{"id":"1221.7.2.a","row":14,"stored":{"file":"master_catalog_large.json","row":14,"construction":{"family":"two-group","k":7,"N":18,"s_total":8,"s_O":7},"columns_sha256":"0a678bf6d30b7bb58fb8e1275fd6004f0d44c5717f9affb118ecfb8424542780"},"parameters":{"n":1221,"k":7,"d":2,"N":18,"r":11,"level":3},"gate":{"string":"0+1+2+3+4+5+6","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6","monomials":[[0],[1],[2],[3],[4],[5],[6]],"sk_key":[[0],[1],[2],[3],[4],[5],[6]],"sk_fingerprint":"4227720e4bdc2b66","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,7,8,9,10,11,12,13,14],[0,7,8,9,10,11,12,13,15],[0,7,8,9,10,11,12,13,16],[0,7,8,9,10,11,12,13,17],[0,7,8,9,10,11,12,14,15],[0,7,8,9,10,11,12,14,16],[0,7,8,9,10,11,12,14,17],[0,7,8,9,10,11,12,15,16],[0,7,8,9,10,11,12,15,17],[0,7,8,9,10,11,12,16,17],[0,7,8,9,10,11,13,14,15],[0,7,8,9,10,11,13,14,16],[0,7,8,9,10,11,13,14,17],[0,7,8,9,10,11,13,15,16],[0,7,8,9,10,11,13,15,17],[0,7,8,9,10,11,13,16,17],[0,7,8,9,10,11,14,15,16],[0,7,8,9,10,11,14,15,17],[0,7,8,9,10,11,14,16,17],[0,7,8,9,10,11,15,16,17],[0,7,8,9,10,12,13,14,15],[0,7,8,9,10,12,13,14,16],[0,7,8,9,10,12,13,14,17],[0,7,8,9,10,12,13,15,16],[0,7,8,9,10,12,13,15,17],[0,7,8,9,10,12,13,16,17],[0,7,8,9,10,12,14,15,16],[0,7,8,9,10,12,14,15,17],[0,7,8,9,10,12,14,16,17],[0,7,8,9,10,12,15,16,17],[0,7,8,9,10,13,14,15,16],[0,7,8,9,10,13,14,15,17],[0,7,8,9,10,13,14,16,17],[0,7,8,9,10,13,15,16,17],[0,7,8,9,10,14,15,16,17],[0,7,8,9,11,12,13,14,15],[0,7,8,9,11,12,13,14,16],[0,7,8,9,11,12,13,14,17],[0,7,8,9,11,12,13,15,16],[0,7,8,9,11,12,13,15,17],[0,7,8,9,11,12,13,16,17],[0,7,8,9,11,12,14,15,16],[0,7,8,9,11,12,14,15,17],[0,7,8,9,11,12,14,16,17],[0,7,8,9,11,12,15,16,17],[0,7,8,9,11,13,14,15,16],[0,7,8,9,11,13,14,15,17],[0,7,8,9,11,13,14,16,17],[0,7,8,9,11,13,15,16,17],[0,7,8,9,11,14,15,16,17],[0,7,8,9,12,13,14,15,16],[0,7,8,9,12,13,14,15,17],[0,7,8,9,12,13,14,16,17],[0,7,8,9,12,13,15,16,17],[0,7,8,9,12,14,15,16,17],[0,7,8,9,13,14,15,16,17],[0,7,8,10,11,12,13,14,15],[0,7,8,10,11,12,13,14,16],[0,7,8,10,11,12,13,14,17],[0,7,8,10,11,12,13,15,16],[0,7,8,10,11,12,13,15,17],[0,7,8,10,11,12,13,16,17],[0,7,8,10,11,12,14,15,16],[0,7,8,10,11,12,14,15,17],[0,7,8,10,11,12,14,16,17],[0,7,8,10,11,12,15,16,17],[0,7,8,10,11,13,14,15,16],[0,7,8,10,11,13,14,15,17],[0,7,8,10,11,13,14,16,17],[0,7,8,10,11,13,15,16,17],[0,7,8,10,11,14,15,16,17],[0,7,8,10,12,13,14,15,16],[0,7,8,10,12,13,14,15,17],[0,7,8,10,12,13,14,16,17],[0,7,8,10,12,13,15,16,17],[0,7,8,10,12,14,15,16,17],[0,7,8,10,13,14,15,16,17],[0,7,8,11,12,13,14,15,16],[0,7,8,11,12,13,14,15,17],[0,7,8,11,12,13,14,16,17],[0,7,8,11,12,13,15,16,17],[0,7,8,11,12,14,15,16,17],[0,7,8,11,13,14,15,16,17],[0,7,8,12,13,14,15,16,17],[0,7,9,10,11,12,13,14,15],[0,7,9,10,11,12,13,14,16],[0,7,9,10,11,12,13,14,17],[0,7,9,10,11,12,13,15,16],[0,7,9,10,11,12,13,15,17],[0,7,9,10,11,12,13,16,17],[0,7,9,10,11,12,14,15,16],[0,7,9,10,11,12,14,15,17],[0,7,9,10,11,12,14,16,17],[0,7,9,10,11,12,15,16,17],[0,7,9,10,11,13,14,15,16],[0,7,9,10,11,13,14,15,17],[0,7,9,10,11,13,14,16,17],[0,7,9,10,11,13,15,16,17],[0,7,9,10,11,14,15,16,17],[0,7,9,10,12,13,14,15,16],[0,7,9,10,12,13,14,15,17],[0,7,9,10,12,13,14,16,17],[0,7,9,10,12,13,15,16,17],[0,7,9,10,12,14,15,16,17],[0,7,9,10,13,14,15,16,17],[0,7,9,11,12,13,14,15,16],[0,7,9,11,12,13,14,15,17],[0,7,9,11,12,13,14,16,17],[0,7,9,11,12,13,15,16,17],[0,7,9,11,12,14,15,16,17],[0,7,9,11,13,14,15,16,17],[0,7,9,12,13,14,15,16,17],[0,7,10,11,12,13,14,15,16],[0,7,10,11,12,13,14,15,17],[0,7,10,11,12,13,14,16,17],[0,7,10,11,12,13,15,16,17],[0,7,10,11,12,14,15,16,17],[0,7,10,11,13,14,15,16,17],[0,7,10,12,13,14,15,16,17],[0,7,11,12,13,14,15,16,17],[0,8,9,10,11,12,13,14,15],[0,8,9,10,11,12,13,14,16],[0,8,9,10,11,12,13,14,17],[0,8,9,10,11,12,13,15,16],[0,8,9,10,11,12,13,15,17],[0,8,9,10,11,12,13,16,17],[0,8,9,10,11,12,14,15,16],[0,8,9,10,11,12,14,15,17],[0,8,9,10,11,12,14,16,17],[0,8,9,10,11,12,15,16,17],[0,8,9,10,11,13,14,15,16],[0,8,9,10,11,13,14,15,17],[0,8,9,10,11,13,14,16,17],[0,8,9,10,11,13,15,16,17],[0,8,9,10,11,14,15,16,17],[0,8,9,10,12,13,14,15,16],[0,8,9,10,12,13,14,15,17],[0,8,9,10,12,13,14,16,17],[0,8,9,10,12,13,15,16,17],[0,8,9,10,12,14,15,16,17],[0,8,9,10,13,14,15,16,17],[0,8,9,11,12,13,14,15,16],[0,8,9,11,12,13,14,15,17],[0,8,9,11,12,13,14,16,17],[0,8,9,11,12,13,15,16,17],[0,8,9,11,12,14,15,16,17],[0,8,9,11,13,14,15,16,17],[0,8,9,12,13,14,15,16,17],[0,8,10,11,12,13,14,15,16],[0,8,10,11,12,13,14,15,17],[0,8,10,11,12,13,14,16,17],[0,8,10,11,12,13,15,16,17],[0,8,10,11,12,14,15,16,17],[0,8,10,11,13,14,15,16,17],[0,8,10,12,13,14,15,16,17],[0,8,11,12,13,14,15,16,17],[0,9,10,11,12,13,14,15,16],[0,9,10,11,12,13,14,15,17],[0,9,10,11,12,13,14,16,17],[0,9,10,11,12,13,15,16,17],[0,9,10,11,12,14,15,16,17],[0,9,10,11,13,14,15,16,17],[0,9,10,12,13,14,15,16,17],[0,9,11,12,13,14,15,16,17],[0,10,11,12,13,14,15,16,17],[1,7,8,9,10,11,12,13,14],[1,7,8,9,10,11,12,13,15],[1,7,8,9,10,11,12,13,16],[1,7,8,9,10,11,12,13,17],[1,7,8,9,10,11,12,14,15],[1,7,8,9,10,11,12,14,16],[1,7,8,9,10,11,12,14,17],[1,7,8,9,10,11,12,15,16],[1,7,8,9,10,11,12,15,17],[1,7,8,9,10,11,12,16,17],[1,7,8,9,10,11,13,14,15],[1,7,8,9,10,11,13,14,16],[1,7,8,9,10,11,13,14,17],[1,7,8,9,10,11,13,15,16],[1,7,8,9,10,11,13,15,17],[1,7,8,9,10,11,13,16,17],[1,7,8,9,10,11,14,15,16],[1,7,8,9,10,11,14,15,17],[1,7,8,9,10,11,14,16,17],[1,7,8,9,10,11,15,16,17],[1,7,8,9,10,12,13,14,15],[1,7,8,9,10,12,13,14,16],[1,7,8,9,10,12,13,14,17],[1,7,8,9,10,12,13,15,16],[1,7,8,9,10,12,13,15,17],[1,7,8,9,10,12,13,16,17],[1,7,8,9,10,12,14,15,16],[1,7,8,9,10,12,14,15,17],[1,7,8,9,10,12,14,16,17],[1,7,8,9,10,12,15,16,17],[1,7,8,9,10,13,14,15,16],[1,7,8,9,10,13,14,15,17],[1,7,8,9,10,13,14,16,17],[1,7,8,9,10,13,15,16,17],[1,7,8,9,10,14,15,16,17],[1,7,8,9,11,12,13,14,15],[1,7,8,9,11,12,13,14,16],[1,7,8,9,11,12,13,14,17],[1,7,8,9,11,12,13,15,16],[1,7,8,9,11,12,13,15,17],[1,7,8,9,11,12,13,16,17],[1,7,8,9,11,12,14,15,16],[1,7,8,9,11,12,14,15,17],[1,7,8,9,11,12,14,16,17],[1,7,8,9,11,12,15,16,17],[1,7,8,9,11,13,14,15,16],[1,7,8,9,11,13,14,15,17],[1,7,8,9,11,13,14,16,17],[1,7,8,9,11,13,15,16,17],[1,7,8,9,11,14,15,16,17],[1,7,8,9,12,13,14,15,16],[1,7,8,9,12,13,14,15,17],[1,7,8,9,12,13,14,16,17],[1,7,8,9,12,13,15,16,17],[1,7,8,9,12,14,15,16,17],[1,7,8,9,13,14,15,16,17],[1,7,8,10,11,12,13,14,15],[1,7,8,10,11,12,13,14,16],[1,7,8,10,11,12,13,14,17],[1,7,8,10,11,12,13,15,16],[1,7,8,10,11,12,13,15,17],[1,7,8,10,11,12,13,16,17],[1,7,8,10,11,12,14,15,16],[1,7,8,10,11,12,14,15,17],[1,7,8,10,11,12,14,16,17],[1,7,8,10,11,12,15,16,17],[1,7,8,10,11,13,14,15,16],[1,7,8,10,11,13,14,15,17],[1,7,8,10,11,13,14,16,17],[1,7,8,10,11,13,15,16,17],[1,7,8,10,11,14,15,16,17],[1,7,8,10,12,13,14,15,16],[1,7,8,10,12,13,14,15,17],[1,7,8,10,12,13,14,16,17],[1,7,8,10,12,13,15,16,17],[1,7,8,10,12,14,15,16,17],[1,7,8,10,13,14,15,16,17],[1,7,8,11,12,13,14,15,16],[1,7,8,11,12,13,14,15,17],[1,7,8,11,12,13,14,16,17],[1,7,8,11,12,13,15,16,17],[1,7,8,11,12,14,15,16,17],[1,7,8,11,13,14,15,16,17],[1,7,8,12,13,14,15,16,17],[1,7,9,10,11,12,13,14,15],[1,7,9,10,11,12,13,14,16],[1,7,9,10,11,12,13,14,17],[1,7,9,10,11,12,13,15,16],[1,7,9,10,11,12,13,15,17],[1,7,9,10,11,12,13,16,17],[1,7,9,10,11,12,14,15,16],[1,7,9,10,11,12,14,15,17],[1,7,9,10,11,12,14,16,17],[1,7,9,10,11,12,15,16,17],[1,7,9,10,11,13,14,15,16],[1,7,9,10,11,13,14,15,17],[1,7,9,10,11,13,14,16,17],[1,7,9,10,11,13,15,16,17],[1,7,9,10,11,14,15,16,17],[1,7,9,10,12,13,14,15,16],[1,7,9,10,12,13,14,15,17],[1,7,9,10,12,13,14,16,17],[1,7,9,10,12,13,15,16,17],[1,7,9,10,12,14,15,16,17],[1,7,9,10,13,14,15,16,17],[1,7,9,11,12,13,14,15,16],[1,7,9,11,12,13,14,15,17],[1,7,9,11,12,13,14,16,17],[1,7,9,11,12,13,15,16,17],[1,7,9,11,12,14,15,16,17],[1,7,9,11,13,14,15,16,17],[1,7,9,12,13,14,15,16,17],[1,7,10,11,12,13,14,15,16],[1,7,10,11,12,13,14,15,17],[1,7,10,11,12,13,14,16,17],[1,7,10,11,12,13,15,16,17],[1,7,10,11,12,14,15,16,17],[1,7,10,11,13,14,15,16,17],[1,7,10,12,13,14,15,16,17],[1,7,11,12,13,14,15,16,17],[1,8,9,10,11,12,13,14,15],[1,8,9,10,11,12,13,14,16],[1,8,9,10,11,12,13,14,17],[1,8,9,10,11,12,13,15,16],[1,8,9,10,11,12,13,15,17],[1,8,9,10,11,12,13,16,17],[1,8,9,10,11,12,14,15,16],[1,8,9,10,11,12,14,15,17],[1,8,9,10,11,12,14,16,17],[1,8,9,10,11,12,15,16,17],[1,8,9,10,11,13,14,15,16],[1,8,9,10,11,13,14,15,17],[1,8,9,10,11,13,14,16,17],[1,8,9,10,11,13,15,16,17],[1,8,9,10,11,14,15,16,17],[1,8,9,10,12,13,14,15,16],[1,8,9,10,12,13,14,15,17],[1,8,9,10,12,13,14,16,17],[1,8,9,10,12,13,15,16,17],[1,8,9,10,12,14,15,16,17],[1,8,9,10,13,14,15,16,17],[1,8,9,11,12,13,14,15,16],[1,8,9,11,12,13,14,15,17],[1,8,9,11,12,13,14,16,17],[1,8,9,11,12,13,15,16,17],[1,8,9,11,12,14,15,16,17],[1,8,9,11,13,14,15,16,17],[1,8,9,12,13,14,15,16,17],[1,8,10,11,12,13,14,15,16],[1,8,10,11,12,13,14,15,17],[1,8,10,11,12,13,14,16,17],[1,8,10,11,12,13,15,16,17],[1,8,10,11,12,14,15,16,17],[1,8,10,11,13,14,15,16,17],[1,8,10,12,13,14,15,16,17],[1,8,11,12,13,14,15,16,17],[1,9,10,11,12,13,14,15,16],[1,9,10,11,12,13,14,15,17],[1,9,10,11,12,13,14,16,17],[1,9,10,11,12,13,15,16,17],[1,9,10,11,12,14,15,16,17],[1,9,10,11,13,14,15,16,17],[1,9,10,12,13,14,15,16,17],[1,9,11,12,13,14,15,16,17],[1,10,11,12,13,14,15,16,17],[2,7,8,9,10,11,12,13,14],[2,7,8,9,10,11,12,13,15],[2,7,8,9,10,11,12,13,16],[2,7,8,9,10,11,12,13,17],[2,7,8,9,10,11,12,14,15],[2,7,8,9,10,11,12,14,16],[2,7,8,9,10,11,12,14,17],[2,7,8,9,10,11,12,15,16],[2,7,8,9,10,11,12,15,17],[2,7,8,9,10,11,12,16,17],[2,7,8,9,10,11,13,14,15],[2,7,8,9,10,11,13,14,16],[2,7,8,9,10,11,13,14,17],[2,7,8,9,10,11,13,15,16],[2,7,8,9,10,11,13,15,17],[2,7,8,9,10,11,13,16,17],[2,7,8,9,10,11,14,15,16],[2,7,8,9,10,11,14,15,17],[2,7,8,9,10,11,14,16,17],[2,7,8,9,10,11,15,16,17],[2,7,8,9,10,12,13,14,15],[2,7,8,9,10,12,13,14,16],[2,7,8,9,10,12,13,14,17],[2,7,8,9,10,12,13,15,16],[2,7,8,9,10,12,13,15,17],[2,7,8,9,10,12,13,16,17],[2,7,8,9,10,12,14,15,16],[2,7,8,9,10,12,14,15,17],[2,7,8,9,10,12,14,16,17],[2,7,8,9,10,12,15,16,17],[2,7,8,9,10,13,14,15,16],[2,7,8,9,10,13,14,15,17],[2,7,8,9,10,13,14,16,17],[2,7,8,9,10,13,15,16,17],[2,7,8,9,10,14,15,16,17],[2,7,8,9,11,12,13,14,15],[2,7,8,9,11,12,13,14,16],[2,7,8,9,11,12,13,14,17],[2,7,8,9,11,12,13,15,16],[2,7,8,9,11,12,13,15,17],[2,7,8,9,11,12,13,16,17],[2,7,8,9,11,12,14,15,16],[2,7,8,9,11,12,14,15,17],[2,7,8,9,11,12,14,16,17],[2,7,8,9,11,12,15,16,17],[2,7,8,9,11,13,14,15,16],[2,7,8,9,11,13,14,15,17],[2,7,8,9,11,13,14,16,17],[2,7,8,9,11,13,15,16,17],[2,7,8,9,11,14,15,16,17],[2,7,8,9,12,13,14,15,16],[2,7,8,9,12,13,14,15,17],[2,7,8,9,12,13,14,16,17],[2,7,8,9,12,13,15,16,17],[2,7,8,9,12,14,15,16,17],[2,7,8,9,13,14,15,16,17],[2,7,8,10,11,12,13,14,15],[2,7,8,10,11,12,13,14,16],[2,7,8,10,11,12,13,14,17],[2,7,8,10,11,12,13,15,16],[2,7,8,10,11,12,13,15,17],[2,7,8,10,11,12,13,16,17],[2,7,8,10,11,12,14,15,16],[2,7,8,10,11,12,14,15,17],[2,7,8,10,11,12,14,16,17],[2,7,8,10,11,12,15,16,17],[2,7,8,10,11,13,14,15,16],[2,7,8,10,11,13,14,15,17],[2,7,8,10,11,13,14,16,17],[2,7,8,10,11,13,15,16,17],[2,7,8,10,11,14,15,16,17],[2,7,8,10,12,13,14,15,16],[2,7,8,10,12,13,14,15,17],[2,7,8,10,12,13,14,16,17],[2,7,8,10,12,13,15,16,17],[2,7,8,10,12,14,15,16,17],[2,7,8,10,13,14,15,16,17],[2,7,8,11,12,13,14,15,16],[2,7,8,11,12,13,14,15,17],[2,7,8,11,12,13,14,16,17],[2,7,8,11,12,13,15,16,17],[2,7,8,11,12,14,15,16,17],[2,7,8,11,13,14,15,16,17],[2,7,8,12,13,14,15,16,17],[2,7,9,10,11,12,13,14,15],[2,7,9,10,11,12,13,14,16],[2,7,9,10,11,12,13,14,17],[2,7,9,10,11,12,13,15,16],[2,7,9,10,11,12,13,15,17],[2,7,9,10,11,12,13,16,17],[2,7,9,10,11,12,14,15,16],[2,7,9,10,11,12,14,15,17],[2,7,9,10,11,12,14,16,17],[2,7,9,10,11,12,15,16,17],[2,7,9,10,11,13,14,15,16],[2,7,9,10,11,13,14,15,17],[2,7,9,10,11,13,14,16,17],[2,7,9,10,11,13,15,16,17],[2,7,9,10,11,14,15,16,17],[2,7,9,10,12,13,14,15,16],[2,7,9,10,12,13,14,15,17],[2,7,9,10,12,13,14,16,17],[2,7,9,10,12,13,15,16,17],[2,7,9,10,12,14,15,16,17],[2,7,9,10,13,14,15,16,17],[2,7,9,11,12,13,14,15,16],[2,7,9,11,12,13,14,15,17],[2,7,9,11,12,13,14,16,17],[2,7,9,11,12,13,15,16,17],[2,7,9,11,12,14,15,16,17],[2,7,9,11,13,14,15,16,17],[2,7,9,12,13,14,15,16,17],[2,7,10,11,12,13,14,15,16],[2,7,10,11,12,13,14,15,17],[2,7,10,11,12,13,14,16,17],[2,7,10,11,12,13,15,16,17],[2,7,10,11,12,14,15,16,17],[2,7,10,11,13,14,15,16,17],[2,7,10,12,13,14,15,16,17],[2,7,11,12,13,14,15,16,17],[2,8,9,10,11,12,13,14,15],[2,8,9,10,11,12,13,14,16],[2,8,9,10,11,12,13,14,17],[2,8,9,10,11,12,13,15,16],[2,8,9,10,11,12,13,15,17],[2,8,9,10,11,12,13,16,17],[2,8,9,10,11,12,14,15,16],[2,8,9,10,11,12,14,15,17],[2,8,9,10,11,12,14,16,17],[2,8,9,10,11,12,15,16,17],[2,8,9,10,11,13,14,15,16],[2,8,9,10,11,13,14,15,17],[2,8,9,10,11,13,14,16,17],[2,8,9,10,11,13,15,16,17],[2,8,9,10,11,14,15,16,17],[2,8,9,10,12,13,14,15,16],[2,8,9,10,12,13,14,15,17],[2,8,9,10,12,13,14,16,17],[2,8,9,10,12,13,15,16,17],[2,8,9,10,12,14,15,16,17],[2,8,9,10,13,14,15,16,17],[2,8,9,11,12,13,14,15,16],[2,8,9,11,12,13,14,15,17],[2,8,9,11,12,13,14,16,17],[2,8,9,11,12,13,15,16,17],[2,8,9,11,12,14,15,16,17],[2,8,9,11,13,14,15,16,17],[2,8,9,12,13,14,15,16,17],[2,8,10,11,12,13,14,15,16],[2,8,10,11,12,13,14,15,17],[2,8,10,11,12,13,14,16,17],[2,8,10,11,12,13,15,16,17],[2,8,10,11,12,14,15,16,17],[2,8,10,11,13,14,15,16,17],[2,8,10,12,13,14,15,16,17],[2,8,11,12,13,14,15,16,17],[2,9,10,11,12,13,14,15,16],[2,9,10,11,12,13,14,15,17],[2,9,10,11,12,13,14,16,17],[2,9,10,11,12,13,15,16,17],[2,9,10,11,12,14,15,16,17],[2,9,10,11,13,14,15,16,17],[2,9,10,12,13,14,15,16,17],[2,9,11,12,13,14,15,16,17],[2,10,11,12,13,14,15,16,17],[3,7,8,9,10,11,12,13,14],[3,7,8,9,10,11,12,13,15],[3,7,8,9,10,11,12,13,16],[3,7,8,9,10,11,12,13,17],[3,7,8,9,10,11,12,14,15],[3,7,8,9,10,11,12,14,16],[3,7,8,9,10,11,12,14,17],[3,7,8,9,10,11,12,15,16],[3,7,8,9,10,11,12,15,17],[3,7,8,9,10,11,12,16,17],[3,7,8,9,10,11,13,14,15],[3,7,8,9,10,11,13,14,16],[3,7,8,9,10,11,13,14,17],[3,7,8,9,10,11,13,15,16],[3,7,8,9,10,11,13,15,17],[3,7,8,9,10,11,13,16,17],[3,7,8,9,10,11,14,15,16],[3,7,8,9,10,11,14,15,17],[3,7,8,9,10,11,14,16,17],[3,7,8,9,10,11,15,16,17],[3,7,8,9,10,12,13,14,15],[3,7,8,9,10,12,13,14,16],[3,7,8,9,10,12,13,14,17],[3,7,8,9,10,12,13,15,16],[3,7,8,9,10,12,13,15,17],[3,7,8,9,10,12,13,16,17],[3,7,8,9,10,12,14,15,16],[3,7,8,9,10,12,14,15,17],[3,7,8,9,10,12,14,16,17],[3,7,8,9,10,12,15,16,17],[3,7,8,9,10,13,14,15,16],[3,7,8,9,10,13,14,15,17],[3,7,8,9,10,13,14,16,17],[3,7,8,9,10,13,15,16,17],[3,7,8,9,10,14,15,16,17],[3,7,8,9,11,12,13,14,15],[3,7,8,9,11,12,13,14,16],[3,7,8,9,11,12,13,14,17],[3,7,8,9,11,12,13,15,16],[3,7,8,9,11,12,13,15,17],[3,7,8,9,11,12,13,16,17],[3,7,8,9,11,12,14,15,16],[3,7,8,9,11,12,14,15,17],[3,7,8,9,11,12,14,16,17],[3,7,8,9,11,12,15,16,17],[3,7,8,9,11,13,14,15,16],[3,7,8,9,11,13,14,15,17],[3,7,8,9,11,13,14,16,17],[3,7,8,9,11,13,15,16,17],[3,7,8,9,11,14,15,16,17],[3,7,8,9,12,13,14,15,16],[3,7,8,9,12,13,14,15,17],[3,7,8,9,12,13,14,16,17],[3,7,8,9,12,13,15,16,17],[3,7,8,9,12,14,15,16,17],[3,7,8,9,13,14,15,16,17],[3,7,8,10,11,12,13,14,15],[3,7,8,10,11,12,13,14,16],[3,7,8,10,11,12,13,14,17],[3,7,8,10,11,12,13,15,16],[3,7,8,10,11,12,13,15,17],[3,7,8,10,11,12,13,16,17],[3,7,8,10,11,12,14,15,16],[3,7,8,10,11,12,14,15,17],[3,7,8,10,11,12,14,16,17],[3,7,8,10,11,12,15,16,17],[3,7,8,10,11,13,14,15,16],[3,7,8,10,11,13,14,15,17],[3,7,8,10,11,13,14,16,17],[3,7,8,10,11,13,15,16,17],[3,7,8,10,11,14,15,16,17],[3,7,8,10,12,13,14,15,16],[3,7,8,10,12,13,14,15,17],[3,7,8,10,12,13,14,16,17],[3,7,8,10,12,13,15,16,17],[3,7,8,10,12,14,15,16,17],[3,7,8,10,13,14,15,16,17],[3,7,8,11,12,13,14,15,16],[3,7,8,11,12,13,14,15,17],[3,7,8,11,12,13,14,16,17],[3,7,8,11,12,13,15,16,17],[3,7,8,11,12,14,15,16,17],[3,7,8,11,13,14,15,16,17],[3,7,8,12,13,14,15,16,17],[3,7,9,10,11,12,13,14,15],[3,7,9,10,11,12,13,14,16],[3,7,9,10,11,12,13,14,17],[3,7,9,10,11,12,13,15,16],[3,7,9,10,11,12,13,15,17],[3,7,9,10,11,12,13,16,17],[3,7,9,10,11,12,14,15,16],[3,7,9,10,11,12,14,15,17],[3,7,9,10,11,12,14,16,17],[3,7,9,10,11,12,15,16,17],[3,7,9,10,11,13,14,15,16],[3,7,9,10,11,13,14,15,17],[3,7,9,10,11,13,14,16,17],[3,7,9,10,11,13,15,16,17],[3,7,9,10,11,14,15,16,17],[3,7,9,10,12,13,14,15,16],[3,7,9,10,12,13,14,15,17],[3,7,9,10,12,13,14,16,17],[3,7,9,10,12,13,15,16,17],[3,7,9,10,12,14,15,16,17],[3,7,9,10,13,14,15,16,17],[3,7,9,11,12,13,14,15,16],[3,7,9,11,12,13,14,15,17],[3,7,9,11,12,13,14,16,17],[3,7,9,11,12,13,15,16,17],[3,7,9,11,12,14,15,16,17],[3,7,9,11,13,14,15,16,17],[3,7,9,12,13,14,15,16,17],[3,7,10,11,12,13,14,15,16],[3,7,10,11,12,13,14,15,17],[3,7,10,11,12,13,14,16,17],[3,7,10,11,12,13,15,16,17],[3,7,10,11,12,14,15,16,17],[3,7,10,11,13,14,15,16,17],[3,7,10,12,13,14,15,16,17],[3,7,11,12,13,14,15,16,17],[3,8,9,10,11,12,13,14,15],[3,8,9,10,11,12,13,14,16],[3,8,9,10,11,12,13,14,17],[3,8,9,10,11,12,13,15,16],[3,8,9,10,11,12,13,15,17],[3,8,9,10,11,12,13,16,17],[3,8,9,10,11,12,14,15,16],[3,8,9,10,11,12,14,15,17],[3,8,9,10,11,12,14,16,17],[3,8,9,10,11,12,15,16,17],[3,8,9,10,11,13,14,15,16],[3,8,9,10,11,13,14,15,17],[3,8,9,10,11,13,14,16,17],[3,8,9,10,11,13,15,16,17],[3,8,9,10,11,14,15,16,17],[3,8,9,10,12,13,14,15,16],[3,8,9,10,12,13,14,15,17],[3,8,9,10,12,13,14,16,17],[3,8,9,10,12,13,15,16,17],[3,8,9,10,12,14,15,16,17],[3,8,9,10,13,14,15,16,17],[3,8,9,11,12,13,14,15,16],[3,8,9,11,12,13,14,15,17],[3,8,9,11,12,13,14,16,17],[3,8,9,11,12,13,15,16,17],[3,8,9,11,12,14,15,16,17],[3,8,9,11,13,14,15,16,17],[3,8,9,12,13,14,15,16,17],[3,8,10,11,12,13,14,15,16],[3,8,10,11,12,13,14,15,17],[3,8,10,11,12,13,14,16,17],[3,8,10,11,12,13,15,16,17],[3,8,10,11,12,14,15,16,17],[3,8,10,11,13,14,15,16,17],[3,8,10,12,13,14,15,16,17],[3,8,11,12,13,14,15,16,17],[3,9,10,11,12,13,14,15,16],[3,9,10,11,12,13,14,15,17],[3,9,10,11,12,13,14,16,17],[3,9,10,11,12,13,15,16,17],[3,9,10,11,12,14,15,16,17],[3,9,10,11,13,14,15,16,17],[3,9,10,12,13,14,15,16,17],[3,9,11,12,13,14,15,16,17],[3,10,11,12,13,14,15,16,17],[4,7,8,9,10,11,12,13,14],[4,7,8,9,10,11,12,13,15],[4,7,8,9,10,11,12,13,16],[4,7,8,9,10,11,12,13,17],[4,7,8,9,10,11,12,14,15],[4,7,8,9,10,11,12,14,16],[4,7,8,9,10,11,12,14,17],[4,7,8,9,10,11,12,15,16],[4,7,8,9,10,11,12,15,17],[4,7,8,9,10,11,12,16,17],[4,7,8,9,10,11,13,14,15],[4,7,8,9,10,11,13,14,16],[4,7,8,9,10,11,13,14,17],[4,7,8,9,10,11,13,15,16],[4,7,8,9,10,11,13,15,17],[4,7,8,9,10,11,13,16,17],[4,7,8,9,10,11,14,15,16],[4,7,8,9,10,11,14,15,17],[4,7,8,9,10,11,14,16,17],[4,7,8,9,10,11,15,16,17],[4,7,8,9,10,12,13,14,15],[4,7,8,9,10,12,13,14,16],[4,7,8,9,10,12,13,14,17],[4,7,8,9,10,12,13,15,16],[4,7,8,9,10,12,13,15,17],[4,7,8,9,10,12,13,16,17],[4,7,8,9,10,12,14,15,16],[4,7,8,9,10,12,14,15,17],[4,7,8,9,10,12,14,16,17],[4,7,8,9,10,12,15,16,17],[4,7,8,9,10,13,14,15,16],[4,7,8,9,10,13,14,15,17],[4,7,8,9,10,13,14,16,17],[4,7,8,9,10,13,15,16,17],[4,7,8,9,10,14,15,16,17],[4,7,8,9,11,12,13,14,15],[4,7,8,9,11,12,13,14,16],[4,7,8,9,11,12,13,14,17],[4,7,8,9,11,12,13,15,16],[4,7,8,9,11,12,13,15,17],[4,7,8,9,11,12,13,16,17],[4,7,8,9,11,12,14,15,16],[4,7,8,9,11,12,14,15,17],[4,7,8,9,11,12,14,16,17],[4,7,8,9,11,12,15,16,17],[4,7,8,9,11,13,14,15,16],[4,7,8,9,11,13,14,15,17],[4,7,8,9,11,13,14,16,17],[4,7,8,9,11,13,15,16,17],[4,7,8,9,11,14,15,16,17],[4,7,8,9,12,13,14,15,16],[4,7,8,9,12,13,14,15,17],[4,7,8,9,12,13,14,16,17],[4,7,8,9,12,13,15,16,17],[4,7,8,9,12,14,15,16,17],[4,7,8,9,13,14,15,16,17],[4,7,8,10,11,12,13,14,15],[4,7,8,10,11,12,13,14,16],[4,7,8,10,11,12,13,14,17],[4,7,8,10,11,12,13,15,16],[4,7,8,10,11,12,13,15,17],[4,7,8,10,11,12,13,16,17],[4,7,8,10,11,12,14,15,16],[4,7,8,10,11,12,14,15,17],[4,7,8,10,11,12,14,16,17],[4,7,8,10,11,12,15,16,17],[4,7,8,10,11,13,14,15,16],[4,7,8,10,11,13,14,15,17],[4,7,8,10,11,13,14,16,17],[4,7,8,10,11,13,15,16,17],[4,7,8,10,11,14,15,16,17],[4,7,8,10,12,13,14,15,16],[4,7,8,10,12,13,14,15,17],[4,7,8,10,12,13,14,16,17],[4,7,8,10,12,13,15,16,17],[4,7,8,10,12,14,15,16,17],[4,7,8,10,13,14,15,16,17],[4,7,8,11,12,13,14,15,16],[4,7,8,11,12,13,14,15,17],[4,7,8,11,12,13,14,16,17],[4,7,8,11,12,13,15,16,17],[4,7,8,11,12,14,15,16,17],[4,7,8,11,13,14,15,16,17],[4,7,8,12,13,14,15,16,17],[4,7,9,10,11,12,13,14,15],[4,7,9,10,11,12,13,14,16],[4,7,9,10,11,12,13,14,17],[4,7,9,10,11,12,13,15,16],[4,7,9,10,11,12,13,15,17],[4,7,9,10,11,12,13,16,17],[4,7,9,10,11,12,14,15,16],[4,7,9,10,11,12,14,15,17],[4,7,9,10,11,12,14,16,17],[4,7,9,10,11,12,15,16,17],[4,7,9,10,11,13,14,15,16],[4,7,9,10,11,13,14,15,17],[4,7,9,10,11,13,14,16,17],[4,7,9,10,11,13,15,16,17],[4,7,9,10,11,14,15,16,17],[4,7,9,10,12,13,14,15,16],[4,7,9,10,12,13,14,15,17],[4,7,9,10,12,13,14,16,17],[4,7,9,10,12,13,15,16,17],[4,7,9,10,12,14,15,16,17],[4,7,9,10,13,14,15,16,17],[4,7,9,11,12,13,14,15,16],[4,7,9,11,12,13,14,15,17],[4,7,9,11,12,13,14,16,17],[4,7,9,11,12,13,15,16,17],[4,7,9,11,12,14,15,16,17],[4,7,9,11,13,14,15,16,17],[4,7,9,12,13,14,15,16,17],[4,7,10,11,12,13,14,15,16],[4,7,10,11,12,13,14,15,17],[4,7,10,11,12,13,14,16,17],[4,7,10,11,12,13,15,16,17],[4,7,10,11,12,14,15,16,17],[4,7,10,11,13,14,15,16,17],[4,7,10,12,13,14,15,16,17],[4,7,11,12,13,14,15,16,17],[4,8,9,10,11,12,13,14,15],[4,8,9,10,11,12,13,14,16],[4,8,9,10,11,12,13,14,17],[4,8,9,10,11,12,13,15,16],[4,8,9,10,11,12,13,15,17],[4,8,9,10,11,12,13,16,17],[4,8,9,10,11,12,14,15,16],[4,8,9,10,11,12,14,15,17],[4,8,9,10,11,12,14,16,17],[4,8,9,10,11,12,15,16,17],[4,8,9,10,11,13,14,15,16],[4,8,9,10,11,13,14,15,17],[4,8,9,10,11,13,14,16,17],[4,8,9,10,11,13,15,16,17],[4,8,9,10,11,14,15,16,17],[4,8,9,10,12,13,14,15,16],[4,8,9,10,12,13,14,15,17],[4,8,9,10,12,13,14,16,17],[4,8,9,10,12,13,15,16,17],[4,8,9,10,12,14,15,16,17],[4,8,9,10,13,14,15,16,17],[4,8,9,11,12,13,14,15,16],[4,8,9,11,12,13,14,15,17],[4,8,9,11,12,13,14,16,17],[4,8,9,11,12,13,15,16,17],[4,8,9,11,12,14,15,16,17],[4,8,9,11,13,14,15,16,17],[4,8,9,12,13,14,15,16,17],[4,8,10,11,12,13,14,15,16],[4,8,10,11,12,13,14,15,17],[4,8,10,11,12,13,14,16,17],[4,8,10,11,12,13,15,16,17],[4,8,10,11,12,14,15,16,17],[4,8,10,11,13,14,15,16,17],[4,8,10,12,13,14,15,16,17],[4,8,11,12,13,14,15,16,17],[4,9,10,11,12,13,14,15,16],[4,9,10,11,12,13,14,15,17],[4,9,10,11,12,13,14,16,17],[4,9,10,11,12,13,15,16,17],[4,9,10,11,12,14,15,16,17],[4,9,10,11,13,14,15,16,17],[4,9,10,12,13,14,15,16,17],[4,9,11,12,13,14,15,16,17],[4,10,11,12,13,14,15,16,17],[5,7,8,9,10,11,12,13,14],[5,7,8,9,10,11,12,13,15],[5,7,8,9,10,11,12,13,16],[5,7,8,9,10,11,12,13,17],[5,7,8,9,10,11,12,14,15],[5,7,8,9,10,11,12,14,16],[5,7,8,9,10,11,12,14,17],[5,7,8,9,10,11,12,15,16],[5,7,8,9,10,11,12,15,17],[5,7,8,9,10,11,12,16,17],[5,7,8,9,10,11,13,14,15],[5,7,8,9,10,11,13,14,16],[5,7,8,9,10,11,13,14,17],[5,7,8,9,10,11,13,15,16],[5,7,8,9,10,11,13,15,17],[5,7,8,9,10,11,13,16,17],[5,7,8,9,10,11,14,15,16],[5,7,8,9,10,11,14,15,17],[5,7,8,9,10,11,14,16,17],[5,7,8,9,10,11,15,16,17],[5,7,8,9,10,12,13,14,15],[5,7,8,9,10,12,13,14,16],[5,7,8,9,10,12,13,14,17],[5,7,8,9,10,12,13,15,16],[5,7,8,9,10,12,13,15,17],[5,7,8,9,10,12,13,16,17],[5,7,8,9,10,12,14,15,16],[5,7,8,9,10,12,14,15,17],[5,7,8,9,10,12,14,16,17],[5,7,8,9,10,12,15,16,17],[5,7,8,9,10,13,14,15,16],[5,7,8,9,10,13,14,15,17],[5,7,8,9,10,13,14,16,17],[5,7,8,9,10,13,15,16,17],[5,7,8,9,10,14,15,16,17],[5,7,8,9,11,12,13,14,15],[5,7,8,9,11,12,13,14,16],[5,7,8,9,11,12,13,14,17],[5,7,8,9,11,12,13,15,16],[5,7,8,9,11,12,13,15,17],[5,7,8,9,11,12,13,16,17],[5,7,8,9,11,12,14,15,16],[5,7,8,9,11,12,14,15,17],[5,7,8,9,11,12,14,16,17],[5,7,8,9,11,12,15,16,17],[5,7,8,9,11,13,14,15,16],[5,7,8,9,11,13,14,15,17],[5,7,8,9,11,13,14,16,17],[5,7,8,9,11,13,15,16,17],[5,7,8,9,11,14,15,16,17],[5,7,8,9,12,13,14,15,16],[5,7,8,9,12,13,14,15,17],[5,7,8,9,12,13,14,16,17],[5,7,8,9,12,13,15,16,17],[5,7,8,9,12,14,15,16,17],[5,7,8,9,13,14,15,16,17],[5,7,8,10,11,12,13,14,15],[5,7,8,10,11,12,13,14,16],[5,7,8,10,11,12,13,14,17],[5,7,8,10,11,12,13,15,16],[5,7,8,10,11,12,13,15,17],[5,7,8,10,11,12,13,16,17],[5,7,8,10,11,12,14,15,16],[5,7,8,10,11,12,14,15,17],[5,7,8,10,11,12,14,16,17],[5,7,8,10,11,12,15,16,17],[5,7,8,10,11,13,14,15,16],[5,7,8,10,11,13,14,15,17],[5,7,8,10,11,13,14,16,17],[5,7,8,10,11,13,15,16,17],[5,7,8,10,11,14,15,16,17],[5,7,8,10,12,13,14,15,16],[5,7,8,10,12,13,14,15,17],[5,7,8,10,12,13,14,16,17],[5,7,8,10,12,13,15,16,17],[5,7,8,10,12,14,15,16,17],[5,7,8,10,13,14,15,16,17],[5,7,8,11,12,13,14,15,16],[5,7,8,11,12,13,14,15,17],[5,7,8,11,12,13,14,16,17],[5,7,8,11,12,13,15,16,17],[5,7,8,11,12,14,15,16,17],[5,7,8,11,13,14,15,16,17],[5,7,8,12,13,14,15,16,17],[5,7,9,10,11,12,13,14,15],[5,7,9,10,11,12,13,14,16],[5,7,9,10,11,12,13,14,17],[5,7,9,10,11,12,13,15,16],[5,7,9,10,11,12,13,15,17],[5,7,9,10,11,12,13,16,17],[5,7,9,10,11,12,14,15,16],[5,7,9,10,11,12,14,15,17],[5,7,9,10,11,12,14,16,17],[5,7,9,10,11,12,15,16,17],[5,7,9,10,11,13,14,15,16],[5,7,9,10,11,13,14,15,17],[5,7,9,10,11,13,14,16,17],[5,7,9,10,11,13,15,16,17],[5,7,9,10,11,14,15,16,17],[5,7,9,10,12,13,14,15,16],[5,7,9,10,12,13,14,15,17],[5,7,9,10,12,13,14,16,17],[5,7,9,10,12,13,15,16,17],[5,7,9,10,12,14,15,16,17],[5,7,9,10,13,14,15,16,17],[5,7,9,11,12,13,14,15,16],[5,7,9,11,12,13,14,15,17],[5,7,9,11,12,13,14,16,17],[5,7,9,11,12,13,15,16,17],[5,7,9,11,12,14,15,16,17],[5,7,9,11,13,14,15,16,17],[5,7,9,12,13,14,15,16,17],[5,7,10,11,12,13,14,15,16],[5,7,10,11,12,13,14,15,17],[5,7,10,11,12,13,14,16,17],[5,7,10,11,12,13,15,16,17],[5,7,10,11,12,14,15,16,17],[5,7,10,11,13,14,15,16,17],[5,7,10,12,13,14,15,16,17],[5,7,11,12,13,14,15,16,17],[5,8,9,10,11,12,13,14,15],[5,8,9,10,11,12,13,14,16],[5,8,9,10,11,12,13,14,17],[5,8,9,10,11,12,13,15,16],[5,8,9,10,11,12,13,15,17],[5,8,9,10,11,12,13,16,17],[5,8,9,10,11,12,14,15,16],[5,8,9,10,11,12,14,15,17],[5,8,9,10,11,12,14,16,17],[5,8,9,10,11,12,15,16,17],[5,8,9,10,11,13,14,15,16],[5,8,9,10,11,13,14,15,17],[5,8,9,10,11,13,14,16,17],[5,8,9,10,11,13,15,16,17],[5,8,9,10,11,14,15,16,17],[5,8,9,10,12,13,14,15,16],[5,8,9,10,12,13,14,15,17],[5,8,9,10,12,13,14,16,17],[5,8,9,10,12,13,15,16,17],[5,8,9,10,12,14,15,16,17],[5,8,9,10,13,14,15,16,17],[5,8,9,11,12,13,14,15,16],[5,8,9,11,12,13,14,15,17],[5,8,9,11,12,13,14,16,17],[5,8,9,11,12,13,15,16,17],[5,8,9,11,12,14,15,16,17],[5,8,9,11,13,14,15,16,17],[5,8,9,12,13,14,15,16,17],[5,8,10,11,12,13,14,15,16],[5,8,10,11,12,13,14,15,17],[5,8,10,11,12,13,14,16,17],[5,8,10,11,12,13,15,16,17],[5,8,10,11,12,14,15,16,17],[5,8,10,11,13,14,15,16,17],[5,8,10,12,13,14,15,16,17],[5,8,11,12,13,14,15,16,17],[5,9,10,11,12,13,14,15,16],[5,9,10,11,12,13,14,15,17],[5,9,10,11,12,13,14,16,17],[5,9,10,11,12,13,15,16,17],[5,9,10,11,12,14,15,16,17],[5,9,10,11,13,14,15,16,17],[5,9,10,12,13,14,15,16,17],[5,9,11,12,13,14,15,16,17],[5,10,11,12,13,14,15,16,17],[6,7,8,9,10,11,12,13,14],[6,7,8,9,10,11,12,13,15],[6,7,8,9,10,11,12,13,16],[6,7,8,9,10,11,12,13,17],[6,7,8,9,10,11,12,14,15],[6,7,8,9,10,11,12,14,16],[6,7,8,9,10,11,12,14,17],[6,7,8,9,10,11,12,15,16],[6,7,8,9,10,11,12,15,17],[6,7,8,9,10,11,12,16,17],[6,7,8,9,10,11,13,14,15],[6,7,8,9,10,11,13,14,16],[6,7,8,9,10,11,13,14,17],[6,7,8,9,10,11,13,15,16],[6,7,8,9,10,11,13,15,17],[6,7,8,9,10,11,13,16,17],[6,7,8,9,10,11,14,15,16],[6,7,8,9,10,11,14,15,17],[6,7,8,9,10,11,14,16,17],[6,7,8,9,10,11,15,16,17],[6,7,8,9,10,12,13,14,15],[6,7,8,9,10,12,13,14,16],[6,7,8,9,10,12,13,14,17],[6,7,8,9,10,12,13,15,16],[6,7,8,9,10,12,13,15,17],[6,7,8,9,10,12,13,16,17],[6,7,8,9,10,12,14,15,16],[6,7,8,9,10,12,14,15,17],[6,7,8,9,10,12,14,16,17],[6,7,8,9,10,12,15,16,17],[6,7,8,9,10,13,14,15,16],[6,7,8,9,10,13,14,15,17],[6,7,8,9,10,13,14,16,17],[6,7,8,9,10,13,15,16,17],[6,7,8,9,10,14,15,16,17],[6,7,8,9,11,12,13,14,15],[6,7,8,9,11,12,13,14,16],[6,7,8,9,11,12,13,14,17],[6,7,8,9,11,12,13,15,16],[6,7,8,9,11,12,13,15,17],[6,7,8,9,11,12,13,16,17],[6,7,8,9,11,12,14,15,16],[6,7,8,9,11,12,14,15,17],[6,7,8,9,11,12,14,16,17],[6,7,8,9,11,12,15,16,17],[6,7,8,9,11,13,14,15,16],[6,7,8,9,11,13,14,15,17],[6,7,8,9,11,13,14,16,17],[6,7,8,9,11,13,15,16,17],[6,7,8,9,11,14,15,16,17],[6,7,8,9,12,13,14,15,16],[6,7,8,9,12,13,14,15,17],[6,7,8,9,12,13,14,16,17],[6,7,8,9,12,13,15,16,17],[6,7,8,9,12,14,15,16,17],[6,7,8,9,13,14,15,16,17],[6,7,8,10,11,12,13,14,15],[6,7,8,10,11,12,13,14,16],[6,7,8,10,11,12,13,14,17],[6,7,8,10,11,12,13,15,16],[6,7,8,10,11,12,13,15,17],[6,7,8,10,11,12,13,16,17],[6,7,8,10,11,12,14,15,16],[6,7,8,10,11,12,14,15,17],[6,7,8,10,11,12,14,16,17],[6,7,8,10,11,12,15,16,17],[6,7,8,10,11,13,14,15,16],[6,7,8,10,11,13,14,15,17],[6,7,8,10,11,13,14,16,17],[6,7,8,10,11,13,15,16,17],[6,7,8,10,11,14,15,16,17],[6,7,8,10,12,13,14,15,16],[6,7,8,10,12,13,14,15,17],[6,7,8,10,12,13,14,16,17],[6,7,8,10,12,13,15,16,17],[6,7,8,10,12,14,15,16,17],[6,7,8,10,13,14,15,16,17],[6,7,8,11,12,13,14,15,16],[6,7,8,11,12,13,14,15,17],[6,7,8,11,12,13,14,16,17],[6,7,8,11,12,13,15,16,17],[6,7,8,11,12,14,15,16,17],[6,7,8,11,13,14,15,16,17],[6,7,8,12,13,14,15,16,17],[6,7,9,10,11,12,13,14,15],[6,7,9,10,11,12,13,14,16],[6,7,9,10,11,12,13,14,17],[6,7,9,10,11,12,13,15,16],[6,7,9,10,11,12,13,15,17],[6,7,9,10,11,12,13,16,17],[6,7,9,10,11,12,14,15,16],[6,7,9,10,11,12,14,15,17],[6,7,9,10,11,12,14,16,17],[6,7,9,10,11,12,15,16,17],[6,7,9,10,11,13,14,15,16],[6,7,9,10,11,13,14,15,17],[6,7,9,10,11,13,14,16,17],[6,7,9,10,11,13,15,16,17],[6,7,9,10,11,14,15,16,17],[6,7,9,10,12,13,14,15,16],[6,7,9,10,12,13,14,15,17],[6,7,9,10,12,13,14,16,17],[6,7,9,10,12,13,15,16,17],[6,7,9,10,12,14,15,16,17],[6,7,9,10,13,14,15,16,17],[6,7,9,11,12,13,14,15,16],[6,7,9,11,12,13,14,15,17],[6,7,9,11,12,13,14,16,17],[6,7,9,11,12,13,15,16,17],[6,7,9,11,12,14,15,16,17],[6,7,9,11,13,14,15,16,17],[6,7,9,12,13,14,15,16,17],[6,7,10,11,12,13,14,15,16],[6,7,10,11,12,13,14,15,17],[6,7,10,11,12,13,14,16,17],[6,7,10,11,12,13,15,16,17],[6,7,10,11,12,14,15,16,17],[6,7,10,11,13,14,15,16,17],[6,7,10,12,13,14,15,16,17],[6,7,11,12,13,14,15,16,17],[6,8,9,10,11,12,13,14,15],[6,8,9,10,11,12,13,14,16],[6,8,9,10,11,12,13,14,17],[6,8,9,10,11,12,13,15,16],[6,8,9,10,11,12,13,15,17],[6,8,9,10,11,12,13,16,17],[6,8,9,10,11,12,14,15,16],[6,8,9,10,11,12,14,15,17],[6,8,9,10,11,12,14,16,17],[6,8,9,10,11,12,15,16,17],[6,8,9,10,11,13,14,15,16],[6,8,9,10,11,13,14,15,17],[6,8,9,10,11,13,14,16,17],[6,8,9,10,11,13,15,16,17],[6,8,9,10,11,14,15,16,17],[6,8,9,10,12,13,14,15,16],[6,8,9,10,12,13,14,15,17],[6,8,9,10,12,13,14,16,17],[6,8,9,10,12,13,15,16,17],[6,8,9,10,12,14,15,16,17],[6,8,9,10,13,14,15,16,17],[6,8,9,11,12,13,14,15,16],[6,8,9,11,12,13,14,15,17],[6,8,9,11,12,13,14,16,17],[6,8,9,11,12,13,15,16,17],[6,8,9,11,12,14,15,16,17],[6,8,9,11,13,14,15,16,17],[6,8,9,12,13,14,15,16,17],[6,8,10,11,12,13,14,15,16],[6,8,10,11,12,13,14,15,17],[6,8,10,11,12,13,14,16,17],[6,8,10,11,12,13,15,16,17],[6,8,10,11,12,14,15,16,17],[6,8,10,11,13,14,15,16,17],[6,8,10,12,13,14,15,16,17],[6,8,11,12,13,14,15,16,17],[6,9,10,11,12,13,14,15,16],[6,9,10,11,12,13,14,15,17],[6,9,10,11,12,13,14,16,17],[6,9,10,11,12,13,15,16,17],[6,9,10,11,12,14,15,16,17],[6,9,10,11,13,14,15,16,17],[6,9,10,12,13,14,15,16,17],[6,9,11,12,13,14,15,16,17],[6,10,11,12,13,14,15,16,17],[7],[7,8,9,10,11,12,13,14,15],[7,8,9,10,11,12,13,14,16],[7,8,9,10,11,12,13,14,17],[7,8,9,10,11,12,13,15,16],[7,8,9,10,11,12,13,15,17],[7,8,9,10,11,12,13,16,17],[7,8,9,10,11,12,14,15,16],[7,8,9,10,11,12,14,15,17],[7,8,9,10,11,12,14,16,17],[7,8,9,10,11,12,15,16,17],[7,8,9,10,11,13,14,15,16],[7,8,9,10,11,13,14,15,17],[7,8,9,10,11,13,14,16,17],[7,8,9,10,11,13,15,16,17],[7,8,9,10,11,14,15,16,17],[7,8,9,10,12,13,14,15,16],[7,8,9,10,12,13,14,15,17],[7,8,9,10,12,13,14,16,17],[7,8,9,10,12,13,15,16,17],[7,8,9,10,12,14,15,16,17],[7,8,9,10,13,14,15,16,17],[7,8,9,11,12,13,14,15,16],[7,8,9,11,12,13,14,15,17],[7,8,9,11,12,13,14,16,17],[7,8,9,11,12,13,15,16,17],[7,8,9,11,12,14,15,16,17],[7,8,9,11,13,14,15,16,17],[7,8,9,12,13,14,15,16,17],[7,8,10,11,12,13,14,15,16],[7,8,10,11,12,13,14,15,17],[7,8,10,11,12,13,14,16,17],[7,8,10,11,12,13,15,16,17],[7,8,10,11,12,14,15,16,17],[7,8,10,11,13,14,15,16,17],[7,8,10,12,13,14,15,16,17],[7,8,11,12,13,14,15,16,17],[7,9,10,11,12,13,14,15,16],[7,9,10,11,12,13,14,15,17],[7,9,10,11,12,13,14,16,17],[7,9,10,11,12,13,15,16,17],[7,9,10,11,12,14,15,16,17],[7,9,10,11,13,14,15,16,17],[7,9,10,12,13,14,15,16,17],[7,9,11,12,13,14,15,16,17],[7,10,11,12,13,14,15,16,17],[8],[8,9,10,11,12,13,14,15,16],[8,9,10,11,12,13,14,15,17],[8,9,10,11,12,13,14,16,17],[8,9,10,11,12,13,15,16,17],[8,9,10,11,12,14,15,16,17],[8,9,10,11,13,14,15,16,17],[8,9,10,12,13,14,15,16,17],[8,9,11,12,13,14,15,16,17],[8,10,11,12,13,14,15,16,17],[9],[9,10,11,12,13,14,15,16,17],[10],[11],[12],[13],[14],[15],[16],[17]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,165],"A_d":3465,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,2],[2,2],[3,2],[4,2],[5,2],[6,2],[7,1],[8,1],[9,1],[10,1],[11,1],[12,1],[13,1],[14,1],[15,1],[16,1],[17,1]],"CZ":[]},"rotation_powers":[[0,5],[1,5],[4,5],[10,5],[20,5],[35,5],[56,5],[84,5],[120,5],[165,5],[330,5],[495,5],[660,5],[825,5],[990,5],[1155,3],[1202,3],[1203,3],[1204,3],[1205,3],[1206,3],[1207,3],[1208,3],[1209,3],[1210,3],[1212,3]]},"metrics":{"gamma":7.446492562929799,"gamma_t":null,"gamma_rho":7.446492562929799,"gamma_claim":7.446492562929799,"gamma_t_claim":null,"gamma_rho_claim":7.446492562929799,"v_ex":7,"rate":0.005733005733005733,"t_count":null,"poly_degree":null,"effective_width":7},"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-0770","N":18,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 770","provenance":"larger unified search l=3, two-group s_total=8,s_O=7"}]},"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"}]}