{"id":"3738.10.2.a","row":122,"stored":{"file":"master_catalog_large.json","row":122,"construction":{"family":"two-group","k":10,"N":17,"s_total":4,"s_O":6},"columns_sha256":"a4a0e46e1849cd0128c843707dd87a0625bf2f30efd61967225a38b183702c3e"},"parameters":{"n":3738,"k":10,"d":2,"N":17,"r":7,"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":[[0,1,2,3,4,5,6,10,11],[0,1,2,3,4,5,6,10,11,12,13,14,15],[0,1,2,3,4,5,6,10,11,12,13,14,16],[0,1,2,3,4,5,6,10,11,12,13,15,16],[0,1,2,3,4,5,6,10,11,12,14,15,16],[0,1,2,3,4,5,6,10,11,13,14,15,16],[0,1,2,3,4,5,6,10,12],[0,1,2,3,4,5,6,10,12,13,14,15,16],[0,1,2,3,4,5,6,10,13],[0,1,2,3,4,5,6,10,14],[0,1,2,3,4,5,6,10,15],[0,1,2,3,4,5,6,10,16],[0,1,2,3,4,5,6,11,12],[0,1,2,3,4,5,6,11,12,13,14,15,16],[0,1,2,3,4,5,6,11,13],[0,1,2,3,4,5,6,11,14],[0,1,2,3,4,5,6,11,15],[0,1,2,3,4,5,6,11,16],[0,1,2,3,4,5,6,12,13],[0,1,2,3,4,5,6,12,14],[0,1,2,3,4,5,6,12,15],[0,1,2,3,4,5,6,12,16],[0,1,2,3,4,5,6,13,14],[0,1,2,3,4,5,6,13,15],[0,1,2,3,4,5,6,13,16],[0,1,2,3,4,5,6,14,15],[0,1,2,3,4,5,6,14,16],[0,1,2,3,4,5,6,15,16],[0,1,2,3,4,5,7,10,11],[0,1,2,3,4,5,7,10,11,12,13,14,15],[0,1,2,3,4,5,7,10,11,12,13,14,16],[0,1,2,3,4,5,7,10,11,12,13,15,16],[0,1,2,3,4,5,7,10,11,12,14,15,16],[0,1,2,3,4,5,7,10,11,13,14,15,16],[0,1,2,3,4,5,7,10,12],[0,1,2,3,4,5,7,10,12,13,14,15,16],[0,1,2,3,4,5,7,10,13],[0,1,2,3,4,5,7,10,14],[0,1,2,3,4,5,7,10,15],[0,1,2,3,4,5,7,10,16],[0,1,2,3,4,5,7,11,12],[0,1,2,3,4,5,7,11,12,13,14,15,16],[0,1,2,3,4,5,7,11,13],[0,1,2,3,4,5,7,11,14],[0,1,2,3,4,5,7,11,15],[0,1,2,3,4,5,7,11,16],[0,1,2,3,4,5,7,12,13],[0,1,2,3,4,5,7,12,14],[0,1,2,3,4,5,7,12,15],[0,1,2,3,4,5,7,12,16],[0,1,2,3,4,5,7,13,14],[0,1,2,3,4,5,7,13,15],[0,1,2,3,4,5,7,13,16],[0,1,2,3,4,5,7,14,15],[0,1,2,3,4,5,7,14,16],[0,1,2,3,4,5,7,15,16],[0,1,2,3,4,5,8,10,11],[0,1,2,3,4,5,8,10,11,12,13,14,15],[0,1,2,3,4,5,8,10,11,12,13,14,16],[0,1,2,3,4,5,8,10,11,12,13,15,16],[0,1,2,3,4,5,8,10,11,12,14,15,16],[0,1,2,3,4,5,8,10,11,13,14,15,16],[0,1,2,3,4,5,8,10,12],[0,1,2,3,4,5,8,10,12,13,14,15,16],[0,1,2,3,4,5,8,10,13],[0,1,2,3,4,5,8,10,14],[0,1,2,3,4,5,8,10,15],[0,1,2,3,4,5,8,10,16],[0,1,2,3,4,5,8,11,12],[0,1,2,3,4,5,8,11,12,13,14,15,16],[0,1,2,3,4,5,8,11,13],[0,1,2,3,4,5,8,11,14],[0,1,2,3,4,5,8,11,15],[0,1,2,3,4,5,8,11,16],[0,1,2,3,4,5,8,12,13],[0,1,2,3,4,5,8,12,14],[0,1,2,3,4,5,8,12,15],[0,1,2,3,4,5,8,12,16],[0,1,2,3,4,5,8,13,14],[0,1,2,3,4,5,8,13,15],[0,1,2,3,4,5,8,13,16],[0,1,2,3,4,5,8,14,15],[0,1,2,3,4,5,8,14,16],[0,1,2,3,4,5,8,15,16],[0,1,2,3,4,5,9,10,11],[0,1,2,3,4,5,9,10,11,12,13,14,15],[0,1,2,3,4,5,9,10,11,12,13,14,16],[0,1,2,3,4,5,9,10,11,12,13,15,16],[0,1,2,3,4,5,9,10,11,12,14,15,16],[0,1,2,3,4,5,9,10,11,13,14,15,16],[0,1,2,3,4,5,9,10,12],[0,1,2,3,4,5,9,10,12,13,14,15,16],[0,1,2,3,4,5,9,10,13],[0,1,2,3,4,5,9,10,14],[0,1,2,3,4,5,9,10,15],[0,1,2,3,4,5,9,10,16],[0,1,2,3,4,5,9,11,12],[0,1,2,3,4,5,9,11,12,13,14,15,16],[0,1,2,3,4,5,9,11,13],[0,1,2,3,4,5,9,11,14],[0,1,2,3,4,5,9,11,15],[0,1,2,3,4,5,9,11,16],[0,1,2,3,4,5,9,12,13],[0,1,2,3,4,5,9,12,14],[0,1,2,3,4,5,9,12,15],[0,1,2,3,4,5,9,12,16],[0,1,2,3,4,5,9,13,14],[0,1,2,3,4,5,9,13,15],[0,1,2,3,4,5,9,13,16],[0,1,2,3,4,5,9,14,15],[0,1,2,3,4,5,9,14,16],[0,1,2,3,4,5,9,15,16],[0,1,2,3,4,6,7,10,11],[0,1,2,3,4,6,7,10,11,12,13,14,15],[0,1,2,3,4,6,7,10,11,12,13,14,16],[0,1,2,3,4,6,7,10,11,12,13,15,16],[0,1,2,3,4,6,7,10,11,12,14,15,16],[0,1,2,3,4,6,7,10,11,13,14,15,16],[0,1,2,3,4,6,7,10,12],[0,1,2,3,4,6,7,10,12,13,14,15,16],[0,1,2,3,4,6,7,10,13],[0,1,2,3,4,6,7,10,14],[0,1,2,3,4,6,7,10,15],[0,1,2,3,4,6,7,10,16],[0,1,2,3,4,6,7,11,12],[0,1,2,3,4,6,7,11,12,13,14,15,16],[0,1,2,3,4,6,7,11,13],[0,1,2,3,4,6,7,11,14],[0,1,2,3,4,6,7,11,15],[0,1,2,3,4,6,7,11,16],[0,1,2,3,4,6,7,12,13],[0,1,2,3,4,6,7,12,14],[0,1,2,3,4,6,7,12,15],[0,1,2,3,4,6,7,12,16],[0,1,2,3,4,6,7,13,14],[0,1,2,3,4,6,7,13,15],[0,1,2,3,4,6,7,13,16],[0,1,2,3,4,6,7,14,15],[0,1,2,3,4,6,7,14,16],[0,1,2,3,4,6,7,15,16],[0,1,2,3,4,6,8,10,11],[0,1,2,3,4,6,8,10,11,12,13,14,15],[0,1,2,3,4,6,8,10,11,12,13,14,16],[0,1,2,3,4,6,8,10,11,12,13,15,16],[0,1,2,3,4,6,8,10,11,12,14,15,16],[0,1,2,3,4,6,8,10,11,13,14,15,16],[0,1,2,3,4,6,8,10,12],[0,1,2,3,4,6,8,10,12,13,14,15,16],[0,1,2,3,4,6,8,10,13],[0,1,2,3,4,6,8,10,14],[0,1,2,3,4,6,8,10,15],[0,1,2,3,4,6,8,10,16],[0,1,2,3,4,6,8,11,12],[0,1,2,3,4,6,8,11,12,13,14,15,16],[0,1,2,3,4,6,8,11,13],[0,1,2,3,4,6,8,11,14],[0,1,2,3,4,6,8,11,15],[0,1,2,3,4,6,8,11,16],[0,1,2,3,4,6,8,12,13],[0,1,2,3,4,6,8,12,14],[0,1,2,3,4,6,8,12,15],[0,1,2,3,4,6,8,12,16],[0,1,2,3,4,6,8,13,14],[0,1,2,3,4,6,8,13,15],[0,1,2,3,4,6,8,13,16],[0,1,2,3,4,6,8,14,15],[0,1,2,3,4,6,8,14,16],[0,1,2,3,4,6,8,15,16],[0,1,2,3,4,6,9,10,11],[0,1,2,3,4,6,9,10,11,12,13,14,15],[0,1,2,3,4,6,9,10,11,12,13,14,16],[0,1,2,3,4,6,9,10,11,12,13,15,16],[0,1,2,3,4,6,9,10,11,12,14,15,16],[0,1,2,3,4,6,9,10,11,13,14,15,16],[0,1,2,3,4,6,9,10,12],[0,1,2,3,4,6,9,10,12,13,14,15,16],[0,1,2,3,4,6,9,10,13],[0,1,2,3,4,6,9,10,14],[0,1,2,3,4,6,9,10,15],[0,1,2,3,4,6,9,10,16],[0,1,2,3,4,6,9,11,12],[0,1,2,3,4,6,9,11,12,13,14,15,16],[0,1,2,3,4,6,9,11,13],[0,1,2,3,4,6,9,11,14],[0,1,2,3,4,6,9,11,15],[0,1,2,3,4,6,9,11,16],[0,1,2,3,4,6,9,12,13],[0,1,2,3,4,6,9,12,14],[0,1,2,3,4,6,9,12,15],[0,1,2,3,4,6,9,12,16],[0,1,2,3,4,6,9,13,14],[0,1,2,3,4,6,9,13,15],[0,1,2,3,4,6,9,13,16],[0,1,2,3,4,6,9,14,15],[0,1,2,3,4,6,9,14,16],[0,1,2,3,4,6,9,15,16],[0,1,2,3,4,7,8,10,11],[0,1,2,3,4,7,8,10,11,12,13,14,15],[0,1,2,3,4,7,8,10,11,12,13,14,16],[0,1,2,3,4,7,8,10,11,12,13,15,16],[0,1,2,3,4,7,8,10,11,12,14,15,16],[0,1,2,3,4,7,8,10,11,13,14,15,16],[0,1,2,3,4,7,8,10,12],[0,1,2,3,4,7,8,10,12,13,14,15,16],[0,1,2,3,4,7,8,10,13],[0,1,2,3,4,7,8,10,14],[0,1,2,3,4,7,8,10,15],[0,1,2,3,4,7,8,10,16],[0,1,2,3,4,7,8,11,12],[0,1,2,3,4,7,8,11,12,13,14,15,16],[0,1,2,3,4,7,8,11,13],[0,1,2,3,4,7,8,11,14],[0,1,2,3,4,7,8,11,15],[0,1,2,3,4,7,8,11,16],[0,1,2,3,4,7,8,12,13],[0,1,2,3,4,7,8,12,14],[0,1,2,3,4,7,8,12,15],[0,1,2,3,4,7,8,12,16],[0,1,2,3,4,7,8,13,14],[0,1,2,3,4,7,8,13,15],[0,1,2,3,4,7,8,13,16],[0,1,2,3,4,7,8,14,15],[0,1,2,3,4,7,8,14,16],[0,1,2,3,4,7,8,15,16],[0,1,2,3,4,7,9,10,11],[0,1,2,3,4,7,9,10,11,12,13,14,15],[0,1,2,3,4,7,9,10,11,12,13,14,16],[0,1,2,3,4,7,9,10,11,12,13,15,16],[0,1,2,3,4,7,9,10,11,12,14,15,16],[0,1,2,3,4,7,9,10,11,13,14,15,16],[0,1,2,3,4,7,9,10,12],[0,1,2,3,4,7,9,10,12,13,14,15,16],[0,1,2,3,4,7,9,10,13],[0,1,2,3,4,7,9,10,14],[0,1,2,3,4,7,9,10,15],[0,1,2,3,4,7,9,10,16],[0,1,2,3,4,7,9,11,12],[0,1,2,3,4,7,9,11,12,13,14,15,16],[0,1,2,3,4,7,9,11,13],[0,1,2,3,4,7,9,11,14],[0,1,2,3,4,7,9,11,15],[0,1,2,3,4,7,9,11,16],[0,1,2,3,4,7,9,12,13],[0,1,2,3,4,7,9,12,14],[0,1,2,3,4,7,9,12,15],[0,1,2,3,4,7,9,12,16],[0,1,2,3,4,7,9,13,14],[0,1,2,3,4,7,9,13,15],[0,1,2,3,4,7,9,13,16],[0,1,2,3,4,7,9,14,15],[0,1,2,3,4,7,9,14,16],[0,1,2,3,4,7,9,15,16],[0,1,2,3,4,8,9,10,11],[0,1,2,3,4,8,9,10,11,12,13,14,15],[0,1,2,3,4,8,9,10,11,12,13,14,16],[0,1,2,3,4,8,9,10,11,12,13,15,16],[0,1,2,3,4,8,9,10,11,12,14,15,16],[0,1,2,3,4,8,9,10,11,13,14,15,16],[0,1,2,3,4,8,9,10,12],[0,1,2,3,4,8,9,10,12,13,14,15,16],[0,1,2,3,4,8,9,10,13],[0,1,2,3,4,8,9,10,14],[0,1,2,3,4,8,9,10,15],[0,1,2,3,4,8,9,10,16],[0,1,2,3,4,8,9,11,12],[0,1,2,3,4,8,9,11,12,13,14,15,16],[0,1,2,3,4,8,9,11,13],[0,1,2,3,4,8,9,11,14],[0,1,2,3,4,8,9,11,15],[0,1,2,3,4,8,9,11,16],[0,1,2,3,4,8,9,12,13],[0,1,2,3,4,8,9,12,14],[0,1,2,3,4,8,9,12,15],[0,1,2,3,4,8,9,12,16],[0,1,2,3,4,8,9,13,14],[0,1,2,3,4,8,9,13,15],[0,1,2,3,4,8,9,13,16],[0,1,2,3,4,8,9,14,15],[0,1,2,3,4,8,9,14,16],[0,1,2,3,4,8,9,15,16],[0,1,2,3,5,6,7,10,11],[0,1,2,3,5,6,7,10,11,12,13,14,15],[0,1,2,3,5,6,7,10,11,12,13,14,16],[0,1,2,3,5,6,7,10,11,12,13,15,16],[0,1,2,3,5,6,7,10,11,12,14,15,16],[0,1,2,3,5,6,7,10,11,13,14,15,16],[0,1,2,3,5,6,7,10,12],[0,1,2,3,5,6,7,10,12,13,14,15,16],[0,1,2,3,5,6,7,10,13],[0,1,2,3,5,6,7,10,14],[0,1,2,3,5,6,7,10,15],[0,1,2,3,5,6,7,10,16],[0,1,2,3,5,6,7,11,12],[0,1,2,3,5,6,7,11,12,13,14,15,16],[0,1,2,3,5,6,7,11,13],[0,1,2,3,5,6,7,11,14],[0,1,2,3,5,6,7,11,15],[0,1,2,3,5,6,7,11,16],[0,1,2,3,5,6,7,12,13],[0,1,2,3,5,6,7,12,14],[0,1,2,3,5,6,7,12,15],[0,1,2,3,5,6,7,12,16],[0,1,2,3,5,6,7,13,14],[0,1,2,3,5,6,7,13,15],[0,1,2,3,5,6,7,13,16],[0,1,2,3,5,6,7,14,15],[0,1,2,3,5,6,7,14,16],[0,1,2,3,5,6,7,15,16],[0,1,2,3,5,6,8,10,11],[0,1,2,3,5,6,8,10,11,12,13,14,15],[0,1,2,3,5,6,8,10,11,12,13,14,16],[0,1,2,3,5,6,8,10,11,12,13,15,16],[0,1,2,3,5,6,8,10,11,12,14,15,16],[0,1,2,3,5,6,8,10,11,13,14,15,16],[0,1,2,3,5,6,8,10,12],[0,1,2,3,5,6,8,10,12,13,14,15,16],[0,1,2,3,5,6,8,10,13],[0,1,2,3,5,6,8,10,14],[0,1,2,3,5,6,8,10,15],[0,1,2,3,5,6,8,10,16],[0,1,2,3,5,6,8,11,12],[0,1,2,3,5,6,8,11,12,13,14,15,16],[0,1,2,3,5,6,8,11,13],[0,1,2,3,5,6,8,11,14],[0,1,2,3,5,6,8,11,15],[0,1,2,3,5,6,8,11,16],[0,1,2,3,5,6,8,12,13],[0,1,2,3,5,6,8,12,14],[0,1,2,3,5,6,8,12,15],[0,1,2,3,5,6,8,12,16],[0,1,2,3,5,6,8,13,14],[0,1,2,3,5,6,8,13,15],[0,1,2,3,5,6,8,13,16],[0,1,2,3,5,6,8,14,15],[0,1,2,3,5,6,8,14,16],[0,1,2,3,5,6,8,15,16],[0,1,2,3,5,6,9,10,11],[0,1,2,3,5,6,9,10,11,12,13,14,15],[0,1,2,3,5,6,9,10,11,12,13,14,16],[0,1,2,3,5,6,9,10,11,12,13,15,16],[0,1,2,3,5,6,9,10,11,12,14,15,16],[0,1,2,3,5,6,9,10,11,13,14,15,16],[0,1,2,3,5,6,9,10,12],[0,1,2,3,5,6,9,10,12,13,14,15,16],[0,1,2,3,5,6,9,10,13],[0,1,2,3,5,6,9,10,14],[0,1,2,3,5,6,9,10,15],[0,1,2,3,5,6,9,10,16],[0,1,2,3,5,6,9,11,12],[0,1,2,3,5,6,9,11,12,13,14,15,16],[0,1,2,3,5,6,9,11,13],[0,1,2,3,5,6,9,11,14],[0,1,2,3,5,6,9,11,15],[0,1,2,3,5,6,9,11,16],[0,1,2,3,5,6,9,12,13],[0,1,2,3,5,6,9,12,14],[0,1,2,3,5,6,9,12,15],[0,1,2,3,5,6,9,12,16],[0,1,2,3,5,6,9,13,14],[0,1,2,3,5,6,9,13,15],[0,1,2,3,5,6,9,13,16],[0,1,2,3,5,6,9,14,15],[0,1,2,3,5,6,9,14,16],[0,1,2,3,5,6,9,15,16],[0,1,2,3,5,7,8,10,11],[0,1,2,3,5,7,8,10,11,12,13,14,15],[0,1,2,3,5,7,8,10,11,12,13,14,16],[0,1,2,3,5,7,8,10,11,12,13,15,16],[0,1,2,3,5,7,8,10,11,12,14,15,16],[0,1,2,3,5,7,8,10,11,13,14,15,16],[0,1,2,3,5,7,8,10,12],[0,1,2,3,5,7,8,10,12,13,14,15,16],[0,1,2,3,5,7,8,10,13],[0,1,2,3,5,7,8,10,14],[0,1,2,3,5,7,8,10,15],[0,1,2,3,5,7,8,10,16],[0,1,2,3,5,7,8,11,12],[0,1,2,3,5,7,8,11,12,13,14,15,16],[0,1,2,3,5,7,8,11,13],[0,1,2,3,5,7,8,11,14],[0,1,2,3,5,7,8,11,15],[0,1,2,3,5,7,8,11,16],[0,1,2,3,5,7,8,12,13],[0,1,2,3,5,7,8,12,14],[0,1,2,3,5,7,8,12,15],[0,1,2,3,5,7,8,12,16],[0,1,2,3,5,7,8,13,14],[0,1,2,3,5,7,8,13,15],[0,1,2,3,5,7,8,13,16],[0,1,2,3,5,7,8,14,15],[0,1,2,3,5,7,8,14,16],[0,1,2,3,5,7,8,15,16],[0,1,2,3,5,7,9,10,11],[0,1,2,3,5,7,9,10,11,12,13,14,15],[0,1,2,3,5,7,9,10,11,12,13,14,16],[0,1,2,3,5,7,9,10,11,12,13,15,16],[0,1,2,3,5,7,9,10,11,12,14,15,16],[0,1,2,3,5,7,9,10,11,13,14,15,16],[0,1,2,3,5,7,9,10,12],[0,1,2,3,5,7,9,10,12,13,14,15,16],[0,1,2,3,5,7,9,10,13],[0,1,2,3,5,7,9,10,14],[0,1,2,3,5,7,9,10,15],[0,1,2,3,5,7,9,10,16],[0,1,2,3,5,7,9,11,12],[0,1,2,3,5,7,9,11,12,13,14,15,16],[0,1,2,3,5,7,9,11,13],[0,1,2,3,5,7,9,11,14],[0,1,2,3,5,7,9,11,15],[0,1,2,3,5,7,9,11,16],[0,1,2,3,5,7,9,12,13],[0,1,2,3,5,7,9,12,14],[0,1,2,3,5,7,9,12,15],[0,1,2,3,5,7,9,12,16],[0,1,2,3,5,7,9,13,14],[0,1,2,3,5,7,9,13,15],[0,1,2,3,5,7,9,13,16],[0,1,2,3,5,7,9,14,15],[0,1,2,3,5,7,9,14,16],[0,1,2,3,5,7,9,15,16],[0,1,2,3,5,8,9,10,11],[0,1,2,3,5,8,9,10,11,12,13,14,15],[0,1,2,3,5,8,9,10,11,12,13,14,16],[0,1,2,3,5,8,9,10,11,12,13,15,16],[0,1,2,3,5,8,9,10,11,12,14,15,16],[0,1,2,3,5,8,9,10,11,13,14,15,16],[0,1,2,3,5,8,9,10,12],[0,1,2,3,5,8,9,10,12,13,14,15,16],[0,1,2,3,5,8,9,10,13],[0,1,2,3,5,8,9,10,14],[0,1,2,3,5,8,9,10,15],[0,1,2,3,5,8,9,10,16],[0,1,2,3,5,8,9,11,12],[0,1,2,3,5,8,9,11,12,13,14,15,16],[0,1,2,3,5,8,9,11,13],[0,1,2,3,5,8,9,11,14],[0,1,2,3,5,8,9,11,15],[0,1,2,3,5,8,9,11,16],[0,1,2,3,5,8,9,12,13],[0,1,2,3,5,8,9,12,14],[0,1,2,3,5,8,9,12,15],[0,1,2,3,5,8,9,12,16],[0,1,2,3,5,8,9,13,14],[0,1,2,3,5,8,9,13,15],[0,1,2,3,5,8,9,13,16],[0,1,2,3,5,8,9,14,15],[0,1,2,3,5,8,9,14,16],[0,1,2,3,5,8,9,15,16],[0,1,2,3,6,7,8,10,11],[0,1,2,3,6,7,8,10,11,12,13,14,15],[0,1,2,3,6,7,8,10,11,12,13,14,16],[0,1,2,3,6,7,8,10,11,12,13,15,16],[0,1,2,3,6,7,8,10,11,12,14,15,16],[0,1,2,3,6,7,8,10,11,13,14,15,16],[0,1,2,3,6,7,8,10,12],[0,1,2,3,6,7,8,10,12,13,14,15,16],[0,1,2,3,6,7,8,10,13],[0,1,2,3,6,7,8,10,14],[0,1,2,3,6,7,8,10,15],[0,1,2,3,6,7,8,10,16],[0,1,2,3,6,7,8,11,12],[0,1,2,3,6,7,8,11,12,13,14,15,16],[0,1,2,3,6,7,8,11,13],[0,1,2,3,6,7,8,11,14],[0,1,2,3,6,7,8,11,15],[0,1,2,3,6,7,8,11,16],[0,1,2,3,6,7,8,12,13],[0,1,2,3,6,7,8,12,14],[0,1,2,3,6,7,8,12,15],[0,1,2,3,6,7,8,12,16],[0,1,2,3,6,7,8,13,14],[0,1,2,3,6,7,8,13,15],[0,1,2,3,6,7,8,13,16],[0,1,2,3,6,7,8,14,15],[0,1,2,3,6,7,8,14,16],[0,1,2,3,6,7,8,15,16],[0,1,2,3,6,7,9,10,11],[0,1,2,3,6,7,9,10,11,12,13,14,15],[0,1,2,3,6,7,9,10,11,12,13,14,16],[0,1,2,3,6,7,9,10,11,12,13,15,16],[0,1,2,3,6,7,9,10,11,12,14,15,16],[0,1,2,3,6,7,9,10,11,13,14,15,16],[0,1,2,3,6,7,9,10,12],[0,1,2,3,6,7,9,10,12,13,14,15,16],[0,1,2,3,6,7,9,10,13],[0,1,2,3,6,7,9,10,14],[0,1,2,3,6,7,9,10,15],[0,1,2,3,6,7,9,10,16],[0,1,2,3,6,7,9,11,12],[0,1,2,3,6,7,9,11,12,13,14,15,16],[0,1,2,3,6,7,9,11,13],[0,1,2,3,6,7,9,11,14],[0,1,2,3,6,7,9,11,15],[0,1,2,3,6,7,9,11,16],[0,1,2,3,6,7,9,12,13],[0,1,2,3,6,7,9,12,14],[0,1,2,3,6,7,9,12,15],[0,1,2,3,6,7,9,12,16],[0,1,2,3,6,7,9,13,14],[0,1,2,3,6,7,9,13,15],[0,1,2,3,6,7,9,13,16],[0,1,2,3,6,7,9,14,15],[0,1,2,3,6,7,9,14,16],[0,1,2,3,6,7,9,15,16],[0,1,2,3,6,8,9,10,11],[0,1,2,3,6,8,9,10,11,12,13,14,15],[0,1,2,3,6,8,9,10,11,12,13,14,16],[0,1,2,3,6,8,9,10,11,12,13,15,16],[0,1,2,3,6,8,9,10,11,12,14,15,16],[0,1,2,3,6,8,9,10,11,13,14,15,16],[0,1,2,3,6,8,9,10,12],[0,1,2,3,6,8,9,10,12,13,14,15,16],[0,1,2,3,6,8,9,10,13],[0,1,2,3,6,8,9,10,14],[0,1,2,3,6,8,9,10,15],[0,1,2,3,6,8,9,10,16],[0,1,2,3,6,8,9,11,12],[0,1,2,3,6,8,9,11,12,13,14,15,16],[0,1,2,3,6,8,9,11,13],[0,1,2,3,6,8,9,11,14],[0,1,2,3,6,8,9,11,15],[0,1,2,3,6,8,9,11,16],[0,1,2,3,6,8,9,12,13],[0,1,2,3,6,8,9,12,14],[0,1,2,3,6,8,9,12,15],[0,1,2,3,6,8,9,12,16],[0,1,2,3,6,8,9,13,14],[0,1,2,3,6,8,9,13,15],[0,1,2,3,6,8,9,13,16],[0,1,2,3,6,8,9,14,15],[0,1,2,3,6,8,9,14,16],[0,1,2,3,6,8,9,15,16],[0,1,2,3,7,8,9,10,11],[0,1,2,3,7,8,9,10,11,12,13,14,15],[0,1,2,3,7,8,9,10,11,12,13,14,16],[0,1,2,3,7,8,9,10,11,12,13,15,16],[0,1,2,3,7,8,9,10,11,12,14,15,16],[0,1,2,3,7,8,9,10,11,13,14,15,16],[0,1,2,3,7,8,9,10,12],[0,1,2,3,7,8,9,10,12,13,14,15,16],[0,1,2,3,7,8,9,10,13],[0,1,2,3,7,8,9,10,14],[0,1,2,3,7,8,9,10,15],[0,1,2,3,7,8,9,10,16],[0,1,2,3,7,8,9,11,12],[0,1,2,3,7,8,9,11,12,13,14,15,16],[0,1,2,3,7,8,9,11,13],[0,1,2,3,7,8,9,11,14],[0,1,2,3,7,8,9,11,15],[0,1,2,3,7,8,9,11,16],[0,1,2,3,7,8,9,12,13],[0,1,2,3,7,8,9,12,14],[0,1,2,3,7,8,9,12,15],[0,1,2,3,7,8,9,12,16],[0,1,2,3,7,8,9,13,14],[0,1,2,3,7,8,9,13,15],[0,1,2,3,7,8,9,13,16],[0,1,2,3,7,8,9,14,15],[0,1,2,3,7,8,9,14,16],[0,1,2,3,7,8,9,15,16],[0,1,2,4,5,6,7,10,11],[0,1,2,4,5,6,7,10,11,12,13,14,15],[0,1,2,4,5,6,7,10,11,12,13,14,16],[0,1,2,4,5,6,7,10,11,12,13,15,16],[0,1,2,4,5,6,7,10,11,12,14,15,16],[0,1,2,4,5,6,7,10,11,13,14,15,16],[0,1,2,4,5,6,7,10,12],[0,1,2,4,5,6,7,10,12,13,14,15,16],[0,1,2,4,5,6,7,10,13],[0,1,2,4,5,6,7,10,14],[0,1,2,4,5,6,7,10,15],[0,1,2,4,5,6,7,10,16],[0,1,2,4,5,6,7,11,12],[0,1,2,4,5,6,7,11,12,13,14,15,16],[0,1,2,4,5,6,7,11,13],[0,1,2,4,5,6,7,11,14],[0,1,2,4,5,6,7,11,15],[0,1,2,4,5,6,7,11,16],[0,1,2,4,5,6,7,12,13],[0,1,2,4,5,6,7,12,14],[0,1,2,4,5,6,7,12,15],[0,1,2,4,5,6,7,12,16],[0,1,2,4,5,6,7,13,14],[0,1,2,4,5,6,7,13,15],[0,1,2,4,5,6,7,13,16],[0,1,2,4,5,6,7,14,15],[0,1,2,4,5,6,7,14,16],[0,1,2,4,5,6,7,15,16],[0,1,2,4,5,6,8,10,11],[0,1,2,4,5,6,8,10,11,12,13,14,15],[0,1,2,4,5,6,8,10,11,12,13,14,16],[0,1,2,4,5,6,8,10,11,12,13,15,16],[0,1,2,4,5,6,8,10,11,12,14,15,16],[0,1,2,4,5,6,8,10,11,13,14,15,16],[0,1,2,4,5,6,8,10,12],[0,1,2,4,5,6,8,10,12,13,14,15,16],[0,1,2,4,5,6,8,10,13],[0,1,2,4,5,6,8,10,14],[0,1,2,4,5,6,8,10,15],[0,1,2,4,5,6,8,10,16],[0,1,2,4,5,6,8,11,12],[0,1,2,4,5,6,8,11,12,13,14,15,16],[0,1,2,4,5,6,8,11,13],[0,1,2,4,5,6,8,11,14],[0,1,2,4,5,6,8,11,15],[0,1,2,4,5,6,8,11,16],[0,1,2,4,5,6,8,12,13],[0,1,2,4,5,6,8,12,14],[0,1,2,4,5,6,8,12,15],[0,1,2,4,5,6,8,12,16],[0,1,2,4,5,6,8,13,14],[0,1,2,4,5,6,8,13,15],[0,1,2,4,5,6,8,13,16],[0,1,2,4,5,6,8,14,15],[0,1,2,4,5,6,8,14,16],[0,1,2,4,5,6,8,15,16],[0,1,2,4,5,6,9,10,11],[0,1,2,4,5,6,9,10,11,12,13,14,15],[0,1,2,4,5,6,9,10,11,12,13,14,16],[0,1,2,4,5,6,9,10,11,12,13,15,16],[0,1,2,4,5,6,9,10,11,12,14,15,16],[0,1,2,4,5,6,9,10,11,13,14,15,16],[0,1,2,4,5,6,9,10,12],[0,1,2,4,5,6,9,10,12,13,14,15,16],[0,1,2,4,5,6,9,10,13],[0,1,2,4,5,6,9,10,14],[0,1,2,4,5,6,9,10,15],[0,1,2,4,5,6,9,10,16],[0,1,2,4,5,6,9,11,12],[0,1,2,4,5,6,9,11,12,13,14,15,16],[0,1,2,4,5,6,9,11,13],[0,1,2,4,5,6,9,11,14],[0,1,2,4,5,6,9,11,15],[0,1,2,4,5,6,9,11,16],[0,1,2,4,5,6,9,12,13],[0,1,2,4,5,6,9,12,14],[0,1,2,4,5,6,9,12,15],[0,1,2,4,5,6,9,12,16],[0,1,2,4,5,6,9,13,14],[0,1,2,4,5,6,9,13,15],[0,1,2,4,5,6,9,13,16],[0,1,2,4,5,6,9,14,15],[0,1,2,4,5,6,9,14,16],[0,1,2,4,5,6,9,15,16],[0,1,2,4,5,7,8,10,11],[0,1,2,4,5,7,8,10,11,12,13,14,15],[0,1,2,4,5,7,8,10,11,12,13,14,16],[0,1,2,4,5,7,8,10,11,12,13,15,16],[0,1,2,4,5,7,8,10,11,12,14,15,16],[0,1,2,4,5,7,8,10,11,13,14,15,16],[0,1,2,4,5,7,8,10,12],[0,1,2,4,5,7,8,10,12,13,14,15,16],[0,1,2,4,5,7,8,10,13],[0,1,2,4,5,7,8,10,14],[0,1,2,4,5,7,8,10,15],[0,1,2,4,5,7,8,10,16],[0,1,2,4,5,7,8,11,12],[0,1,2,4,5,7,8,11,12,13,14,15,16],[0,1,2,4,5,7,8,11,13],[0,1,2,4,5,7,8,11,14],[0,1,2,4,5,7,8,11,15],[0,1,2,4,5,7,8,11,16],[0,1,2,4,5,7,8,12,13],[0,1,2,4,5,7,8,12,14],[0,1,2,4,5,7,8,12,15],[0,1,2,4,5,7,8,12,16],[0,1,2,4,5,7,8,13,14],[0,1,2,4,5,7,8,13,15],[0,1,2,4,5,7,8,13,16],[0,1,2,4,5,7,8,14,15],[0,1,2,4,5,7,8,14,16],[0,1,2,4,5,7,8,15,16],[0,1,2,4,5,7,9,10,11],[0,1,2,4,5,7,9,10,11,12,13,14,15],[0,1,2,4,5,7,9,10,11,12,13,14,16],[0,1,2,4,5,7,9,10,11,12,13,15,16],[0,1,2,4,5,7,9,10,11,12,14,15,16],[0,1,2,4,5,7,9,10,11,13,14,15,16],[0,1,2,4,5,7,9,10,12],[0,1,2,4,5,7,9,10,12,13,14,15,16],[0,1,2,4,5,7,9,10,13],[0,1,2,4,5,7,9,10,14],[0,1,2,4,5,7,9,10,15],[0,1,2,4,5,7,9,10,16],[0,1,2,4,5,7,9,11,12],[0,1,2,4,5,7,9,11,12,13,14,15,16],[0,1,2,4,5,7,9,11,13],[0,1,2,4,5,7,9,11,14],[0,1,2,4,5,7,9,11,15],[0,1,2,4,5,7,9,11,16],[0,1,2,4,5,7,9,12,13],[0,1,2,4,5,7,9,12,14],[0,1,2,4,5,7,9,12,15],[0,1,2,4,5,7,9,12,16],[0,1,2,4,5,7,9,13,14],[0,1,2,4,5,7,9,13,15],[0,1,2,4,5,7,9,13,16],[0,1,2,4,5,7,9,14,15],[0,1,2,4,5,7,9,14,16],[0,1,2,4,5,7,9,15,16],[0,1,2,4,5,8,9,10,11],[0,1,2,4,5,8,9,10,11,12,13,14,15],[0,1,2,4,5,8,9,10,11,12,13,14,16],[0,1,2,4,5,8,9,10,11,12,13,15,16],[0,1,2,4,5,8,9,10,11,12,14,15,16],[0,1,2,4,5,8,9,10,11,13,14,15,16],[0,1,2,4,5,8,9,10,12],[0,1,2,4,5,8,9,10,12,13,14,15,16],[0,1,2,4,5,8,9,10,13],[0,1,2,4,5,8,9,10,14],[0,1,2,4,5,8,9,10,15],[0,1,2,4,5,8,9,10,16],[0,1,2,4,5,8,9,11,12],[0,1,2,4,5,8,9,11,12,13,14,15,16],[0,1,2,4,5,8,9,11,13],[0,1,2,4,5,8,9,11,14],[0,1,2,4,5,8,9,11,15],[0,1,2,4,5,8,9,11,16],[0,1,2,4,5,8,9,12,13],[0,1,2,4,5,8,9,12,14],[0,1,2,4,5,8,9,12,15],[0,1,2,4,5,8,9,12,16],[0,1,2,4,5,8,9,13,14],[0,1,2,4,5,8,9,13,15],[0,1,2,4,5,8,9,13,16],[0,1,2,4,5,8,9,14,15],[0,1,2,4,5,8,9,14,16],[0,1,2,4,5,8,9,15,16],[0,1,2,4,6,7,8,10,11],[0,1,2,4,6,7,8,10,11,12,13,14,15],[0,1,2,4,6,7,8,10,11,12,13,14,16],[0,1,2,4,6,7,8,10,11,12,13,15,16],[0,1,2,4,6,7,8,10,11,12,14,15,16],[0,1,2,4,6,7,8,10,11,13,14,15,16],[0,1,2,4,6,7,8,10,12],[0,1,2,4,6,7,8,10,12,13,14,15,16],[0,1,2,4,6,7,8,10,13],[0,1,2,4,6,7,8,10,14],[0,1,2,4,6,7,8,10,15],[0,1,2,4,6,7,8,10,16],[0,1,2,4,6,7,8,11,12],[0,1,2,4,6,7,8,11,12,13,14,15,16],[0,1,2,4,6,7,8,11,13],[0,1,2,4,6,7,8,11,14],[0,1,2,4,6,7,8,11,15],[0,1,2,4,6,7,8,11,16],[0,1,2,4,6,7,8,12,13],[0,1,2,4,6,7,8,12,14],[0,1,2,4,6,7,8,12,15],[0,1,2,4,6,7,8,12,16],[0,1,2,4,6,7,8,13,14],[0,1,2,4,6,7,8,13,15],[0,1,2,4,6,7,8,13,16],[0,1,2,4,6,7,8,14,15],[0,1,2,4,6,7,8,14,16],[0,1,2,4,6,7,8,15,16],[0,1,2,4,6,7,9,10,11],[0,1,2,4,6,7,9,10,11,12,13,14,15],[0,1,2,4,6,7,9,10,11,12,13,14,16],[0,1,2,4,6,7,9,10,11,12,13,15,16],[0,1,2,4,6,7,9,10,11,12,14,15,16],[0,1,2,4,6,7,9,10,11,13,14,15,16],[0,1,2,4,6,7,9,10,12],[0,1,2,4,6,7,9,10,12,13,14,15,16],[0,1,2,4,6,7,9,10,13],[0,1,2,4,6,7,9,10,14],[0,1,2,4,6,7,9,10,15],[0,1,2,4,6,7,9,10,16],[0,1,2,4,6,7,9,11,12],[0,1,2,4,6,7,9,11,12,13,14,15,16],[0,1,2,4,6,7,9,11,13],[0,1,2,4,6,7,9,11,14],[0,1,2,4,6,7,9,11,15],[0,1,2,4,6,7,9,11,16],[0,1,2,4,6,7,9,12,13],[0,1,2,4,6,7,9,12,14],[0,1,2,4,6,7,9,12,15],[0,1,2,4,6,7,9,12,16],[0,1,2,4,6,7,9,13,14],[0,1,2,4,6,7,9,13,15],[0,1,2,4,6,7,9,13,16],[0,1,2,4,6,7,9,14,15],[0,1,2,4,6,7,9,14,16],[0,1,2,4,6,7,9,15,16],[0,1,2,4,6,8,9,10,11],[0,1,2,4,6,8,9,10,11,12,13,14,15],[0,1,2,4,6,8,9,10,11,12,13,14,16],[0,1,2,4,6,8,9,10,11,12,13,15,16],[0,1,2,4,6,8,9,10,11,12,14,15,16],[0,1,2,4,6,8,9,10,11,13,14,15,16],[0,1,2,4,6,8,9,10,12],[0,1,2,4,6,8,9,10,12,13,14,15,16],[0,1,2,4,6,8,9,10,13],[0,1,2,4,6,8,9,10,14],[0,1,2,4,6,8,9,10,15],[0,1,2,4,6,8,9,10,16],[0,1,2,4,6,8,9,11,12],[0,1,2,4,6,8,9,11,12,13,14,15,16],[0,1,2,4,6,8,9,11,13],[0,1,2,4,6,8,9,11,14],[0,1,2,4,6,8,9,11,15],[0,1,2,4,6,8,9,11,16],[0,1,2,4,6,8,9,12,13],[0,1,2,4,6,8,9,12,14],[0,1,2,4,6,8,9,12,15],[0,1,2,4,6,8,9,12,16],[0,1,2,4,6,8,9,13,14],[0,1,2,4,6,8,9,13,15],[0,1,2,4,6,8,9,13,16],[0,1,2,4,6,8,9,14,15],[0,1,2,4,6,8,9,14,16],[0,1,2,4,6,8,9,15,16],[0,1,2,4,7,8,9,10,11],[0,1,2,4,7,8,9,10,11,12,13,14,15],[0,1,2,4,7,8,9,10,11,12,13,14,16],[0,1,2,4,7,8,9,10,11,12,13,15,16],[0,1,2,4,7,8,9,10,11,12,14,15,16],[0,1,2,4,7,8,9,10,11,13,14,15,16],[0,1,2,4,7,8,9,10,12],[0,1,2,4,7,8,9,10,12,13,14,15,16],[0,1,2,4,7,8,9,10,13],[0,1,2,4,7,8,9,10,14],[0,1,2,4,7,8,9,10,15],[0,1,2,4,7,8,9,10,16],[0,1,2,4,7,8,9,11,12],[0,1,2,4,7,8,9,11,12,13,14,15,16],[0,1,2,4,7,8,9,11,13],[0,1,2,4,7,8,9,11,14],[0,1,2,4,7,8,9,11,15],[0,1,2,4,7,8,9,11,16],[0,1,2,4,7,8,9,12,13],[0,1,2,4,7,8,9,12,14],[0,1,2,4,7,8,9,12,15],[0,1,2,4,7,8,9,12,16],[0,1,2,4,7,8,9,13,14],[0,1,2,4,7,8,9,13,15],[0,1,2,4,7,8,9,13,16],[0,1,2,4,7,8,9,14,15],[0,1,2,4,7,8,9,14,16],[0,1,2,4,7,8,9,15,16],[0,1,2,5,6,7,8,10,11],[0,1,2,5,6,7,8,10,11,12,13,14,15],[0,1,2,5,6,7,8,10,11,12,13,14,16],[0,1,2,5,6,7,8,10,11,12,13,15,16],[0,1,2,5,6,7,8,10,11,12,14,15,16],[0,1,2,5,6,7,8,10,11,13,14,15,16],[0,1,2,5,6,7,8,10,12],[0,1,2,5,6,7,8,10,12,13,14,15,16],[0,1,2,5,6,7,8,10,13],[0,1,2,5,6,7,8,10,14],[0,1,2,5,6,7,8,10,15],[0,1,2,5,6,7,8,10,16],[0,1,2,5,6,7,8,11,12],[0,1,2,5,6,7,8,11,12,13,14,15,16],[0,1,2,5,6,7,8,11,13],[0,1,2,5,6,7,8,11,14],[0,1,2,5,6,7,8,11,15],[0,1,2,5,6,7,8,11,16],[0,1,2,5,6,7,8,12,13],[0,1,2,5,6,7,8,12,14],[0,1,2,5,6,7,8,12,15],[0,1,2,5,6,7,8,12,16],[0,1,2,5,6,7,8,13,14],[0,1,2,5,6,7,8,13,15],[0,1,2,5,6,7,8,13,16],[0,1,2,5,6,7,8,14,15],[0,1,2,5,6,7,8,14,16],[0,1,2,5,6,7,8,15,16],[0,1,2,5,6,7,9,10,11],[0,1,2,5,6,7,9,10,11,12,13,14,15],[0,1,2,5,6,7,9,10,11,12,13,14,16],[0,1,2,5,6,7,9,10,11,12,13,15,16],[0,1,2,5,6,7,9,10,11,12,14,15,16],[0,1,2,5,6,7,9,10,11,13,14,15,16],[0,1,2,5,6,7,9,10,12],[0,1,2,5,6,7,9,10,12,13,14,15,16],[0,1,2,5,6,7,9,10,13],[0,1,2,5,6,7,9,10,14],[0,1,2,5,6,7,9,10,15],[0,1,2,5,6,7,9,10,16],[0,1,2,5,6,7,9,11,12],[0,1,2,5,6,7,9,11,12,13,14,15,16],[0,1,2,5,6,7,9,11,13],[0,1,2,5,6,7,9,11,14],[0,1,2,5,6,7,9,11,15],[0,1,2,5,6,7,9,11,16],[0,1,2,5,6,7,9,12,13],[0,1,2,5,6,7,9,12,14],[0,1,2,5,6,7,9,12,15],[0,1,2,5,6,7,9,12,16],[0,1,2,5,6,7,9,13,14],[0,1,2,5,6,7,9,13,15],[0,1,2,5,6,7,9,13,16],[0,1,2,5,6,7,9,14,15],[0,1,2,5,6,7,9,14,16],[0,1,2,5,6,7,9,15,16],[0,1,2,5,6,8,9,10,11],[0,1,2,5,6,8,9,10,11,12,13,14,15],[0,1,2,5,6,8,9,10,11,12,13,14,16],[0,1,2,5,6,8,9,10,11,12,13,15,16],[0,1,2,5,6,8,9,10,11,12,14,15,16],[0,1,2,5,6,8,9,10,11,13,14,15,16],[0,1,2,5,6,8,9,10,12],[0,1,2,5,6,8,9,10,12,13,14,15,16],[0,1,2,5,6,8,9,10,13],[0,1,2,5,6,8,9,10,14],[0,1,2,5,6,8,9,10,15],[0,1,2,5,6,8,9,10,16],[0,1,2,5,6,8,9,11,12],[0,1,2,5,6,8,9,11,12,13,14,15,16],[0,1,2,5,6,8,9,11,13],[0,1,2,5,6,8,9,11,14],[0,1,2,5,6,8,9,11,15],[0,1,2,5,6,8,9,11,16],[0,1,2,5,6,8,9,12,13],[0,1,2,5,6,8,9,12,14],[0,1,2,5,6,8,9,12,15],[0,1,2,5,6,8,9,12,16],[0,1,2,5,6,8,9,13,14],[0,1,2,5,6,8,9,13,15],[0,1,2,5,6,8,9,13,16],[0,1,2,5,6,8,9,14,15],[0,1,2,5,6,8,9,14,16],[0,1,2,5,6,8,9,15,16],[0,1,2,5,7,8,9,10,11],[0,1,2,5,7,8,9,10,11,12,13,14,15],[0,1,2,5,7,8,9,10,11,12,13,14,16],[0,1,2,5,7,8,9,10,11,12,13,15,16],[0,1,2,5,7,8,9,10,11,12,14,15,16],[0,1,2,5,7,8,9,10,11,13,14,15,16],[0,1,2,5,7,8,9,10,12],[0,1,2,5,7,8,9,10,12,13,14,15,16],[0,1,2,5,7,8,9,10,13],[0,1,2,5,7,8,9,10,14],[0,1,2,5,7,8,9,10,15],[0,1,2,5,7,8,9,10,16],[0,1,2,5,7,8,9,11,12],[0,1,2,5,7,8,9,11,12,13,14,15,16],[0,1,2,5,7,8,9,11,13],[0,1,2,5,7,8,9,11,14],[0,1,2,5,7,8,9,11,15],[0,1,2,5,7,8,9,11,16],[0,1,2,5,7,8,9,12,13],[0,1,2,5,7,8,9,12,14],[0,1,2,5,7,8,9,12,15],[0,1,2,5,7,8,9,12,16],[0,1,2,5,7,8,9,13,14],[0,1,2,5,7,8,9,13,15],[0,1,2,5,7,8,9,13,16],[0,1,2,5,7,8,9,14,15],[0,1,2,5,7,8,9,14,16],[0,1,2,5,7,8,9,15,16],[0,1,2,6,7,8,9,10,11],[0,1,2,6,7,8,9,10,11,12,13,14,15],[0,1,2,6,7,8,9,10,11,12,13,14,16],[0,1,2,6,7,8,9,10,11,12,13,15,16],[0,1,2,6,7,8,9,10,11,12,14,15,16],[0,1,2,6,7,8,9,10,11,13,14,15,16],[0,1,2,6,7,8,9,10,12],[0,1,2,6,7,8,9,10,12,13,14,15,16],[0,1,2,6,7,8,9,10,13],[0,1,2,6,7,8,9,10,14],[0,1,2,6,7,8,9,10,15],[0,1,2,6,7,8,9,10,16],[0,1,2,6,7,8,9,11,12],[0,1,2,6,7,8,9,11,12,13,14,15,16],[0,1,2,6,7,8,9,11,13],[0,1,2,6,7,8,9,11,14],[0,1,2,6,7,8,9,11,15],[0,1,2,6,7,8,9,11,16],[0,1,2,6,7,8,9,12,13],[0,1,2,6,7,8,9,12,14],[0,1,2,6,7,8,9,12,15],[0,1,2,6,7,8,9,12,16],[0,1,2,6,7,8,9,13,14],[0,1,2,6,7,8,9,13,15],[0,1,2,6,7,8,9,13,16],[0,1,2,6,7,8,9,14,15],[0,1,2,6,7,8,9,14,16],[0,1,2,6,7,8,9,15,16],[0,1,3,4,5,6,7,10,11],[0,1,3,4,5,6,7,10,11,12,13,14,15],[0,1,3,4,5,6,7,10,11,12,13,14,16],[0,1,3,4,5,6,7,10,11,12,13,15,16],[0,1,3,4,5,6,7,10,11,12,14,15,16],[0,1,3,4,5,6,7,10,11,13,14,15,16],[0,1,3,4,5,6,7,10,12],[0,1,3,4,5,6,7,10,12,13,14,15,16],[0,1,3,4,5,6,7,10,13],[0,1,3,4,5,6,7,10,14],[0,1,3,4,5,6,7,10,15],[0,1,3,4,5,6,7,10,16],[0,1,3,4,5,6,7,11,12],[0,1,3,4,5,6,7,11,12,13,14,15,16],[0,1,3,4,5,6,7,11,13],[0,1,3,4,5,6,7,11,14],[0,1,3,4,5,6,7,11,15],[0,1,3,4,5,6,7,11,16],[0,1,3,4,5,6,7,12,13],[0,1,3,4,5,6,7,12,14],[0,1,3,4,5,6,7,12,15],[0,1,3,4,5,6,7,12,16],[0,1,3,4,5,6,7,13,14],[0,1,3,4,5,6,7,13,15],[0,1,3,4,5,6,7,13,16],[0,1,3,4,5,6,7,14,15],[0,1,3,4,5,6,7,14,16],[0,1,3,4,5,6,7,15,16],[0,1,3,4,5,6,8,10,11],[0,1,3,4,5,6,8,10,11,12,13,14,15],[0,1,3,4,5,6,8,10,11,12,13,14,16],[0,1,3,4,5,6,8,10,11,12,13,15,16],[0,1,3,4,5,6,8,10,11,12,14,15,16],[0,1,3,4,5,6,8,10,11,13,14,15,16],[0,1,3,4,5,6,8,10,12],[0,1,3,4,5,6,8,10,12,13,14,15,16],[0,1,3,4,5,6,8,10,13],[0,1,3,4,5,6,8,10,14],[0,1,3,4,5,6,8,10,15],[0,1,3,4,5,6,8,10,16],[0,1,3,4,5,6,8,11,12],[0,1,3,4,5,6,8,11,12,13,14,15,16],[0,1,3,4,5,6,8,11,13],[0,1,3,4,5,6,8,11,14],[0,1,3,4,5,6,8,11,15],[0,1,3,4,5,6,8,11,16],[0,1,3,4,5,6,8,12,13],[0,1,3,4,5,6,8,12,14],[0,1,3,4,5,6,8,12,15],[0,1,3,4,5,6,8,12,16],[0,1,3,4,5,6,8,13,14],[0,1,3,4,5,6,8,13,15],[0,1,3,4,5,6,8,13,16],[0,1,3,4,5,6,8,14,15],[0,1,3,4,5,6,8,14,16],[0,1,3,4,5,6,8,15,16],[0,1,3,4,5,6,9,10,11],[0,1,3,4,5,6,9,10,11,12,13,14,15],[0,1,3,4,5,6,9,10,11,12,13,14,16],[0,1,3,4,5,6,9,10,11,12,13,15,16],[0,1,3,4,5,6,9,10,11,12,14,15,16],[0,1,3,4,5,6,9,10,11,13,14,15,16],[0,1,3,4,5,6,9,10,12],[0,1,3,4,5,6,9,10,12,13,14,15,16],[0,1,3,4,5,6,9,10,13],[0,1,3,4,5,6,9,10,14],[0,1,3,4,5,6,9,10,15],[0,1,3,4,5,6,9,10,16],[0,1,3,4,5,6,9,11,12],[0,1,3,4,5,6,9,11,12,13,14,15,16],[0,1,3,4,5,6,9,11,13],[0,1,3,4,5,6,9,11,14],[0,1,3,4,5,6,9,11,15],[0,1,3,4,5,6,9,11,16],[0,1,3,4,5,6,9,12,13],[0,1,3,4,5,6,9,12,14],[0,1,3,4,5,6,9,12,15],[0,1,3,4,5,6,9,12,16],[0,1,3,4,5,6,9,13,14],[0,1,3,4,5,6,9,13,15],[0,1,3,4,5,6,9,13,16],[0,1,3,4,5,6,9,14,15],[0,1,3,4,5,6,9,14,16],[0,1,3,4,5,6,9,15,16],[0,1,3,4,5,7,8,10,11],[0,1,3,4,5,7,8,10,11,12,13,14,15],[0,1,3,4,5,7,8,10,11,12,13,14,16],[0,1,3,4,5,7,8,10,11,12,13,15,16],[0,1,3,4,5,7,8,10,11,12,14,15,16],[0,1,3,4,5,7,8,10,11,13,14,15,16],[0,1,3,4,5,7,8,10,12],[0,1,3,4,5,7,8,10,12,13,14,15,16],[0,1,3,4,5,7,8,10,13],[0,1,3,4,5,7,8,10,14],[0,1,3,4,5,7,8,10,15],[0,1,3,4,5,7,8,10,16],[0,1,3,4,5,7,8,11,12],[0,1,3,4,5,7,8,11,12,13,14,15,16],[0,1,3,4,5,7,8,11,13],[0,1,3,4,5,7,8,11,14],[0,1,3,4,5,7,8,11,15],[0,1,3,4,5,7,8,11,16],[0,1,3,4,5,7,8,12,13],[0,1,3,4,5,7,8,12,14],[0,1,3,4,5,7,8,12,15],[0,1,3,4,5,7,8,12,16],[0,1,3,4,5,7,8,13,14],[0,1,3,4,5,7,8,13,15],[0,1,3,4,5,7,8,13,16],[0,1,3,4,5,7,8,14,15],[0,1,3,4,5,7,8,14,16],[0,1,3,4,5,7,8,15,16],[0,1,3,4,5,7,9,10,11],[0,1,3,4,5,7,9,10,11,12,13,14,15],[0,1,3,4,5,7,9,10,11,12,13,14,16],[0,1,3,4,5,7,9,10,11,12,13,15,16],[0,1,3,4,5,7,9,10,11,12,14,15,16],[0,1,3,4,5,7,9,10,11,13,14,15,16],[0,1,3,4,5,7,9,10,12],[0,1,3,4,5,7,9,10,12,13,14,15,16],[0,1,3,4,5,7,9,10,13],[0,1,3,4,5,7,9,10,14],[0,1,3,4,5,7,9,10,15],[0,1,3,4,5,7,9,10,16],[0,1,3,4,5,7,9,11,12],[0,1,3,4,5,7,9,11,12,13,14,15,16],[0,1,3,4,5,7,9,11,13],[0,1,3,4,5,7,9,11,14],[0,1,3,4,5,7,9,11,15],[0,1,3,4,5,7,9,11,16],[0,1,3,4,5,7,9,12,13],[0,1,3,4,5,7,9,12,14],[0,1,3,4,5,7,9,12,15],[0,1,3,4,5,7,9,12,16],[0,1,3,4,5,7,9,13,14],[0,1,3,4,5,7,9,13,15],[0,1,3,4,5,7,9,13,16],[0,1,3,4,5,7,9,14,15],[0,1,3,4,5,7,9,14,16],[0,1,3,4,5,7,9,15,16],[0,1,3,4,5,8,9,10,11],[0,1,3,4,5,8,9,10,11,12,13,14,15],[0,1,3,4,5,8,9,10,11,12,13,14,16],[0,1,3,4,5,8,9,10,11,12,13,15,16],[0,1,3,4,5,8,9,10,11,12,14,15,16],[0,1,3,4,5,8,9,10,11,13,14,15,16],[0,1,3,4,5,8,9,10,12],[0,1,3,4,5,8,9,10,12,13,14,15,16],[0,1,3,4,5,8,9,10,13],[0,1,3,4,5,8,9,10,14],[0,1,3,4,5,8,9,10,15],[0,1,3,4,5,8,9,10,16],[0,1,3,4,5,8,9,11,12],[0,1,3,4,5,8,9,11,12,13,14,15,16],[0,1,3,4,5,8,9,11,13],[0,1,3,4,5,8,9,11,14],[0,1,3,4,5,8,9,11,15],[0,1,3,4,5,8,9,11,16],[0,1,3,4,5,8,9,12,13],[0,1,3,4,5,8,9,12,14],[0,1,3,4,5,8,9,12,15],[0,1,3,4,5,8,9,12,16],[0,1,3,4,5,8,9,13,14],[0,1,3,4,5,8,9,13,15],[0,1,3,4,5,8,9,13,16],[0,1,3,4,5,8,9,14,15],[0,1,3,4,5,8,9,14,16],[0,1,3,4,5,8,9,15,16],[0,1,3,4,6,7,8,10,11],[0,1,3,4,6,7,8,10,11,12,13,14,15],[0,1,3,4,6,7,8,10,11,12,13,14,16],[0,1,3,4,6,7,8,10,11,12,13,15,16],[0,1,3,4,6,7,8,10,11,12,14,15,16],[0,1,3,4,6,7,8,10,11,13,14,15,16],[0,1,3,4,6,7,8,10,12],[0,1,3,4,6,7,8,10,12,13,14,15,16],[0,1,3,4,6,7,8,10,13],[0,1,3,4,6,7,8,10,14],[0,1,3,4,6,7,8,10,15],[0,1,3,4,6,7,8,10,16],[0,1,3,4,6,7,8,11,12],[0,1,3,4,6,7,8,11,12,13,14,15,16],[0,1,3,4,6,7,8,11,13],[0,1,3,4,6,7,8,11,14],[0,1,3,4,6,7,8,11,15],[0,1,3,4,6,7,8,11,16],[0,1,3,4,6,7,8,12,13],[0,1,3,4,6,7,8,12,14],[0,1,3,4,6,7,8,12,15],[0,1,3,4,6,7,8,12,16],[0,1,3,4,6,7,8,13,14],[0,1,3,4,6,7,8,13,15],[0,1,3,4,6,7,8,13,16],[0,1,3,4,6,7,8,14,15],[0,1,3,4,6,7,8,14,16],[0,1,3,4,6,7,8,15,16],[0,1,3,4,6,7,9,10,11],[0,1,3,4,6,7,9,10,11,12,13,14,15],[0,1,3,4,6,7,9,10,11,12,13,14,16],[0,1,3,4,6,7,9,10,11,12,13,15,16],[0,1,3,4,6,7,9,10,11,12,14,15,16],[0,1,3,4,6,7,9,10,11,13,14,15,16],[0,1,3,4,6,7,9,10,12],[0,1,3,4,6,7,9,10,12,13,14,15,16],[0,1,3,4,6,7,9,10,13],[0,1,3,4,6,7,9,10,14],[0,1,3,4,6,7,9,10,15],[0,1,3,4,6,7,9,10,16],[0,1,3,4,6,7,9,11,12],[0,1,3,4,6,7,9,11,12,13,14,15,16],[0,1,3,4,6,7,9,11,13],[0,1,3,4,6,7,9,11,14],[0,1,3,4,6,7,9,11,15],[0,1,3,4,6,7,9,11,16],[0,1,3,4,6,7,9,12,13],[0,1,3,4,6,7,9,12,14],[0,1,3,4,6,7,9,12,15],[0,1,3,4,6,7,9,12,16],[0,1,3,4,6,7,9,13,14],[0,1,3,4,6,7,9,13,15],[0,1,3,4,6,7,9,13,16],[0,1,3,4,6,7,9,14,15],[0,1,3,4,6,7,9,14,16],[0,1,3,4,6,7,9,15,16],[0,1,3,4,6,8,9,10,11],[0,1,3,4,6,8,9,10,11,12,13,14,15],[0,1,3,4,6,8,9,10,11,12,13,14,16],[0,1,3,4,6,8,9,10,11,12,13,15,16],[0,1,3,4,6,8,9,10,11,12,14,15,16],[0,1,3,4,6,8,9,10,11,13,14,15,16],[0,1,3,4,6,8,9,10,12],[0,1,3,4,6,8,9,10,12,13,14,15,16],[0,1,3,4,6,8,9,10,13],[0,1,3,4,6,8,9,10,14],[0,1,3,4,6,8,9,10,15],[0,1,3,4,6,8,9,10,16],[0,1,3,4,6,8,9,11,12],[0,1,3,4,6,8,9,11,12,13,14,15,16],[0,1,3,4,6,8,9,11,13],[0,1,3,4,6,8,9,11,14],[0,1,3,4,6,8,9,11,15],[0,1,3,4,6,8,9,11,16],[0,1,3,4,6,8,9,12,13],[0,1,3,4,6,8,9,12,14],[0,1,3,4,6,8,9,12,15],[0,1,3,4,6,8,9,12,16],[0,1,3,4,6,8,9,13,14],[0,1,3,4,6,8,9,13,15],[0,1,3,4,6,8,9,13,16],[0,1,3,4,6,8,9,14,15],[0,1,3,4,6,8,9,14,16],[0,1,3,4,6,8,9,15,16],[0,1,3,4,7,8,9,10,11],[0,1,3,4,7,8,9,10,11,12,13,14,15],[0,1,3,4,7,8,9,10,11,12,13,14,16],[0,1,3,4,7,8,9,10,11,12,13,15,16],[0,1,3,4,7,8,9,10,11,12,14,15,16],[0,1,3,4,7,8,9,10,11,13,14,15,16],[0,1,3,4,7,8,9,10,12],[0,1,3,4,7,8,9,10,12,13,14,15,16],[0,1,3,4,7,8,9,10,13],[0,1,3,4,7,8,9,10,14],[0,1,3,4,7,8,9,10,15],[0,1,3,4,7,8,9,10,16],[0,1,3,4,7,8,9,11,12],[0,1,3,4,7,8,9,11,12,13,14,15,16],[0,1,3,4,7,8,9,11,13],[0,1,3,4,7,8,9,11,14],[0,1,3,4,7,8,9,11,15],[0,1,3,4,7,8,9,11,16],[0,1,3,4,7,8,9,12,13],[0,1,3,4,7,8,9,12,14],[0,1,3,4,7,8,9,12,15],[0,1,3,4,7,8,9,12,16],[0,1,3,4,7,8,9,13,14],[0,1,3,4,7,8,9,13,15],[0,1,3,4,7,8,9,13,16],[0,1,3,4,7,8,9,14,15],[0,1,3,4,7,8,9,14,16],[0,1,3,4,7,8,9,15,16],[0,1,3,5,6,7,8,10,11],[0,1,3,5,6,7,8,10,11,12,13,14,15],[0,1,3,5,6,7,8,10,11,12,13,14,16],[0,1,3,5,6,7,8,10,11,12,13,15,16],[0,1,3,5,6,7,8,10,11,12,14,15,16],[0,1,3,5,6,7,8,10,11,13,14,15,16],[0,1,3,5,6,7,8,10,12],[0,1,3,5,6,7,8,10,12,13,14,15,16],[0,1,3,5,6,7,8,10,13],[0,1,3,5,6,7,8,10,14],[0,1,3,5,6,7,8,10,15],[0,1,3,5,6,7,8,10,16],[0,1,3,5,6,7,8,11,12],[0,1,3,5,6,7,8,11,12,13,14,15,16],[0,1,3,5,6,7,8,11,13],[0,1,3,5,6,7,8,11,14],[0,1,3,5,6,7,8,11,15],[0,1,3,5,6,7,8,11,16],[0,1,3,5,6,7,8,12,13],[0,1,3,5,6,7,8,12,14],[0,1,3,5,6,7,8,12,15],[0,1,3,5,6,7,8,12,16],[0,1,3,5,6,7,8,13,14],[0,1,3,5,6,7,8,13,15],[0,1,3,5,6,7,8,13,16],[0,1,3,5,6,7,8,14,15],[0,1,3,5,6,7,8,14,16],[0,1,3,5,6,7,8,15,16],[0,1,3,5,6,7,9,10,11],[0,1,3,5,6,7,9,10,11,12,13,14,15],[0,1,3,5,6,7,9,10,11,12,13,14,16],[0,1,3,5,6,7,9,10,11,12,13,15,16],[0,1,3,5,6,7,9,10,11,12,14,15,16],[0,1,3,5,6,7,9,10,11,13,14,15,16],[0,1,3,5,6,7,9,10,12],[0,1,3,5,6,7,9,10,12,13,14,15,16],[0,1,3,5,6,7,9,10,13],[0,1,3,5,6,7,9,10,14],[0,1,3,5,6,7,9,10,15],[0,1,3,5,6,7,9,10,16],[0,1,3,5,6,7,9,11,12],[0,1,3,5,6,7,9,11,12,13,14,15,16],[0,1,3,5,6,7,9,11,13],[0,1,3,5,6,7,9,11,14],[0,1,3,5,6,7,9,11,15],[0,1,3,5,6,7,9,11,16],[0,1,3,5,6,7,9,12,13],[0,1,3,5,6,7,9,12,14],[0,1,3,5,6,7,9,12,15],[0,1,3,5,6,7,9,12,16],[0,1,3,5,6,7,9,13,14],[0,1,3,5,6,7,9,13,15],[0,1,3,5,6,7,9,13,16],[0,1,3,5,6,7,9,14,15],[0,1,3,5,6,7,9,14,16],[0,1,3,5,6,7,9,15,16],[0,1,3,5,6,8,9,10,11],[0,1,3,5,6,8,9,10,11,12,13,14,15],[0,1,3,5,6,8,9,10,11,12,13,14,16],[0,1,3,5,6,8,9,10,11,12,13,15,16],[0,1,3,5,6,8,9,10,11,12,14,15,16],[0,1,3,5,6,8,9,10,11,13,14,15,16],[0,1,3,5,6,8,9,10,12],[0,1,3,5,6,8,9,10,12,13,14,15,16],[0,1,3,5,6,8,9,10,13],[0,1,3,5,6,8,9,10,14],[0,1,3,5,6,8,9,10,15],[0,1,3,5,6,8,9,10,16],[0,1,3,5,6,8,9,11,12],[0,1,3,5,6,8,9,11,12,13,14,15,16],[0,1,3,5,6,8,9,11,13],[0,1,3,5,6,8,9,11,14],[0,1,3,5,6,8,9,11,15],[0,1,3,5,6,8,9,11,16],[0,1,3,5,6,8,9,12,13],[0,1,3,5,6,8,9,12,14],[0,1,3,5,6,8,9,12,15],[0,1,3,5,6,8,9,12,16],[0,1,3,5,6,8,9,13,14],[0,1,3,5,6,8,9,13,15],[0,1,3,5,6,8,9,13,16],[0,1,3,5,6,8,9,14,15],[0,1,3,5,6,8,9,14,16],[0,1,3,5,6,8,9,15,16],[0,1,3,5,7,8,9,10,11],[0,1,3,5,7,8,9,10,11,12,13,14,15],[0,1,3,5,7,8,9,10,11,12,13,14,16],[0,1,3,5,7,8,9,10,11,12,13,15,16],[0,1,3,5,7,8,9,10,11,12,14,15,16],[0,1,3,5,7,8,9,10,11,13,14,15,16],[0,1,3,5,7,8,9,10,12],[0,1,3,5,7,8,9,10,12,13,14,15,16],[0,1,3,5,7,8,9,10,13],[0,1,3,5,7,8,9,10,14],[0,1,3,5,7,8,9,10,15],[0,1,3,5,7,8,9,10,16],[0,1,3,5,7,8,9,11,12],[0,1,3,5,7,8,9,11,12,13,14,15,16],[0,1,3,5,7,8,9,11,13],[0,1,3,5,7,8,9,11,14],[0,1,3,5,7,8,9,11,15],[0,1,3,5,7,8,9,11,16],[0,1,3,5,7,8,9,12,13],[0,1,3,5,7,8,9,12,14],[0,1,3,5,7,8,9,12,15],[0,1,3,5,7,8,9,12,16],[0,1,3,5,7,8,9,13,14],[0,1,3,5,7,8,9,13,15],[0,1,3,5,7,8,9,13,16],[0,1,3,5,7,8,9,14,15],[0,1,3,5,7,8,9,14,16],[0,1,3,5,7,8,9,15,16],[0,1,3,6,7,8,9,10,11],[0,1,3,6,7,8,9,10,11,12,13,14,15],[0,1,3,6,7,8,9,10,11,12,13,14,16],[0,1,3,6,7,8,9,10,11,12,13,15,16],[0,1,3,6,7,8,9,10,11,12,14,15,16],[0,1,3,6,7,8,9,10,11,13,14,15,16],[0,1,3,6,7,8,9,10,12],[0,1,3,6,7,8,9,10,12,13,14,15,16],[0,1,3,6,7,8,9,10,13],[0,1,3,6,7,8,9,10,14],[0,1,3,6,7,8,9,10,15],[0,1,3,6,7,8,9,10,16],[0,1,3,6,7,8,9,11,12],[0,1,3,6,7,8,9,11,12,13,14,15,16],[0,1,3,6,7,8,9,11,13],[0,1,3,6,7,8,9,11,14],[0,1,3,6,7,8,9,11,15],[0,1,3,6,7,8,9,11,16],[0,1,3,6,7,8,9,12,13],[0,1,3,6,7,8,9,12,14],[0,1,3,6,7,8,9,12,15],[0,1,3,6,7,8,9,12,16],[0,1,3,6,7,8,9,13,14],[0,1,3,6,7,8,9,13,15],[0,1,3,6,7,8,9,13,16],[0,1,3,6,7,8,9,14,15],[0,1,3,6,7,8,9,14,16],[0,1,3,6,7,8,9,15,16],[0,1,4,5,6,7,8,10,11],[0,1,4,5,6,7,8,10,11,12,13,14,15],[0,1,4,5,6,7,8,10,11,12,13,14,16],[0,1,4,5,6,7,8,10,11,12,13,15,16],[0,1,4,5,6,7,8,10,11,12,14,15,16],[0,1,4,5,6,7,8,10,11,13,14,15,16],[0,1,4,5,6,7,8,10,12],[0,1,4,5,6,7,8,10,12,13,14,15,16],[0,1,4,5,6,7,8,10,13],[0,1,4,5,6,7,8,10,14],[0,1,4,5,6,7,8,10,15],[0,1,4,5,6,7,8,10,16],[0,1,4,5,6,7,8,11,12],[0,1,4,5,6,7,8,11,12,13,14,15,16],[0,1,4,5,6,7,8,11,13],[0,1,4,5,6,7,8,11,14],[0,1,4,5,6,7,8,11,15],[0,1,4,5,6,7,8,11,16],[0,1,4,5,6,7,8,12,13],[0,1,4,5,6,7,8,12,14],[0,1,4,5,6,7,8,12,15],[0,1,4,5,6,7,8,12,16],[0,1,4,5,6,7,8,13,14],[0,1,4,5,6,7,8,13,15],[0,1,4,5,6,7,8,13,16],[0,1,4,5,6,7,8,14,15],[0,1,4,5,6,7,8,14,16],[0,1,4,5,6,7,8,15,16],[0,1,4,5,6,7,9,10,11],[0,1,4,5,6,7,9,10,11,12,13,14,15],[0,1,4,5,6,7,9,10,11,12,13,14,16],[0,1,4,5,6,7,9,10,11,12,13,15,16],[0,1,4,5,6,7,9,10,11,12,14,15,16],[0,1,4,5,6,7,9,10,11,13,14,15,16],[0,1,4,5,6,7,9,10,12],[0,1,4,5,6,7,9,10,12,13,14,15,16],[0,1,4,5,6,7,9,10,13],[0,1,4,5,6,7,9,10,14],[0,1,4,5,6,7,9,10,15],[0,1,4,5,6,7,9,10,16],[0,1,4,5,6,7,9,11,12],[0,1,4,5,6,7,9,11,12,13,14,15,16],[0,1,4,5,6,7,9,11,13],[0,1,4,5,6,7,9,11,14],[0,1,4,5,6,7,9,11,15],[0,1,4,5,6,7,9,11,16],[0,1,4,5,6,7,9,12,13],[0,1,4,5,6,7,9,12,14],[0,1,4,5,6,7,9,12,15],[0,1,4,5,6,7,9,12,16],[0,1,4,5,6,7,9,13,14],[0,1,4,5,6,7,9,13,15],[0,1,4,5,6,7,9,13,16],[0,1,4,5,6,7,9,14,15],[0,1,4,5,6,7,9,14,16],[0,1,4,5,6,7,9,15,16],[0,1,4,5,6,8,9,10,11],[0,1,4,5,6,8,9,10,11,12,13,14,15],[0,1,4,5,6,8,9,10,11,12,13,14,16],[0,1,4,5,6,8,9,10,11,12,13,15,16],[0,1,4,5,6,8,9,10,11,12,14,15,16],[0,1,4,5,6,8,9,10,11,13,14,15,16],[0,1,4,5,6,8,9,10,12],[0,1,4,5,6,8,9,10,12,13,14,15,16],[0,1,4,5,6,8,9,10,13],[0,1,4,5,6,8,9,10,14],[0,1,4,5,6,8,9,10,15],[0,1,4,5,6,8,9,10,16],[0,1,4,5,6,8,9,11,12],[0,1,4,5,6,8,9,11,12,13,14,15,16],[0,1,4,5,6,8,9,11,13],[0,1,4,5,6,8,9,11,14],[0,1,4,5,6,8,9,11,15],[0,1,4,5,6,8,9,11,16],[0,1,4,5,6,8,9,12,13],[0,1,4,5,6,8,9,12,14],[0,1,4,5,6,8,9,12,15],[0,1,4,5,6,8,9,12,16],[0,1,4,5,6,8,9,13,14],[0,1,4,5,6,8,9,13,15],[0,1,4,5,6,8,9,13,16],[0,1,4,5,6,8,9,14,15],[0,1,4,5,6,8,9,14,16],[0,1,4,5,6,8,9,15,16],[0,1,4,5,7,8,9,10,11],[0,1,4,5,7,8,9,10,11,12,13,14,15],[0,1,4,5,7,8,9,10,11,12,13,14,16],[0,1,4,5,7,8,9,10,11,12,13,15,16],[0,1,4,5,7,8,9,10,11,12,14,15,16],[0,1,4,5,7,8,9,10,11,13,14,15,16],[0,1,4,5,7,8,9,10,12],[0,1,4,5,7,8,9,10,12,13,14,15,16],[0,1,4,5,7,8,9,10,13],[0,1,4,5,7,8,9,10,14],[0,1,4,5,7,8,9,10,15],[0,1,4,5,7,8,9,10,16],[0,1,4,5,7,8,9,11,12],[0,1,4,5,7,8,9,11,12,13,14,15,16],[0,1,4,5,7,8,9,11,13],[0,1,4,5,7,8,9,11,14],[0,1,4,5,7,8,9,11,15],[0,1,4,5,7,8,9,11,16],[0,1,4,5,7,8,9,12,13],[0,1,4,5,7,8,9,12,14],[0,1,4,5,7,8,9,12,15],[0,1,4,5,7,8,9,12,16],[0,1,4,5,7,8,9,13,14],[0,1,4,5,7,8,9,13,15],[0,1,4,5,7,8,9,13,16],[0,1,4,5,7,8,9,14,15],[0,1,4,5,7,8,9,14,16],[0,1,4,5,7,8,9,15,16],[0,1,4,6,7,8,9,10,11],[0,1,4,6,7,8,9,10,11,12,13,14,15],[0,1,4,6,7,8,9,10,11,12,13,14,16],[0,1,4,6,7,8,9,10,11,12,13,15,16],[0,1,4,6,7,8,9,10,11,12,14,15,16],[0,1,4,6,7,8,9,10,11,13,14,15,16],[0,1,4,6,7,8,9,10,12],[0,1,4,6,7,8,9,10,12,13,14,15,16],[0,1,4,6,7,8,9,10,13],[0,1,4,6,7,8,9,10,14],[0,1,4,6,7,8,9,10,15],[0,1,4,6,7,8,9,10,16],[0,1,4,6,7,8,9,11,12],[0,1,4,6,7,8,9,11,12,13,14,15,16],[0,1,4,6,7,8,9,11,13],[0,1,4,6,7,8,9,11,14],[0,1,4,6,7,8,9,11,15],[0,1,4,6,7,8,9,11,16],[0,1,4,6,7,8,9,12,13],[0,1,4,6,7,8,9,12,14],[0,1,4,6,7,8,9,12,15],[0,1,4,6,7,8,9,12,16],[0,1,4,6,7,8,9,13,14],[0,1,4,6,7,8,9,13,15],[0,1,4,6,7,8,9,13,16],[0,1,4,6,7,8,9,14,15],[0,1,4,6,7,8,9,14,16],[0,1,4,6,7,8,9,15,16],[0,1,5,6,7,8,9,10,11],[0,1,5,6,7,8,9,10,11,12,13,14,15],[0,1,5,6,7,8,9,10,11,12,13,14,16],[0,1,5,6,7,8,9,10,11,12,13,15,16],[0,1,5,6,7,8,9,10,11,12,14,15,16],[0,1,5,6,7,8,9,10,11,13,14,15,16],[0,1,5,6,7,8,9,10,12],[0,1,5,6,7,8,9,10,12,13,14,15,16],[0,1,5,6,7,8,9,10,13],[0,1,5,6,7,8,9,10,14],[0,1,5,6,7,8,9,10,15],[0,1,5,6,7,8,9,10,16],[0,1,5,6,7,8,9,11,12],[0,1,5,6,7,8,9,11,12,13,14,15,16],[0,1,5,6,7,8,9,11,13],[0,1,5,6,7,8,9,11,14],[0,1,5,6,7,8,9,11,15],[0,1,5,6,7,8,9,11,16],[0,1,5,6,7,8,9,12,13],[0,1,5,6,7,8,9,12,14],[0,1,5,6,7,8,9,12,15],[0,1,5,6,7,8,9,12,16],[0,1,5,6,7,8,9,13,14],[0,1,5,6,7,8,9,13,15],[0,1,5,6,7,8,9,13,16],[0,1,5,6,7,8,9,14,15],[0,1,5,6,7,8,9,14,16],[0,1,5,6,7,8,9,15,16],[0,2,3,4,5,6,7,10,11],[0,2,3,4,5,6,7,10,11,12,13,14,15],[0,2,3,4,5,6,7,10,11,12,13,14,16],[0,2,3,4,5,6,7,10,11,12,13,15,16],[0,2,3,4,5,6,7,10,11,12,14,15,16],[0,2,3,4,5,6,7,10,11,13,14,15,16],[0,2,3,4,5,6,7,10,12],[0,2,3,4,5,6,7,10,12,13,14,15,16],[0,2,3,4,5,6,7,10,13],[0,2,3,4,5,6,7,10,14],[0,2,3,4,5,6,7,10,15],[0,2,3,4,5,6,7,10,16],[0,2,3,4,5,6,7,11,12],[0,2,3,4,5,6,7,11,12,13,14,15,16],[0,2,3,4,5,6,7,11,13],[0,2,3,4,5,6,7,11,14],[0,2,3,4,5,6,7,11,15],[0,2,3,4,5,6,7,11,16],[0,2,3,4,5,6,7,12,13],[0,2,3,4,5,6,7,12,14],[0,2,3,4,5,6,7,12,15],[0,2,3,4,5,6,7,12,16],[0,2,3,4,5,6,7,13,14],[0,2,3,4,5,6,7,13,15],[0,2,3,4,5,6,7,13,16],[0,2,3,4,5,6,7,14,15],[0,2,3,4,5,6,7,14,16],[0,2,3,4,5,6,7,15,16],[0,2,3,4,5,6,8,10,11],[0,2,3,4,5,6,8,10,11,12,13,14,15],[0,2,3,4,5,6,8,10,11,12,13,14,16],[0,2,3,4,5,6,8,10,11,12,13,15,16],[0,2,3,4,5,6,8,10,11,12,14,15,16],[0,2,3,4,5,6,8,10,11,13,14,15,16],[0,2,3,4,5,6,8,10,12],[0,2,3,4,5,6,8,10,12,13,14,15,16],[0,2,3,4,5,6,8,10,13],[0,2,3,4,5,6,8,10,14],[0,2,3,4,5,6,8,10,15],[0,2,3,4,5,6,8,10,16],[0,2,3,4,5,6,8,11,12],[0,2,3,4,5,6,8,11,12,13,14,15,16],[0,2,3,4,5,6,8,11,13],[0,2,3,4,5,6,8,11,14],[0,2,3,4,5,6,8,11,15],[0,2,3,4,5,6,8,11,16],[0,2,3,4,5,6,8,12,13],[0,2,3,4,5,6,8,12,14],[0,2,3,4,5,6,8,12,15],[0,2,3,4,5,6,8,12,16],[0,2,3,4,5,6,8,13,14],[0,2,3,4,5,6,8,13,15],[0,2,3,4,5,6,8,13,16],[0,2,3,4,5,6,8,14,15],[0,2,3,4,5,6,8,14,16],[0,2,3,4,5,6,8,15,16],[0,2,3,4,5,6,9,10,11],[0,2,3,4,5,6,9,10,11,12,13,14,15],[0,2,3,4,5,6,9,10,11,12,13,14,16],[0,2,3,4,5,6,9,10,11,12,13,15,16],[0,2,3,4,5,6,9,10,11,12,14,15,16],[0,2,3,4,5,6,9,10,11,13,14,15,16],[0,2,3,4,5,6,9,10,12],[0,2,3,4,5,6,9,10,12,13,14,15,16],[0,2,3,4,5,6,9,10,13],[0,2,3,4,5,6,9,10,14],[0,2,3,4,5,6,9,10,15],[0,2,3,4,5,6,9,10,16],[0,2,3,4,5,6,9,11,12],[0,2,3,4,5,6,9,11,12,13,14,15,16],[0,2,3,4,5,6,9,11,13],[0,2,3,4,5,6,9,11,14],[0,2,3,4,5,6,9,11,15],[0,2,3,4,5,6,9,11,16],[0,2,3,4,5,6,9,12,13],[0,2,3,4,5,6,9,12,14],[0,2,3,4,5,6,9,12,15],[0,2,3,4,5,6,9,12,16],[0,2,3,4,5,6,9,13,14],[0,2,3,4,5,6,9,13,15],[0,2,3,4,5,6,9,13,16],[0,2,3,4,5,6,9,14,15],[0,2,3,4,5,6,9,14,16],[0,2,3,4,5,6,9,15,16],[0,2,3,4,5,7,8,10,11],[0,2,3,4,5,7,8,10,11,12,13,14,15],[0,2,3,4,5,7,8,10,11,12,13,14,16],[0,2,3,4,5,7,8,10,11,12,13,15,16],[0,2,3,4,5,7,8,10,11,12,14,15,16],[0,2,3,4,5,7,8,10,11,13,14,15,16],[0,2,3,4,5,7,8,10,12],[0,2,3,4,5,7,8,10,12,13,14,15,16],[0,2,3,4,5,7,8,10,13],[0,2,3,4,5,7,8,10,14],[0,2,3,4,5,7,8,10,15],[0,2,3,4,5,7,8,10,16],[0,2,3,4,5,7,8,11,12],[0,2,3,4,5,7,8,11,12,13,14,15,16],[0,2,3,4,5,7,8,11,13],[0,2,3,4,5,7,8,11,14],[0,2,3,4,5,7,8,11,15],[0,2,3,4,5,7,8,11,16],[0,2,3,4,5,7,8,12,13],[0,2,3,4,5,7,8,12,14],[0,2,3,4,5,7,8,12,15],[0,2,3,4,5,7,8,12,16],[0,2,3,4,5,7,8,13,14],[0,2,3,4,5,7,8,13,15],[0,2,3,4,5,7,8,13,16],[0,2,3,4,5,7,8,14,15],[0,2,3,4,5,7,8,14,16],[0,2,3,4,5,7,8,15,16],[0,2,3,4,5,7,9,10,11],[0,2,3,4,5,7,9,10,11,12,13,14,15],[0,2,3,4,5,7,9,10,11,12,13,14,16],[0,2,3,4,5,7,9,10,11,12,13,15,16],[0,2,3,4,5,7,9,10,11,12,14,15,16],[0,2,3,4,5,7,9,10,11,13,14,15,16],[0,2,3,4,5,7,9,10,12],[0,2,3,4,5,7,9,10,12,13,14,15,16],[0,2,3,4,5,7,9,10,13],[0,2,3,4,5,7,9,10,14],[0,2,3,4,5,7,9,10,15],[0,2,3,4,5,7,9,10,16],[0,2,3,4,5,7,9,11,12],[0,2,3,4,5,7,9,11,12,13,14,15,16],[0,2,3,4,5,7,9,11,13],[0,2,3,4,5,7,9,11,14],[0,2,3,4,5,7,9,11,15],[0,2,3,4,5,7,9,11,16],[0,2,3,4,5,7,9,12,13],[0,2,3,4,5,7,9,12,14],[0,2,3,4,5,7,9,12,15],[0,2,3,4,5,7,9,12,16],[0,2,3,4,5,7,9,13,14],[0,2,3,4,5,7,9,13,15],[0,2,3,4,5,7,9,13,16],[0,2,3,4,5,7,9,14,15],[0,2,3,4,5,7,9,14,16],[0,2,3,4,5,7,9,15,16],[0,2,3,4,5,8,9,10,11],[0,2,3,4,5,8,9,10,11,12,13,14,15],[0,2,3,4,5,8,9,10,11,12,13,14,16],[0,2,3,4,5,8,9,10,11,12,13,15,16],[0,2,3,4,5,8,9,10,11,12,14,15,16],[0,2,3,4,5,8,9,10,11,13,14,15,16],[0,2,3,4,5,8,9,10,12],[0,2,3,4,5,8,9,10,12,13,14,15,16],[0,2,3,4,5,8,9,10,13],[0,2,3,4,5,8,9,10,14],[0,2,3,4,5,8,9,10,15],[0,2,3,4,5,8,9,10,16],[0,2,3,4,5,8,9,11,12],[0,2,3,4,5,8,9,11,12,13,14,15,16],[0,2,3,4,5,8,9,11,13],[0,2,3,4,5,8,9,11,14],[0,2,3,4,5,8,9,11,15],[0,2,3,4,5,8,9,11,16],[0,2,3,4,5,8,9,12,13],[0,2,3,4,5,8,9,12,14],[0,2,3,4,5,8,9,12,15],[0,2,3,4,5,8,9,12,16],[0,2,3,4,5,8,9,13,14],[0,2,3,4,5,8,9,13,15],[0,2,3,4,5,8,9,13,16],[0,2,3,4,5,8,9,14,15],[0,2,3,4,5,8,9,14,16],[0,2,3,4,5,8,9,15,16],[0,2,3,4,6,7,8,10,11],[0,2,3,4,6,7,8,10,11,12,13,14,15],[0,2,3,4,6,7,8,10,11,12,13,14,16],[0,2,3,4,6,7,8,10,11,12,13,15,16],[0,2,3,4,6,7,8,10,11,12,14,15,16],[0,2,3,4,6,7,8,10,11,13,14,15,16],[0,2,3,4,6,7,8,10,12],[0,2,3,4,6,7,8,10,12,13,14,15,16],[0,2,3,4,6,7,8,10,13],[0,2,3,4,6,7,8,10,14],[0,2,3,4,6,7,8,10,15],[0,2,3,4,6,7,8,10,16],[0,2,3,4,6,7,8,11,12],[0,2,3,4,6,7,8,11,12,13,14,15,16],[0,2,3,4,6,7,8,11,13],[0,2,3,4,6,7,8,11,14],[0,2,3,4,6,7,8,11,15],[0,2,3,4,6,7,8,11,16],[0,2,3,4,6,7,8,12,13],[0,2,3,4,6,7,8,12,14],[0,2,3,4,6,7,8,12,15],[0,2,3,4,6,7,8,12,16],[0,2,3,4,6,7,8,13,14],[0,2,3,4,6,7,8,13,15],[0,2,3,4,6,7,8,13,16],[0,2,3,4,6,7,8,14,15],[0,2,3,4,6,7,8,14,16],[0,2,3,4,6,7,8,15,16],[0,2,3,4,6,7,9,10,11],[0,2,3,4,6,7,9,10,11,12,13,14,15],[0,2,3,4,6,7,9,10,11,12,13,14,16],[0,2,3,4,6,7,9,10,11,12,13,15,16],[0,2,3,4,6,7,9,10,11,12,14,15,16],[0,2,3,4,6,7,9,10,11,13,14,15,16],[0,2,3,4,6,7,9,10,12],[0,2,3,4,6,7,9,10,12,13,14,15,16],[0,2,3,4,6,7,9,10,13],[0,2,3,4,6,7,9,10,14],[0,2,3,4,6,7,9,10,15],[0,2,3,4,6,7,9,10,16],[0,2,3,4,6,7,9,11,12],[0,2,3,4,6,7,9,11,12,13,14,15,16],[0,2,3,4,6,7,9,11,13],[0,2,3,4,6,7,9,11,14],[0,2,3,4,6,7,9,11,15],[0,2,3,4,6,7,9,11,16],[0,2,3,4,6,7,9,12,13],[0,2,3,4,6,7,9,12,14],[0,2,3,4,6,7,9,12,15],[0,2,3,4,6,7,9,12,16],[0,2,3,4,6,7,9,13,14],[0,2,3,4,6,7,9,13,15],[0,2,3,4,6,7,9,13,16],[0,2,3,4,6,7,9,14,15],[0,2,3,4,6,7,9,14,16],[0,2,3,4,6,7,9,15,16],[0,2,3,4,6,8,9,10,11],[0,2,3,4,6,8,9,10,11,12,13,14,15],[0,2,3,4,6,8,9,10,11,12,13,14,16],[0,2,3,4,6,8,9,10,11,12,13,15,16],[0,2,3,4,6,8,9,10,11,12,14,15,16],[0,2,3,4,6,8,9,10,11,13,14,15,16],[0,2,3,4,6,8,9,10,12],[0,2,3,4,6,8,9,10,12,13,14,15,16],[0,2,3,4,6,8,9,10,13],[0,2,3,4,6,8,9,10,14],[0,2,3,4,6,8,9,10,15],[0,2,3,4,6,8,9,10,16],[0,2,3,4,6,8,9,11,12],[0,2,3,4,6,8,9,11,12,13,14,15,16],[0,2,3,4,6,8,9,11,13],[0,2,3,4,6,8,9,11,14],[0,2,3,4,6,8,9,11,15],[0,2,3,4,6,8,9,11,16],[0,2,3,4,6,8,9,12,13],[0,2,3,4,6,8,9,12,14],[0,2,3,4,6,8,9,12,15],[0,2,3,4,6,8,9,12,16],[0,2,3,4,6,8,9,13,14],[0,2,3,4,6,8,9,13,15],[0,2,3,4,6,8,9,13,16],[0,2,3,4,6,8,9,14,15],[0,2,3,4,6,8,9,14,16],[0,2,3,4,6,8,9,15,16],[0,2,3,4,7,8,9,10,11],[0,2,3,4,7,8,9,10,11,12,13,14,15],[0,2,3,4,7,8,9,10,11,12,13,14,16],[0,2,3,4,7,8,9,10,11,12,13,15,16],[0,2,3,4,7,8,9,10,11,12,14,15,16],[0,2,3,4,7,8,9,10,11,13,14,15,16],[0,2,3,4,7,8,9,10,12],[0,2,3,4,7,8,9,10,12,13,14,15,16],[0,2,3,4,7,8,9,10,13],[0,2,3,4,7,8,9,10,14],[0,2,3,4,7,8,9,10,15],[0,2,3,4,7,8,9,10,16],[0,2,3,4,7,8,9,11,12],[0,2,3,4,7,8,9,11,12,13,14,15,16],[0,2,3,4,7,8,9,11,13],[0,2,3,4,7,8,9,11,14],[0,2,3,4,7,8,9,11,15],[0,2,3,4,7,8,9,11,16],[0,2,3,4,7,8,9,12,13],[0,2,3,4,7,8,9,12,14],[0,2,3,4,7,8,9,12,15],[0,2,3,4,7,8,9,12,16],[0,2,3,4,7,8,9,13,14],[0,2,3,4,7,8,9,13,15],[0,2,3,4,7,8,9,13,16],[0,2,3,4,7,8,9,14,15],[0,2,3,4,7,8,9,14,16],[0,2,3,4,7,8,9,15,16],[0,2,3,5,6,7,8,10,11],[0,2,3,5,6,7,8,10,11,12,13,14,15],[0,2,3,5,6,7,8,10,11,12,13,14,16],[0,2,3,5,6,7,8,10,11,12,13,15,16],[0,2,3,5,6,7,8,10,11,12,14,15,16],[0,2,3,5,6,7,8,10,11,13,14,15,16],[0,2,3,5,6,7,8,10,12],[0,2,3,5,6,7,8,10,12,13,14,15,16],[0,2,3,5,6,7,8,10,13],[0,2,3,5,6,7,8,10,14],[0,2,3,5,6,7,8,10,15],[0,2,3,5,6,7,8,10,16],[0,2,3,5,6,7,8,11,12],[0,2,3,5,6,7,8,11,12,13,14,15,16],[0,2,3,5,6,7,8,11,13],[0,2,3,5,6,7,8,11,14],[0,2,3,5,6,7,8,11,15],[0,2,3,5,6,7,8,11,16],[0,2,3,5,6,7,8,12,13],[0,2,3,5,6,7,8,12,14],[0,2,3,5,6,7,8,12,15],[0,2,3,5,6,7,8,12,16],[0,2,3,5,6,7,8,13,14],[0,2,3,5,6,7,8,13,15],[0,2,3,5,6,7,8,13,16],[0,2,3,5,6,7,8,14,15],[0,2,3,5,6,7,8,14,16],[0,2,3,5,6,7,8,15,16],[0,2,3,5,6,7,9,10,11],[0,2,3,5,6,7,9,10,11,12,13,14,15],[0,2,3,5,6,7,9,10,11,12,13,14,16],[0,2,3,5,6,7,9,10,11,12,13,15,16],[0,2,3,5,6,7,9,10,11,12,14,15,16],[0,2,3,5,6,7,9,10,11,13,14,15,16],[0,2,3,5,6,7,9,10,12],[0,2,3,5,6,7,9,10,12,13,14,15,16],[0,2,3,5,6,7,9,10,13],[0,2,3,5,6,7,9,10,14],[0,2,3,5,6,7,9,10,15],[0,2,3,5,6,7,9,10,16],[0,2,3,5,6,7,9,11,12],[0,2,3,5,6,7,9,11,12,13,14,15,16],[0,2,3,5,6,7,9,11,13],[0,2,3,5,6,7,9,11,14],[0,2,3,5,6,7,9,11,15],[0,2,3,5,6,7,9,11,16],[0,2,3,5,6,7,9,12,13],[0,2,3,5,6,7,9,12,14],[0,2,3,5,6,7,9,12,15],[0,2,3,5,6,7,9,12,16],[0,2,3,5,6,7,9,13,14],[0,2,3,5,6,7,9,13,15],[0,2,3,5,6,7,9,13,16],[0,2,3,5,6,7,9,14,15],[0,2,3,5,6,7,9,14,16],[0,2,3,5,6,7,9,15,16],[0,2,3,5,6,8,9,10,11],[0,2,3,5,6,8,9,10,11,12,13,14,15],[0,2,3,5,6,8,9,10,11,12,13,14,16],[0,2,3,5,6,8,9,10,11,12,13,15,16],[0,2,3,5,6,8,9,10,11,12,14,15,16],[0,2,3,5,6,8,9,10,11,13,14,15,16],[0,2,3,5,6,8,9,10,12],[0,2,3,5,6,8,9,10,12,13,14,15,16],[0,2,3,5,6,8,9,10,13],[0,2,3,5,6,8,9,10,14],[0,2,3,5,6,8,9,10,15],[0,2,3,5,6,8,9,10,16],[0,2,3,5,6,8,9,11,12],[0,2,3,5,6,8,9,11,12,13,14,15,16],[0,2,3,5,6,8,9,11,13],[0,2,3,5,6,8,9,11,14],[0,2,3,5,6,8,9,11,15],[0,2,3,5,6,8,9,11,16],[0,2,3,5,6,8,9,12,13],[0,2,3,5,6,8,9,12,14],[0,2,3,5,6,8,9,12,15],[0,2,3,5,6,8,9,12,16],[0,2,3,5,6,8,9,13,14],[0,2,3,5,6,8,9,13,15],[0,2,3,5,6,8,9,13,16],[0,2,3,5,6,8,9,14,15],[0,2,3,5,6,8,9,14,16],[0,2,3,5,6,8,9,15,16],[0,2,3,5,7,8,9,10,11],[0,2,3,5,7,8,9,10,11,12,13,14,15],[0,2,3,5,7,8,9,10,11,12,13,14,16],[0,2,3,5,7,8,9,10,11,12,13,15,16],[0,2,3,5,7,8,9,10,11,12,14,15,16],[0,2,3,5,7,8,9,10,11,13,14,15,16],[0,2,3,5,7,8,9,10,12],[0,2,3,5,7,8,9,10,12,13,14,15,16],[0,2,3,5,7,8,9,10,13],[0,2,3,5,7,8,9,10,14],[0,2,3,5,7,8,9,10,15],[0,2,3,5,7,8,9,10,16],[0,2,3,5,7,8,9,11,12],[0,2,3,5,7,8,9,11,12,13,14,15,16],[0,2,3,5,7,8,9,11,13],[0,2,3,5,7,8,9,11,14],[0,2,3,5,7,8,9,11,15],[0,2,3,5,7,8,9,11,16],[0,2,3,5,7,8,9,12,13],[0,2,3,5,7,8,9,12,14],[0,2,3,5,7,8,9,12,15],[0,2,3,5,7,8,9,12,16],[0,2,3,5,7,8,9,13,14],[0,2,3,5,7,8,9,13,15],[0,2,3,5,7,8,9,13,16],[0,2,3,5,7,8,9,14,15],[0,2,3,5,7,8,9,14,16],[0,2,3,5,7,8,9,15,16],[0,2,3,6,7,8,9,10,11],[0,2,3,6,7,8,9,10,11,12,13,14,15],[0,2,3,6,7,8,9,10,11,12,13,14,16],[0,2,3,6,7,8,9,10,11,12,13,15,16],[0,2,3,6,7,8,9,10,11,12,14,15,16],[0,2,3,6,7,8,9,10,11,13,14,15,16],[0,2,3,6,7,8,9,10,12],[0,2,3,6,7,8,9,10,12,13,14,15,16],[0,2,3,6,7,8,9,10,13],[0,2,3,6,7,8,9,10,14],[0,2,3,6,7,8,9,10,15],[0,2,3,6,7,8,9,10,16],[0,2,3,6,7,8,9,11,12],[0,2,3,6,7,8,9,11,12,13,14,15,16],[0,2,3,6,7,8,9,11,13],[0,2,3,6,7,8,9,11,14],[0,2,3,6,7,8,9,11,15],[0,2,3,6,7,8,9,11,16],[0,2,3,6,7,8,9,12,13],[0,2,3,6,7,8,9,12,14],[0,2,3,6,7,8,9,12,15],[0,2,3,6,7,8,9,12,16],[0,2,3,6,7,8,9,13,14],[0,2,3,6,7,8,9,13,15],[0,2,3,6,7,8,9,13,16],[0,2,3,6,7,8,9,14,15],[0,2,3,6,7,8,9,14,16],[0,2,3,6,7,8,9,15,16],[0,2,4,5,6,7,8,10,11],[0,2,4,5,6,7,8,10,11,12,13,14,15],[0,2,4,5,6,7,8,10,11,12,13,14,16],[0,2,4,5,6,7,8,10,11,12,13,15,16],[0,2,4,5,6,7,8,10,11,12,14,15,16],[0,2,4,5,6,7,8,10,11,13,14,15,16],[0,2,4,5,6,7,8,10,12],[0,2,4,5,6,7,8,10,12,13,14,15,16],[0,2,4,5,6,7,8,10,13],[0,2,4,5,6,7,8,10,14],[0,2,4,5,6,7,8,10,15],[0,2,4,5,6,7,8,10,16],[0,2,4,5,6,7,8,11,12],[0,2,4,5,6,7,8,11,12,13,14,15,16],[0,2,4,5,6,7,8,11,13],[0,2,4,5,6,7,8,11,14],[0,2,4,5,6,7,8,11,15],[0,2,4,5,6,7,8,11,16],[0,2,4,5,6,7,8,12,13],[0,2,4,5,6,7,8,12,14],[0,2,4,5,6,7,8,12,15],[0,2,4,5,6,7,8,12,16],[0,2,4,5,6,7,8,13,14],[0,2,4,5,6,7,8,13,15],[0,2,4,5,6,7,8,13,16],[0,2,4,5,6,7,8,14,15],[0,2,4,5,6,7,8,14,16],[0,2,4,5,6,7,8,15,16],[0,2,4,5,6,7,9,10,11],[0,2,4,5,6,7,9,10,11,12,13,14,15],[0,2,4,5,6,7,9,10,11,12,13,14,16],[0,2,4,5,6,7,9,10,11,12,13,15,16],[0,2,4,5,6,7,9,10,11,12,14,15,16],[0,2,4,5,6,7,9,10,11,13,14,15,16],[0,2,4,5,6,7,9,10,12],[0,2,4,5,6,7,9,10,12,13,14,15,16],[0,2,4,5,6,7,9,10,13],[0,2,4,5,6,7,9,10,14],[0,2,4,5,6,7,9,10,15],[0,2,4,5,6,7,9,10,16],[0,2,4,5,6,7,9,11,12],[0,2,4,5,6,7,9,11,12,13,14,15,16],[0,2,4,5,6,7,9,11,13],[0,2,4,5,6,7,9,11,14],[0,2,4,5,6,7,9,11,15],[0,2,4,5,6,7,9,11,16],[0,2,4,5,6,7,9,12,13],[0,2,4,5,6,7,9,12,14],[0,2,4,5,6,7,9,12,15],[0,2,4,5,6,7,9,12,16],[0,2,4,5,6,7,9,13,14],[0,2,4,5,6,7,9,13,15],[0,2,4,5,6,7,9,13,16],[0,2,4,5,6,7,9,14,15],[0,2,4,5,6,7,9,14,16],[0,2,4,5,6,7,9,15,16],[0,2,4,5,6,8,9,10,11],[0,2,4,5,6,8,9,10,11,12,13,14,15],[0,2,4,5,6,8,9,10,11,12,13,14,16],[0,2,4,5,6,8,9,10,11,12,13,15,16],[0,2,4,5,6,8,9,10,11,12,14,15,16],[0,2,4,5,6,8,9,10,11,13,14,15,16],[0,2,4,5,6,8,9,10,12],[0,2,4,5,6,8,9,10,12,13,14,15,16],[0,2,4,5,6,8,9,10,13],[0,2,4,5,6,8,9,10,14],[0,2,4,5,6,8,9,10,15],[0,2,4,5,6,8,9,10,16],[0,2,4,5,6,8,9,11,12],[0,2,4,5,6,8,9,11,12,13,14,15,16],[0,2,4,5,6,8,9,11,13],[0,2,4,5,6,8,9,11,14],[0,2,4,5,6,8,9,11,15],[0,2,4,5,6,8,9,11,16],[0,2,4,5,6,8,9,12,13],[0,2,4,5,6,8,9,12,14],[0,2,4,5,6,8,9,12,15],[0,2,4,5,6,8,9,12,16],[0,2,4,5,6,8,9,13,14],[0,2,4,5,6,8,9,13,15],[0,2,4,5,6,8,9,13,16],[0,2,4,5,6,8,9,14,15],[0,2,4,5,6,8,9,14,16],[0,2,4,5,6,8,9,15,16],[0,2,4,5,7,8,9,10,11],[0,2,4,5,7,8,9,10,11,12,13,14,15],[0,2,4,5,7,8,9,10,11,12,13,14,16],[0,2,4,5,7,8,9,10,11,12,13,15,16],[0,2,4,5,7,8,9,10,11,12,14,15,16],[0,2,4,5,7,8,9,10,11,13,14,15,16],[0,2,4,5,7,8,9,10,12],[0,2,4,5,7,8,9,10,12,13,14,15,16],[0,2,4,5,7,8,9,10,13],[0,2,4,5,7,8,9,10,14],[0,2,4,5,7,8,9,10,15],[0,2,4,5,7,8,9,10,16],[0,2,4,5,7,8,9,11,12],[0,2,4,5,7,8,9,11,12,13,14,15,16],[0,2,4,5,7,8,9,11,13],[0,2,4,5,7,8,9,11,14],[0,2,4,5,7,8,9,11,15],[0,2,4,5,7,8,9,11,16],[0,2,4,5,7,8,9,12,13],[0,2,4,5,7,8,9,12,14],[0,2,4,5,7,8,9,12,15],[0,2,4,5,7,8,9,12,16],[0,2,4,5,7,8,9,13,14],[0,2,4,5,7,8,9,13,15],[0,2,4,5,7,8,9,13,16],[0,2,4,5,7,8,9,14,15],[0,2,4,5,7,8,9,14,16],[0,2,4,5,7,8,9,15,16],[0,2,4,6,7,8,9,10,11],[0,2,4,6,7,8,9,10,11,12,13,14,15],[0,2,4,6,7,8,9,10,11,12,13,14,16],[0,2,4,6,7,8,9,10,11,12,13,15,16],[0,2,4,6,7,8,9,10,11,12,14,15,16],[0,2,4,6,7,8,9,10,11,13,14,15,16],[0,2,4,6,7,8,9,10,12],[0,2,4,6,7,8,9,10,12,13,14,15,16],[0,2,4,6,7,8,9,10,13],[0,2,4,6,7,8,9,10,14],[0,2,4,6,7,8,9,10,15],[0,2,4,6,7,8,9,10,16],[0,2,4,6,7,8,9,11,12],[0,2,4,6,7,8,9,11,12,13,14,15,16],[0,2,4,6,7,8,9,11,13],[0,2,4,6,7,8,9,11,14],[0,2,4,6,7,8,9,11,15],[0,2,4,6,7,8,9,11,16],[0,2,4,6,7,8,9,12,13],[0,2,4,6,7,8,9,12,14],[0,2,4,6,7,8,9,12,15],[0,2,4,6,7,8,9,12,16],[0,2,4,6,7,8,9,13,14],[0,2,4,6,7,8,9,13,15],[0,2,4,6,7,8,9,13,16],[0,2,4,6,7,8,9,14,15],[0,2,4,6,7,8,9,14,16],[0,2,4,6,7,8,9,15,16],[0,2,5,6,7,8,9,10,11],[0,2,5,6,7,8,9,10,11,12,13,14,15],[0,2,5,6,7,8,9,10,11,12,13,14,16],[0,2,5,6,7,8,9,10,11,12,13,15,16],[0,2,5,6,7,8,9,10,11,12,14,15,16],[0,2,5,6,7,8,9,10,11,13,14,15,16],[0,2,5,6,7,8,9,10,12],[0,2,5,6,7,8,9,10,12,13,14,15,16],[0,2,5,6,7,8,9,10,13],[0,2,5,6,7,8,9,10,14],[0,2,5,6,7,8,9,10,15],[0,2,5,6,7,8,9,10,16],[0,2,5,6,7,8,9,11,12],[0,2,5,6,7,8,9,11,12,13,14,15,16],[0,2,5,6,7,8,9,11,13],[0,2,5,6,7,8,9,11,14],[0,2,5,6,7,8,9,11,15],[0,2,5,6,7,8,9,11,16],[0,2,5,6,7,8,9,12,13],[0,2,5,6,7,8,9,12,14],[0,2,5,6,7,8,9,12,15],[0,2,5,6,7,8,9,12,16],[0,2,5,6,7,8,9,13,14],[0,2,5,6,7,8,9,13,15],[0,2,5,6,7,8,9,13,16],[0,2,5,6,7,8,9,14,15],[0,2,5,6,7,8,9,14,16],[0,2,5,6,7,8,9,15,16],[0,3,4,5,6,7,8,10,11],[0,3,4,5,6,7,8,10,11,12,13,14,15],[0,3,4,5,6,7,8,10,11,12,13,14,16],[0,3,4,5,6,7,8,10,11,12,13,15,16],[0,3,4,5,6,7,8,10,11,12,14,15,16],[0,3,4,5,6,7,8,10,11,13,14,15,16],[0,3,4,5,6,7,8,10,12],[0,3,4,5,6,7,8,10,12,13,14,15,16],[0,3,4,5,6,7,8,10,13],[0,3,4,5,6,7,8,10,14],[0,3,4,5,6,7,8,10,15],[0,3,4,5,6,7,8,10,16],[0,3,4,5,6,7,8,11,12],[0,3,4,5,6,7,8,11,12,13,14,15,16],[0,3,4,5,6,7,8,11,13],[0,3,4,5,6,7,8,11,14],[0,3,4,5,6,7,8,11,15],[0,3,4,5,6,7,8,11,16],[0,3,4,5,6,7,8,12,13],[0,3,4,5,6,7,8,12,14],[0,3,4,5,6,7,8,12,15],[0,3,4,5,6,7,8,12,16],[0,3,4,5,6,7,8,13,14],[0,3,4,5,6,7,8,13,15],[0,3,4,5,6,7,8,13,16],[0,3,4,5,6,7,8,14,15],[0,3,4,5,6,7,8,14,16],[0,3,4,5,6,7,8,15,16],[0,3,4,5,6,7,9,10,11],[0,3,4,5,6,7,9,10,11,12,13,14,15],[0,3,4,5,6,7,9,10,11,12,13,14,16],[0,3,4,5,6,7,9,10,11,12,13,15,16],[0,3,4,5,6,7,9,10,11,12,14,15,16],[0,3,4,5,6,7,9,10,11,13,14,15,16],[0,3,4,5,6,7,9,10,12],[0,3,4,5,6,7,9,10,12,13,14,15,16],[0,3,4,5,6,7,9,10,13],[0,3,4,5,6,7,9,10,14],[0,3,4,5,6,7,9,10,15],[0,3,4,5,6,7,9,10,16],[0,3,4,5,6,7,9,11,12],[0,3,4,5,6,7,9,11,12,13,14,15,16],[0,3,4,5,6,7,9,11,13],[0,3,4,5,6,7,9,11,14],[0,3,4,5,6,7,9,11,15],[0,3,4,5,6,7,9,11,16],[0,3,4,5,6,7,9,12,13],[0,3,4,5,6,7,9,12,14],[0,3,4,5,6,7,9,12,15],[0,3,4,5,6,7,9,12,16],[0,3,4,5,6,7,9,13,14],[0,3,4,5,6,7,9,13,15],[0,3,4,5,6,7,9,13,16],[0,3,4,5,6,7,9,14,15],[0,3,4,5,6,7,9,14,16],[0,3,4,5,6,7,9,15,16],[0,3,4,5,6,8,9,10,11],[0,3,4,5,6,8,9,10,11,12,13,14,15],[0,3,4,5,6,8,9,10,11,12,13,14,16],[0,3,4,5,6,8,9,10,11,12,13,15,16],[0,3,4,5,6,8,9,10,11,12,14,15,16],[0,3,4,5,6,8,9,10,11,13,14,15,16],[0,3,4,5,6,8,9,10,12],[0,3,4,5,6,8,9,10,12,13,14,15,16],[0,3,4,5,6,8,9,10,13],[0,3,4,5,6,8,9,10,14],[0,3,4,5,6,8,9,10,15],[0,3,4,5,6,8,9,10,16],[0,3,4,5,6,8,9,11,12],[0,3,4,5,6,8,9,11,12,13,14,15,16],[0,3,4,5,6,8,9,11,13],[0,3,4,5,6,8,9,11,14],[0,3,4,5,6,8,9,11,15],[0,3,4,5,6,8,9,11,16],[0,3,4,5,6,8,9,12,13],[0,3,4,5,6,8,9,12,14],[0,3,4,5,6,8,9,12,15],[0,3,4,5,6,8,9,12,16],[0,3,4,5,6,8,9,13,14],[0,3,4,5,6,8,9,13,15],[0,3,4,5,6,8,9,13,16],[0,3,4,5,6,8,9,14,15],[0,3,4,5,6,8,9,14,16],[0,3,4,5,6,8,9,15,16],[0,3,4,5,7,8,9,10,11],[0,3,4,5,7,8,9,10,11,12,13,14,15],[0,3,4,5,7,8,9,10,11,12,13,14,16],[0,3,4,5,7,8,9,10,11,12,13,15,16],[0,3,4,5,7,8,9,10,11,12,14,15,16],[0,3,4,5,7,8,9,10,11,13,14,15,16],[0,3,4,5,7,8,9,10,12],[0,3,4,5,7,8,9,10,12,13,14,15,16],[0,3,4,5,7,8,9,10,13],[0,3,4,5,7,8,9,10,14],[0,3,4,5,7,8,9,10,15],[0,3,4,5,7,8,9,10,16],[0,3,4,5,7,8,9,11,12],[0,3,4,5,7,8,9,11,12,13,14,15,16],[0,3,4,5,7,8,9,11,13],[0,3,4,5,7,8,9,11,14],[0,3,4,5,7,8,9,11,15],[0,3,4,5,7,8,9,11,16],[0,3,4,5,7,8,9,12,13],[0,3,4,5,7,8,9,12,14],[0,3,4,5,7,8,9,12,15],[0,3,4,5,7,8,9,12,16],[0,3,4,5,7,8,9,13,14],[0,3,4,5,7,8,9,13,15],[0,3,4,5,7,8,9,13,16],[0,3,4,5,7,8,9,14,15],[0,3,4,5,7,8,9,14,16],[0,3,4,5,7,8,9,15,16],[0,3,4,6,7,8,9,10,11],[0,3,4,6,7,8,9,10,11,12,13,14,15],[0,3,4,6,7,8,9,10,11,12,13,14,16],[0,3,4,6,7,8,9,10,11,12,13,15,16],[0,3,4,6,7,8,9,10,11,12,14,15,16],[0,3,4,6,7,8,9,10,11,13,14,15,16],[0,3,4,6,7,8,9,10,12],[0,3,4,6,7,8,9,10,12,13,14,15,16],[0,3,4,6,7,8,9,10,13],[0,3,4,6,7,8,9,10,14],[0,3,4,6,7,8,9,10,15],[0,3,4,6,7,8,9,10,16],[0,3,4,6,7,8,9,11,12],[0,3,4,6,7,8,9,11,12,13,14,15,16],[0,3,4,6,7,8,9,11,13],[0,3,4,6,7,8,9,11,14],[0,3,4,6,7,8,9,11,15],[0,3,4,6,7,8,9,11,16],[0,3,4,6,7,8,9,12,13],[0,3,4,6,7,8,9,12,14],[0,3,4,6,7,8,9,12,15],[0,3,4,6,7,8,9,12,16],[0,3,4,6,7,8,9,13,14],[0,3,4,6,7,8,9,13,15],[0,3,4,6,7,8,9,13,16],[0,3,4,6,7,8,9,14,15],[0,3,4,6,7,8,9,14,16],[0,3,4,6,7,8,9,15,16],[0,3,5,6,7,8,9,10,11],[0,3,5,6,7,8,9,10,11,12,13,14,15],[0,3,5,6,7,8,9,10,11,12,13,14,16],[0,3,5,6,7,8,9,10,11,12,13,15,16],[0,3,5,6,7,8,9,10,11,12,14,15,16],[0,3,5,6,7,8,9,10,11,13,14,15,16],[0,3,5,6,7,8,9,10,12],[0,3,5,6,7,8,9,10,12,13,14,15,16],[0,3,5,6,7,8,9,10,13],[0,3,5,6,7,8,9,10,14],[0,3,5,6,7,8,9,10,15],[0,3,5,6,7,8,9,10,16],[0,3,5,6,7,8,9,11,12],[0,3,5,6,7,8,9,11,12,13,14,15,16],[0,3,5,6,7,8,9,11,13],[0,3,5,6,7,8,9,11,14],[0,3,5,6,7,8,9,11,15],[0,3,5,6,7,8,9,11,16],[0,3,5,6,7,8,9,12,13],[0,3,5,6,7,8,9,12,14],[0,3,5,6,7,8,9,12,15],[0,3,5,6,7,8,9,12,16],[0,3,5,6,7,8,9,13,14],[0,3,5,6,7,8,9,13,15],[0,3,5,6,7,8,9,13,16],[0,3,5,6,7,8,9,14,15],[0,3,5,6,7,8,9,14,16],[0,3,5,6,7,8,9,15,16],[0,4,5,6,7,8,9,10,11],[0,4,5,6,7,8,9,10,11,12,13,14,15],[0,4,5,6,7,8,9,10,11,12,13,14,16],[0,4,5,6,7,8,9,10,11,12,13,15,16],[0,4,5,6,7,8,9,10,11,12,14,15,16],[0,4,5,6,7,8,9,10,11,13,14,15,16],[0,4,5,6,7,8,9,10,12],[0,4,5,6,7,8,9,10,12,13,14,15,16],[0,4,5,6,7,8,9,10,13],[0,4,5,6,7,8,9,10,14],[0,4,5,6,7,8,9,10,15],[0,4,5,6,7,8,9,10,16],[0,4,5,6,7,8,9,11,12],[0,4,5,6,7,8,9,11,12,13,14,15,16],[0,4,5,6,7,8,9,11,13],[0,4,5,6,7,8,9,11,14],[0,4,5,6,7,8,9,11,15],[0,4,5,6,7,8,9,11,16],[0,4,5,6,7,8,9,12,13],[0,4,5,6,7,8,9,12,14],[0,4,5,6,7,8,9,12,15],[0,4,5,6,7,8,9,12,16],[0,4,5,6,7,8,9,13,14],[0,4,5,6,7,8,9,13,15],[0,4,5,6,7,8,9,13,16],[0,4,5,6,7,8,9,14,15],[0,4,5,6,7,8,9,14,16],[0,4,5,6,7,8,9,15,16],[0,10,11,12,13],[0,10,11,12,14],[0,10,11,12,15],[0,10,11,12,16],[0,10,11,13,14],[0,10,11,13,15],[0,10,11,13,16],[0,10,11,14,15],[0,10,11,14,16],[0,10,11,15,16],[0,10,12,13,14],[0,10,12,13,15],[0,10,12,13,16],[0,10,12,14,15],[0,10,12,14,16],[0,10,12,15,16],[0,10,13,14,15],[0,10,13,14,16],[0,10,13,15,16],[0,10,14,15,16],[0,11,12,13,14],[0,11,12,13,15],[0,11,12,13,16],[0,11,12,14,15],[0,11,12,14,16],[0,11,12,15,16],[0,11,13,14,15],[0,11,13,14,16],[0,11,13,15,16],[0,11,14,15,16],[0,12,13,14,15],[0,12,13,14,16],[0,12,13,15,16],[0,12,14,15,16],[0,13,14,15,16],[1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,10,11,12,13,14,15],[1,2,3,4,5,6,7,10,11,12,13,14,16],[1,2,3,4,5,6,7,10,11,12,13,15,16],[1,2,3,4,5,6,7,10,11,12,14,15,16],[1,2,3,4,5,6,7,10,11,13,14,15,16],[1,2,3,4,5,6,7,10,12],[1,2,3,4,5,6,7,10,12,13,14,15,16],[1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,10,14],[1,2,3,4,5,6,7,10,15],[1,2,3,4,5,6,7,10,16],[1,2,3,4,5,6,7,11,12],[1,2,3,4,5,6,7,11,12,13,14,15,16],[1,2,3,4,5,6,7,11,13],[1,2,3,4,5,6,7,11,14],[1,2,3,4,5,6,7,11,15],[1,2,3,4,5,6,7,11,16],[1,2,3,4,5,6,7,12,13],[1,2,3,4,5,6,7,12,14],[1,2,3,4,5,6,7,12,15],[1,2,3,4,5,6,7,12,16],[1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,7,13,15],[1,2,3,4,5,6,7,13,16],[1,2,3,4,5,6,7,14,15],[1,2,3,4,5,6,7,14,16],[1,2,3,4,5,6,7,15,16],[1,2,3,4,5,6,8,10,11],[1,2,3,4,5,6,8,10,11,12,13,14,15],[1,2,3,4,5,6,8,10,11,12,13,14,16],[1,2,3,4,5,6,8,10,11,12,13,15,16],[1,2,3,4,5,6,8,10,11,12,14,15,16],[1,2,3,4,5,6,8,10,11,13,14,15,16],[1,2,3,4,5,6,8,10,12],[1,2,3,4,5,6,8,10,12,13,14,15,16],[1,2,3,4,5,6,8,10,13],[1,2,3,4,5,6,8,10,14],[1,2,3,4,5,6,8,10,15],[1,2,3,4,5,6,8,10,16],[1,2,3,4,5,6,8,11,12],[1,2,3,4,5,6,8,11,12,13,14,15,16],[1,2,3,4,5,6,8,11,13],[1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,8,11,15],[1,2,3,4,5,6,8,11,16],[1,2,3,4,5,6,8,12,13],[1,2,3,4,5,6,8,12,14],[1,2,3,4,5,6,8,12,15],[1,2,3,4,5,6,8,12,16],[1,2,3,4,5,6,8,13,14],[1,2,3,4,5,6,8,13,15],[1,2,3,4,5,6,8,13,16],[1,2,3,4,5,6,8,14,15],[1,2,3,4,5,6,8,14,16],[1,2,3,4,5,6,8,15,16],[1,2,3,4,5,6,9,10,11],[1,2,3,4,5,6,9,10,11,12,13,14,15],[1,2,3,4,5,6,9,10,11,12,13,14,16],[1,2,3,4,5,6,9,10,11,12,13,15,16],[1,2,3,4,5,6,9,10,11,12,14,15,16],[1,2,3,4,5,6,9,10,11,13,14,15,16],[1,2,3,4,5,6,9,10,12],[1,2,3,4,5,6,9,10,12,13,14,15,16],[1,2,3,4,5,6,9,10,13],[1,2,3,4,5,6,9,10,14],[1,2,3,4,5,6,9,10,15],[1,2,3,4,5,6,9,10,16],[1,2,3,4,5,6,9,11,12],[1,2,3,4,5,6,9,11,12,13,14,15,16],[1,2,3,4,5,6,9,11,13],[1,2,3,4,5,6,9,11,14],[1,2,3,4,5,6,9,11,15],[1,2,3,4,5,6,9,11,16],[1,2,3,4,5,6,9,12,13],[1,2,3,4,5,6,9,12,14],[1,2,3,4,5,6,9,12,15],[1,2,3,4,5,6,9,12,16],[1,2,3,4,5,6,9,13,14],[1,2,3,4,5,6,9,13,15],[1,2,3,4,5,6,9,13,16],[1,2,3,4,5,6,9,14,15],[1,2,3,4,5,6,9,14,16],[1,2,3,4,5,6,9,15,16],[1,2,3,4,5,7,8,10,11],[1,2,3,4,5,7,8,10,11,12,13,14,15],[1,2,3,4,5,7,8,10,11,12,13,14,16],[1,2,3,4,5,7,8,10,11,12,13,15,16],[1,2,3,4,5,7,8,10,11,12,14,15,16],[1,2,3,4,5,7,8,10,11,13,14,15,16],[1,2,3,4,5,7,8,10,12],[1,2,3,4,5,7,8,10,12,13,14,15,16],[1,2,3,4,5,7,8,10,13],[1,2,3,4,5,7,8,10,14],[1,2,3,4,5,7,8,10,15],[1,2,3,4,5,7,8,10,16],[1,2,3,4,5,7,8,11,12],[1,2,3,4,5,7,8,11,12,13,14,15,16],[1,2,3,4,5,7,8,11,13],[1,2,3,4,5,7,8,11,14],[1,2,3,4,5,7,8,11,15],[1,2,3,4,5,7,8,11,16],[1,2,3,4,5,7,8,12,13],[1,2,3,4,5,7,8,12,14],[1,2,3,4,5,7,8,12,15],[1,2,3,4,5,7,8,12,16],[1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,8,13,15],[1,2,3,4,5,7,8,13,16],[1,2,3,4,5,7,8,14,15],[1,2,3,4,5,7,8,14,16],[1,2,3,4,5,7,8,15,16],[1,2,3,4,5,7,9,10,11],[1,2,3,4,5,7,9,10,11,12,13,14,15],[1,2,3,4,5,7,9,10,11,12,13,14,16],[1,2,3,4,5,7,9,10,11,12,13,15,16],[1,2,3,4,5,7,9,10,11,12,14,15,16],[1,2,3,4,5,7,9,10,11,13,14,15,16],[1,2,3,4,5,7,9,10,12],[1,2,3,4,5,7,9,10,12,13,14,15,16],[1,2,3,4,5,7,9,10,13],[1,2,3,4,5,7,9,10,14],[1,2,3,4,5,7,9,10,15],[1,2,3,4,5,7,9,10,16],[1,2,3,4,5,7,9,11,12],[1,2,3,4,5,7,9,11,12,13,14,15,16],[1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,9,11,14],[1,2,3,4,5,7,9,11,15],[1,2,3,4,5,7,9,11,16],[1,2,3,4,5,7,9,12,13],[1,2,3,4,5,7,9,12,14],[1,2,3,4,5,7,9,12,15],[1,2,3,4,5,7,9,12,16],[1,2,3,4,5,7,9,13,14],[1,2,3,4,5,7,9,13,15],[1,2,3,4,5,7,9,13,16],[1,2,3,4,5,7,9,14,15],[1,2,3,4,5,7,9,14,16],[1,2,3,4,5,7,9,15,16],[1,2,3,4,5,8,9,10,11],[1,2,3,4,5,8,9,10,11,12,13,14,15],[1,2,3,4,5,8,9,10,11,12,13,14,16],[1,2,3,4,5,8,9,10,11,12,13,15,16],[1,2,3,4,5,8,9,10,11,12,14,15,16],[1,2,3,4,5,8,9,10,11,13,14,15,16],[1,2,3,4,5,8,9,10,12],[1,2,3,4,5,8,9,10,12,13,14,15,16],[1,2,3,4,5,8,9,10,13],[1,2,3,4,5,8,9,10,14],[1,2,3,4,5,8,9,10,15],[1,2,3,4,5,8,9,10,16],[1,2,3,4,5,8,9,11,12],[1,2,3,4,5,8,9,11,12,13,14,15,16],[1,2,3,4,5,8,9,11,13],[1,2,3,4,5,8,9,11,14],[1,2,3,4,5,8,9,11,15],[1,2,3,4,5,8,9,11,16],[1,2,3,4,5,8,9,12,13],[1,2,3,4,5,8,9,12,14],[1,2,3,4,5,8,9,12,15],[1,2,3,4,5,8,9,12,16],[1,2,3,4,5,8,9,13,14],[1,2,3,4,5,8,9,13,15],[1,2,3,4,5,8,9,13,16],[1,2,3,4,5,8,9,14,15],[1,2,3,4,5,8,9,14,16],[1,2,3,4,5,8,9,15,16],[1,2,3,4,6,7,8,10,11],[1,2,3,4,6,7,8,10,11,12,13,14,15],[1,2,3,4,6,7,8,10,11,12,13,14,16],[1,2,3,4,6,7,8,10,11,12,13,15,16],[1,2,3,4,6,7,8,10,11,12,14,15,16],[1,2,3,4,6,7,8,10,11,13,14,15,16],[1,2,3,4,6,7,8,10,12],[1,2,3,4,6,7,8,10,12,13,14,15,16],[1,2,3,4,6,7,8,10,13],[1,2,3,4,6,7,8,10,14],[1,2,3,4,6,7,8,10,15],[1,2,3,4,6,7,8,10,16],[1,2,3,4,6,7,8,11,12],[1,2,3,4,6,7,8,11,12,13,14,15,16],[1,2,3,4,6,7,8,11,13],[1,2,3,4,6,7,8,11,14],[1,2,3,4,6,7,8,11,15],[1,2,3,4,6,7,8,11,16],[1,2,3,4,6,7,8,12,13],[1,2,3,4,6,7,8,12,14],[1,2,3,4,6,7,8,12,15],[1,2,3,4,6,7,8,12,16],[1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,8,13,15],[1,2,3,4,6,7,8,13,16],[1,2,3,4,6,7,8,14,15],[1,2,3,4,6,7,8,14,16],[1,2,3,4,6,7,8,15,16],[1,2,3,4,6,7,9,10,11],[1,2,3,4,6,7,9,10,11,12,13,14,15],[1,2,3,4,6,7,9,10,11,12,13,14,16],[1,2,3,4,6,7,9,10,11,12,13,15,16],[1,2,3,4,6,7,9,10,11,12,14,15,16],[1,2,3,4,6,7,9,10,11,13,14,15,16],[1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,9,10,12,13,14,15,16],[1,2,3,4,6,7,9,10,13],[1,2,3,4,6,7,9,10,14],[1,2,3,4,6,7,9,10,15],[1,2,3,4,6,7,9,10,16],[1,2,3,4,6,7,9,11,12],[1,2,3,4,6,7,9,11,12,13,14,15,16],[1,2,3,4,6,7,9,11,13],[1,2,3,4,6,7,9,11,14],[1,2,3,4,6,7,9,11,15],[1,2,3,4,6,7,9,11,16],[1,2,3,4,6,7,9,12,13],[1,2,3,4,6,7,9,12,14],[1,2,3,4,6,7,9,12,15],[1,2,3,4,6,7,9,12,16],[1,2,3,4,6,7,9,13,14],[1,2,3,4,6,7,9,13,15],[1,2,3,4,6,7,9,13,16],[1,2,3,4,6,7,9,14,15],[1,2,3,4,6,7,9,14,16],[1,2,3,4,6,7,9,15,16],[1,2,3,4,6,8,9,10,11],[1,2,3,4,6,8,9,10,11,12,13,14,15],[1,2,3,4,6,8,9,10,11,12,13,14,16],[1,2,3,4,6,8,9,10,11,12,13,15,16],[1,2,3,4,6,8,9,10,11,12,14,15,16],[1,2,3,4,6,8,9,10,11,13,14,15,16],[1,2,3,4,6,8,9,10,12],[1,2,3,4,6,8,9,10,12,13,14,15,16],[1,2,3,4,6,8,9,10,13],[1,2,3,4,6,8,9,10,14],[1,2,3,4,6,8,9,10,15],[1,2,3,4,6,8,9,10,16],[1,2,3,4,6,8,9,11,12],[1,2,3,4,6,8,9,11,12,13,14,15,16],[1,2,3,4,6,8,9,11,13],[1,2,3,4,6,8,9,11,14],[1,2,3,4,6,8,9,11,15],[1,2,3,4,6,8,9,11,16],[1,2,3,4,6,8,9,12,13],[1,2,3,4,6,8,9,12,14],[1,2,3,4,6,8,9,12,15],[1,2,3,4,6,8,9,12,16],[1,2,3,4,6,8,9,13,14],[1,2,3,4,6,8,9,13,15],[1,2,3,4,6,8,9,13,16],[1,2,3,4,6,8,9,14,15],[1,2,3,4,6,8,9,14,16],[1,2,3,4,6,8,9,15,16],[1,2,3,4,7,8,9,10,11],[1,2,3,4,7,8,9,10,11,12,13,14,15],[1,2,3,4,7,8,9,10,11,12,13,14,16],[1,2,3,4,7,8,9,10,11,12,13,15,16],[1,2,3,4,7,8,9,10,11,12,14,15,16],[1,2,3,4,7,8,9,10,11,13,14,15,16],[1,2,3,4,7,8,9,10,12],[1,2,3,4,7,8,9,10,12,13,14,15,16],[1,2,3,4,7,8,9,10,13],[1,2,3,4,7,8,9,10,14],[1,2,3,4,7,8,9,10,15],[1,2,3,4,7,8,9,10,16],[1,2,3,4,7,8,9,11,12],[1,2,3,4,7,8,9,11,12,13,14,15,16],[1,2,3,4,7,8,9,11,13],[1,2,3,4,7,8,9,11,14],[1,2,3,4,7,8,9,11,15],[1,2,3,4,7,8,9,11,16],[1,2,3,4,7,8,9,12,13],[1,2,3,4,7,8,9,12,14],[1,2,3,4,7,8,9,12,15],[1,2,3,4,7,8,9,12,16],[1,2,3,4,7,8,9,13,14],[1,2,3,4,7,8,9,13,15],[1,2,3,4,7,8,9,13,16],[1,2,3,4,7,8,9,14,15],[1,2,3,4,7,8,9,14,16],[1,2,3,4,7,8,9,15,16],[1,2,3,5,6,7,8,10,11],[1,2,3,5,6,7,8,10,11,12,13,14,15],[1,2,3,5,6,7,8,10,11,12,13,14,16],[1,2,3,5,6,7,8,10,11,12,13,15,16],[1,2,3,5,6,7,8,10,11,12,14,15,16],[1,2,3,5,6,7,8,10,11,13,14,15,16],[1,2,3,5,6,7,8,10,12],[1,2,3,5,6,7,8,10,12,13,14,15,16],[1,2,3,5,6,7,8,10,13],[1,2,3,5,6,7,8,10,14],[1,2,3,5,6,7,8,10,15],[1,2,3,5,6,7,8,10,16],[1,2,3,5,6,7,8,11,12],[1,2,3,5,6,7,8,11,12,13,14,15,16],[1,2,3,5,6,7,8,11,13],[1,2,3,5,6,7,8,11,14],[1,2,3,5,6,7,8,11,15],[1,2,3,5,6,7,8,11,16],[1,2,3,5,6,7,8,12,13],[1,2,3,5,6,7,8,12,14],[1,2,3,5,6,7,8,12,15],[1,2,3,5,6,7,8,12,16],[1,2,3,5,6,7,8,13,14],[1,2,3,5,6,7,8,13,15],[1,2,3,5,6,7,8,13,16],[1,2,3,5,6,7,8,14,15],[1,2,3,5,6,7,8,14,16],[1,2,3,5,6,7,8,15,16],[1,2,3,5,6,7,9,10,11],[1,2,3,5,6,7,9,10,11,12,13,14,15],[1,2,3,5,6,7,9,10,11,12,13,14,16],[1,2,3,5,6,7,9,10,11,12,13,15,16],[1,2,3,5,6,7,9,10,11,12,14,15,16],[1,2,3,5,6,7,9,10,11,13,14,15,16],[1,2,3,5,6,7,9,10,12],[1,2,3,5,6,7,9,10,12,13,14,15,16],[1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,10,14],[1,2,3,5,6,7,9,10,15],[1,2,3,5,6,7,9,10,16],[1,2,3,5,6,7,9,11,12],[1,2,3,5,6,7,9,11,12,13,14,15,16],[1,2,3,5,6,7,9,11,13],[1,2,3,5,6,7,9,11,14],[1,2,3,5,6,7,9,11,15],[1,2,3,5,6,7,9,11,16],[1,2,3,5,6,7,9,12,13],[1,2,3,5,6,7,9,12,14],[1,2,3,5,6,7,9,12,15],[1,2,3,5,6,7,9,12,16],[1,2,3,5,6,7,9,13,14],[1,2,3,5,6,7,9,13,15],[1,2,3,5,6,7,9,13,16],[1,2,3,5,6,7,9,14,15],[1,2,3,5,6,7,9,14,16],[1,2,3,5,6,7,9,15,16],[1,2,3,5,6,8,9,10,11],[1,2,3,5,6,8,9,10,11,12,13,14,15],[1,2,3,5,6,8,9,10,11,12,13,14,16],[1,2,3,5,6,8,9,10,11,12,13,15,16],[1,2,3,5,6,8,9,10,11,12,14,15,16],[1,2,3,5,6,8,9,10,11,13,14,15,16],[1,2,3,5,6,8,9,10,12],[1,2,3,5,6,8,9,10,12,13,14,15,16],[1,2,3,5,6,8,9,10,13],[1,2,3,5,6,8,9,10,14],[1,2,3,5,6,8,9,10,15],[1,2,3,5,6,8,9,10,16],[1,2,3,5,6,8,9,11,12],[1,2,3,5,6,8,9,11,12,13,14,15,16],[1,2,3,5,6,8,9,11,13],[1,2,3,5,6,8,9,11,14],[1,2,3,5,6,8,9,11,15],[1,2,3,5,6,8,9,11,16],[1,2,3,5,6,8,9,12,13],[1,2,3,5,6,8,9,12,14],[1,2,3,5,6,8,9,12,15],[1,2,3,5,6,8,9,12,16],[1,2,3,5,6,8,9,13,14],[1,2,3,5,6,8,9,13,15],[1,2,3,5,6,8,9,13,16],[1,2,3,5,6,8,9,14,15],[1,2,3,5,6,8,9,14,16],[1,2,3,5,6,8,9,15,16],[1,2,3,5,7,8,9,10,11],[1,2,3,5,7,8,9,10,11,12,13,14,15],[1,2,3,5,7,8,9,10,11,12,13,14,16],[1,2,3,5,7,8,9,10,11,12,13,15,16],[1,2,3,5,7,8,9,10,11,12,14,15,16],[1,2,3,5,7,8,9,10,11,13,14,15,16],[1,2,3,5,7,8,9,10,12],[1,2,3,5,7,8,9,10,12,13,14,15,16],[1,2,3,5,7,8,9,10,13],[1,2,3,5,7,8,9,10,14],[1,2,3,5,7,8,9,10,15],[1,2,3,5,7,8,9,10,16],[1,2,3,5,7,8,9,11,12],[1,2,3,5,7,8,9,11,12,13,14,15,16],[1,2,3,5,7,8,9,11,13],[1,2,3,5,7,8,9,11,14],[1,2,3,5,7,8,9,11,15],[1,2,3,5,7,8,9,11,16],[1,2,3,5,7,8,9,12,13],[1,2,3,5,7,8,9,12,14],[1,2,3,5,7,8,9,12,15],[1,2,3,5,7,8,9,12,16],[1,2,3,5,7,8,9,13,14],[1,2,3,5,7,8,9,13,15],[1,2,3,5,7,8,9,13,16],[1,2,3,5,7,8,9,14,15],[1,2,3,5,7,8,9,14,16],[1,2,3,5,7,8,9,15,16],[1,2,3,6,7,8,9,10,11],[1,2,3,6,7,8,9,10,11,12,13,14,15],[1,2,3,6,7,8,9,10,11,12,13,14,16],[1,2,3,6,7,8,9,10,11,12,13,15,16],[1,2,3,6,7,8,9,10,11,12,14,15,16],[1,2,3,6,7,8,9,10,11,13,14,15,16],[1,2,3,6,7,8,9,10,12],[1,2,3,6,7,8,9,10,12,13,14,15,16],[1,2,3,6,7,8,9,10,13],[1,2,3,6,7,8,9,10,14],[1,2,3,6,7,8,9,10,15],[1,2,3,6,7,8,9,10,16],[1,2,3,6,7,8,9,11,12],[1,2,3,6,7,8,9,11,12,13,14,15,16],[1,2,3,6,7,8,9,11,13],[1,2,3,6,7,8,9,11,14],[1,2,3,6,7,8,9,11,15],[1,2,3,6,7,8,9,11,16],[1,2,3,6,7,8,9,12,13],[1,2,3,6,7,8,9,12,14],[1,2,3,6,7,8,9,12,15],[1,2,3,6,7,8,9,12,16],[1,2,3,6,7,8,9,13,14],[1,2,3,6,7,8,9,13,15],[1,2,3,6,7,8,9,13,16],[1,2,3,6,7,8,9,14,15],[1,2,3,6,7,8,9,14,16],[1,2,3,6,7,8,9,15,16],[1,2,4,5,6,7,8,10,11],[1,2,4,5,6,7,8,10,11,12,13,14,15],[1,2,4,5,6,7,8,10,11,12,13,14,16],[1,2,4,5,6,7,8,10,11,12,13,15,16],[1,2,4,5,6,7,8,10,11,12,14,15,16],[1,2,4,5,6,7,8,10,11,13,14,15,16],[1,2,4,5,6,7,8,10,12],[1,2,4,5,6,7,8,10,12,13,14,15,16],[1,2,4,5,6,7,8,10,13],[1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,8,10,15],[1,2,4,5,6,7,8,10,16],[1,2,4,5,6,7,8,11,12],[1,2,4,5,6,7,8,11,12,13,14,15,16],[1,2,4,5,6,7,8,11,13],[1,2,4,5,6,7,8,11,14],[1,2,4,5,6,7,8,11,15],[1,2,4,5,6,7,8,11,16],[1,2,4,5,6,7,8,12,13],[1,2,4,5,6,7,8,12,14],[1,2,4,5,6,7,8,12,15],[1,2,4,5,6,7,8,12,16],[1,2,4,5,6,7,8,13,14],[1,2,4,5,6,7,8,13,15],[1,2,4,5,6,7,8,13,16],[1,2,4,5,6,7,8,14,15],[1,2,4,5,6,7,8,14,16],[1,2,4,5,6,7,8,15,16],[1,2,4,5,6,7,9,10,11],[1,2,4,5,6,7,9,10,11,12,13,14,15],[1,2,4,5,6,7,9,10,11,12,13,14,16],[1,2,4,5,6,7,9,10,11,12,13,15,16],[1,2,4,5,6,7,9,10,11,12,14,15,16],[1,2,4,5,6,7,9,10,11,13,14,15,16],[1,2,4,5,6,7,9,10,12],[1,2,4,5,6,7,9,10,12,13,14,15,16],[1,2,4,5,6,7,9,10,13],[1,2,4,5,6,7,9,10,14],[1,2,4,5,6,7,9,10,15],[1,2,4,5,6,7,9,10,16],[1,2,4,5,6,7,9,11,12],[1,2,4,5,6,7,9,11,12,13,14,15,16],[1,2,4,5,6,7,9,11,13],[1,2,4,5,6,7,9,11,14],[1,2,4,5,6,7,9,11,15],[1,2,4,5,6,7,9,11,16],[1,2,4,5,6,7,9,12,13],[1,2,4,5,6,7,9,12,14],[1,2,4,5,6,7,9,12,15],[1,2,4,5,6,7,9,12,16],[1,2,4,5,6,7,9,13,14],[1,2,4,5,6,7,9,13,15],[1,2,4,5,6,7,9,13,16],[1,2,4,5,6,7,9,14,15],[1,2,4,5,6,7,9,14,16],[1,2,4,5,6,7,9,15,16],[1,2,4,5,6,8,9,10,11],[1,2,4,5,6,8,9,10,11,12,13,14,15],[1,2,4,5,6,8,9,10,11,12,13,14,16],[1,2,4,5,6,8,9,10,11,12,13,15,16],[1,2,4,5,6,8,9,10,11,12,14,15,16],[1,2,4,5,6,8,9,10,11,13,14,15,16],[1,2,4,5,6,8,9,10,12],[1,2,4,5,6,8,9,10,12,13,14,15,16],[1,2,4,5,6,8,9,10,13],[1,2,4,5,6,8,9,10,14],[1,2,4,5,6,8,9,10,15],[1,2,4,5,6,8,9,10,16],[1,2,4,5,6,8,9,11,12],[1,2,4,5,6,8,9,11,12,13,14,15,16],[1,2,4,5,6,8,9,11,13],[1,2,4,5,6,8,9,11,14],[1,2,4,5,6,8,9,11,15],[1,2,4,5,6,8,9,11,16],[1,2,4,5,6,8,9,12,13],[1,2,4,5,6,8,9,12,14],[1,2,4,5,6,8,9,12,15],[1,2,4,5,6,8,9,12,16],[1,2,4,5,6,8,9,13,14],[1,2,4,5,6,8,9,13,15],[1,2,4,5,6,8,9,13,16],[1,2,4,5,6,8,9,14,15],[1,2,4,5,6,8,9,14,16],[1,2,4,5,6,8,9,15,16],[1,2,4,5,7,8,9,10,11],[1,2,4,5,7,8,9,10,11,12,13,14,15],[1,2,4,5,7,8,9,10,11,12,13,14,16],[1,2,4,5,7,8,9,10,11,12,13,15,16],[1,2,4,5,7,8,9,10,11,12,14,15,16],[1,2,4,5,7,8,9,10,11,13,14,15,16],[1,2,4,5,7,8,9,10,12],[1,2,4,5,7,8,9,10,12,13,14,15,16],[1,2,4,5,7,8,9,10,13],[1,2,4,5,7,8,9,10,14],[1,2,4,5,7,8,9,10,15],[1,2,4,5,7,8,9,10,16],[1,2,4,5,7,8,9,11,12],[1,2,4,5,7,8,9,11,12,13,14,15,16],[1,2,4,5,7,8,9,11,13],[1,2,4,5,7,8,9,11,14],[1,2,4,5,7,8,9,11,15],[1,2,4,5,7,8,9,11,16],[1,2,4,5,7,8,9,12,13],[1,2,4,5,7,8,9,12,14],[1,2,4,5,7,8,9,12,15],[1,2,4,5,7,8,9,12,16],[1,2,4,5,7,8,9,13,14],[1,2,4,5,7,8,9,13,15],[1,2,4,5,7,8,9,13,16],[1,2,4,5,7,8,9,14,15],[1,2,4,5,7,8,9,14,16],[1,2,4,5,7,8,9,15,16],[1,2,4,6,7,8,9,10,11],[1,2,4,6,7,8,9,10,11,12,13,14,15],[1,2,4,6,7,8,9,10,11,12,13,14,16],[1,2,4,6,7,8,9,10,11,12,13,15,16],[1,2,4,6,7,8,9,10,11,12,14,15,16],[1,2,4,6,7,8,9,10,11,13,14,15,16],[1,2,4,6,7,8,9,10,12],[1,2,4,6,7,8,9,10,12,13,14,15,16],[1,2,4,6,7,8,9,10,13],[1,2,4,6,7,8,9,10,14],[1,2,4,6,7,8,9,10,15],[1,2,4,6,7,8,9,10,16],[1,2,4,6,7,8,9,11,12],[1,2,4,6,7,8,9,11,12,13,14,15,16],[1,2,4,6,7,8,9,11,13],[1,2,4,6,7,8,9,11,14],[1,2,4,6,7,8,9,11,15],[1,2,4,6,7,8,9,11,16],[1,2,4,6,7,8,9,12,13],[1,2,4,6,7,8,9,12,14],[1,2,4,6,7,8,9,12,15],[1,2,4,6,7,8,9,12,16],[1,2,4,6,7,8,9,13,14],[1,2,4,6,7,8,9,13,15],[1,2,4,6,7,8,9,13,16],[1,2,4,6,7,8,9,14,15],[1,2,4,6,7,8,9,14,16],[1,2,4,6,7,8,9,15,16],[1,2,5,6,7,8,9,10,11],[1,2,5,6,7,8,9,10,11,12,13,14,15],[1,2,5,6,7,8,9,10,11,12,13,14,16],[1,2,5,6,7,8,9,10,11,12,13,15,16],[1,2,5,6,7,8,9,10,11,12,14,15,16],[1,2,5,6,7,8,9,10,11,13,14,15,16],[1,2,5,6,7,8,9,10,12],[1,2,5,6,7,8,9,10,12,13,14,15,16],[1,2,5,6,7,8,9,10,13],[1,2,5,6,7,8,9,10,14],[1,2,5,6,7,8,9,10,15],[1,2,5,6,7,8,9,10,16],[1,2,5,6,7,8,9,11,12],[1,2,5,6,7,8,9,11,12,13,14,15,16],[1,2,5,6,7,8,9,11,13],[1,2,5,6,7,8,9,11,14],[1,2,5,6,7,8,9,11,15],[1,2,5,6,7,8,9,11,16],[1,2,5,6,7,8,9,12,13],[1,2,5,6,7,8,9,12,14],[1,2,5,6,7,8,9,12,15],[1,2,5,6,7,8,9,12,16],[1,2,5,6,7,8,9,13,14],[1,2,5,6,7,8,9,13,15],[1,2,5,6,7,8,9,13,16],[1,2,5,6,7,8,9,14,15],[1,2,5,6,7,8,9,14,16],[1,2,5,6,7,8,9,15,16],[1,3,4,5,6,7,8,10,11],[1,3,4,5,6,7,8,10,11,12,13,14,15],[1,3,4,5,6,7,8,10,11,12,13,14,16],[1,3,4,5,6,7,8,10,11,12,13,15,16],[1,3,4,5,6,7,8,10,11,12,14,15,16],[1,3,4,5,6,7,8,10,11,13,14,15,16],[1,3,4,5,6,7,8,10,12],[1,3,4,5,6,7,8,10,12,13,14,15,16],[1,3,4,5,6,7,8,10,13],[1,3,4,5,6,7,8,10,14],[1,3,4,5,6,7,8,10,15],[1,3,4,5,6,7,8,10,16],[1,3,4,5,6,7,8,11,12],[1,3,4,5,6,7,8,11,12,13,14,15,16],[1,3,4,5,6,7,8,11,13],[1,3,4,5,6,7,8,11,14],[1,3,4,5,6,7,8,11,15],[1,3,4,5,6,7,8,11,16],[1,3,4,5,6,7,8,12,13],[1,3,4,5,6,7,8,12,14],[1,3,4,5,6,7,8,12,15],[1,3,4,5,6,7,8,12,16],[1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,8,13,15],[1,3,4,5,6,7,8,13,16],[1,3,4,5,6,7,8,14,15],[1,3,4,5,6,7,8,14,16],[1,3,4,5,6,7,8,15,16],[1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,10,11,12,13,14,15],[1,3,4,5,6,7,9,10,11,12,13,14,16],[1,3,4,5,6,7,9,10,11,12,13,15,16],[1,3,4,5,6,7,9,10,11,12,14,15,16],[1,3,4,5,6,7,9,10,11,13,14,15,16],[1,3,4,5,6,7,9,10,12],[1,3,4,5,6,7,9,10,12,13,14,15,16],[1,3,4,5,6,7,9,10,13],[1,3,4,5,6,7,9,10,14],[1,3,4,5,6,7,9,10,15],[1,3,4,5,6,7,9,10,16],[1,3,4,5,6,7,9,11,12],[1,3,4,5,6,7,9,11,12,13,14,15,16],[1,3,4,5,6,7,9,11,13],[1,3,4,5,6,7,9,11,14],[1,3,4,5,6,7,9,11,15],[1,3,4,5,6,7,9,11,16],[1,3,4,5,6,7,9,12,13],[1,3,4,5,6,7,9,12,14],[1,3,4,5,6,7,9,12,15],[1,3,4,5,6,7,9,12,16],[1,3,4,5,6,7,9,13,14],[1,3,4,5,6,7,9,13,15],[1,3,4,5,6,7,9,13,16],[1,3,4,5,6,7,9,14,15],[1,3,4,5,6,7,9,14,16],[1,3,4,5,6,7,9,15,16],[1,3,4,5,6,8,9,10,11],[1,3,4,5,6,8,9,10,11,12,13,14,15],[1,3,4,5,6,8,9,10,11,12,13,14,16],[1,3,4,5,6,8,9,10,11,12,13,15,16],[1,3,4,5,6,8,9,10,11,12,14,15,16],[1,3,4,5,6,8,9,10,11,13,14,15,16],[1,3,4,5,6,8,9,10,12],[1,3,4,5,6,8,9,10,12,13,14,15,16],[1,3,4,5,6,8,9,10,13],[1,3,4,5,6,8,9,10,14],[1,3,4,5,6,8,9,10,15],[1,3,4,5,6,8,9,10,16],[1,3,4,5,6,8,9,11,12],[1,3,4,5,6,8,9,11,12,13,14,15,16],[1,3,4,5,6,8,9,11,13],[1,3,4,5,6,8,9,11,14],[1,3,4,5,6,8,9,11,15],[1,3,4,5,6,8,9,11,16],[1,3,4,5,6,8,9,12,13],[1,3,4,5,6,8,9,12,14],[1,3,4,5,6,8,9,12,15],[1,3,4,5,6,8,9,12,16],[1,3,4,5,6,8,9,13,14],[1,3,4,5,6,8,9,13,15],[1,3,4,5,6,8,9,13,16],[1,3,4,5,6,8,9,14,15],[1,3,4,5,6,8,9,14,16],[1,3,4,5,6,8,9,15,16],[1,3,4,5,7,8,9,10,11],[1,3,4,5,7,8,9,10,11,12,13,14,15],[1,3,4,5,7,8,9,10,11,12,13,14,16],[1,3,4,5,7,8,9,10,11,12,13,15,16],[1,3,4,5,7,8,9,10,11,12,14,15,16],[1,3,4,5,7,8,9,10,11,13,14,15,16],[1,3,4,5,7,8,9,10,12],[1,3,4,5,7,8,9,10,12,13,14,15,16],[1,3,4,5,7,8,9,10,13],[1,3,4,5,7,8,9,10,14],[1,3,4,5,7,8,9,10,15],[1,3,4,5,7,8,9,10,16],[1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,9,11,12,13,14,15,16],[1,3,4,5,7,8,9,11,13],[1,3,4,5,7,8,9,11,14],[1,3,4,5,7,8,9,11,15],[1,3,4,5,7,8,9,11,16],[1,3,4,5,7,8,9,12,13],[1,3,4,5,7,8,9,12,14],[1,3,4,5,7,8,9,12,15],[1,3,4,5,7,8,9,12,16],[1,3,4,5,7,8,9,13,14],[1,3,4,5,7,8,9,13,15],[1,3,4,5,7,8,9,13,16],[1,3,4,5,7,8,9,14,15],[1,3,4,5,7,8,9,14,16],[1,3,4,5,7,8,9,15,16],[1,3,4,6,7,8,9,10,11],[1,3,4,6,7,8,9,10,11,12,13,14,15],[1,3,4,6,7,8,9,10,11,12,13,14,16],[1,3,4,6,7,8,9,10,11,12,13,15,16],[1,3,4,6,7,8,9,10,11,12,14,15,16],[1,3,4,6,7,8,9,10,11,13,14,15,16],[1,3,4,6,7,8,9,10,12],[1,3,4,6,7,8,9,10,12,13,14,15,16],[1,3,4,6,7,8,9,10,13],[1,3,4,6,7,8,9,10,14],[1,3,4,6,7,8,9,10,15],[1,3,4,6,7,8,9,10,16],[1,3,4,6,7,8,9,11,12],[1,3,4,6,7,8,9,11,12,13,14,15,16],[1,3,4,6,7,8,9,11,13],[1,3,4,6,7,8,9,11,14],[1,3,4,6,7,8,9,11,15],[1,3,4,6,7,8,9,11,16],[1,3,4,6,7,8,9,12,13],[1,3,4,6,7,8,9,12,14],[1,3,4,6,7,8,9,12,15],[1,3,4,6,7,8,9,12,16],[1,3,4,6,7,8,9,13,14],[1,3,4,6,7,8,9,13,15],[1,3,4,6,7,8,9,13,16],[1,3,4,6,7,8,9,14,15],[1,3,4,6,7,8,9,14,16],[1,3,4,6,7,8,9,15,16],[1,3,5,6,7,8,9,10,11],[1,3,5,6,7,8,9,10,11,12,13,14,15],[1,3,5,6,7,8,9,10,11,12,13,14,16],[1,3,5,6,7,8,9,10,11,12,13,15,16],[1,3,5,6,7,8,9,10,11,12,14,15,16],[1,3,5,6,7,8,9,10,11,13,14,15,16],[1,3,5,6,7,8,9,10,12],[1,3,5,6,7,8,9,10,12,13,14,15,16],[1,3,5,6,7,8,9,10,13],[1,3,5,6,7,8,9,10,14],[1,3,5,6,7,8,9,10,15],[1,3,5,6,7,8,9,10,16],[1,3,5,6,7,8,9,11,12],[1,3,5,6,7,8,9,11,12,13,14,15,16],[1,3,5,6,7,8,9,11,13],[1,3,5,6,7,8,9,11,14],[1,3,5,6,7,8,9,11,15],[1,3,5,6,7,8,9,11,16],[1,3,5,6,7,8,9,12,13],[1,3,5,6,7,8,9,12,14],[1,3,5,6,7,8,9,12,15],[1,3,5,6,7,8,9,12,16],[1,3,5,6,7,8,9,13,14],[1,3,5,6,7,8,9,13,15],[1,3,5,6,7,8,9,13,16],[1,3,5,6,7,8,9,14,15],[1,3,5,6,7,8,9,14,16],[1,3,5,6,7,8,9,15,16],[1,4,5,6,7,8,9,10,11],[1,4,5,6,7,8,9,10,11,12,13,14,15],[1,4,5,6,7,8,9,10,11,12,13,14,16],[1,4,5,6,7,8,9,10,11,12,13,15,16],[1,4,5,6,7,8,9,10,11,12,14,15,16],[1,4,5,6,7,8,9,10,11,13,14,15,16],[1,4,5,6,7,8,9,10,12],[1,4,5,6,7,8,9,10,12,13,14,15,16],[1,4,5,6,7,8,9,10,13],[1,4,5,6,7,8,9,10,14],[1,4,5,6,7,8,9,10,15],[1,4,5,6,7,8,9,10,16],[1,4,5,6,7,8,9,11,12],[1,4,5,6,7,8,9,11,12,13,14,15,16],[1,4,5,6,7,8,9,11,13],[1,4,5,6,7,8,9,11,14],[1,4,5,6,7,8,9,11,15],[1,4,5,6,7,8,9,11,16],[1,4,5,6,7,8,9,12,13],[1,4,5,6,7,8,9,12,14],[1,4,5,6,7,8,9,12,15],[1,4,5,6,7,8,9,12,16],[1,4,5,6,7,8,9,13,14],[1,4,5,6,7,8,9,13,15],[1,4,5,6,7,8,9,13,16],[1,4,5,6,7,8,9,14,15],[1,4,5,6,7,8,9,14,16],[1,4,5,6,7,8,9,15,16],[1,10,11,12,13],[1,10,11,12,14],[1,10,11,12,15],[1,10,11,12,16],[1,10,11,13,14],[1,10,11,13,15],[1,10,11,13,16],[1,10,11,14,15],[1,10,11,14,16],[1,10,11,15,16],[1,10,12,13,14],[1,10,12,13,15],[1,10,12,13,16],[1,10,12,14,15],[1,10,12,14,16],[1,10,12,15,16],[1,10,13,14,15],[1,10,13,14,16],[1,10,13,15,16],[1,10,14,15,16],[1,11,12,13,14],[1,11,12,13,15],[1,11,12,13,16],[1,11,12,14,15],[1,11,12,14,16],[1,11,12,15,16],[1,11,13,14,15],[1,11,13,14,16],[1,11,13,15,16],[1,11,14,15,16],[1,12,13,14,15],[1,12,13,14,16],[1,12,13,15,16],[1,12,14,15,16],[1,13,14,15,16],[2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,10,11,12,13,14,15],[2,3,4,5,6,7,8,10,11,12,13,14,16],[2,3,4,5,6,7,8,10,11,12,13,15,16],[2,3,4,5,6,7,8,10,11,12,14,15,16],[2,3,4,5,6,7,8,10,11,13,14,15,16],[2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,10,12,13,14,15,16],[2,3,4,5,6,7,8,10,13],[2,3,4,5,6,7,8,10,14],[2,3,4,5,6,7,8,10,15],[2,3,4,5,6,7,8,10,16],[2,3,4,5,6,7,8,11,12],[2,3,4,5,6,7,8,11,12,13,14,15,16],[2,3,4,5,6,7,8,11,13],[2,3,4,5,6,7,8,11,14],[2,3,4,5,6,7,8,11,15],[2,3,4,5,6,7,8,11,16],[2,3,4,5,6,7,8,12,13],[2,3,4,5,6,7,8,12,14],[2,3,4,5,6,7,8,12,15],[2,3,4,5,6,7,8,12,16],[2,3,4,5,6,7,8,13,14],[2,3,4,5,6,7,8,13,15],[2,3,4,5,6,7,8,13,16],[2,3,4,5,6,7,8,14,15],[2,3,4,5,6,7,8,14,16],[2,3,4,5,6,7,8,15,16],[2,3,4,5,6,7,9,10,11],[2,3,4,5,6,7,9,10,11,12,13,14,15],[2,3,4,5,6,7,9,10,11,12,13,14,16],[2,3,4,5,6,7,9,10,11,12,13,15,16],[2,3,4,5,6,7,9,10,11,12,14,15,16],[2,3,4,5,6,7,9,10,11,13,14,15,16],[2,3,4,5,6,7,9,10,12],[2,3,4,5,6,7,9,10,12,13,14,15,16],[2,3,4,5,6,7,9,10,13],[2,3,4,5,6,7,9,10,14],[2,3,4,5,6,7,9,10,15],[2,3,4,5,6,7,9,10,16],[2,3,4,5,6,7,9,11,12],[2,3,4,5,6,7,9,11,12,13,14,15,16],[2,3,4,5,6,7,9,11,13],[2,3,4,5,6,7,9,11,14],[2,3,4,5,6,7,9,11,15],[2,3,4,5,6,7,9,11,16],[2,3,4,5,6,7,9,12,13],[2,3,4,5,6,7,9,12,14],[2,3,4,5,6,7,9,12,15],[2,3,4,5,6,7,9,12,16],[2,3,4,5,6,7,9,13,14],[2,3,4,5,6,7,9,13,15],[2,3,4,5,6,7,9,13,16],[2,3,4,5,6,7,9,14,15],[2,3,4,5,6,7,9,14,16],[2,3,4,5,6,7,9,15,16],[2,3,4,5,6,8,9,10,11],[2,3,4,5,6,8,9,10,11,12,13,14,15],[2,3,4,5,6,8,9,10,11,12,13,14,16],[2,3,4,5,6,8,9,10,11,12,13,15,16],[2,3,4,5,6,8,9,10,11,12,14,15,16],[2,3,4,5,6,8,9,10,11,13,14,15,16],[2,3,4,5,6,8,9,10,12],[2,3,4,5,6,8,9,10,12,13,14,15,16],[2,3,4,5,6,8,9,10,13],[2,3,4,5,6,8,9,10,14],[2,3,4,5,6,8,9,10,15],[2,3,4,5,6,8,9,10,16],[2,3,4,5,6,8,9,11,12],[2,3,4,5,6,8,9,11,12,13,14,15,16],[2,3,4,5,6,8,9,11,13],[2,3,4,5,6,8,9,11,14],[2,3,4,5,6,8,9,11,15],[2,3,4,5,6,8,9,11,16],[2,3,4,5,6,8,9,12,13],[2,3,4,5,6,8,9,12,14],[2,3,4,5,6,8,9,12,15],[2,3,4,5,6,8,9,12,16],[2,3,4,5,6,8,9,13,14],[2,3,4,5,6,8,9,13,15],[2,3,4,5,6,8,9,13,16],[2,3,4,5,6,8,9,14,15],[2,3,4,5,6,8,9,14,16],[2,3,4,5,6,8,9,15,16],[2,3,4,5,7,8,9,10,11],[2,3,4,5,7,8,9,10,11,12,13,14,15],[2,3,4,5,7,8,9,10,11,12,13,14,16],[2,3,4,5,7,8,9,10,11,12,13,15,16],[2,3,4,5,7,8,9,10,11,12,14,15,16],[2,3,4,5,7,8,9,10,11,13,14,15,16],[2,3,4,5,7,8,9,10,12],[2,3,4,5,7,8,9,10,12,13,14,15,16],[2,3,4,5,7,8,9,10,13],[2,3,4,5,7,8,9,10,14],[2,3,4,5,7,8,9,10,15],[2,3,4,5,7,8,9,10,16],[2,3,4,5,7,8,9,11,12],[2,3,4,5,7,8,9,11,12,13,14,15,16],[2,3,4,5,7,8,9,11,13],[2,3,4,5,7,8,9,11,14],[2,3,4,5,7,8,9,11,15],[2,3,4,5,7,8,9,11,16],[2,3,4,5,7,8,9,12,13],[2,3,4,5,7,8,9,12,14],[2,3,4,5,7,8,9,12,15],[2,3,4,5,7,8,9,12,16],[2,3,4,5,7,8,9,13,14],[2,3,4,5,7,8,9,13,15],[2,3,4,5,7,8,9,13,16],[2,3,4,5,7,8,9,14,15],[2,3,4,5,7,8,9,14,16],[2,3,4,5,7,8,9,15,16],[2,3,4,6,7,8,9,10,11],[2,3,4,6,7,8,9,10,11,12,13,14,15],[2,3,4,6,7,8,9,10,11,12,13,14,16],[2,3,4,6,7,8,9,10,11,12,13,15,16],[2,3,4,6,7,8,9,10,11,12,14,15,16],[2,3,4,6,7,8,9,10,11,13,14,15,16],[2,3,4,6,7,8,9,10,12],[2,3,4,6,7,8,9,10,12,13,14,15,16],[2,3,4,6,7,8,9,10,13],[2,3,4,6,7,8,9,10,14],[2,3,4,6,7,8,9,10,15],[2,3,4,6,7,8,9,10,16],[2,3,4,6,7,8,9,11,12],[2,3,4,6,7,8,9,11,12,13,14,15,16],[2,3,4,6,7,8,9,11,13],[2,3,4,6,7,8,9,11,14],[2,3,4,6,7,8,9,11,15],[2,3,4,6,7,8,9,11,16],[2,3,4,6,7,8,9,12,13],[2,3,4,6,7,8,9,12,14],[2,3,4,6,7,8,9,12,15],[2,3,4,6,7,8,9,12,16],[2,3,4,6,7,8,9,13,14],[2,3,4,6,7,8,9,13,15],[2,3,4,6,7,8,9,13,16],[2,3,4,6,7,8,9,14,15],[2,3,4,6,7,8,9,14,16],[2,3,4,6,7,8,9,15,16],[2,3,5,6,7,8,9,10,11],[2,3,5,6,7,8,9,10,11,12,13,14,15],[2,3,5,6,7,8,9,10,11,12,13,14,16],[2,3,5,6,7,8,9,10,11,12,13,15,16],[2,3,5,6,7,8,9,10,11,12,14,15,16],[2,3,5,6,7,8,9,10,11,13,14,15,16],[2,3,5,6,7,8,9,10,12],[2,3,5,6,7,8,9,10,12,13,14,15,16],[2,3,5,6,7,8,9,10,13],[2,3,5,6,7,8,9,10,14],[2,3,5,6,7,8,9,10,15],[2,3,5,6,7,8,9,10,16],[2,3,5,6,7,8,9,11,12],[2,3,5,6,7,8,9,11,12,13,14,15,16],[2,3,5,6,7,8,9,11,13],[2,3,5,6,7,8,9,11,14],[2,3,5,6,7,8,9,11,15],[2,3,5,6,7,8,9,11,16],[2,3,5,6,7,8,9,12,13],[2,3,5,6,7,8,9,12,14],[2,3,5,6,7,8,9,12,15],[2,3,5,6,7,8,9,12,16],[2,3,5,6,7,8,9,13,14],[2,3,5,6,7,8,9,13,15],[2,3,5,6,7,8,9,13,16],[2,3,5,6,7,8,9,14,15],[2,3,5,6,7,8,9,14,16],[2,3,5,6,7,8,9,15,16],[2,4,5,6,7,8,9,10,11],[2,4,5,6,7,8,9,10,11,12,13,14,15],[2,4,5,6,7,8,9,10,11,12,13,14,16],[2,4,5,6,7,8,9,10,11,12,13,15,16],[2,4,5,6,7,8,9,10,11,12,14,15,16],[2,4,5,6,7,8,9,10,11,13,14,15,16],[2,4,5,6,7,8,9,10,12],[2,4,5,6,7,8,9,10,12,13,14,15,16],[2,4,5,6,7,8,9,10,13],[2,4,5,6,7,8,9,10,14],[2,4,5,6,7,8,9,10,15],[2,4,5,6,7,8,9,10,16],[2,4,5,6,7,8,9,11,12],[2,4,5,6,7,8,9,11,12,13,14,15,16],[2,4,5,6,7,8,9,11,13],[2,4,5,6,7,8,9,11,14],[2,4,5,6,7,8,9,11,15],[2,4,5,6,7,8,9,11,16],[2,4,5,6,7,8,9,12,13],[2,4,5,6,7,8,9,12,14],[2,4,5,6,7,8,9,12,15],[2,4,5,6,7,8,9,12,16],[2,4,5,6,7,8,9,13,14],[2,4,5,6,7,8,9,13,15],[2,4,5,6,7,8,9,13,16],[2,4,5,6,7,8,9,14,15],[2,4,5,6,7,8,9,14,16],[2,4,5,6,7,8,9,15,16],[2,10,11,12,13],[2,10,11,12,14],[2,10,11,12,15],[2,10,11,12,16],[2,10,11,13,14],[2,10,11,13,15],[2,10,11,13,16],[2,10,11,14,15],[2,10,11,14,16],[2,10,11,15,16],[2,10,12,13,14],[2,10,12,13,15],[2,10,12,13,16],[2,10,12,14,15],[2,10,12,14,16],[2,10,12,15,16],[2,10,13,14,15],[2,10,13,14,16],[2,10,13,15,16],[2,10,14,15,16],[2,11,12,13,14],[2,11,12,13,15],[2,11,12,13,16],[2,11,12,14,15],[2,11,12,14,16],[2,11,12,15,16],[2,11,13,14,15],[2,11,13,14,16],[2,11,13,15,16],[2,11,14,15,16],[2,12,13,14,15],[2,12,13,14,16],[2,12,13,15,16],[2,12,14,15,16],[2,13,14,15,16],[3,4,5,6,7,8,9,10,11],[3,4,5,6,7,8,9,10,11,12,13,14,15],[3,4,5,6,7,8,9,10,11,12,13,14,16],[3,4,5,6,7,8,9,10,11,12,13,15,16],[3,4,5,6,7,8,9,10,11,12,14,15,16],[3,4,5,6,7,8,9,10,11,13,14,15,16],[3,4,5,6,7,8,9,10,12],[3,4,5,6,7,8,9,10,12,13,14,15,16],[3,4,5,6,7,8,9,10,13],[3,4,5,6,7,8,9,10,14],[3,4,5,6,7,8,9,10,15],[3,4,5,6,7,8,9,10,16],[3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,11,12,13,14,15,16],[3,4,5,6,7,8,9,11,13],[3,4,5,6,7,8,9,11,14],[3,4,5,6,7,8,9,11,15],[3,4,5,6,7,8,9,11,16],[3,4,5,6,7,8,9,12,13],[3,4,5,6,7,8,9,12,14],[3,4,5,6,7,8,9,12,15],[3,4,5,6,7,8,9,12,16],[3,4,5,6,7,8,9,13,14],[3,4,5,6,7,8,9,13,15],[3,4,5,6,7,8,9,13,16],[3,4,5,6,7,8,9,14,15],[3,4,5,6,7,8,9,14,16],[3,4,5,6,7,8,9,15,16],[3,10,11,12,13],[3,10,11,12,14],[3,10,11,12,15],[3,10,11,12,16],[3,10,11,13,14],[3,10,11,13,15],[3,10,11,13,16],[3,10,11,14,15],[3,10,11,14,16],[3,10,11,15,16],[3,10,12,13,14],[3,10,12,13,15],[3,10,12,13,16],[3,10,12,14,15],[3,10,12,14,16],[3,10,12,15,16],[3,10,13,14,15],[3,10,13,14,16],[3,10,13,15,16],[3,10,14,15,16],[3,11,12,13,14],[3,11,12,13,15],[3,11,12,13,16],[3,11,12,14,15],[3,11,12,14,16],[3,11,12,15,16],[3,11,13,14,15],[3,11,13,14,16],[3,11,13,15,16],[3,11,14,15,16],[3,12,13,14,15],[3,12,13,14,16],[3,12,13,15,16],[3,12,14,15,16],[3,13,14,15,16],[4,10,11,12,13],[4,10,11,12,14],[4,10,11,12,15],[4,10,11,12,16],[4,10,11,13,14],[4,10,11,13,15],[4,10,11,13,16],[4,10,11,14,15],[4,10,11,14,16],[4,10,11,15,16],[4,10,12,13,14],[4,10,12,13,15],[4,10,12,13,16],[4,10,12,14,15],[4,10,12,14,16],[4,10,12,15,16],[4,10,13,14,15],[4,10,13,14,16],[4,10,13,15,16],[4,10,14,15,16],[4,11,12,13,14],[4,11,12,13,15],[4,11,12,13,16],[4,11,12,14,15],[4,11,12,14,16],[4,11,12,15,16],[4,11,13,14,15],[4,11,13,14,16],[4,11,13,15,16],[4,11,14,15,16],[4,12,13,14,15],[4,12,13,14,16],[4,12,13,15,16],[4,12,14,15,16],[4,13,14,15,16],[5,10,11,12,13],[5,10,11,12,14],[5,10,11,12,15],[5,10,11,12,16],[5,10,11,13,14],[5,10,11,13,15],[5,10,11,13,16],[5,10,11,14,15],[5,10,11,14,16],[5,10,11,15,16],[5,10,12,13,14],[5,10,12,13,15],[5,10,12,13,16],[5,10,12,14,15],[5,10,12,14,16],[5,10,12,15,16],[5,10,13,14,15],[5,10,13,14,16],[5,10,13,15,16],[5,10,14,15,16],[5,11,12,13,14],[5,11,12,13,15],[5,11,12,13,16],[5,11,12,14,15],[5,11,12,14,16],[5,11,12,15,16],[5,11,13,14,15],[5,11,13,14,16],[5,11,13,15,16],[5,11,14,15,16],[5,12,13,14,15],[5,12,13,14,16],[5,12,13,15,16],[5,12,14,15,16],[5,13,14,15,16],[6,10,11,12,13],[6,10,11,12,14],[6,10,11,12,15],[6,10,11,12,16],[6,10,11,13,14],[6,10,11,13,15],[6,10,11,13,16],[6,10,11,14,15],[6,10,11,14,16],[6,10,11,15,16],[6,10,12,13,14],[6,10,12,13,15],[6,10,12,13,16],[6,10,12,14,15],[6,10,12,14,16],[6,10,12,15,16],[6,10,13,14,15],[6,10,13,14,16],[6,10,13,15,16],[6,10,14,15,16],[6,11,12,13,14],[6,11,12,13,15],[6,11,12,13,16],[6,11,12,14,15],[6,11,12,14,16],[6,11,12,15,16],[6,11,13,14,15],[6,11,13,14,16],[6,11,13,15,16],[6,11,14,15,16],[6,12,13,14,15],[6,12,13,14,16],[6,12,13,15,16],[6,12,14,15,16],[6,13,14,15,16],[7,10,11,12,13],[7,10,11,12,14],[7,10,11,12,15],[7,10,11,12,16],[7,10,11,13,14],[7,10,11,13,15],[7,10,11,13,16],[7,10,11,14,15],[7,10,11,14,16],[7,10,11,15,16],[7,10,12,13,14],[7,10,12,13,15],[7,10,12,13,16],[7,10,12,14,15],[7,10,12,14,16],[7,10,12,15,16],[7,10,13,14,15],[7,10,13,14,16],[7,10,13,15,16],[7,10,14,15,16],[7,11,12,13,14],[7,11,12,13,15],[7,11,12,13,16],[7,11,12,14,15],[7,11,12,14,16],[7,11,12,15,16],[7,11,13,14,15],[7,11,13,14,16],[7,11,13,15,16],[7,11,14,15,16],[7,12,13,14,15],[7,12,13,14,16],[7,12,13,15,16],[7,12,14,15,16],[7,13,14,15,16],[8,10,11,12,13],[8,10,11,12,14],[8,10,11,12,15],[8,10,11,12,16],[8,10,11,13,14],[8,10,11,13,15],[8,10,11,13,16],[8,10,11,14,15],[8,10,11,14,16],[8,10,11,15,16],[8,10,12,13,14],[8,10,12,13,15],[8,10,12,13,16],[8,10,12,14,15],[8,10,12,14,16],[8,10,12,15,16],[8,10,13,14,15],[8,10,13,14,16],[8,10,13,15,16],[8,10,14,15,16],[8,11,12,13,14],[8,11,12,13,15],[8,11,12,13,16],[8,11,12,14,15],[8,11,12,14,16],[8,11,12,15,16],[8,11,13,14,15],[8,11,13,14,16],[8,11,13,15,16],[8,11,14,15,16],[8,12,13,14,15],[8,12,13,14,16],[8,12,13,15,16],[8,12,14,15,16],[8,13,14,15,16],[9,10,11,12,13],[9,10,11,12,14],[9,10,11,12,15],[9,10,11,12,16],[9,10,11,13,14],[9,10,11,13,15],[9,10,11,13,16],[9,10,11,14,15],[9,10,11,14,16],[9,10,11,15,16],[9,10,12,13,14],[9,10,12,13,15],[9,10,12,13,16],[9,10,12,14,15],[9,10,12,14,16],[9,10,12,15,16],[9,10,13,14,15],[9,10,13,14,16],[9,10,13,15,16],[9,10,14,15,16],[9,11,12,13,14],[9,11,12,13,15],[9,11,12,13,16],[9,11,12,14,15],[9,11,12,14,16],[9,11,12,15,16],[9,11,13,14,15],[9,11,13,14,16],[9,11,13,15,16],[9,11,14,15,16],[9,12,13,14,15],[9,12,13,14,16],[9,12,13,15,16],[9,12,14,15,16],[9,13,14,15,16],[10],[10,11,12,13,14],[10,11,12,13,15],[10,11,12,13,16],[10,11,12,14,15],[10,11,12,14,16],[10,11,12,15,16],[10,11,13,14,15],[10,11,13,14,16],[10,11,13,15,16],[10,11,14,15,16],[10,12,13,14,15],[10,12,13,14,16],[10,12,13,15,16],[10,12,14,15,16],[10,13,14,15,16],[11],[11,12,13,14,15],[11,12,13,14,16],[11,12,13,15,16],[11,12,14,15,16],[11,13,14,15,16],[12],[12,13,14,15,16],[13],[14],[15],[16]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,28],"A_d":201495,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,3],[2,3],[3,3],[4,3],[5,3],[6,3],[7,3],[8,3],[9,3]],"CZ":[[10,11],[10,12],[10,13],[10,14],[10,15],[10,16],[11,12],[11,13],[11,14],[11,15],[11,16],[12,13],[12,14],[12,15],[12,16],[13,14],[13,15],[13,16],[14,15],[14,16],[15,16]]},"rotation_powers":null},"metrics":{"gamma":8.546122758857797,"gamma_t":null,"gamma_rho":8.546122758857797,"gamma_claim":8.546122758857797,"gamma_t_claim":null,"gamma_rho_claim":8.546122758857797,"v_ex":10,"rate":0.002675227394328518,"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-1133","N":17,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 1133","provenance":"larger unified search l=3, two-group s_total=4,s_O=6"}]},"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"}]}