{"id":"2424.8.2.a","row":76,"stored":{"file":"master_catalog_large.json","row":76,"construction":{"family":"two-group","k":8,"N":16,"s_total":4,"s_O":5},"columns_sha256":"9a938e3a89724a4954937392ff9058d02a7da734aa3f1b9f8a4eadce21215f89"},"parameters":{"n":2424,"k":8,"d":2,"N":16,"r":8,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7","monomials":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_fingerprint":"2daea1c2f1d6f117","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,5,8,9,10],[0,1,2,3,4,5,8,9,10,11,12,13,14],[0,1,2,3,4,5,8,9,10,11,12,13,15],[0,1,2,3,4,5,8,9,10,11,12,14,15],[0,1,2,3,4,5,8,9,10,11,13,14,15],[0,1,2,3,4,5,8,9,10,12,13,14,15],[0,1,2,3,4,5,8,9,11],[0,1,2,3,4,5,8,9,11,12,13,14,15],[0,1,2,3,4,5,8,9,12],[0,1,2,3,4,5,8,9,13],[0,1,2,3,4,5,8,9,14],[0,1,2,3,4,5,8,9,15],[0,1,2,3,4,5,8,10,11],[0,1,2,3,4,5,8,10,11,12,13,14,15],[0,1,2,3,4,5,8,10,12],[0,1,2,3,4,5,8,10,13],[0,1,2,3,4,5,8,10,14],[0,1,2,3,4,5,8,10,15],[0,1,2,3,4,5,8,11,12],[0,1,2,3,4,5,8,11,13],[0,1,2,3,4,5,8,11,14],[0,1,2,3,4,5,8,11,15],[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],[0,1,2,3,4,5,8,13,14],[0,1,2,3,4,5,8,13,15],[0,1,2,3,4,5,8,14,15],[0,1,2,3,4,5,9,10,11],[0,1,2,3,4,5,9,10,11,12,13,14,15],[0,1,2,3,4,5,9,10,12],[0,1,2,3,4,5,9,10,13],[0,1,2,3,4,5,9,10,14],[0,1,2,3,4,5,9,10,15],[0,1,2,3,4,5,9,11,12],[0,1,2,3,4,5,9,11,13],[0,1,2,3,4,5,9,11,14],[0,1,2,3,4,5,9,11,15],[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],[0,1,2,3,4,5,9,13,14],[0,1,2,3,4,5,9,13,15],[0,1,2,3,4,5,9,14,15],[0,1,2,3,4,5,10,11,12],[0,1,2,3,4,5,10,11,13],[0,1,2,3,4,5,10,11,14],[0,1,2,3,4,5,10,11,15],[0,1,2,3,4,5,10,12,13],[0,1,2,3,4,5,10,12,14],[0,1,2,3,4,5,10,12,15],[0,1,2,3,4,5,10,13,14],[0,1,2,3,4,5,10,13,15],[0,1,2,3,4,5,10,14,15],[0,1,2,3,4,5,11,12,13],[0,1,2,3,4,5,11,12,14],[0,1,2,3,4,5,11,12,15],[0,1,2,3,4,5,11,13,14],[0,1,2,3,4,5,11,13,15],[0,1,2,3,4,5,11,14,15],[0,1,2,3,4,5,12,13,14],[0,1,2,3,4,5,12,13,15],[0,1,2,3,4,5,12,14,15],[0,1,2,3,4,5,13,14,15],[0,1,2,3,4,6,8,9,10],[0,1,2,3,4,6,8,9,10,11,12,13,14],[0,1,2,3,4,6,8,9,10,11,12,13,15],[0,1,2,3,4,6,8,9,10,11,12,14,15],[0,1,2,3,4,6,8,9,10,11,13,14,15],[0,1,2,3,4,6,8,9,10,12,13,14,15],[0,1,2,3,4,6,8,9,11],[0,1,2,3,4,6,8,9,11,12,13,14,15],[0,1,2,3,4,6,8,9,12],[0,1,2,3,4,6,8,9,13],[0,1,2,3,4,6,8,9,14],[0,1,2,3,4,6,8,9,15],[0,1,2,3,4,6,8,10,11],[0,1,2,3,4,6,8,10,11,12,13,14,15],[0,1,2,3,4,6,8,10,12],[0,1,2,3,4,6,8,10,13],[0,1,2,3,4,6,8,10,14],[0,1,2,3,4,6,8,10,15],[0,1,2,3,4,6,8,11,12],[0,1,2,3,4,6,8,11,13],[0,1,2,3,4,6,8,11,14],[0,1,2,3,4,6,8,11,15],[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],[0,1,2,3,4,6,8,13,14],[0,1,2,3,4,6,8,13,15],[0,1,2,3,4,6,8,14,15],[0,1,2,3,4,6,9,10,11],[0,1,2,3,4,6,9,10,11,12,13,14,15],[0,1,2,3,4,6,9,10,12],[0,1,2,3,4,6,9,10,13],[0,1,2,3,4,6,9,10,14],[0,1,2,3,4,6,9,10,15],[0,1,2,3,4,6,9,11,12],[0,1,2,3,4,6,9,11,13],[0,1,2,3,4,6,9,11,14],[0,1,2,3,4,6,9,11,15],[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],[0,1,2,3,4,6,9,13,14],[0,1,2,3,4,6,9,13,15],[0,1,2,3,4,6,9,14,15],[0,1,2,3,4,6,10,11,12],[0,1,2,3,4,6,10,11,13],[0,1,2,3,4,6,10,11,14],[0,1,2,3,4,6,10,11,15],[0,1,2,3,4,6,10,12,13],[0,1,2,3,4,6,10,12,14],[0,1,2,3,4,6,10,12,15],[0,1,2,3,4,6,10,13,14],[0,1,2,3,4,6,10,13,15],[0,1,2,3,4,6,10,14,15],[0,1,2,3,4,6,11,12,13],[0,1,2,3,4,6,11,12,14],[0,1,2,3,4,6,11,12,15],[0,1,2,3,4,6,11,13,14],[0,1,2,3,4,6,11,13,15],[0,1,2,3,4,6,11,14,15],[0,1,2,3,4,6,12,13,14],[0,1,2,3,4,6,12,13,15],[0,1,2,3,4,6,12,14,15],[0,1,2,3,4,6,13,14,15],[0,1,2,3,4,7,8,9,10],[0,1,2,3,4,7,8,9,10,11,12,13,14],[0,1,2,3,4,7,8,9,10,11,12,13,15],[0,1,2,3,4,7,8,9,10,11,12,14,15],[0,1,2,3,4,7,8,9,10,11,13,14,15],[0,1,2,3,4,7,8,9,10,12,13,14,15],[0,1,2,3,4,7,8,9,11],[0,1,2,3,4,7,8,9,11,12,13,14,15],[0,1,2,3,4,7,8,9,12],[0,1,2,3,4,7,8,9,13],[0,1,2,3,4,7,8,9,14],[0,1,2,3,4,7,8,9,15],[0,1,2,3,4,7,8,10,11],[0,1,2,3,4,7,8,10,11,12,13,14,15],[0,1,2,3,4,7,8,10,12],[0,1,2,3,4,7,8,10,13],[0,1,2,3,4,7,8,10,14],[0,1,2,3,4,7,8,10,15],[0,1,2,3,4,7,8,11,12],[0,1,2,3,4,7,8,11,13],[0,1,2,3,4,7,8,11,14],[0,1,2,3,4,7,8,11,15],[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],[0,1,2,3,4,7,8,13,14],[0,1,2,3,4,7,8,13,15],[0,1,2,3,4,7,8,14,15],[0,1,2,3,4,7,9,10,11],[0,1,2,3,4,7,9,10,11,12,13,14,15],[0,1,2,3,4,7,9,10,12],[0,1,2,3,4,7,9,10,13],[0,1,2,3,4,7,9,10,14],[0,1,2,3,4,7,9,10,15],[0,1,2,3,4,7,9,11,12],[0,1,2,3,4,7,9,11,13],[0,1,2,3,4,7,9,11,14],[0,1,2,3,4,7,9,11,15],[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],[0,1,2,3,4,7,9,13,14],[0,1,2,3,4,7,9,13,15],[0,1,2,3,4,7,9,14,15],[0,1,2,3,4,7,10,11,12],[0,1,2,3,4,7,10,11,13],[0,1,2,3,4,7,10,11,14],[0,1,2,3,4,7,10,11,15],[0,1,2,3,4,7,10,12,13],[0,1,2,3,4,7,10,12,14],[0,1,2,3,4,7,10,12,15],[0,1,2,3,4,7,10,13,14],[0,1,2,3,4,7,10,13,15],[0,1,2,3,4,7,10,14,15],[0,1,2,3,4,7,11,12,13],[0,1,2,3,4,7,11,12,14],[0,1,2,3,4,7,11,12,15],[0,1,2,3,4,7,11,13,14],[0,1,2,3,4,7,11,13,15],[0,1,2,3,4,7,11,14,15],[0,1,2,3,4,7,12,13,14],[0,1,2,3,4,7,12,13,15],[0,1,2,3,4,7,12,14,15],[0,1,2,3,4,7,13,14,15],[0,1,2,3,5,6,8,9,10],[0,1,2,3,5,6,8,9,10,11,12,13,14],[0,1,2,3,5,6,8,9,10,11,12,13,15],[0,1,2,3,5,6,8,9,10,11,12,14,15],[0,1,2,3,5,6,8,9,10,11,13,14,15],[0,1,2,3,5,6,8,9,10,12,13,14,15],[0,1,2,3,5,6,8,9,11],[0,1,2,3,5,6,8,9,11,12,13,14,15],[0,1,2,3,5,6,8,9,12],[0,1,2,3,5,6,8,9,13],[0,1,2,3,5,6,8,9,14],[0,1,2,3,5,6,8,9,15],[0,1,2,3,5,6,8,10,11],[0,1,2,3,5,6,8,10,11,12,13,14,15],[0,1,2,3,5,6,8,10,12],[0,1,2,3,5,6,8,10,13],[0,1,2,3,5,6,8,10,14],[0,1,2,3,5,6,8,10,15],[0,1,2,3,5,6,8,11,12],[0,1,2,3,5,6,8,11,13],[0,1,2,3,5,6,8,11,14],[0,1,2,3,5,6,8,11,15],[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],[0,1,2,3,5,6,8,13,14],[0,1,2,3,5,6,8,13,15],[0,1,2,3,5,6,8,14,15],[0,1,2,3,5,6,9,10,11],[0,1,2,3,5,6,9,10,11,12,13,14,15],[0,1,2,3,5,6,9,10,12],[0,1,2,3,5,6,9,10,13],[0,1,2,3,5,6,9,10,14],[0,1,2,3,5,6,9,10,15],[0,1,2,3,5,6,9,11,12],[0,1,2,3,5,6,9,11,13],[0,1,2,3,5,6,9,11,14],[0,1,2,3,5,6,9,11,15],[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],[0,1,2,3,5,6,9,13,14],[0,1,2,3,5,6,9,13,15],[0,1,2,3,5,6,9,14,15],[0,1,2,3,5,6,10,11,12],[0,1,2,3,5,6,10,11,13],[0,1,2,3,5,6,10,11,14],[0,1,2,3,5,6,10,11,15],[0,1,2,3,5,6,10,12,13],[0,1,2,3,5,6,10,12,14],[0,1,2,3,5,6,10,12,15],[0,1,2,3,5,6,10,13,14],[0,1,2,3,5,6,10,13,15],[0,1,2,3,5,6,10,14,15],[0,1,2,3,5,6,11,12,13],[0,1,2,3,5,6,11,12,14],[0,1,2,3,5,6,11,12,15],[0,1,2,3,5,6,11,13,14],[0,1,2,3,5,6,11,13,15],[0,1,2,3,5,6,11,14,15],[0,1,2,3,5,6,12,13,14],[0,1,2,3,5,6,12,13,15],[0,1,2,3,5,6,12,14,15],[0,1,2,3,5,6,13,14,15],[0,1,2,3,5,7,8,9,10],[0,1,2,3,5,7,8,9,10,11,12,13,14],[0,1,2,3,5,7,8,9,10,11,12,13,15],[0,1,2,3,5,7,8,9,10,11,12,14,15],[0,1,2,3,5,7,8,9,10,11,13,14,15],[0,1,2,3,5,7,8,9,10,12,13,14,15],[0,1,2,3,5,7,8,9,11],[0,1,2,3,5,7,8,9,11,12,13,14,15],[0,1,2,3,5,7,8,9,12],[0,1,2,3,5,7,8,9,13],[0,1,2,3,5,7,8,9,14],[0,1,2,3,5,7,8,9,15],[0,1,2,3,5,7,8,10,11],[0,1,2,3,5,7,8,10,11,12,13,14,15],[0,1,2,3,5,7,8,10,12],[0,1,2,3,5,7,8,10,13],[0,1,2,3,5,7,8,10,14],[0,1,2,3,5,7,8,10,15],[0,1,2,3,5,7,8,11,12],[0,1,2,3,5,7,8,11,13],[0,1,2,3,5,7,8,11,14],[0,1,2,3,5,7,8,11,15],[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],[0,1,2,3,5,7,8,13,14],[0,1,2,3,5,7,8,13,15],[0,1,2,3,5,7,8,14,15],[0,1,2,3,5,7,9,10,11],[0,1,2,3,5,7,9,10,11,12,13,14,15],[0,1,2,3,5,7,9,10,12],[0,1,2,3,5,7,9,10,13],[0,1,2,3,5,7,9,10,14],[0,1,2,3,5,7,9,10,15],[0,1,2,3,5,7,9,11,12],[0,1,2,3,5,7,9,11,13],[0,1,2,3,5,7,9,11,14],[0,1,2,3,5,7,9,11,15],[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],[0,1,2,3,5,7,9,13,14],[0,1,2,3,5,7,9,13,15],[0,1,2,3,5,7,9,14,15],[0,1,2,3,5,7,10,11,12],[0,1,2,3,5,7,10,11,13],[0,1,2,3,5,7,10,11,14],[0,1,2,3,5,7,10,11,15],[0,1,2,3,5,7,10,12,13],[0,1,2,3,5,7,10,12,14],[0,1,2,3,5,7,10,12,15],[0,1,2,3,5,7,10,13,14],[0,1,2,3,5,7,10,13,15],[0,1,2,3,5,7,10,14,15],[0,1,2,3,5,7,11,12,13],[0,1,2,3,5,7,11,12,14],[0,1,2,3,5,7,11,12,15],[0,1,2,3,5,7,11,13,14],[0,1,2,3,5,7,11,13,15],[0,1,2,3,5,7,11,14,15],[0,1,2,3,5,7,12,13,14],[0,1,2,3,5,7,12,13,15],[0,1,2,3,5,7,12,14,15],[0,1,2,3,5,7,13,14,15],[0,1,2,3,6,7,8,9,10],[0,1,2,3,6,7,8,9,10,11,12,13,14],[0,1,2,3,6,7,8,9,10,11,12,13,15],[0,1,2,3,6,7,8,9,10,11,12,14,15],[0,1,2,3,6,7,8,9,10,11,13,14,15],[0,1,2,3,6,7,8,9,10,12,13,14,15],[0,1,2,3,6,7,8,9,11],[0,1,2,3,6,7,8,9,11,12,13,14,15],[0,1,2,3,6,7,8,9,12],[0,1,2,3,6,7,8,9,13],[0,1,2,3,6,7,8,9,14],[0,1,2,3,6,7,8,9,15],[0,1,2,3,6,7,8,10,11],[0,1,2,3,6,7,8,10,11,12,13,14,15],[0,1,2,3,6,7,8,10,12],[0,1,2,3,6,7,8,10,13],[0,1,2,3,6,7,8,10,14],[0,1,2,3,6,7,8,10,15],[0,1,2,3,6,7,8,11,12],[0,1,2,3,6,7,8,11,13],[0,1,2,3,6,7,8,11,14],[0,1,2,3,6,7,8,11,15],[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],[0,1,2,3,6,7,8,13,14],[0,1,2,3,6,7,8,13,15],[0,1,2,3,6,7,8,14,15],[0,1,2,3,6,7,9,10,11],[0,1,2,3,6,7,9,10,11,12,13,14,15],[0,1,2,3,6,7,9,10,12],[0,1,2,3,6,7,9,10,13],[0,1,2,3,6,7,9,10,14],[0,1,2,3,6,7,9,10,15],[0,1,2,3,6,7,9,11,12],[0,1,2,3,6,7,9,11,13],[0,1,2,3,6,7,9,11,14],[0,1,2,3,6,7,9,11,15],[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],[0,1,2,3,6,7,9,13,14],[0,1,2,3,6,7,9,13,15],[0,1,2,3,6,7,9,14,15],[0,1,2,3,6,7,10,11,12],[0,1,2,3,6,7,10,11,13],[0,1,2,3,6,7,10,11,14],[0,1,2,3,6,7,10,11,15],[0,1,2,3,6,7,10,12,13],[0,1,2,3,6,7,10,12,14],[0,1,2,3,6,7,10,12,15],[0,1,2,3,6,7,10,13,14],[0,1,2,3,6,7,10,13,15],[0,1,2,3,6,7,10,14,15],[0,1,2,3,6,7,11,12,13],[0,1,2,3,6,7,11,12,14],[0,1,2,3,6,7,11,12,15],[0,1,2,3,6,7,11,13,14],[0,1,2,3,6,7,11,13,15],[0,1,2,3,6,7,11,14,15],[0,1,2,3,6,7,12,13,14],[0,1,2,3,6,7,12,13,15],[0,1,2,3,6,7,12,14,15],[0,1,2,3,6,7,13,14,15],[0,1,2,4,5,6,8,9,10],[0,1,2,4,5,6,8,9,10,11,12,13,14],[0,1,2,4,5,6,8,9,10,11,12,13,15],[0,1,2,4,5,6,8,9,10,11,12,14,15],[0,1,2,4,5,6,8,9,10,11,13,14,15],[0,1,2,4,5,6,8,9,10,12,13,14,15],[0,1,2,4,5,6,8,9,11],[0,1,2,4,5,6,8,9,11,12,13,14,15],[0,1,2,4,5,6,8,9,12],[0,1,2,4,5,6,8,9,13],[0,1,2,4,5,6,8,9,14],[0,1,2,4,5,6,8,9,15],[0,1,2,4,5,6,8,10,11],[0,1,2,4,5,6,8,10,11,12,13,14,15],[0,1,2,4,5,6,8,10,12],[0,1,2,4,5,6,8,10,13],[0,1,2,4,5,6,8,10,14],[0,1,2,4,5,6,8,10,15],[0,1,2,4,5,6,8,11,12],[0,1,2,4,5,6,8,11,13],[0,1,2,4,5,6,8,11,14],[0,1,2,4,5,6,8,11,15],[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],[0,1,2,4,5,6,8,13,14],[0,1,2,4,5,6,8,13,15],[0,1,2,4,5,6,8,14,15],[0,1,2,4,5,6,9,10,11],[0,1,2,4,5,6,9,10,11,12,13,14,15],[0,1,2,4,5,6,9,10,12],[0,1,2,4,5,6,9,10,13],[0,1,2,4,5,6,9,10,14],[0,1,2,4,5,6,9,10,15],[0,1,2,4,5,6,9,11,12],[0,1,2,4,5,6,9,11,13],[0,1,2,4,5,6,9,11,14],[0,1,2,4,5,6,9,11,15],[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],[0,1,2,4,5,6,9,13,14],[0,1,2,4,5,6,9,13,15],[0,1,2,4,5,6,9,14,15],[0,1,2,4,5,6,10,11,12],[0,1,2,4,5,6,10,11,13],[0,1,2,4,5,6,10,11,14],[0,1,2,4,5,6,10,11,15],[0,1,2,4,5,6,10,12,13],[0,1,2,4,5,6,10,12,14],[0,1,2,4,5,6,10,12,15],[0,1,2,4,5,6,10,13,14],[0,1,2,4,5,6,10,13,15],[0,1,2,4,5,6,10,14,15],[0,1,2,4,5,6,11,12,13],[0,1,2,4,5,6,11,12,14],[0,1,2,4,5,6,11,12,15],[0,1,2,4,5,6,11,13,14],[0,1,2,4,5,6,11,13,15],[0,1,2,4,5,6,11,14,15],[0,1,2,4,5,6,12,13,14],[0,1,2,4,5,6,12,13,15],[0,1,2,4,5,6,12,14,15],[0,1,2,4,5,6,13,14,15],[0,1,2,4,5,7,8,9,10],[0,1,2,4,5,7,8,9,10,11,12,13,14],[0,1,2,4,5,7,8,9,10,11,12,13,15],[0,1,2,4,5,7,8,9,10,11,12,14,15],[0,1,2,4,5,7,8,9,10,11,13,14,15],[0,1,2,4,5,7,8,9,10,12,13,14,15],[0,1,2,4,5,7,8,9,11],[0,1,2,4,5,7,8,9,11,12,13,14,15],[0,1,2,4,5,7,8,9,12],[0,1,2,4,5,7,8,9,13],[0,1,2,4,5,7,8,9,14],[0,1,2,4,5,7,8,9,15],[0,1,2,4,5,7,8,10,11],[0,1,2,4,5,7,8,10,11,12,13,14,15],[0,1,2,4,5,7,8,10,12],[0,1,2,4,5,7,8,10,13],[0,1,2,4,5,7,8,10,14],[0,1,2,4,5,7,8,10,15],[0,1,2,4,5,7,8,11,12],[0,1,2,4,5,7,8,11,13],[0,1,2,4,5,7,8,11,14],[0,1,2,4,5,7,8,11,15],[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],[0,1,2,4,5,7,8,13,14],[0,1,2,4,5,7,8,13,15],[0,1,2,4,5,7,8,14,15],[0,1,2,4,5,7,9,10,11],[0,1,2,4,5,7,9,10,11,12,13,14,15],[0,1,2,4,5,7,9,10,12],[0,1,2,4,5,7,9,10,13],[0,1,2,4,5,7,9,10,14],[0,1,2,4,5,7,9,10,15],[0,1,2,4,5,7,9,11,12],[0,1,2,4,5,7,9,11,13],[0,1,2,4,5,7,9,11,14],[0,1,2,4,5,7,9,11,15],[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],[0,1,2,4,5,7,9,13,14],[0,1,2,4,5,7,9,13,15],[0,1,2,4,5,7,9,14,15],[0,1,2,4,5,7,10,11,12],[0,1,2,4,5,7,10,11,13],[0,1,2,4,5,7,10,11,14],[0,1,2,4,5,7,10,11,15],[0,1,2,4,5,7,10,12,13],[0,1,2,4,5,7,10,12,14],[0,1,2,4,5,7,10,12,15],[0,1,2,4,5,7,10,13,14],[0,1,2,4,5,7,10,13,15],[0,1,2,4,5,7,10,14,15],[0,1,2,4,5,7,11,12,13],[0,1,2,4,5,7,11,12,14],[0,1,2,4,5,7,11,12,15],[0,1,2,4,5,7,11,13,14],[0,1,2,4,5,7,11,13,15],[0,1,2,4,5,7,11,14,15],[0,1,2,4,5,7,12,13,14],[0,1,2,4,5,7,12,13,15],[0,1,2,4,5,7,12,14,15],[0,1,2,4,5,7,13,14,15],[0,1,2,4,6,7,8,9,10],[0,1,2,4,6,7,8,9,10,11,12,13,14],[0,1,2,4,6,7,8,9,10,11,12,13,15],[0,1,2,4,6,7,8,9,10,11,12,14,15],[0,1,2,4,6,7,8,9,10,11,13,14,15],[0,1,2,4,6,7,8,9,10,12,13,14,15],[0,1,2,4,6,7,8,9,11],[0,1,2,4,6,7,8,9,11,12,13,14,15],[0,1,2,4,6,7,8,9,12],[0,1,2,4,6,7,8,9,13],[0,1,2,4,6,7,8,9,14],[0,1,2,4,6,7,8,9,15],[0,1,2,4,6,7,8,10,11],[0,1,2,4,6,7,8,10,11,12,13,14,15],[0,1,2,4,6,7,8,10,12],[0,1,2,4,6,7,8,10,13],[0,1,2,4,6,7,8,10,14],[0,1,2,4,6,7,8,10,15],[0,1,2,4,6,7,8,11,12],[0,1,2,4,6,7,8,11,13],[0,1,2,4,6,7,8,11,14],[0,1,2,4,6,7,8,11,15],[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],[0,1,2,4,6,7,8,13,14],[0,1,2,4,6,7,8,13,15],[0,1,2,4,6,7,8,14,15],[0,1,2,4,6,7,9,10,11],[0,1,2,4,6,7,9,10,11,12,13,14,15],[0,1,2,4,6,7,9,10,12],[0,1,2,4,6,7,9,10,13],[0,1,2,4,6,7,9,10,14],[0,1,2,4,6,7,9,10,15],[0,1,2,4,6,7,9,11,12],[0,1,2,4,6,7,9,11,13],[0,1,2,4,6,7,9,11,14],[0,1,2,4,6,7,9,11,15],[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],[0,1,2,4,6,7,9,13,14],[0,1,2,4,6,7,9,13,15],[0,1,2,4,6,7,9,14,15],[0,1,2,4,6,7,10,11,12],[0,1,2,4,6,7,10,11,13],[0,1,2,4,6,7,10,11,14],[0,1,2,4,6,7,10,11,15],[0,1,2,4,6,7,10,12,13],[0,1,2,4,6,7,10,12,14],[0,1,2,4,6,7,10,12,15],[0,1,2,4,6,7,10,13,14],[0,1,2,4,6,7,10,13,15],[0,1,2,4,6,7,10,14,15],[0,1,2,4,6,7,11,12,13],[0,1,2,4,6,7,11,12,14],[0,1,2,4,6,7,11,12,15],[0,1,2,4,6,7,11,13,14],[0,1,2,4,6,7,11,13,15],[0,1,2,4,6,7,11,14,15],[0,1,2,4,6,7,12,13,14],[0,1,2,4,6,7,12,13,15],[0,1,2,4,6,7,12,14,15],[0,1,2,4,6,7,13,14,15],[0,1,2,5,6,7,8,9,10],[0,1,2,5,6,7,8,9,10,11,12,13,14],[0,1,2,5,6,7,8,9,10,11,12,13,15],[0,1,2,5,6,7,8,9,10,11,12,14,15],[0,1,2,5,6,7,8,9,10,11,13,14,15],[0,1,2,5,6,7,8,9,10,12,13,14,15],[0,1,2,5,6,7,8,9,11],[0,1,2,5,6,7,8,9,11,12,13,14,15],[0,1,2,5,6,7,8,9,12],[0,1,2,5,6,7,8,9,13],[0,1,2,5,6,7,8,9,14],[0,1,2,5,6,7,8,9,15],[0,1,2,5,6,7,8,10,11],[0,1,2,5,6,7,8,10,11,12,13,14,15],[0,1,2,5,6,7,8,10,12],[0,1,2,5,6,7,8,10,13],[0,1,2,5,6,7,8,10,14],[0,1,2,5,6,7,8,10,15],[0,1,2,5,6,7,8,11,12],[0,1,2,5,6,7,8,11,13],[0,1,2,5,6,7,8,11,14],[0,1,2,5,6,7,8,11,15],[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],[0,1,2,5,6,7,8,13,14],[0,1,2,5,6,7,8,13,15],[0,1,2,5,6,7,8,14,15],[0,1,2,5,6,7,9,10,11],[0,1,2,5,6,7,9,10,11,12,13,14,15],[0,1,2,5,6,7,9,10,12],[0,1,2,5,6,7,9,10,13],[0,1,2,5,6,7,9,10,14],[0,1,2,5,6,7,9,10,15],[0,1,2,5,6,7,9,11,12],[0,1,2,5,6,7,9,11,13],[0,1,2,5,6,7,9,11,14],[0,1,2,5,6,7,9,11,15],[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],[0,1,2,5,6,7,9,13,14],[0,1,2,5,6,7,9,13,15],[0,1,2,5,6,7,9,14,15],[0,1,2,5,6,7,10,11,12],[0,1,2,5,6,7,10,11,13],[0,1,2,5,6,7,10,11,14],[0,1,2,5,6,7,10,11,15],[0,1,2,5,6,7,10,12,13],[0,1,2,5,6,7,10,12,14],[0,1,2,5,6,7,10,12,15],[0,1,2,5,6,7,10,13,14],[0,1,2,5,6,7,10,13,15],[0,1,2,5,6,7,10,14,15],[0,1,2,5,6,7,11,12,13],[0,1,2,5,6,7,11,12,14],[0,1,2,5,6,7,11,12,15],[0,1,2,5,6,7,11,13,14],[0,1,2,5,6,7,11,13,15],[0,1,2,5,6,7,11,14,15],[0,1,2,5,6,7,12,13,14],[0,1,2,5,6,7,12,13,15],[0,1,2,5,6,7,12,14,15],[0,1,2,5,6,7,13,14,15],[0,1,3,4,5,6,8,9,10],[0,1,3,4,5,6,8,9,10,11,12,13,14],[0,1,3,4,5,6,8,9,10,11,12,13,15],[0,1,3,4,5,6,8,9,10,11,12,14,15],[0,1,3,4,5,6,8,9,10,11,13,14,15],[0,1,3,4,5,6,8,9,10,12,13,14,15],[0,1,3,4,5,6,8,9,11],[0,1,3,4,5,6,8,9,11,12,13,14,15],[0,1,3,4,5,6,8,9,12],[0,1,3,4,5,6,8,9,13],[0,1,3,4,5,6,8,9,14],[0,1,3,4,5,6,8,9,15],[0,1,3,4,5,6,8,10,11],[0,1,3,4,5,6,8,10,11,12,13,14,15],[0,1,3,4,5,6,8,10,12],[0,1,3,4,5,6,8,10,13],[0,1,3,4,5,6,8,10,14],[0,1,3,4,5,6,8,10,15],[0,1,3,4,5,6,8,11,12],[0,1,3,4,5,6,8,11,13],[0,1,3,4,5,6,8,11,14],[0,1,3,4,5,6,8,11,15],[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],[0,1,3,4,5,6,8,13,14],[0,1,3,4,5,6,8,13,15],[0,1,3,4,5,6,8,14,15],[0,1,3,4,5,6,9,10,11],[0,1,3,4,5,6,9,10,11,12,13,14,15],[0,1,3,4,5,6,9,10,12],[0,1,3,4,5,6,9,10,13],[0,1,3,4,5,6,9,10,14],[0,1,3,4,5,6,9,10,15],[0,1,3,4,5,6,9,11,12],[0,1,3,4,5,6,9,11,13],[0,1,3,4,5,6,9,11,14],[0,1,3,4,5,6,9,11,15],[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],[0,1,3,4,5,6,9,13,14],[0,1,3,4,5,6,9,13,15],[0,1,3,4,5,6,9,14,15],[0,1,3,4,5,6,10,11,12],[0,1,3,4,5,6,10,11,13],[0,1,3,4,5,6,10,11,14],[0,1,3,4,5,6,10,11,15],[0,1,3,4,5,6,10,12,13],[0,1,3,4,5,6,10,12,14],[0,1,3,4,5,6,10,12,15],[0,1,3,4,5,6,10,13,14],[0,1,3,4,5,6,10,13,15],[0,1,3,4,5,6,10,14,15],[0,1,3,4,5,6,11,12,13],[0,1,3,4,5,6,11,12,14],[0,1,3,4,5,6,11,12,15],[0,1,3,4,5,6,11,13,14],[0,1,3,4,5,6,11,13,15],[0,1,3,4,5,6,11,14,15],[0,1,3,4,5,6,12,13,14],[0,1,3,4,5,6,12,13,15],[0,1,3,4,5,6,12,14,15],[0,1,3,4,5,6,13,14,15],[0,1,3,4,5,7,8,9,10],[0,1,3,4,5,7,8,9,10,11,12,13,14],[0,1,3,4,5,7,8,9,10,11,12,13,15],[0,1,3,4,5,7,8,9,10,11,12,14,15],[0,1,3,4,5,7,8,9,10,11,13,14,15],[0,1,3,4,5,7,8,9,10,12,13,14,15],[0,1,3,4,5,7,8,9,11],[0,1,3,4,5,7,8,9,11,12,13,14,15],[0,1,3,4,5,7,8,9,12],[0,1,3,4,5,7,8,9,13],[0,1,3,4,5,7,8,9,14],[0,1,3,4,5,7,8,9,15],[0,1,3,4,5,7,8,10,11],[0,1,3,4,5,7,8,10,11,12,13,14,15],[0,1,3,4,5,7,8,10,12],[0,1,3,4,5,7,8,10,13],[0,1,3,4,5,7,8,10,14],[0,1,3,4,5,7,8,10,15],[0,1,3,4,5,7,8,11,12],[0,1,3,4,5,7,8,11,13],[0,1,3,4,5,7,8,11,14],[0,1,3,4,5,7,8,11,15],[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],[0,1,3,4,5,7,8,13,14],[0,1,3,4,5,7,8,13,15],[0,1,3,4,5,7,8,14,15],[0,1,3,4,5,7,9,10,11],[0,1,3,4,5,7,9,10,11,12,13,14,15],[0,1,3,4,5,7,9,10,12],[0,1,3,4,5,7,9,10,13],[0,1,3,4,5,7,9,10,14],[0,1,3,4,5,7,9,10,15],[0,1,3,4,5,7,9,11,12],[0,1,3,4,5,7,9,11,13],[0,1,3,4,5,7,9,11,14],[0,1,3,4,5,7,9,11,15],[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],[0,1,3,4,5,7,9,13,14],[0,1,3,4,5,7,9,13,15],[0,1,3,4,5,7,9,14,15],[0,1,3,4,5,7,10,11,12],[0,1,3,4,5,7,10,11,13],[0,1,3,4,5,7,10,11,14],[0,1,3,4,5,7,10,11,15],[0,1,3,4,5,7,10,12,13],[0,1,3,4,5,7,10,12,14],[0,1,3,4,5,7,10,12,15],[0,1,3,4,5,7,10,13,14],[0,1,3,4,5,7,10,13,15],[0,1,3,4,5,7,10,14,15],[0,1,3,4,5,7,11,12,13],[0,1,3,4,5,7,11,12,14],[0,1,3,4,5,7,11,12,15],[0,1,3,4,5,7,11,13,14],[0,1,3,4,5,7,11,13,15],[0,1,3,4,5,7,11,14,15],[0,1,3,4,5,7,12,13,14],[0,1,3,4,5,7,12,13,15],[0,1,3,4,5,7,12,14,15],[0,1,3,4,5,7,13,14,15],[0,1,3,4,6,7,8,9,10],[0,1,3,4,6,7,8,9,10,11,12,13,14],[0,1,3,4,6,7,8,9,10,11,12,13,15],[0,1,3,4,6,7,8,9,10,11,12,14,15],[0,1,3,4,6,7,8,9,10,11,13,14,15],[0,1,3,4,6,7,8,9,10,12,13,14,15],[0,1,3,4,6,7,8,9,11],[0,1,3,4,6,7,8,9,11,12,13,14,15],[0,1,3,4,6,7,8,9,12],[0,1,3,4,6,7,8,9,13],[0,1,3,4,6,7,8,9,14],[0,1,3,4,6,7,8,9,15],[0,1,3,4,6,7,8,10,11],[0,1,3,4,6,7,8,10,11,12,13,14,15],[0,1,3,4,6,7,8,10,12],[0,1,3,4,6,7,8,10,13],[0,1,3,4,6,7,8,10,14],[0,1,3,4,6,7,8,10,15],[0,1,3,4,6,7,8,11,12],[0,1,3,4,6,7,8,11,13],[0,1,3,4,6,7,8,11,14],[0,1,3,4,6,7,8,11,15],[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],[0,1,3,4,6,7,8,13,14],[0,1,3,4,6,7,8,13,15],[0,1,3,4,6,7,8,14,15],[0,1,3,4,6,7,9,10,11],[0,1,3,4,6,7,9,10,11,12,13,14,15],[0,1,3,4,6,7,9,10,12],[0,1,3,4,6,7,9,10,13],[0,1,3,4,6,7,9,10,14],[0,1,3,4,6,7,9,10,15],[0,1,3,4,6,7,9,11,12],[0,1,3,4,6,7,9,11,13],[0,1,3,4,6,7,9,11,14],[0,1,3,4,6,7,9,11,15],[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],[0,1,3,4,6,7,9,13,14],[0,1,3,4,6,7,9,13,15],[0,1,3,4,6,7,9,14,15],[0,1,3,4,6,7,10,11,12],[0,1,3,4,6,7,10,11,13],[0,1,3,4,6,7,10,11,14],[0,1,3,4,6,7,10,11,15],[0,1,3,4,6,7,10,12,13],[0,1,3,4,6,7,10,12,14],[0,1,3,4,6,7,10,12,15],[0,1,3,4,6,7,10,13,14],[0,1,3,4,6,7,10,13,15],[0,1,3,4,6,7,10,14,15],[0,1,3,4,6,7,11,12,13],[0,1,3,4,6,7,11,12,14],[0,1,3,4,6,7,11,12,15],[0,1,3,4,6,7,11,13,14],[0,1,3,4,6,7,11,13,15],[0,1,3,4,6,7,11,14,15],[0,1,3,4,6,7,12,13,14],[0,1,3,4,6,7,12,13,15],[0,1,3,4,6,7,12,14,15],[0,1,3,4,6,7,13,14,15],[0,1,3,5,6,7,8,9,10],[0,1,3,5,6,7,8,9,10,11,12,13,14],[0,1,3,5,6,7,8,9,10,11,12,13,15],[0,1,3,5,6,7,8,9,10,11,12,14,15],[0,1,3,5,6,7,8,9,10,11,13,14,15],[0,1,3,5,6,7,8,9,10,12,13,14,15],[0,1,3,5,6,7,8,9,11],[0,1,3,5,6,7,8,9,11,12,13,14,15],[0,1,3,5,6,7,8,9,12],[0,1,3,5,6,7,8,9,13],[0,1,3,5,6,7,8,9,14],[0,1,3,5,6,7,8,9,15],[0,1,3,5,6,7,8,10,11],[0,1,3,5,6,7,8,10,11,12,13,14,15],[0,1,3,5,6,7,8,10,12],[0,1,3,5,6,7,8,10,13],[0,1,3,5,6,7,8,10,14],[0,1,3,5,6,7,8,10,15],[0,1,3,5,6,7,8,11,12],[0,1,3,5,6,7,8,11,13],[0,1,3,5,6,7,8,11,14],[0,1,3,5,6,7,8,11,15],[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],[0,1,3,5,6,7,8,13,14],[0,1,3,5,6,7,8,13,15],[0,1,3,5,6,7,8,14,15],[0,1,3,5,6,7,9,10,11],[0,1,3,5,6,7,9,10,11,12,13,14,15],[0,1,3,5,6,7,9,10,12],[0,1,3,5,6,7,9,10,13],[0,1,3,5,6,7,9,10,14],[0,1,3,5,6,7,9,10,15],[0,1,3,5,6,7,9,11,12],[0,1,3,5,6,7,9,11,13],[0,1,3,5,6,7,9,11,14],[0,1,3,5,6,7,9,11,15],[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],[0,1,3,5,6,7,9,13,14],[0,1,3,5,6,7,9,13,15],[0,1,3,5,6,7,9,14,15],[0,1,3,5,6,7,10,11,12],[0,1,3,5,6,7,10,11,13],[0,1,3,5,6,7,10,11,14],[0,1,3,5,6,7,10,11,15],[0,1,3,5,6,7,10,12,13],[0,1,3,5,6,7,10,12,14],[0,1,3,5,6,7,10,12,15],[0,1,3,5,6,7,10,13,14],[0,1,3,5,6,7,10,13,15],[0,1,3,5,6,7,10,14,15],[0,1,3,5,6,7,11,12,13],[0,1,3,5,6,7,11,12,14],[0,1,3,5,6,7,11,12,15],[0,1,3,5,6,7,11,13,14],[0,1,3,5,6,7,11,13,15],[0,1,3,5,6,7,11,14,15],[0,1,3,5,6,7,12,13,14],[0,1,3,5,6,7,12,13,15],[0,1,3,5,6,7,12,14,15],[0,1,3,5,6,7,13,14,15],[0,1,4,5,6,7,8,9,10],[0,1,4,5,6,7,8,9,10,11,12,13,14],[0,1,4,5,6,7,8,9,10,11,12,13,15],[0,1,4,5,6,7,8,9,10,11,12,14,15],[0,1,4,5,6,7,8,9,10,11,13,14,15],[0,1,4,5,6,7,8,9,10,12,13,14,15],[0,1,4,5,6,7,8,9,11],[0,1,4,5,6,7,8,9,11,12,13,14,15],[0,1,4,5,6,7,8,9,12],[0,1,4,5,6,7,8,9,13],[0,1,4,5,6,7,8,9,14],[0,1,4,5,6,7,8,9,15],[0,1,4,5,6,7,8,10,11],[0,1,4,5,6,7,8,10,11,12,13,14,15],[0,1,4,5,6,7,8,10,12],[0,1,4,5,6,7,8,10,13],[0,1,4,5,6,7,8,10,14],[0,1,4,5,6,7,8,10,15],[0,1,4,5,6,7,8,11,12],[0,1,4,5,6,7,8,11,13],[0,1,4,5,6,7,8,11,14],[0,1,4,5,6,7,8,11,15],[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],[0,1,4,5,6,7,8,13,14],[0,1,4,5,6,7,8,13,15],[0,1,4,5,6,7,8,14,15],[0,1,4,5,6,7,9,10,11],[0,1,4,5,6,7,9,10,11,12,13,14,15],[0,1,4,5,6,7,9,10,12],[0,1,4,5,6,7,9,10,13],[0,1,4,5,6,7,9,10,14],[0,1,4,5,6,7,9,10,15],[0,1,4,5,6,7,9,11,12],[0,1,4,5,6,7,9,11,13],[0,1,4,5,6,7,9,11,14],[0,1,4,5,6,7,9,11,15],[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],[0,1,4,5,6,7,9,13,14],[0,1,4,5,6,7,9,13,15],[0,1,4,5,6,7,9,14,15],[0,1,4,5,6,7,10,11,12],[0,1,4,5,6,7,10,11,13],[0,1,4,5,6,7,10,11,14],[0,1,4,5,6,7,10,11,15],[0,1,4,5,6,7,10,12,13],[0,1,4,5,6,7,10,12,14],[0,1,4,5,6,7,10,12,15],[0,1,4,5,6,7,10,13,14],[0,1,4,5,6,7,10,13,15],[0,1,4,5,6,7,10,14,15],[0,1,4,5,6,7,11,12,13],[0,1,4,5,6,7,11,12,14],[0,1,4,5,6,7,11,12,15],[0,1,4,5,6,7,11,13,14],[0,1,4,5,6,7,11,13,15],[0,1,4,5,6,7,11,14,15],[0,1,4,5,6,7,12,13,14],[0,1,4,5,6,7,12,13,15],[0,1,4,5,6,7,12,14,15],[0,1,4,5,6,7,13,14,15],[0,2,3,4,5,6,8,9,10],[0,2,3,4,5,6,8,9,10,11,12,13,14],[0,2,3,4,5,6,8,9,10,11,12,13,15],[0,2,3,4,5,6,8,9,10,11,12,14,15],[0,2,3,4,5,6,8,9,10,11,13,14,15],[0,2,3,4,5,6,8,9,10,12,13,14,15],[0,2,3,4,5,6,8,9,11],[0,2,3,4,5,6,8,9,11,12,13,14,15],[0,2,3,4,5,6,8,9,12],[0,2,3,4,5,6,8,9,13],[0,2,3,4,5,6,8,9,14],[0,2,3,4,5,6,8,9,15],[0,2,3,4,5,6,8,10,11],[0,2,3,4,5,6,8,10,11,12,13,14,15],[0,2,3,4,5,6,8,10,12],[0,2,3,4,5,6,8,10,13],[0,2,3,4,5,6,8,10,14],[0,2,3,4,5,6,8,10,15],[0,2,3,4,5,6,8,11,12],[0,2,3,4,5,6,8,11,13],[0,2,3,4,5,6,8,11,14],[0,2,3,4,5,6,8,11,15],[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],[0,2,3,4,5,6,8,13,14],[0,2,3,4,5,6,8,13,15],[0,2,3,4,5,6,8,14,15],[0,2,3,4,5,6,9,10,11],[0,2,3,4,5,6,9,10,11,12,13,14,15],[0,2,3,4,5,6,9,10,12],[0,2,3,4,5,6,9,10,13],[0,2,3,4,5,6,9,10,14],[0,2,3,4,5,6,9,10,15],[0,2,3,4,5,6,9,11,12],[0,2,3,4,5,6,9,11,13],[0,2,3,4,5,6,9,11,14],[0,2,3,4,5,6,9,11,15],[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],[0,2,3,4,5,6,9,13,14],[0,2,3,4,5,6,9,13,15],[0,2,3,4,5,6,9,14,15],[0,2,3,4,5,6,10,11,12],[0,2,3,4,5,6,10,11,13],[0,2,3,4,5,6,10,11,14],[0,2,3,4,5,6,10,11,15],[0,2,3,4,5,6,10,12,13],[0,2,3,4,5,6,10,12,14],[0,2,3,4,5,6,10,12,15],[0,2,3,4,5,6,10,13,14],[0,2,3,4,5,6,10,13,15],[0,2,3,4,5,6,10,14,15],[0,2,3,4,5,6,11,12,13],[0,2,3,4,5,6,11,12,14],[0,2,3,4,5,6,11,12,15],[0,2,3,4,5,6,11,13,14],[0,2,3,4,5,6,11,13,15],[0,2,3,4,5,6,11,14,15],[0,2,3,4,5,6,12,13,14],[0,2,3,4,5,6,12,13,15],[0,2,3,4,5,6,12,14,15],[0,2,3,4,5,6,13,14,15],[0,2,3,4,5,7,8,9,10],[0,2,3,4,5,7,8,9,10,11,12,13,14],[0,2,3,4,5,7,8,9,10,11,12,13,15],[0,2,3,4,5,7,8,9,10,11,12,14,15],[0,2,3,4,5,7,8,9,10,11,13,14,15],[0,2,3,4,5,7,8,9,10,12,13,14,15],[0,2,3,4,5,7,8,9,11],[0,2,3,4,5,7,8,9,11,12,13,14,15],[0,2,3,4,5,7,8,9,12],[0,2,3,4,5,7,8,9,13],[0,2,3,4,5,7,8,9,14],[0,2,3,4,5,7,8,9,15],[0,2,3,4,5,7,8,10,11],[0,2,3,4,5,7,8,10,11,12,13,14,15],[0,2,3,4,5,7,8,10,12],[0,2,3,4,5,7,8,10,13],[0,2,3,4,5,7,8,10,14],[0,2,3,4,5,7,8,10,15],[0,2,3,4,5,7,8,11,12],[0,2,3,4,5,7,8,11,13],[0,2,3,4,5,7,8,11,14],[0,2,3,4,5,7,8,11,15],[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],[0,2,3,4,5,7,8,13,14],[0,2,3,4,5,7,8,13,15],[0,2,3,4,5,7,8,14,15],[0,2,3,4,5,7,9,10,11],[0,2,3,4,5,7,9,10,11,12,13,14,15],[0,2,3,4,5,7,9,10,12],[0,2,3,4,5,7,9,10,13],[0,2,3,4,5,7,9,10,14],[0,2,3,4,5,7,9,10,15],[0,2,3,4,5,7,9,11,12],[0,2,3,4,5,7,9,11,13],[0,2,3,4,5,7,9,11,14],[0,2,3,4,5,7,9,11,15],[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],[0,2,3,4,5,7,9,13,14],[0,2,3,4,5,7,9,13,15],[0,2,3,4,5,7,9,14,15],[0,2,3,4,5,7,10,11,12],[0,2,3,4,5,7,10,11,13],[0,2,3,4,5,7,10,11,14],[0,2,3,4,5,7,10,11,15],[0,2,3,4,5,7,10,12,13],[0,2,3,4,5,7,10,12,14],[0,2,3,4,5,7,10,12,15],[0,2,3,4,5,7,10,13,14],[0,2,3,4,5,7,10,13,15],[0,2,3,4,5,7,10,14,15],[0,2,3,4,5,7,11,12,13],[0,2,3,4,5,7,11,12,14],[0,2,3,4,5,7,11,12,15],[0,2,3,4,5,7,11,13,14],[0,2,3,4,5,7,11,13,15],[0,2,3,4,5,7,11,14,15],[0,2,3,4,5,7,12,13,14],[0,2,3,4,5,7,12,13,15],[0,2,3,4,5,7,12,14,15],[0,2,3,4,5,7,13,14,15],[0,2,3,4,6,7,8,9,10],[0,2,3,4,6,7,8,9,10,11,12,13,14],[0,2,3,4,6,7,8,9,10,11,12,13,15],[0,2,3,4,6,7,8,9,10,11,12,14,15],[0,2,3,4,6,7,8,9,10,11,13,14,15],[0,2,3,4,6,7,8,9,10,12,13,14,15],[0,2,3,4,6,7,8,9,11],[0,2,3,4,6,7,8,9,11,12,13,14,15],[0,2,3,4,6,7,8,9,12],[0,2,3,4,6,7,8,9,13],[0,2,3,4,6,7,8,9,14],[0,2,3,4,6,7,8,9,15],[0,2,3,4,6,7,8,10,11],[0,2,3,4,6,7,8,10,11,12,13,14,15],[0,2,3,4,6,7,8,10,12],[0,2,3,4,6,7,8,10,13],[0,2,3,4,6,7,8,10,14],[0,2,3,4,6,7,8,10,15],[0,2,3,4,6,7,8,11,12],[0,2,3,4,6,7,8,11,13],[0,2,3,4,6,7,8,11,14],[0,2,3,4,6,7,8,11,15],[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],[0,2,3,4,6,7,8,13,14],[0,2,3,4,6,7,8,13,15],[0,2,3,4,6,7,8,14,15],[0,2,3,4,6,7,9,10,11],[0,2,3,4,6,7,9,10,11,12,13,14,15],[0,2,3,4,6,7,9,10,12],[0,2,3,4,6,7,9,10,13],[0,2,3,4,6,7,9,10,14],[0,2,3,4,6,7,9,10,15],[0,2,3,4,6,7,9,11,12],[0,2,3,4,6,7,9,11,13],[0,2,3,4,6,7,9,11,14],[0,2,3,4,6,7,9,11,15],[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],[0,2,3,4,6,7,9,13,14],[0,2,3,4,6,7,9,13,15],[0,2,3,4,6,7,9,14,15],[0,2,3,4,6,7,10,11,12],[0,2,3,4,6,7,10,11,13],[0,2,3,4,6,7,10,11,14],[0,2,3,4,6,7,10,11,15],[0,2,3,4,6,7,10,12,13],[0,2,3,4,6,7,10,12,14],[0,2,3,4,6,7,10,12,15],[0,2,3,4,6,7,10,13,14],[0,2,3,4,6,7,10,13,15],[0,2,3,4,6,7,10,14,15],[0,2,3,4,6,7,11,12,13],[0,2,3,4,6,7,11,12,14],[0,2,3,4,6,7,11,12,15],[0,2,3,4,6,7,11,13,14],[0,2,3,4,6,7,11,13,15],[0,2,3,4,6,7,11,14,15],[0,2,3,4,6,7,12,13,14],[0,2,3,4,6,7,12,13,15],[0,2,3,4,6,7,12,14,15],[0,2,3,4,6,7,13,14,15],[0,2,3,5,6,7,8,9,10],[0,2,3,5,6,7,8,9,10,11,12,13,14],[0,2,3,5,6,7,8,9,10,11,12,13,15],[0,2,3,5,6,7,8,9,10,11,12,14,15],[0,2,3,5,6,7,8,9,10,11,13,14,15],[0,2,3,5,6,7,8,9,10,12,13,14,15],[0,2,3,5,6,7,8,9,11],[0,2,3,5,6,7,8,9,11,12,13,14,15],[0,2,3,5,6,7,8,9,12],[0,2,3,5,6,7,8,9,13],[0,2,3,5,6,7,8,9,14],[0,2,3,5,6,7,8,9,15],[0,2,3,5,6,7,8,10,11],[0,2,3,5,6,7,8,10,11,12,13,14,15],[0,2,3,5,6,7,8,10,12],[0,2,3,5,6,7,8,10,13],[0,2,3,5,6,7,8,10,14],[0,2,3,5,6,7,8,10,15],[0,2,3,5,6,7,8,11,12],[0,2,3,5,6,7,8,11,13],[0,2,3,5,6,7,8,11,14],[0,2,3,5,6,7,8,11,15],[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],[0,2,3,5,6,7,8,13,14],[0,2,3,5,6,7,8,13,15],[0,2,3,5,6,7,8,14,15],[0,2,3,5,6,7,9,10,11],[0,2,3,5,6,7,9,10,11,12,13,14,15],[0,2,3,5,6,7,9,10,12],[0,2,3,5,6,7,9,10,13],[0,2,3,5,6,7,9,10,14],[0,2,3,5,6,7,9,10,15],[0,2,3,5,6,7,9,11,12],[0,2,3,5,6,7,9,11,13],[0,2,3,5,6,7,9,11,14],[0,2,3,5,6,7,9,11,15],[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],[0,2,3,5,6,7,9,13,14],[0,2,3,5,6,7,9,13,15],[0,2,3,5,6,7,9,14,15],[0,2,3,5,6,7,10,11,12],[0,2,3,5,6,7,10,11,13],[0,2,3,5,6,7,10,11,14],[0,2,3,5,6,7,10,11,15],[0,2,3,5,6,7,10,12,13],[0,2,3,5,6,7,10,12,14],[0,2,3,5,6,7,10,12,15],[0,2,3,5,6,7,10,13,14],[0,2,3,5,6,7,10,13,15],[0,2,3,5,6,7,10,14,15],[0,2,3,5,6,7,11,12,13],[0,2,3,5,6,7,11,12,14],[0,2,3,5,6,7,11,12,15],[0,2,3,5,6,7,11,13,14],[0,2,3,5,6,7,11,13,15],[0,2,3,5,6,7,11,14,15],[0,2,3,5,6,7,12,13,14],[0,2,3,5,6,7,12,13,15],[0,2,3,5,6,7,12,14,15],[0,2,3,5,6,7,13,14,15],[0,2,4,5,6,7,8,9,10],[0,2,4,5,6,7,8,9,10,11,12,13,14],[0,2,4,5,6,7,8,9,10,11,12,13,15],[0,2,4,5,6,7,8,9,10,11,12,14,15],[0,2,4,5,6,7,8,9,10,11,13,14,15],[0,2,4,5,6,7,8,9,10,12,13,14,15],[0,2,4,5,6,7,8,9,11],[0,2,4,5,6,7,8,9,11,12,13,14,15],[0,2,4,5,6,7,8,9,12],[0,2,4,5,6,7,8,9,13],[0,2,4,5,6,7,8,9,14],[0,2,4,5,6,7,8,9,15],[0,2,4,5,6,7,8,10,11],[0,2,4,5,6,7,8,10,11,12,13,14,15],[0,2,4,5,6,7,8,10,12],[0,2,4,5,6,7,8,10,13],[0,2,4,5,6,7,8,10,14],[0,2,4,5,6,7,8,10,15],[0,2,4,5,6,7,8,11,12],[0,2,4,5,6,7,8,11,13],[0,2,4,5,6,7,8,11,14],[0,2,4,5,6,7,8,11,15],[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],[0,2,4,5,6,7,8,13,14],[0,2,4,5,6,7,8,13,15],[0,2,4,5,6,7,8,14,15],[0,2,4,5,6,7,9,10,11],[0,2,4,5,6,7,9,10,11,12,13,14,15],[0,2,4,5,6,7,9,10,12],[0,2,4,5,6,7,9,10,13],[0,2,4,5,6,7,9,10,14],[0,2,4,5,6,7,9,10,15],[0,2,4,5,6,7,9,11,12],[0,2,4,5,6,7,9,11,13],[0,2,4,5,6,7,9,11,14],[0,2,4,5,6,7,9,11,15],[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],[0,2,4,5,6,7,9,13,14],[0,2,4,5,6,7,9,13,15],[0,2,4,5,6,7,9,14,15],[0,2,4,5,6,7,10,11,12],[0,2,4,5,6,7,10,11,13],[0,2,4,5,6,7,10,11,14],[0,2,4,5,6,7,10,11,15],[0,2,4,5,6,7,10,12,13],[0,2,4,5,6,7,10,12,14],[0,2,4,5,6,7,10,12,15],[0,2,4,5,6,7,10,13,14],[0,2,4,5,6,7,10,13,15],[0,2,4,5,6,7,10,14,15],[0,2,4,5,6,7,11,12,13],[0,2,4,5,6,7,11,12,14],[0,2,4,5,6,7,11,12,15],[0,2,4,5,6,7,11,13,14],[0,2,4,5,6,7,11,13,15],[0,2,4,5,6,7,11,14,15],[0,2,4,5,6,7,12,13,14],[0,2,4,5,6,7,12,13,15],[0,2,4,5,6,7,12,14,15],[0,2,4,5,6,7,13,14,15],[0,3,4,5,6,7,8,9,10],[0,3,4,5,6,7,8,9,10,11,12,13,14],[0,3,4,5,6,7,8,9,10,11,12,13,15],[0,3,4,5,6,7,8,9,10,11,12,14,15],[0,3,4,5,6,7,8,9,10,11,13,14,15],[0,3,4,5,6,7,8,9,10,12,13,14,15],[0,3,4,5,6,7,8,9,11],[0,3,4,5,6,7,8,9,11,12,13,14,15],[0,3,4,5,6,7,8,9,12],[0,3,4,5,6,7,8,9,13],[0,3,4,5,6,7,8,9,14],[0,3,4,5,6,7,8,9,15],[0,3,4,5,6,7,8,10,11],[0,3,4,5,6,7,8,10,11,12,13,14,15],[0,3,4,5,6,7,8,10,12],[0,3,4,5,6,7,8,10,13],[0,3,4,5,6,7,8,10,14],[0,3,4,5,6,7,8,10,15],[0,3,4,5,6,7,8,11,12],[0,3,4,5,6,7,8,11,13],[0,3,4,5,6,7,8,11,14],[0,3,4,5,6,7,8,11,15],[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],[0,3,4,5,6,7,8,13,14],[0,3,4,5,6,7,8,13,15],[0,3,4,5,6,7,8,14,15],[0,3,4,5,6,7,9,10,11],[0,3,4,5,6,7,9,10,11,12,13,14,15],[0,3,4,5,6,7,9,10,12],[0,3,4,5,6,7,9,10,13],[0,3,4,5,6,7,9,10,14],[0,3,4,5,6,7,9,10,15],[0,3,4,5,6,7,9,11,12],[0,3,4,5,6,7,9,11,13],[0,3,4,5,6,7,9,11,14],[0,3,4,5,6,7,9,11,15],[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],[0,3,4,5,6,7,9,13,14],[0,3,4,5,6,7,9,13,15],[0,3,4,5,6,7,9,14,15],[0,3,4,5,6,7,10,11,12],[0,3,4,5,6,7,10,11,13],[0,3,4,5,6,7,10,11,14],[0,3,4,5,6,7,10,11,15],[0,3,4,5,6,7,10,12,13],[0,3,4,5,6,7,10,12,14],[0,3,4,5,6,7,10,12,15],[0,3,4,5,6,7,10,13,14],[0,3,4,5,6,7,10,13,15],[0,3,4,5,6,7,10,14,15],[0,3,4,5,6,7,11,12,13],[0,3,4,5,6,7,11,12,14],[0,3,4,5,6,7,11,12,15],[0,3,4,5,6,7,11,13,14],[0,3,4,5,6,7,11,13,15],[0,3,4,5,6,7,11,14,15],[0,3,4,5,6,7,12,13,14],[0,3,4,5,6,7,12,13,15],[0,3,4,5,6,7,12,14,15],[0,3,4,5,6,7,13,14,15],[0,8,9,10,11],[0,8,9,10,11,12,13,14,15],[0,8,9,10,12],[0,8,9,10,13],[0,8,9,10,14],[0,8,9,10,15],[0,8,9,11,12],[0,8,9,11,13],[0,8,9,11,14],[0,8,9,11,15],[0,8,9,12,13],[0,8,9,12,14],[0,8,9,12,15],[0,8,9,13,14],[0,8,9,13,15],[0,8,9,14,15],[0,8,10,11,12],[0,8,10,11,13],[0,8,10,11,14],[0,8,10,11,15],[0,8,10,12,13],[0,8,10,12,14],[0,8,10,12,15],[0,8,10,13,14],[0,8,10,13,15],[0,8,10,14,15],[0,8,11,12,13],[0,8,11,12,14],[0,8,11,12,15],[0,8,11,13,14],[0,8,11,13,15],[0,8,11,14,15],[0,8,12,13,14],[0,8,12,13,15],[0,8,12,14,15],[0,8,13,14,15],[0,9,10,11,12],[0,9,10,11,13],[0,9,10,11,14],[0,9,10,11,15],[0,9,10,12,13],[0,9,10,12,14],[0,9,10,12,15],[0,9,10,13,14],[0,9,10,13,15],[0,9,10,14,15],[0,9,11,12,13],[0,9,11,12,14],[0,9,11,12,15],[0,9,11,13,14],[0,9,11,13,15],[0,9,11,14,15],[0,9,12,13,14],[0,9,12,13,15],[0,9,12,14,15],[0,9,13,14,15],[0,10,11,12,13],[0,10,11,12,14],[0,10,11,12,15],[0,10,11,13,14],[0,10,11,13,15],[0,10,11,14,15],[0,10,12,13,14],[0,10,12,13,15],[0,10,12,14,15],[0,10,13,14,15],[0,11,12,13,14],[0,11,12,13,15],[0,11,12,14,15],[0,11,13,14,15],[0,12,13,14,15],[1,2,3,4,5,6,8,9,10],[1,2,3,4,5,6,8,9,10,11,12,13,14],[1,2,3,4,5,6,8,9,10,11,12,13,15],[1,2,3,4,5,6,8,9,10,11,12,14,15],[1,2,3,4,5,6,8,9,10,11,13,14,15],[1,2,3,4,5,6,8,9,10,12,13,14,15],[1,2,3,4,5,6,8,9,11],[1,2,3,4,5,6,8,9,11,12,13,14,15],[1,2,3,4,5,6,8,9,12],[1,2,3,4,5,6,8,9,13],[1,2,3,4,5,6,8,9,14],[1,2,3,4,5,6,8,9,15],[1,2,3,4,5,6,8,10,11],[1,2,3,4,5,6,8,10,11,12,13,14,15],[1,2,3,4,5,6,8,10,12],[1,2,3,4,5,6,8,10,13],[1,2,3,4,5,6,8,10,14],[1,2,3,4,5,6,8,10,15],[1,2,3,4,5,6,8,11,12],[1,2,3,4,5,6,8,11,13],[1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,8,11,15],[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],[1,2,3,4,5,6,8,13,14],[1,2,3,4,5,6,8,13,15],[1,2,3,4,5,6,8,14,15],[1,2,3,4,5,6,9,10,11],[1,2,3,4,5,6,9,10,11,12,13,14,15],[1,2,3,4,5,6,9,10,12],[1,2,3,4,5,6,9,10,13],[1,2,3,4,5,6,9,10,14],[1,2,3,4,5,6,9,10,15],[1,2,3,4,5,6,9,11,12],[1,2,3,4,5,6,9,11,13],[1,2,3,4,5,6,9,11,14],[1,2,3,4,5,6,9,11,15],[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],[1,2,3,4,5,6,9,13,14],[1,2,3,4,5,6,9,13,15],[1,2,3,4,5,6,9,14,15],[1,2,3,4,5,6,10,11,12],[1,2,3,4,5,6,10,11,13],[1,2,3,4,5,6,10,11,14],[1,2,3,4,5,6,10,11,15],[1,2,3,4,5,6,10,12,13],[1,2,3,4,5,6,10,12,14],[1,2,3,4,5,6,10,12,15],[1,2,3,4,5,6,10,13,14],[1,2,3,4,5,6,10,13,15],[1,2,3,4,5,6,10,14,15],[1,2,3,4,5,6,11,12,13],[1,2,3,4,5,6,11,12,14],[1,2,3,4,5,6,11,12,15],[1,2,3,4,5,6,11,13,14],[1,2,3,4,5,6,11,13,15],[1,2,3,4,5,6,11,14,15],[1,2,3,4,5,6,12,13,14],[1,2,3,4,5,6,12,13,15],[1,2,3,4,5,6,12,14,15],[1,2,3,4,5,6,13,14,15],[1,2,3,4,5,7,8,9,10],[1,2,3,4,5,7,8,9,10,11,12,13,14],[1,2,3,4,5,7,8,9,10,11,12,13,15],[1,2,3,4,5,7,8,9,10,11,12,14,15],[1,2,3,4,5,7,8,9,10,11,13,14,15],[1,2,3,4,5,7,8,9,10,12,13,14,15],[1,2,3,4,5,7,8,9,11],[1,2,3,4,5,7,8,9,11,12,13,14,15],[1,2,3,4,5,7,8,9,12],[1,2,3,4,5,7,8,9,13],[1,2,3,4,5,7,8,9,14],[1,2,3,4,5,7,8,9,15],[1,2,3,4,5,7,8,10,11],[1,2,3,4,5,7,8,10,11,12,13,14,15],[1,2,3,4,5,7,8,10,12],[1,2,3,4,5,7,8,10,13],[1,2,3,4,5,7,8,10,14],[1,2,3,4,5,7,8,10,15],[1,2,3,4,5,7,8,11,12],[1,2,3,4,5,7,8,11,13],[1,2,3,4,5,7,8,11,14],[1,2,3,4,5,7,8,11,15],[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],[1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,8,13,15],[1,2,3,4,5,7,8,14,15],[1,2,3,4,5,7,9,10,11],[1,2,3,4,5,7,9,10,11,12,13,14,15],[1,2,3,4,5,7,9,10,12],[1,2,3,4,5,7,9,10,13],[1,2,3,4,5,7,9,10,14],[1,2,3,4,5,7,9,10,15],[1,2,3,4,5,7,9,11,12],[1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,9,11,14],[1,2,3,4,5,7,9,11,15],[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],[1,2,3,4,5,7,9,13,14],[1,2,3,4,5,7,9,13,15],[1,2,3,4,5,7,9,14,15],[1,2,3,4,5,7,10,11,12],[1,2,3,4,5,7,10,11,13],[1,2,3,4,5,7,10,11,14],[1,2,3,4,5,7,10,11,15],[1,2,3,4,5,7,10,12,13],[1,2,3,4,5,7,10,12,14],[1,2,3,4,5,7,10,12,15],[1,2,3,4,5,7,10,13,14],[1,2,3,4,5,7,10,13,15],[1,2,3,4,5,7,10,14,15],[1,2,3,4,5,7,11,12,13],[1,2,3,4,5,7,11,12,14],[1,2,3,4,5,7,11,12,15],[1,2,3,4,5,7,11,13,14],[1,2,3,4,5,7,11,13,15],[1,2,3,4,5,7,11,14,15],[1,2,3,4,5,7,12,13,14],[1,2,3,4,5,7,12,13,15],[1,2,3,4,5,7,12,14,15],[1,2,3,4,5,7,13,14,15],[1,2,3,4,6,7,8,9,10],[1,2,3,4,6,7,8,9,10,11,12,13,14],[1,2,3,4,6,7,8,9,10,11,12,13,15],[1,2,3,4,6,7,8,9,10,11,12,14,15],[1,2,3,4,6,7,8,9,10,11,13,14,15],[1,2,3,4,6,7,8,9,10,12,13,14,15],[1,2,3,4,6,7,8,9,11],[1,2,3,4,6,7,8,9,11,12,13,14,15],[1,2,3,4,6,7,8,9,12],[1,2,3,4,6,7,8,9,13],[1,2,3,4,6,7,8,9,14],[1,2,3,4,6,7,8,9,15],[1,2,3,4,6,7,8,10,11],[1,2,3,4,6,7,8,10,11,12,13,14,15],[1,2,3,4,6,7,8,10,12],[1,2,3,4,6,7,8,10,13],[1,2,3,4,6,7,8,10,14],[1,2,3,4,6,7,8,10,15],[1,2,3,4,6,7,8,11,12],[1,2,3,4,6,7,8,11,13],[1,2,3,4,6,7,8,11,14],[1,2,3,4,6,7,8,11,15],[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],[1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,8,13,15],[1,2,3,4,6,7,8,14,15],[1,2,3,4,6,7,9,10,11],[1,2,3,4,6,7,9,10,11,12,13,14,15],[1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,9,10,13],[1,2,3,4,6,7,9,10,14],[1,2,3,4,6,7,9,10,15],[1,2,3,4,6,7,9,11,12],[1,2,3,4,6,7,9,11,13],[1,2,3,4,6,7,9,11,14],[1,2,3,4,6,7,9,11,15],[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],[1,2,3,4,6,7,9,13,14],[1,2,3,4,6,7,9,13,15],[1,2,3,4,6,7,9,14,15],[1,2,3,4,6,7,10,11,12],[1,2,3,4,6,7,10,11,13],[1,2,3,4,6,7,10,11,14],[1,2,3,4,6,7,10,11,15],[1,2,3,4,6,7,10,12,13],[1,2,3,4,6,7,10,12,14],[1,2,3,4,6,7,10,12,15],[1,2,3,4,6,7,10,13,14],[1,2,3,4,6,7,10,13,15],[1,2,3,4,6,7,10,14,15],[1,2,3,4,6,7,11,12,13],[1,2,3,4,6,7,11,12,14],[1,2,3,4,6,7,11,12,15],[1,2,3,4,6,7,11,13,14],[1,2,3,4,6,7,11,13,15],[1,2,3,4,6,7,11,14,15],[1,2,3,4,6,7,12,13,14],[1,2,3,4,6,7,12,13,15],[1,2,3,4,6,7,12,14,15],[1,2,3,4,6,7,13,14,15],[1,2,3,5,6,7,8,9,10],[1,2,3,5,6,7,8,9,10,11,12,13,14],[1,2,3,5,6,7,8,9,10,11,12,13,15],[1,2,3,5,6,7,8,9,10,11,12,14,15],[1,2,3,5,6,7,8,9,10,11,13,14,15],[1,2,3,5,6,7,8,9,10,12,13,14,15],[1,2,3,5,6,7,8,9,11],[1,2,3,5,6,7,8,9,11,12,13,14,15],[1,2,3,5,6,7,8,9,12],[1,2,3,5,6,7,8,9,13],[1,2,3,5,6,7,8,9,14],[1,2,3,5,6,7,8,9,15],[1,2,3,5,6,7,8,10,11],[1,2,3,5,6,7,8,10,11,12,13,14,15],[1,2,3,5,6,7,8,10,12],[1,2,3,5,6,7,8,10,13],[1,2,3,5,6,7,8,10,14],[1,2,3,5,6,7,8,10,15],[1,2,3,5,6,7,8,11,12],[1,2,3,5,6,7,8,11,13],[1,2,3,5,6,7,8,11,14],[1,2,3,5,6,7,8,11,15],[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],[1,2,3,5,6,7,8,13,14],[1,2,3,5,6,7,8,13,15],[1,2,3,5,6,7,8,14,15],[1,2,3,5,6,7,9,10,11],[1,2,3,5,6,7,9,10,11,12,13,14,15],[1,2,3,5,6,7,9,10,12],[1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,10,14],[1,2,3,5,6,7,9,10,15],[1,2,3,5,6,7,9,11,12],[1,2,3,5,6,7,9,11,13],[1,2,3,5,6,7,9,11,14],[1,2,3,5,6,7,9,11,15],[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],[1,2,3,5,6,7,9,13,14],[1,2,3,5,6,7,9,13,15],[1,2,3,5,6,7,9,14,15],[1,2,3,5,6,7,10,11,12],[1,2,3,5,6,7,10,11,13],[1,2,3,5,6,7,10,11,14],[1,2,3,5,6,7,10,11,15],[1,2,3,5,6,7,10,12,13],[1,2,3,5,6,7,10,12,14],[1,2,3,5,6,7,10,12,15],[1,2,3,5,6,7,10,13,14],[1,2,3,5,6,7,10,13,15],[1,2,3,5,6,7,10,14,15],[1,2,3,5,6,7,11,12,13],[1,2,3,5,6,7,11,12,14],[1,2,3,5,6,7,11,12,15],[1,2,3,5,6,7,11,13,14],[1,2,3,5,6,7,11,13,15],[1,2,3,5,6,7,11,14,15],[1,2,3,5,6,7,12,13,14],[1,2,3,5,6,7,12,13,15],[1,2,3,5,6,7,12,14,15],[1,2,3,5,6,7,13,14,15],[1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10,11,12,13,15],[1,2,4,5,6,7,8,9,10,11,12,14,15],[1,2,4,5,6,7,8,9,10,11,13,14,15],[1,2,4,5,6,7,8,9,10,12,13,14,15],[1,2,4,5,6,7,8,9,11],[1,2,4,5,6,7,8,9,11,12,13,14,15],[1,2,4,5,6,7,8,9,12],[1,2,4,5,6,7,8,9,13],[1,2,4,5,6,7,8,9,14],[1,2,4,5,6,7,8,9,15],[1,2,4,5,6,7,8,10,11],[1,2,4,5,6,7,8,10,11,12,13,14,15],[1,2,4,5,6,7,8,10,12],[1,2,4,5,6,7,8,10,13],[1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,8,10,15],[1,2,4,5,6,7,8,11,12],[1,2,4,5,6,7,8,11,13],[1,2,4,5,6,7,8,11,14],[1,2,4,5,6,7,8,11,15],[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],[1,2,4,5,6,7,8,13,14],[1,2,4,5,6,7,8,13,15],[1,2,4,5,6,7,8,14,15],[1,2,4,5,6,7,9,10,11],[1,2,4,5,6,7,9,10,11,12,13,14,15],[1,2,4,5,6,7,9,10,12],[1,2,4,5,6,7,9,10,13],[1,2,4,5,6,7,9,10,14],[1,2,4,5,6,7,9,10,15],[1,2,4,5,6,7,9,11,12],[1,2,4,5,6,7,9,11,13],[1,2,4,5,6,7,9,11,14],[1,2,4,5,6,7,9,11,15],[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],[1,2,4,5,6,7,9,13,14],[1,2,4,5,6,7,9,13,15],[1,2,4,5,6,7,9,14,15],[1,2,4,5,6,7,10,11,12],[1,2,4,5,6,7,10,11,13],[1,2,4,5,6,7,10,11,14],[1,2,4,5,6,7,10,11,15],[1,2,4,5,6,7,10,12,13],[1,2,4,5,6,7,10,12,14],[1,2,4,5,6,7,10,12,15],[1,2,4,5,6,7,10,13,14],[1,2,4,5,6,7,10,13,15],[1,2,4,5,6,7,10,14,15],[1,2,4,5,6,7,11,12,13],[1,2,4,5,6,7,11,12,14],[1,2,4,5,6,7,11,12,15],[1,2,4,5,6,7,11,13,14],[1,2,4,5,6,7,11,13,15],[1,2,4,5,6,7,11,14,15],[1,2,4,5,6,7,12,13,14],[1,2,4,5,6,7,12,13,15],[1,2,4,5,6,7,12,14,15],[1,2,4,5,6,7,13,14,15],[1,3,4,5,6,7,8,9,10],[1,3,4,5,6,7,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,10,11,12,13,15],[1,3,4,5,6,7,8,9,10,11,12,14,15],[1,3,4,5,6,7,8,9,10,11,13,14,15],[1,3,4,5,6,7,8,9,10,12,13,14,15],[1,3,4,5,6,7,8,9,11],[1,3,4,5,6,7,8,9,11,12,13,14,15],[1,3,4,5,6,7,8,9,12],[1,3,4,5,6,7,8,9,13],[1,3,4,5,6,7,8,9,14],[1,3,4,5,6,7,8,9,15],[1,3,4,5,6,7,8,10,11],[1,3,4,5,6,7,8,10,11,12,13,14,15],[1,3,4,5,6,7,8,10,12],[1,3,4,5,6,7,8,10,13],[1,3,4,5,6,7,8,10,14],[1,3,4,5,6,7,8,10,15],[1,3,4,5,6,7,8,11,12],[1,3,4,5,6,7,8,11,13],[1,3,4,5,6,7,8,11,14],[1,3,4,5,6,7,8,11,15],[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],[1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,8,13,15],[1,3,4,5,6,7,8,14,15],[1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,10,11,12,13,14,15],[1,3,4,5,6,7,9,10,12],[1,3,4,5,6,7,9,10,13],[1,3,4,5,6,7,9,10,14],[1,3,4,5,6,7,9,10,15],[1,3,4,5,6,7,9,11,12],[1,3,4,5,6,7,9,11,13],[1,3,4,5,6,7,9,11,14],[1,3,4,5,6,7,9,11,15],[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],[1,3,4,5,6,7,9,13,14],[1,3,4,5,6,7,9,13,15],[1,3,4,5,6,7,9,14,15],[1,3,4,5,6,7,10,11,12],[1,3,4,5,6,7,10,11,13],[1,3,4,5,6,7,10,11,14],[1,3,4,5,6,7,10,11,15],[1,3,4,5,6,7,10,12,13],[1,3,4,5,6,7,10,12,14],[1,3,4,5,6,7,10,12,15],[1,3,4,5,6,7,10,13,14],[1,3,4,5,6,7,10,13,15],[1,3,4,5,6,7,10,14,15],[1,3,4,5,6,7,11,12,13],[1,3,4,5,6,7,11,12,14],[1,3,4,5,6,7,11,12,15],[1,3,4,5,6,7,11,13,14],[1,3,4,5,6,7,11,13,15],[1,3,4,5,6,7,11,14,15],[1,3,4,5,6,7,12,13,14],[1,3,4,5,6,7,12,13,15],[1,3,4,5,6,7,12,14,15],[1,3,4,5,6,7,13,14,15],[1,8,9,10,11],[1,8,9,10,11,12,13,14,15],[1,8,9,10,12],[1,8,9,10,13],[1,8,9,10,14],[1,8,9,10,15],[1,8,9,11,12],[1,8,9,11,13],[1,8,9,11,14],[1,8,9,11,15],[1,8,9,12,13],[1,8,9,12,14],[1,8,9,12,15],[1,8,9,13,14],[1,8,9,13,15],[1,8,9,14,15],[1,8,10,11,12],[1,8,10,11,13],[1,8,10,11,14],[1,8,10,11,15],[1,8,10,12,13],[1,8,10,12,14],[1,8,10,12,15],[1,8,10,13,14],[1,8,10,13,15],[1,8,10,14,15],[1,8,11,12,13],[1,8,11,12,14],[1,8,11,12,15],[1,8,11,13,14],[1,8,11,13,15],[1,8,11,14,15],[1,8,12,13,14],[1,8,12,13,15],[1,8,12,14,15],[1,8,13,14,15],[1,9,10,11,12],[1,9,10,11,13],[1,9,10,11,14],[1,9,10,11,15],[1,9,10,12,13],[1,9,10,12,14],[1,9,10,12,15],[1,9,10,13,14],[1,9,10,13,15],[1,9,10,14,15],[1,9,11,12,13],[1,9,11,12,14],[1,9,11,12,15],[1,9,11,13,14],[1,9,11,13,15],[1,9,11,14,15],[1,9,12,13,14],[1,9,12,13,15],[1,9,12,14,15],[1,9,13,14,15],[1,10,11,12,13],[1,10,11,12,14],[1,10,11,12,15],[1,10,11,13,14],[1,10,11,13,15],[1,10,11,14,15],[1,10,12,13,14],[1,10,12,13,15],[1,10,12,14,15],[1,10,13,14,15],[1,11,12,13,14],[1,11,12,13,15],[1,11,12,14,15],[1,11,13,14,15],[1,12,13,14,15],[2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10,11,12,13,15],[2,3,4,5,6,7,8,9,10,11,12,14,15],[2,3,4,5,6,7,8,9,10,11,13,14,15],[2,3,4,5,6,7,8,9,10,12,13,14,15],[2,3,4,5,6,7,8,9,11],[2,3,4,5,6,7,8,9,11,12,13,14,15],[2,3,4,5,6,7,8,9,12],[2,3,4,5,6,7,8,9,13],[2,3,4,5,6,7,8,9,14],[2,3,4,5,6,7,8,9,15],[2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,10,11,12,13,14,15],[2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,10,13],[2,3,4,5,6,7,8,10,14],[2,3,4,5,6,7,8,10,15],[2,3,4,5,6,7,8,11,12],[2,3,4,5,6,7,8,11,13],[2,3,4,5,6,7,8,11,14],[2,3,4,5,6,7,8,11,15],[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],[2,3,4,5,6,7,8,13,14],[2,3,4,5,6,7,8,13,15],[2,3,4,5,6,7,8,14,15],[2,3,4,5,6,7,9,10,11],[2,3,4,5,6,7,9,10,11,12,13,14,15],[2,3,4,5,6,7,9,10,12],[2,3,4,5,6,7,9,10,13],[2,3,4,5,6,7,9,10,14],[2,3,4,5,6,7,9,10,15],[2,3,4,5,6,7,9,11,12],[2,3,4,5,6,7,9,11,13],[2,3,4,5,6,7,9,11,14],[2,3,4,5,6,7,9,11,15],[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],[2,3,4,5,6,7,9,13,14],[2,3,4,5,6,7,9,13,15],[2,3,4,5,6,7,9,14,15],[2,3,4,5,6,7,10,11,12],[2,3,4,5,6,7,10,11,13],[2,3,4,5,6,7,10,11,14],[2,3,4,5,6,7,10,11,15],[2,3,4,5,6,7,10,12,13],[2,3,4,5,6,7,10,12,14],[2,3,4,5,6,7,10,12,15],[2,3,4,5,6,7,10,13,14],[2,3,4,5,6,7,10,13,15],[2,3,4,5,6,7,10,14,15],[2,3,4,5,6,7,11,12,13],[2,3,4,5,6,7,11,12,14],[2,3,4,5,6,7,11,12,15],[2,3,4,5,6,7,11,13,14],[2,3,4,5,6,7,11,13,15],[2,3,4,5,6,7,11,14,15],[2,3,4,5,6,7,12,13,14],[2,3,4,5,6,7,12,13,15],[2,3,4,5,6,7,12,14,15],[2,3,4,5,6,7,13,14,15],[2,8,9,10,11],[2,8,9,10,11,12,13,14,15],[2,8,9,10,12],[2,8,9,10,13],[2,8,9,10,14],[2,8,9,10,15],[2,8,9,11,12],[2,8,9,11,13],[2,8,9,11,14],[2,8,9,11,15],[2,8,9,12,13],[2,8,9,12,14],[2,8,9,12,15],[2,8,9,13,14],[2,8,9,13,15],[2,8,9,14,15],[2,8,10,11,12],[2,8,10,11,13],[2,8,10,11,14],[2,8,10,11,15],[2,8,10,12,13],[2,8,10,12,14],[2,8,10,12,15],[2,8,10,13,14],[2,8,10,13,15],[2,8,10,14,15],[2,8,11,12,13],[2,8,11,12,14],[2,8,11,12,15],[2,8,11,13,14],[2,8,11,13,15],[2,8,11,14,15],[2,8,12,13,14],[2,8,12,13,15],[2,8,12,14,15],[2,8,13,14,15],[2,9,10,11,12],[2,9,10,11,13],[2,9,10,11,14],[2,9,10,11,15],[2,9,10,12,13],[2,9,10,12,14],[2,9,10,12,15],[2,9,10,13,14],[2,9,10,13,15],[2,9,10,14,15],[2,9,11,12,13],[2,9,11,12,14],[2,9,11,12,15],[2,9,11,13,14],[2,9,11,13,15],[2,9,11,14,15],[2,9,12,13,14],[2,9,12,13,15],[2,9,12,14,15],[2,9,13,14,15],[2,10,11,12,13],[2,10,11,12,14],[2,10,11,12,15],[2,10,11,13,14],[2,10,11,13,15],[2,10,11,14,15],[2,10,12,13,14],[2,10,12,13,15],[2,10,12,14,15],[2,10,13,14,15],[2,11,12,13,14],[2,11,12,13,15],[2,11,12,14,15],[2,11,13,14,15],[2,12,13,14,15],[3,8,9,10,11],[3,8,9,10,11,12,13,14,15],[3,8,9,10,12],[3,8,9,10,13],[3,8,9,10,14],[3,8,9,10,15],[3,8,9,11,12],[3,8,9,11,13],[3,8,9,11,14],[3,8,9,11,15],[3,8,9,12,13],[3,8,9,12,14],[3,8,9,12,15],[3,8,9,13,14],[3,8,9,13,15],[3,8,9,14,15],[3,8,10,11,12],[3,8,10,11,13],[3,8,10,11,14],[3,8,10,11,15],[3,8,10,12,13],[3,8,10,12,14],[3,8,10,12,15],[3,8,10,13,14],[3,8,10,13,15],[3,8,10,14,15],[3,8,11,12,13],[3,8,11,12,14],[3,8,11,12,15],[3,8,11,13,14],[3,8,11,13,15],[3,8,11,14,15],[3,8,12,13,14],[3,8,12,13,15],[3,8,12,14,15],[3,8,13,14,15],[3,9,10,11,12],[3,9,10,11,13],[3,9,10,11,14],[3,9,10,11,15],[3,9,10,12,13],[3,9,10,12,14],[3,9,10,12,15],[3,9,10,13,14],[3,9,10,13,15],[3,9,10,14,15],[3,9,11,12,13],[3,9,11,12,14],[3,9,11,12,15],[3,9,11,13,14],[3,9,11,13,15],[3,9,11,14,15],[3,9,12,13,14],[3,9,12,13,15],[3,9,12,14,15],[3,9,13,14,15],[3,10,11,12,13],[3,10,11,12,14],[3,10,11,12,15],[3,10,11,13,14],[3,10,11,13,15],[3,10,11,14,15],[3,10,12,13,14],[3,10,12,13,15],[3,10,12,14,15],[3,10,13,14,15],[3,11,12,13,14],[3,11,12,13,15],[3,11,12,14,15],[3,11,13,14,15],[3,12,13,14,15],[4,8,9,10,11],[4,8,9,10,11,12,13,14,15],[4,8,9,10,12],[4,8,9,10,13],[4,8,9,10,14],[4,8,9,10,15],[4,8,9,11,12],[4,8,9,11,13],[4,8,9,11,14],[4,8,9,11,15],[4,8,9,12,13],[4,8,9,12,14],[4,8,9,12,15],[4,8,9,13,14],[4,8,9,13,15],[4,8,9,14,15],[4,8,10,11,12],[4,8,10,11,13],[4,8,10,11,14],[4,8,10,11,15],[4,8,10,12,13],[4,8,10,12,14],[4,8,10,12,15],[4,8,10,13,14],[4,8,10,13,15],[4,8,10,14,15],[4,8,11,12,13],[4,8,11,12,14],[4,8,11,12,15],[4,8,11,13,14],[4,8,11,13,15],[4,8,11,14,15],[4,8,12,13,14],[4,8,12,13,15],[4,8,12,14,15],[4,8,13,14,15],[4,9,10,11,12],[4,9,10,11,13],[4,9,10,11,14],[4,9,10,11,15],[4,9,10,12,13],[4,9,10,12,14],[4,9,10,12,15],[4,9,10,13,14],[4,9,10,13,15],[4,9,10,14,15],[4,9,11,12,13],[4,9,11,12,14],[4,9,11,12,15],[4,9,11,13,14],[4,9,11,13,15],[4,9,11,14,15],[4,9,12,13,14],[4,9,12,13,15],[4,9,12,14,15],[4,9,13,14,15],[4,10,11,12,13],[4,10,11,12,14],[4,10,11,12,15],[4,10,11,13,14],[4,10,11,13,15],[4,10,11,14,15],[4,10,12,13,14],[4,10,12,13,15],[4,10,12,14,15],[4,10,13,14,15],[4,11,12,13,14],[4,11,12,13,15],[4,11,12,14,15],[4,11,13,14,15],[4,12,13,14,15],[5,8,9,10,11],[5,8,9,10,11,12,13,14,15],[5,8,9,10,12],[5,8,9,10,13],[5,8,9,10,14],[5,8,9,10,15],[5,8,9,11,12],[5,8,9,11,13],[5,8,9,11,14],[5,8,9,11,15],[5,8,9,12,13],[5,8,9,12,14],[5,8,9,12,15],[5,8,9,13,14],[5,8,9,13,15],[5,8,9,14,15],[5,8,10,11,12],[5,8,10,11,13],[5,8,10,11,14],[5,8,10,11,15],[5,8,10,12,13],[5,8,10,12,14],[5,8,10,12,15],[5,8,10,13,14],[5,8,10,13,15],[5,8,10,14,15],[5,8,11,12,13],[5,8,11,12,14],[5,8,11,12,15],[5,8,11,13,14],[5,8,11,13,15],[5,8,11,14,15],[5,8,12,13,14],[5,8,12,13,15],[5,8,12,14,15],[5,8,13,14,15],[5,9,10,11,12],[5,9,10,11,13],[5,9,10,11,14],[5,9,10,11,15],[5,9,10,12,13],[5,9,10,12,14],[5,9,10,12,15],[5,9,10,13,14],[5,9,10,13,15],[5,9,10,14,15],[5,9,11,12,13],[5,9,11,12,14],[5,9,11,12,15],[5,9,11,13,14],[5,9,11,13,15],[5,9,11,14,15],[5,9,12,13,14],[5,9,12,13,15],[5,9,12,14,15],[5,9,13,14,15],[5,10,11,12,13],[5,10,11,12,14],[5,10,11,12,15],[5,10,11,13,14],[5,10,11,13,15],[5,10,11,14,15],[5,10,12,13,14],[5,10,12,13,15],[5,10,12,14,15],[5,10,13,14,15],[5,11,12,13,14],[5,11,12,13,15],[5,11,12,14,15],[5,11,13,14,15],[5,12,13,14,15],[6,8,9,10,11],[6,8,9,10,11,12,13,14,15],[6,8,9,10,12],[6,8,9,10,13],[6,8,9,10,14],[6,8,9,10,15],[6,8,9,11,12],[6,8,9,11,13],[6,8,9,11,14],[6,8,9,11,15],[6,8,9,12,13],[6,8,9,12,14],[6,8,9,12,15],[6,8,9,13,14],[6,8,9,13,15],[6,8,9,14,15],[6,8,10,11,12],[6,8,10,11,13],[6,8,10,11,14],[6,8,10,11,15],[6,8,10,12,13],[6,8,10,12,14],[6,8,10,12,15],[6,8,10,13,14],[6,8,10,13,15],[6,8,10,14,15],[6,8,11,12,13],[6,8,11,12,14],[6,8,11,12,15],[6,8,11,13,14],[6,8,11,13,15],[6,8,11,14,15],[6,8,12,13,14],[6,8,12,13,15],[6,8,12,14,15],[6,8,13,14,15],[6,9,10,11,12],[6,9,10,11,13],[6,9,10,11,14],[6,9,10,11,15],[6,9,10,12,13],[6,9,10,12,14],[6,9,10,12,15],[6,9,10,13,14],[6,9,10,13,15],[6,9,10,14,15],[6,9,11,12,13],[6,9,11,12,14],[6,9,11,12,15],[6,9,11,13,14],[6,9,11,13,15],[6,9,11,14,15],[6,9,12,13,14],[6,9,12,13,15],[6,9,12,14,15],[6,9,13,14,15],[6,10,11,12,13],[6,10,11,12,14],[6,10,11,12,15],[6,10,11,13,14],[6,10,11,13,15],[6,10,11,14,15],[6,10,12,13,14],[6,10,12,13,15],[6,10,12,14,15],[6,10,13,14,15],[6,11,12,13,14],[6,11,12,13,15],[6,11,12,14,15],[6,11,13,14,15],[6,12,13,14,15],[7,8,9,10,11],[7,8,9,10,11,12,13,14,15],[7,8,9,10,12],[7,8,9,10,13],[7,8,9,10,14],[7,8,9,10,15],[7,8,9,11,12],[7,8,9,11,13],[7,8,9,11,14],[7,8,9,11,15],[7,8,9,12,13],[7,8,9,12,14],[7,8,9,12,15],[7,8,9,13,14],[7,8,9,13,15],[7,8,9,14,15],[7,8,10,11,12],[7,8,10,11,13],[7,8,10,11,14],[7,8,10,11,15],[7,8,10,12,13],[7,8,10,12,14],[7,8,10,12,15],[7,8,10,13,14],[7,8,10,13,15],[7,8,10,14,15],[7,8,11,12,13],[7,8,11,12,14],[7,8,11,12,15],[7,8,11,13,14],[7,8,11,13,15],[7,8,11,14,15],[7,8,12,13,14],[7,8,12,13,15],[7,8,12,14,15],[7,8,13,14,15],[7,9,10,11,12],[7,9,10,11,13],[7,9,10,11,14],[7,9,10,11,15],[7,9,10,12,13],[7,9,10,12,14],[7,9,10,12,15],[7,9,10,13,14],[7,9,10,13,15],[7,9,10,14,15],[7,9,11,12,13],[7,9,11,12,14],[7,9,11,12,15],[7,9,11,13,14],[7,9,11,13,15],[7,9,11,14,15],[7,9,12,13,14],[7,9,12,13,15],[7,9,12,14,15],[7,9,13,14,15],[7,10,11,12,13],[7,10,11,12,14],[7,10,11,12,15],[7,10,11,13,14],[7,10,11,13,15],[7,10,11,14,15],[7,10,12,13,14],[7,10,12,13,15],[7,10,12,14,15],[7,10,13,14,15],[7,11,12,13,14],[7,11,12,13,15],[7,11,12,14,15],[7,11,13,14,15],[7,12,13,14,15],[8],[8,9,10,11,12],[8,9,10,11,13],[8,9,10,11,14],[8,9,10,11,15],[8,9,10,12,13],[8,9,10,12,14],[8,9,10,12,15],[8,9,10,13,14],[8,9,10,13,15],[8,9,10,14,15],[8,9,11,12,13],[8,9,11,12,14],[8,9,11,12,15],[8,9,11,13,14],[8,9,11,13,15],[8,9,11,14,15],[8,9,12,13,14],[8,9,12,13,15],[8,9,12,14,15],[8,9,13,14,15],[8,10,11,12,13],[8,10,11,12,14],[8,10,11,12,15],[8,10,11,13,14],[8,10,11,13,15],[8,10,11,14,15],[8,10,12,13,14],[8,10,12,13,15],[8,10,12,14,15],[8,10,13,14,15],[8,11,12,13,14],[8,11,12,13,15],[8,11,12,14,15],[8,11,13,14,15],[8,12,13,14,15],[9],[9,10,11,12,13],[9,10,11,12,14],[9,10,11,12,15],[9,10,11,13,14],[9,10,11,13,15],[9,10,11,14,15],[9,10,12,13,14],[9,10,12,13,15],[9,10,12,14,15],[9,10,13,14,15],[9,11,12,13,14],[9,11,12,13,15],[9,11,12,14,15],[9,11,13,14,15],[9,12,13,14,15],[10],[10,11,12,13,14],[10,11,12,13,15],[10,11,12,14,15],[10,11,13,14,15],[10,12,13,14,15],[11],[11,12,13,14,15],[12],[13],[14],[15]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,64],"A_d":26180,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,2],[9,2],[10,2],[11,2],[12,2],[13,2],[14,2],[15,2]],"CZ":[]},"rotation_powers":[[0,3],[6,3],[12,3],[28,3],[64,5],[192,5],[384,5],[640,5],[960,5],[1344,7],[1415,5],[1834,3],[1854,3],[1864,3],[1865,3],[1866,3],[1867,3],[1869,3],[1969,3],[1989,3],[1999,3],[2000,3],[2001,3],[2002,3],[2004,3],[2040,3],[2060,3],[2070,3],[2071,3],[2072,3],[2073,3],[2075,3],[2111,3],[2131,3],[2141,3],[2142,3],[2143,3],[2144,3],[2146,3],[2182,3],[2202,3],[2212,3],[2213,3],[2214,3],[2215,3],[2217,3],[2284,3],[2285,3],[2286,3],[2287,3],[2288,3],[2355,3],[2356,3],[2357,3],[2358,3],[2359,3],[2380,3],[2390,3],[2394,3],[2406,3],[2410,3],[2416,3],[2418,3],[2419,3],[2420,3],[2421,3],[2422,3],[2423,3]]},"metrics":{"gamma":8.24317398347295,"gamma_t":null,"gamma_rho":8.24317398347295,"gamma_claim":8.24317398347295,"gamma_t_claim":null,"gamma_rho_claim":8.24317398347295,"v_ex":8,"rate":0.0033003300330033004,"t_count":null,"poly_degree":null,"effective_width":8},"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-0901","N":16,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 901","provenance":"larger unified search l=3, two-group s_total=4,s_O=5"}]},"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"}]}