,14],[2,3,8,9,10],[2,3,8,9,10,11,12,13,14],[2,3,8,9,11],[2,3,8,9,12],[2,3,8,9,13],[2,3,8,9,14],[2,4,5,6,7,8,9,10,11],[2,4,5,6,7,8,9,10,12],[2,4,5,6,7,8,9,10,13],[2,4,5,6,7,8,9,10,14],[2,4,5,6,7,8,9,11,12],[2,4,5,6,7,8,9,11,13],[2,4,5,6,7,8,9,11,14],[2,4,5,6,7,8,9,12,13],[2,4,5,6,7,8,9,12,14],[2,4,5,6,7,8,9,13,14],[2,4,5,6,10],[2,4,5,6,10,11,12,13,14],[2,4,5,6,11],[2,4,5,6,12],[2,4,5,6,13],[2,4,5,6,14],[2,4,5,7,10],[2,4,5,7,10,11,12,13,14],[2,4,5,7,11],[2,4,5,7,12],[2,4,5,7,13],[2,4,5,7,14],[2,4,5,8,10],[2,4,5,8,10,11,12,13,14],[2,4,5,8,11],[2,4,5,8,12],[2,4,5,8,13],[2,4,5,8,14],[2,4,5,9,10],[2,4,5,9,10,11,12,13,14],[2,4,5,9,11],[2,4,5,9,12],[2,4,5,9,13],[2,4,5,9,14],[2,4,6,7,10],[2,4,6,7,10,11,12,13,14],[2,4,6,7,11],[2,4,6,7,12],[2,4,6,7,13],[2,4,6,7,14],[2,4,6,8,10],[2,4,6,8,10,11,12,13,14],[2,4,6,8,11],[2,4,6,8,12],[2,4,6,8,13],[2,4,6,8,14],[2,4,6,9,10],[2,4,6,9,10,11,12,13,14],[2,4,6,9,11],[2,4,6,9,12],[2,4,6,9,13],[2,4,6,9,14],[2,4,7,8,10],[2,4,7,8,10,11,12,13,14],[2,4,7,8,11],[2,4,7,8,12],[2,4,7,8,13],[2,4,7,8,14],[2,4,7,9,10],[2,4,7,9,10,11,12,13,14],[2,4,7,9,11],[2,4,7,9,12],[2,4,7,9,13],[2,4,7,9,14],[2,4,8,9,10],[2,4,8,9,10,11,12,13,14],[2,4,8,9,11],[2,4,8,9,12],[2,4,8,9,13],[2,4,8,9,14],[2,5,6,7,10],[2,5,6,7,10,11,12,13,14],[2,5,6,7,11],[2,5,6,7,12],[2,5,6,7,13],[2,5,6,7,14],[2,5,6,8,10],[2,5,6,8,10,11,12,13,14],[2,5,6,8,11],[2,5,6,8,12],[2,5,6,8,13],[2,5,6,8,14],[2,5,6,9,10],[2,5,6,9,10,11,12,13,14],[2,5,6,9,11],[2,5,6,9,12],[2,5,6,9,13],[2,5,6,9,14],[2,5,7,8,10],[2,5,7,8,10,11,12,13,14],[2,5,7,8,11],[2,5,7,8,12],[2,5,7,8,13],[2,5,7,8,14],[2,5,7,9,10],[2,5,7,9,10,11,12,13,14],[2,5,7,9,11],[2,5,7,9,12],[2,5,7,9,13],[2,5,7,9,14],[2,5,8,9,10],[2,5,8,9,10,11,12,13,14],[2,5,8,9,11],[2,5,8,9,12],[2,5,8,9,13],[2,5,8,9,14],[2,6,7,8,10],[2,6,7,8,10,11,12,13,14],[2,6,7,8,11],[2,6,7,8,12],[2,6,7,8,13],[2,6,7,8,14],[2,6,7,9,10],[2,6,7,9,10,11,12,13,14],[2,6,7,9,11],[2,6,7,9,12],[2,6,7,9,13],[2,6,7,9,14],[2,6,8,9,10],[2,6,8,9,10,11,12,13,14],[2,6,8,9,11],[2,6,8,9,12],[2,6,8,9,13],[2,6,8,9,14],[2,7,8,9,10],[2,7,8,9,10,11,12,13,14],[2,7,8,9,11],[2,7,8,9,12],[2,7,8,9,13],[2,7,8,9,14],[2,10,11,12,13],[2,10,11,12,14],[2,10,11,13,14],[2,10,12,13,14],[2,11,12,13,14],[3,4,5,6,7,8,9,10,11],[3,4,5,6,7,8,9,10,12],[3,4,5,6,7,8,9,10,13],[3,4,5,6,7,8,9,10,14],[3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,11,13],[3,4,5,6,7,8,9,11,14],[3,4,5,6,7,8,9,12,13],[3,4,5,6,7,8,9,12,14],[3,4,5,6,7,8,9,13,14],[3,4,5,6,10],[3,4,5,6,10,11,12,13,14],[3,4,5,6,11],[3,4,5,6,12],[3,4,5,6,13],[3,4,5,6,14],[3,4,5,7,10],[3,4,5,7,10,11,12,13,14],[3,4,5,7,11],[3,4,5,7,12],[3,4,5,7,13],[3,4,5,7,14],[3,4,5,8,10],[3,4,5,8,10,11,12,13,14],[3,4,5,8,11],[3,4,5,8,12],[3,4,5,8,13],[3,4,5,8,14],[3,4,5,9,10],[3,4,5,9,10,11,12,13,14],[3,4,5,9,11],[3,4,5,9,12],[3,4,5,9,13],[3,4,5,9,14],[3,4,6,7,10],[3,4,6,7,10,11,12,13,14],[3,4,6,7,11],[3,4,6,7,12],[3,4,6,7,13],[3,4,6,7,14],[3,4,6,8,10],[3,4,6,8,10,11,12,13,14],[3,4,6,8,11],[3,4,6,8,12],[3,4,6,8,13],[3,4,6,8,14],[3,4,6,9,10],[3,4,6,9,10,11,12,13,14],[3,4,6,9,11],[3,4,6,9,12],[3,4,6,9,13],[3,4,6,9,14],[3,4,7,8,10],[3,4,7,8,10,11,12,13,14],[3,4,7,8,11],[3,4,7,8,12],[3,4,7,8,13],[3,4,7,8,14],[3,4,7,9,10],[3,4,7,9,10,11,12,13,14],[3,4,7,9,11],[3,4,7,9,12],[3,4,7,9,13],[3,4,7,9,14],[3,4,8,9,10],[3,4,8,9,10,11,12,13,14],[3,4,8,9,11],[3,4,8,9,12],[3,4,8,9,13],[3,4,8,9,14],[3,5,6,7,10],[3,5,6,7,10,11,12,13,14],[3,5,6,7,11],[3,5,6,7,12],[3,5,6,7,13],[3,5,6,7,14],[3,5,6,8,10],[3,5,6,8,10,11,12,13,14],[3,5,6,8,11],[3,5,6,8,12],[3,5,6,8,13],[3,5,6,8,14],[3,5,6,9,10],[3,5,6,9,10,11,12,13,14],[3,5,6,9,11],[3,5,6,9,12],[3,5,6,9,13],[3,5,6,9,14],[3,5,7,8,10],[3,5,7,8,10,11,12,13,14],[3,5,7,8,11],[3,5,7,8,12],[3,5,7,8,13],[3,5,7,8,14],[3,5,7,9,10],[3,5,7,9,10,11,12,13,14],[3,5,7,9,11],[3,5,7,9,12],[3,5,7,9,13],[3,5,7,9,14],[3,5,8,9,10],[3,5,8,9,10,11,12,13,14],[3,5,8,9,11],[3,5,8,9,12],[3,5,8,9,13],[3,5,8,9,14],[3,6,7,8,10],[3,6,7,8,10,11,12,13,14],[3,6,7,8,11],[3,6,7,8,12],[3,6,7,8,13],[3,6,7,8,14],[3,6,7,9,10],[3,6,7,9,10,11,12,13,14],[3,6,7,9,11],[3,6,7,9,12],[3,6,7,9,13],[3,6,7,9,14],[3,6,8,9,10],[3,6,8,9,10,11,12,13,14],[3,6,8,9,11],[3,6,8,9,12],[3,6,8,9,13],[3,6,8,9,14],[3,7,8,9,10],[3,7,8,9,10,11,12,13,14],[3,7,8,9,11],[3,7,8,9,12],[3,7,8,9,13],[3,7,8,9,14],[3,10,11,12,13],[3,10,11,12,14],[3,10,11,13,14],[3,10,12,13,14],[3,11,12,13,14],[4,5,6,7,10],[4,5,6,7,10,11,12,13,14],[4,5,6,7,11],[4,5,6,7,12],[4,5,6,7,13],[4,5,6,7,14],[4,5,6,8,10],[4,5,6,8,10,11,12,13,14],[4,5,6,8,11],[4,5,6,8,12],[4,5,6,8,13],[4,5,6,8,14],[4,5,6,9,10],[4,5,6,9,10,11,12,13,14],[4,5,6,9,11],[4,5,6,9,12],[4,5,6,9,13],[4,5,6,9,14],[4,5,7,8,10],[4,5,7,8,10,11,12,13,14],[4,5,7,8,11],[4,5,7,8,12],[4,5,7,8,13],[4,5,7,8,14],[4,5,7,9,10],[4,5,7,9,10,11,12,13,14],[4,5,7,9,11],[4,5,7,9,12],[4,5,7,9,13],[4,5,7,9,14],[4,5,8,9,10],[4,5,8,9,10,11,12,13,14],[4,5,8,9,11],[4,5,8,9,12],[4,5,8,9,13],[4,5,8,9,14],[4,6,7,8,10],[4,6,7,8,10,11,12,13,14],[4,6,7,8,11],[4,6,7,8,12],[4,6,7,8,13],[4,6,7,8,14],[4,6,7,9,10],[4,6,7,9,10,11,12,13,14],[4,6,7,9,11],[4,6,7,9,12],[4,6,7,9,13],[4,6,7,9,14],[4,6,8,9,10],[4,6,8,9,10,11,12,13,14],[4,6,8,9,11],[4,6,8,9,12],[4,6,8,9,13],[4,6,8,9,14],[4,7,8,9,10],[4,7,8,9,10,11,12,13,14],[4,7,8,9,11],[4,7,8,9,12],[4,7,8,9,13],[4,7,8,9,14],[4,10,11,12,13],[4,10,11,12,14],[4,10,11,13,14],[4,10,12,13,14],[4,11,12,13,14],[5,6,7,8,10],[5,6,7,8,10,11,12,13,14],[5,6,7,8,11],[5,6,7,8,12],[5,6,7,8,13],[5,6,7,8,14],[5,6,7,9,10],[5,6,7,9,10,11,12,13,14],[5,6,7,9,11],[5,6,7,9,12],[5,6,7,9,13],[5,6,7,9,14],[5,6,8,9,10],[5,6,8,9,10,11,12,13,14],[5,6,8,9,11],[5,6,8,9,12],[5,6,8,9,13],[5,6,8,9,14],[5,7,8,9,10],[5,7,8,9,10,11,12,13,14],[5,7,8,9,11],[5,7,8,9,12],[5,7,8,9,13],[5,7,8,9,14],[5,10,11,12,13],[5,10,11,12,14],[5,10,11,13,14],[5,10,12,13,14],[5,11,12,13,14],[6,7,8,9,10],[6,7,8,9,10,11,12,13,14],[6,7,8,9,11],[6,7,8,9,12],[6,7,8,9,13],[6,7,8,9,14],[6,10,11,12,13],[6,10,11,12,14],[6,10,11,13,14],[6,10,12,13,14],[6,11,12,13,14],[7,10,11,12,13],[7,10,11,12,14],[7,10,11,13,14],[7,10,12,13,14],[7,11,12,13,14],[8,10,11,12,13],[8,10,11,12,14],[8,10,11,13,14],[8,10,12,13,14],[8,11,12,13,14],[9,10,11,12,13],[9,10,11,12,14],[9,10,11,13,14],[9,10,12,13,14],[9,11,12,13,14],[10],[10,11,12,13,14],[11],[12],[13],[14]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[10,20],"A_d":204555,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,2],[11,2],[12,2],[13,2],[14,2]],"CZ":[[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[0,11],[0,12],[0,13],[0,14],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[1,8],[1,9],[1,10],[1,11],[1,12],[1,13],[1,14],[2,3],[2,4],[2,5],[2,6],[2,7],[2,8],[2,9],[2,10],[2,11],[2,12],[2,13],[2,14],[3,4],[3,5],[3,6],[3,7],[3,8],[3,9],[3,10],[3,11],[3,12],[3,13],[3,14],[4,5],[4,6],[4,7],[4,8],[4,9],[4,10],[4,11],[4,12],[4,13],[4,14],[5,6],[5,7],[5,8],[5,9],[5,10],[5,11],[5,12],[5,13],[5,14],[6,7],[6,8],[6,9],[6,10],[6,11],[6,12],[6,13],[6,14],[7,8],[7,9],[7,10],[7,11],[7,12],[7,13],[7,14],[8,9],[8,10],[8,11],[8,12],[8,13],[8,14],[9,10],[9,11],[9,12],[9,13],[9,14]]},"rotation_powers":null},"metrics":{"gamma":7.9807108289001905,"gamma_t":null,"gamma_rho":7.9807108289001905,"gamma_claim":7.9807108289001905,"gamma_t_claim":null,"gamma_rho_claim":7.9807108289001905,"v_ex":10,"rate":0.00395882818685669,"t_count":null,"poly_degree":null,"effective_width":10},"provenance":{"regimes":["borrowed-identity search: two-group"],"discovery":"pre-existing","strongest_claim":"found by the two-group borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/): an identity circuit symmetric within its output and check blocks, with its output-only gates removed; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: two-group","file":"borrowed_identities/circuits/large_unified_l3.json","label":"lu-1122","N":15,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 1122","provenance":"larger unified search l=3, two-group s_total=4,s_O=3"}]},"references":[{"key":"singh2026borrowed","short":"Singh et al. (2026)","full":"S. Singh, C. Gidney, and C. Jones, \"Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search,\" arXiv:2606.28518 (2026).","url":"https://arxiv.org/abs/2606.28518","date":"2026-06-26"}]}