Identifier
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0Cc0007;cc-rep-2
[1,0]=>[1]=>[[1]]=>[1]
[1,0,1,0]=>[2,1]=>[[1],[2]]=>[1,1]
[1,1,0,0]=>[1,2]=>[[1,2]]=>[2]
[1,0,1,0,1,0]=>[2,1,3]=>[[1,3],[2]]=>[1,2]
[1,0,1,1,0,0]=>[2,3,1]=>[[1,2],[3]]=>[2,1]
[1,1,0,0,1,0]=>[3,1,2]=>[[1,3],[2]]=>[1,2]
[1,1,0,1,0,0]=>[1,3,2]=>[[1,2],[3]]=>[2,1]
[1,1,1,0,0,0]=>[1,2,3]=>[[1,2,3]]=>[3]
[1,0,1,0,1,0,1,0]=>[2,1,4,3]=>[[1,3],[2,4]]=>[1,2,1]
[1,0,1,0,1,1,0,0]=>[2,4,1,3]=>[[1,2],[3,4]]=>[2,2]
[1,0,1,1,0,0,1,0]=>[2,1,3,4]=>[[1,3,4],[2]]=>[1,3]
[1,0,1,1,0,1,0,0]=>[2,3,1,4]=>[[1,2,4],[3]]=>[2,2]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[[1,2,3],[4]]=>[3,1]
[1,1,0,0,1,0,1,0]=>[3,1,4,2]=>[[1,3],[2,4]]=>[1,2,1]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[[1,2],[3,4]]=>[2,2]
[1,1,0,1,0,0,1,0]=>[3,1,2,4]=>[[1,3,4],[2]]=>[1,3]
[1,1,0,1,0,1,0,0]=>[1,3,2,4]=>[[1,2,4],[3]]=>[2,2]
[1,1,0,1,1,0,0,0]=>[1,3,4,2]=>[[1,2,3],[4]]=>[3,1]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[[1,3,4],[2]]=>[1,3]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[[1,2,4],[3]]=>[2,2]
[1,1,1,0,1,0,0,0]=>[1,2,4,3]=>[[1,2,3],[4]]=>[3,1]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[[1,2,3,4]]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>[[1,3,5],[2,4]]=>[1,2,2]
[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>[[1,2,5],[3,4]]=>[2,3]
[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>[[1,3,4],[2,5]]=>[1,3,1]
[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>[[1,2,4],[3,5]]=>[2,2,1]
[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>[[1,2,3],[4,5]]=>[3,2]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>[[1,3,5],[2,4]]=>[1,2,2]
[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>[[1,2,5],[3,4]]=>[2,3]
[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>[[1,3,4],[2,5]]=>[1,3,1]
[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>[[1,2,4],[3,5]]=>[2,2,1]
[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[[1,2,3],[4,5]]=>[3,2]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]=>[1,4]
[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>[[1,2,4,5],[3]]=>[2,3]
[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>[[1,2,3,5],[4]]=>[3,2]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[[1,2,3,4],[5]]=>[4,1]
[1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>[[1,3,5],[2,4]]=>[1,2,2]
[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>[[1,2,5],[3,4]]=>[2,3]
[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>[[1,3,4],[2,5]]=>[1,3,1]
[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>[[1,2,4],[3,5]]=>[2,2,1]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[[1,2,3],[4,5]]=>[3,2]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>[[1,3,5],[2,4]]=>[1,2,2]
[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>[[1,2,5],[3,4]]=>[2,3]
[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>[[1,3,4],[2,5]]=>[1,3,1]
[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>[[1,2,4],[3,5]]=>[2,2,1]
[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[[1,2,3],[4,5]]=>[3,2]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>[[1,3,4,5],[2]]=>[1,4]
[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>[[1,2,4,5],[3]]=>[2,3]
[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>[[1,2,3,5],[4]]=>[3,2]
[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>[[1,2,3,4],[5]]=>[4,1]
[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>[[1,3,5],[2,4]]=>[1,2,2]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[[1,2,5],[3,4]]=>[2,3]
[1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>[[1,3,4],[2,5]]=>[1,3,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>[[1,2,4],[3,5]]=>[2,2,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>[[1,2,3],[4,5]]=>[3,2]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>[[1,3,4,5],[2]]=>[1,4]
[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>[[1,2,4,5],[3]]=>[2,3]
[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>[[1,2,3,5],[4]]=>[3,2]
[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>[[1,2,3,4],[5]]=>[4,1]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[[1,3,4,5],[2]]=>[1,4]
[1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>[[1,2,4,5],[3]]=>[2,3]
[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>[[1,2,3,5],[4]]=>[3,2]
[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>[[1,2,3,4],[5]]=>[4,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[[1,2,3,4,5]]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]=>[1,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>[[1,2,5],[3,4,6]]=>[2,3,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>[[1,3,4],[2,5,6]]=>[1,3,2]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>[[1,2,4],[3,5,6]]=>[2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>[[1,2,3],[4,5,6]]=>[3,3]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>[[1,3,5],[2,4,6]]=>[1,2,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[[1,2,5],[3,4,6]]=>[2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>[[1,3,4],[2,5,6]]=>[1,3,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>[[1,2,4],[3,5,6]]=>[2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>[[1,2,3],[4,5,6]]=>[3,3]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>[[1,2,3,4,6],[5]]=>[4,2]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[[1,2,3,4,5],[6]]=>[5,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>[[1,3,5],[2,4,6]]=>[1,2,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>[[1,2,5],[3,4,6]]=>[2,3,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>[[1,3,4],[2,5,6]]=>[1,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>[[1,2,4],[3,5,6]]=>[2,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>[[1,2,3],[4,5,6]]=>[3,3]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>[[1,3,5],[2,4,6]]=>[1,2,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>[[1,2,5],[3,4,6]]=>[2,3,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>[[1,3,4],[2,5,6]]=>[1,3,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>[[1,2,4],[3,5,6]]=>[2,2,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>[[1,2,3],[4,5,6]]=>[3,3]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>[[1,2,3,4,6],[5]]=>[4,2]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>[[1,2,3,4,5],[6]]=>[5,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>[[1,3,5],[2,4,6]]=>[1,2,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>[[1,2,5],[3,4,6]]=>[2,3,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>[[1,3,4],[2,5,6]]=>[1,3,2]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>[[1,2,4],[3,5,6]]=>[2,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>[[1,2,3,4,6],[5]]=>[4,2]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>[[1,2,3,4,5],[6]]=>[5,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>[[1,3,5,6],[2,4]]=>[1,2,3]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>[[1,3,4,6],[2,5]]=>[1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>[[1,2,4,6],[3,5]]=>[2,2,2]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>[[1,3,4,5],[2,6]]=>[1,4,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>[[1,2,4,5],[3,6]]=>[2,3,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>[[1,2,3,5],[4,6]]=>[3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>[[1,2,4,5,6],[3]]=>[2,4]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>[[1,2,3,5,6],[4]]=>[3,3]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>[[1,2,3,4,6],[5]]=>[4,2]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>[[1,2,3,4,5],[6]]=>[5,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>[[1,2,4,5,6],[3]]=>[2,4]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[[1,2,3,5,6],[4]]=>[3,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>[[1,2,3,4,6],[5]]=>[4,2]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]=>[5,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>[[1,3,5,7],[2,4,6]]=>[1,2,2,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>[[1,3,4,7],[2,5,6]]=>[1,3,3]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>[[1,3,5,6],[2,4,7]]=>[1,2,3,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[[1,3,4,6],[2,5,7]]=>[1,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>[[1,3,4,5],[2,6,7]]=>[1,4,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>[[1,3,5,6,7],[2,4]]=>[1,2,4]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>[[1,3,4,6,7],[2,5]]=>[1,3,3]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>[[1,3,4,5,7],[2,6]]=>[1,4,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[[1,3,4,5,6],[2,7]]=>[1,5,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,8,5,7]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,8,5,7]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,8,3,5,7]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,3,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,6,1,7,3,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,8,5]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,6,7,8,3,5]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,7,8,1,3,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,7,8,3,5,6]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,8,3,5,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,7,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,7,3,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,7,8,3,6]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,7,8,3,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,5,7,1,8,3,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,7,8,1,3,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,8,5,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,4,8,3,5,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,5,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,8,1,3,5,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,4,5,8,3,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,5,8,3,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,8,3,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,8,3,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,6,8,1,3,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,5,1,6,7,8,3]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,5,6,1,7,8,3]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,3]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,8,4,7]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,8,4,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,8,3,4,7]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,8,3,4,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4,8]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4,8]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,7,8,4]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,8,4]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,7,8,4]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,6,7,1,3,8,4]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,5,6,7,8,3,4]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5,6,7,1,8,3,4]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,7,8,4,6]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,8,4,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,7,8,3,4,6]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,7,8,3,4,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,7,1,8,3,4,6]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,7,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,7,4,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,7,1,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,7,8,1,4,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,8,4,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,8,4,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,8,3,4,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,8,3,4,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,5,8,1,3,4,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,5,8,4,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,8,4,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,8,4,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,8,4,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,5,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,6,7,8,1,4]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,8,5]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,8,5]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,6,3,7,8,4,5]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,1,3,7,8,4,5]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,6,7,1,3,8,4,5]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,6,1,7,8,3,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,6,7,1,8,3,4,5]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,6,7,8,4,5]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,8,4,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,6,7,8,1,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,8,4,5,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,8,4,5,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,8,3,4,5,7]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,8,3,4,5,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,6,8,1,3,4,5,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,8,5,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,8,5,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,8,4,5,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,8,5,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,8,1,5,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,6,1,7,8,5]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,7,8,1,5]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,7,3,8,4,5,6]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,7,1,3,8,4,5,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,7,8,3,4,5,6]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,7,8,1,3,4,5,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,7,3,4,8,5,6]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,7,4,8,5,6]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,1,4,8,5,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,7,8,4,5,6]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,1,7,8,4,5,6]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,4,7,1,8,5,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,8,1,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,8,4,5,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,8,4,5,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,8,1,4,5,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,4,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,8,5,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,8,2,5,7]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,8,2,5,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5,8]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,6,2,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,2,7,8,5]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,6,1,2,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,6,7,2,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,6,7,2,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,6,1,7,2,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,6,7,1,2,8,5]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,6,7,8,2,5]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,8,2,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,7,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,7,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,7,2,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,8,2,6]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,7,8,2,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,7,1,8,2,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,7,8,1,2,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,8,5,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,8,2,5,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,8,2,5,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,8,1,2,5,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,8,6,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,4,5,8,2,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,5,8,2,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,8,2,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,8,2,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,8,1,2,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,5,6,7,8,2]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,1,6,7,8,2]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,5,6,1,7,8,2]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,8,4,7]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,8,4,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,8,2,4,7]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,8,2,4,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,7,8,4]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,6,2,7,8,4]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5,6,1,2,7,8,4]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,7,2,8,4]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,8,4]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,6,7,8,2,4]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,8,2,4]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,8,4,6]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,7,8,4,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,7,2,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,7,8,2,4,6]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,7,8,2,4,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,8,4,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,8,2,4,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,8,2,4,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,8,6,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,5,8,4,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,8,4,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,8,4,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,8,4,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,6,8,2,4,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,5,6,2,7,8,4]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,5,6,7,2,8,4]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,6,7,8,2,4]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,8,5]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,8,5]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,8,4,5]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,6,7,2,8,4,5]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,8]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,4,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,6,2,7,4,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,6,7,8,4,5]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,6,7,8,4,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,6,7,8,2,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,8,4,5,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,8,4,5,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,8,2,4,5,7]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,8,2,4,5,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,6,8,1,2,4,5,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,8,5,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,8,5,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,8,4,5,7]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,8,4,5,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,8,5,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,8,2,5,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,6,7,2,8,5]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,7,2,8,4,5,6]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,7,1,2,8,4,5,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,7,1,8,2,4,5,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,7,8,1,2,4,5,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,7,1,2,4,8,5,6]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,7,4,8,5,6]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,7,8,4,5,6]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,3,4,7,8,2,5,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,7,8,2,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,8,1,2,4,5,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,8,4,5,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,2,8,4,5,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,3,2,4,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,8,2,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,8,3,7]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,8,3,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,8,3,7]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,8,2,3,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3,8]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,7,8,3]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,6,1,2,7,8,3]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5,6,1,7,2,8,3]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,8,3]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,5,6,7,8,2,3]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,5,6,1,7,8,2,3]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,3]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,7,8,3,6]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,7,8,3,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,7,2,8,3,6]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,7,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,7,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,7,3,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,7,8,3,6]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,7,8,2,3,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,8,3,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,8,3,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,8,2,3,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,8,6,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,8,6,7]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,8,3,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,8,3,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,6,8,2,3,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,3]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,3]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,5,2,6,7,8,3]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,5,6,2,7,8,3]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,5,6,7,2,8,3]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,5,6,7,8,2,3]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,8,5]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,8,5]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,6,1,2,7,8,3,5]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,6,7,1,2,8,3,5]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,6,7,8,2,3,5]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,6,1,7,8,2,3,5]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5,8]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,2,7,3,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,8,3,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,6,7,8,2,3,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,5,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,8,3,5,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,8,2,3,5,7]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,8,2,3,5,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,8,1,2,3,5,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,8,5,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,8,5,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,8,3,5,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,8,5,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,6,7,8,3,5]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,5,6]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,7,1,2,8,3,5,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,7,8,2,3,5,6]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,7,1,8,2,3,5,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,7,8,1,2,3,5,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,7,2,3,8,5,6]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,7,1,2,3,8,5,6]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,7,2,3,8,5,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,8,3,5,6]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,7,8,3,5,6]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,7,8,2,3,5,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,4,7,3,8,5,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,7,3,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,7,8,3,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,8,2,3,5,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,8,1,2,3,5,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,8,3,5,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,4,8,2,3,5,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,3,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,4,5,8,3,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,8,3,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,3]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,8,4]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,8,4]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,6,1,2,7,8,3,4]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[5,1,6,7,2,8,3,4]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,6,7,8,2,3,4]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,6,1,7,8,2,3,4]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4,8]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4,8]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4,8]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4,8]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,8,4]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,8,4]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,7,8,4]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,8,4]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,1,2,6,7,8,3,4]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,5,6,2,7,8,3,4]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,5,6,7,2,8,3,4]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,8,3,4,7]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,8,3,4,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[5,6,1,8,2,3,4,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,8,1,2,3,4,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,8,4,7]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,8,4,7]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,8,3,4,7]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,8,3,4,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,8,4,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,6,7,8,4]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,5,6,3,7,8,4]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,6,7,3,8,4]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,5,6,7,8,3,4]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,8,3,4,6]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,7,1,2,8,3,4,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,7,8,2,3,4,6]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,8,1,2,3,4,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,7,2,3,8,4,6]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,8,4,6]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,7,3,8,4,6]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,7,8,3,4,6]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,7,8,3,4,6]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,7,8,4,6]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,7,4,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,8,4,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,8,2,3,4,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,8,1,2,3,4,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,2,8,3,4,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,8,2,3,4,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,3,8,4,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,2,3,8,4,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,8,4,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,5]=>[[1,3,5,7,8],[2,4,6]]=>[1,2,2,3]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,7,1,2,8,3,4,5]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,4,5]=>[[1,3,4,7,8],[2,5,6]]=>[1,3,4]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,7,1,8,2,3,4,5]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,7,2,3,8,4,5]=>[[1,3,5,6,8],[2,4,7]]=>[1,2,3,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,7,1,2,3,8,4,5]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[6,1,2,7,3,8,4,5]=>[[1,3,4,6,8],[2,5,7]]=>[1,3,2,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[6,1,2,7,8,3,4,5]=>[[1,3,4,5,8],[2,6,7]]=>[1,4,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,6,2,7,8,3,4,5]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[1,2,4,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[1,3,3,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[1,4,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[6,1,2,3,7,8,4,5]=>[[1,3,4,5,6],[2,7,8]]=>[1,5,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,6,2,3,7,8,4,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,8,4,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5,8]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5,8]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5,8]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5,8]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,7,8,5]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,6,7,4,8,5]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,7,8,4,5]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,8,1,2,3,4,5,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,5,7]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,8,3,4,5,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,6,8,2,3,4,5,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,8,4,5,7]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,8,4,5,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,8,5,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,8,4,5,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6]=>[[1,3,5,6,7,8],[2,4]]=>[1,2,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,8,3,4,5,6]=>[[1,3,4,6,7,8],[2,5]]=>[1,3,4]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,7,2,8,3,4,5,6]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,8,2,3,4,5,6]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1,2,3,8,4,5,6]=>[[1,3,4,5,7,8],[2,6]]=>[1,4,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,7,2,3,8,4,5,6]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1,2,3,4,8,5,6]=>[[1,3,4,5,6,8],[2,7]]=>[1,5,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,6]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[1,6,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,7]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[1,8,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,9,6,7]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,9,1,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,10,7,8]=>[[1,3,4,5,6,7,8,10],[2,9]]=>[1,7,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[1,8,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[6,4]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,9,1,7,8]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,9,7]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,10,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[7,2,1]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,7,8,9,1,6]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6,9]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,9,7,8]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,9,7,8]=>[[1,2,3,4,5,7,9],[6,8]]=>[5,2,2]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,9,7]=>[[1,2,3,4,5,7,8],[6,9]]=>[5,3,1]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,7,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]=>[[1,2,3,4,5,6,7,10],[8,9]]=>[7,3]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,7,8,1,9,6]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[7,2,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,6,7,8,9,1,5]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,2,9,3,4,5,6,7]=>[[1,3,4,6,7,8,9],[2,5]]=>[1,3,5]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[4,6]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,9,1,6,7,8]=>[[1,2,3,4,5,8,9],[6,7]]=>[5,4]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7,9]=>[[1,2,3,4,5,7,9],[6,8]]=>[5,2,2]
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,10,8]=>[[1,2,3,4,5,6,8,9],[7,10]]=>[6,3,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,6,7,8,9,1,4]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,9,10,6]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[1,8,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,9,2,3,4,5,6,7]=>[[1,3,5,6,7,8,9],[2,4]]=>[1,2,6]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,9,1,2,3,4,5,6,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[2,6,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,10,1,7,8,9]=>[[1,2,3,4,5,6,9,10],[7,8]]=>[6,4]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,8,10]=>[[1,2,3,4,5,6,8,10],[7,9]]=>[6,2,2]
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,9,1,6,8]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,2]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,1,3]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,9,2,3,4,5,6,8]=>[[1,3,5,6,7,8,9],[2,4]]=>[1,2,6]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7,9]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,9,1,2,3,4,5,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6,8,9]=>[[1,2,3,4,5,8,9],[6,7]]=>[5,4]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,9,2]=>[[1,2,3,4,5,7,8],[6,9]]=>[5,3,1]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,9,3]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,1,10,2,3,4,5,6,7,8]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[1,2,7]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,10,1,2,3,4,5,6,7,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[1,2,6]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,9,7,8]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,9,7]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,9,6]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,9,1,2,3,4,6,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,8,6,9,7]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4,9]=>[[1,2,3,4,5,7,9],[6,8]]=>[5,2,2]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,9,1,2,8]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,3,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,10,2]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[7,2,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[]=>[]=>[]=>[0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,9,4,6,8]=>[[1,2,3,4,6],[5,7,8,9]]=>[4,2,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,9,6]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8,9]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,6,7,8,9,2,4,5]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[3,2,2,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,8,9,2,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[2,6,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,9,2,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,2]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,9,3]=>[[1,2,4,5,6,7,8],[3,9]]=>[2,6,1]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,4,5,6,7,8,2,9,3]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,5,6,7,8,9,2,3]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[3,2,2,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[[1,2,3,4,7,8,9],[5,6]]=>[4,5]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,3]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,6,7,8,9,3,4]=>[[1,2,4,5,6,7],[3,8,9]]=>[2,5,2]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,5,6,7,8,9,2,3,4]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,5,6,7,3,8,9,4]=>[[1,2,3,4,5,7,8],[6,9]]=>[5,3,1]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,7,8,9,2,3,4,6]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[[1,2,3,4,5,8,9],[6,7]]=>[5,4]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,4]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,9,5]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,6,7,8,2,9,3,4,5]=>[[1,2,3,4,6],[5,7,8,9]]=>[4,2,3]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,6,7,8,9,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,9,8]=>[[1,2,3,5,6,8],[4,7,9]]=>[3,3,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,9]=>[[1,2,3,4,5,7,9],[6,8]]=>[5,2,2]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,9,5,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,5]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,7,8,9,2,3,4,5,6]=>[[1,2,3,4,8,9],[5,6,7]]=>[4,5]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,9,6]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6,9]=>[[1,2,3,4,5,7,9],[6,8]]=>[5,2,2]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,9,6]=>[[1,2,3,4,5,7,8],[6,9]]=>[5,3,1]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,9,6]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,9,5,6,8]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,9,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[2,6,1]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,9,8]=>[[1,2,3,4,5,7,8],[6,9]]=>[5,3,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,9,6,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,6]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,8,2,9,3,4,5,6,7]=>[[1,2,4,6,7,8,9],[3,5]]=>[2,2,5]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,9,6,7]=>[[1,2,3,4,5,7,9],[6,8]]=>[5,2,2]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,9,7]=>[[1,2,4,5,6,7,8],[3,9]]=>[2,6,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,9,7]=>[[1,2,3,4,5,7,8],[6,9]]=>[5,3,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,9,7]=>[[1,2,3,4,5,6,8],[7,9]]=>[6,2,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,8,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,7]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,8]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9]]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[1,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[2,3,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7,10,9]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[2,2,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7,10,9]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[2,2,2,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[2,2,2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8,9]=>[[1,2,4,6,8,9],[3,5,7]]=>[2,2,2,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,9,7]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]]=>[2,2,5]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,1,8,3,9,5,10,7]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[3,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,9]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[3,2,2,2]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,6,7,8,9,1,3,5]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,3,1,9,4,5,6,7,8]=>[[1,2,4,6,7,8,9],[3,5]]=>[2,2,5]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,7,2,8,3,9,4,10,5,6]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[3,2,2,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7,10,9]=>[[1,2,4,5,7,9],[3,6,8,10]]=>[2,3,2,2,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8,9]=>[[1,3,5,7,8,9],[2,4,6]]=>[1,2,2,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[1,2,6]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,6,7,8,9,3,4]=>[[1,3,4,5,6,7],[2,8,9]]=>[1,6,2]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,5,6,7,8,9,1,3,4]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,6,7,8,9,1,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,7,8,9,1,3,4,5,6]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,8,9,1,3,4,5,6,7]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,1,9,3,4,5,6,7,8]=>[[1,3,5,6,7,8,9],[2,4]]=>[1,2,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,7,8,9,1,2,5,6]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[1,2,6]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8,9]=>[[1,3,5,7,8,9],[2,4,6]]=>[1,2,2,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,6,7,8,9,3]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,5,6,7,8,9,2,3]=>[[1,3,4,5,6,7],[2,8,9]]=>[1,6,2]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,6,7,8,9,2,3,4]=>[[1,3,4,5,6],[2,7,8,9]]=>[1,5,3]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,9,4,5]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,8,2,9,3,4,5,6]=>[[1,3,5,7,8,9],[2,4,6]]=>[1,2,2,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,9,10]=>[[1,3,5,7,9,10],[2,4,6,8]]=>[1,2,2,2,3]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,10,7,8,9]=>[[1,3,5,7,9,10],[2,4,6,8]]=>[1,2,2,2,3]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,10,5,6,7,8,9]=>[[1,3,5,7,8,9,10],[2,4,6]]=>[1,2,2,5]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,9,10,3]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[1,8,1]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,5,6,7,8,9,10,1,3,4]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,9,10,5]=>[[1,2,3,7,8,9],[4,5,6,10]]=>[3,6,1]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6,7,8,9,10,1,3,4,5]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,8,9,10,1,3,4,5,6,7]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,1,10,3,4,5,6,7,8,9]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[1,2,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[1,2,2,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[2,3,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,8,10,1,2,5,7,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9,10]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[1,2,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[1,8,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[1,2,2,2,2,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[1,2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,6,7,8,9,10,2,3,4]=>[[1,3,4,5,6,7],[2,8,9,10]]=>[1,6,3]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[1,2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,1,7,8,9,10,2,3,4,5]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[1,5,4]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,1,8,2,9,3,10,4,5,6]=>[[1,3,5,7,9,10],[2,4,6,8]]=>[1,2,2,2,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,1,9,2,10,3,4,5,6,7]=>[[1,3,5,7,8,9,10],[2,4,6]]=>[1,2,2,5]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[[1,3,4,6,8],[2,5,7,9]]=>[1,3,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,8,10]=>[[1,3,5,7,9,10],[2,4,6,8]]=>[1,2,2,2,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8,10]=>[[1,3,4,6,8,10],[2,5,7,9]]=>[1,3,2,2,2]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6,10,9]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[5,2,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,10,7,9]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,10,8]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[7,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,8,7,10,9]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[2,2,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7,9]=>[[1,3,4,5,7,9],[2,6,8]]=>[1,4,2,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,5,7,9]=>[[1,3,5,7,8,9],[2,4,6]]=>[1,2,2,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,9,5,7]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,8,2,3,9,4,5,6]=>[[1,3,5,6,8,9],[2,4,7]]=>[1,2,3,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,9,5]=>[[1,3,5,7,8],[2,4,6,9]]=>[1,2,2,3,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,9,4,8]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[1,2,2,2,2]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[3,2,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7,9]=>[[1,3,4,5,7,9],[2,6,8]]=>[1,4,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[3,2,2,2,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,5,6,7,8,9,1,2,4]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,6,7,8,9,1,2,3,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,7,8,9,1,2,3,4,6]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,8,9,1,2,3,4,5,7]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7,10,9]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[5,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[3,2,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6,9,8]=>[[1,3,4,6,8],[2,5,7,9]]=>[1,3,2,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,9,8]=>[[1,2,3,7,8],[4,5,6,9]]=>[3,5,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,9,1,2,4,6,8]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5,7,8,1,9,2,4,6]=>[[1,2,3,4,6],[5,7,8,9]]=>[4,2,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,7,2,9,4,10,6,8]=>[[1,2,3,4,6,8],[5,7,9,10]]=>[4,2,2,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,8,2,9,4]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,9,6,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,7,8,9,1,2,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[4,9,1,2,3,5,6,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[[1,2,3,4,5,9],[6,7,8]]=>[5,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,8,9,1,2,3,4,6,7]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,6,7,8,1,9,2,3,4]=>[[1,2,3,4,6],[5,7,8,9]]=>[4,2,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[4,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,5,6,7,8,1,9,2,3]=>[[1,2,3,4,5,7],[6,8,9]]=>[5,2,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[6,4]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5,9]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[[1,2,4,6,8,9],[3,5,7,10]]=>[2,2,2,3,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[3,2,2,2,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,7,8,9,10,2,3,4,5,6]=>[[1,2,3,4,5,10],[6,7,8,9]]=>[5,5]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,7,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,2,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,10,2,9]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,10,9]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[5,2,2,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,9,7,10]=>[[1,2,3,4,5,6,8,10],[7,9]]=>[6,2,2]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,9,3]=>[[1,2,3,4,6,8],[5,7,9]]=>[4,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,9,5]=>[[1,2,4,6,8],[3,5,7,9]]=>[2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,1,10,3]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[7,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,8,9,10,2,3,4,5,6,7]=>[[1,2,3,4,8,9,10],[5,6,7]]=>[4,6]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,6,7,8,9,1,4,5]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[7,2,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2,9]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8],[3,9]]=>[2,6,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[[1,2,3,6,7,8,9,10],[4,5]]=>[3,7]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,6,7,8,9,10,2,3,4,5]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,5,6,7,8,9,10,2,3,4]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,5,6,7,8,9,10,2,3]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[4,6]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,8,7,10,9]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[5,2,2,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,9,6,7,10,8]=>[[1,2,3,4,5,6,8,9],[7,10]]=>[6,3,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,10,5,7,9]=>[[1,3,5,7,9,10],[2,4,6,8]]=>[1,2,2,2,3]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,6,7,8,1,9,3,4]=>[[1,2,3,4,5,7],[6,8,9]]=>[5,2,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,9,1,2,3,4,5,8]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,5,6,7,8,9,4]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,10,2,3,4,5,6,7,9]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[1,2,7]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,9,4]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[2,3,4,10,1,5,6,7,8,9]=>[[1,2,3,4,7,8,9,10],[5,6]]=>[4,6]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,9,3]=>[[1,3,4,5,6,7,8],[2,9]]=>[1,7,1]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,6,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,9,2,10,3,4,5,6,7,8]=>[[1,2,4,6,7,8,9,10],[3,5]]=>[2,2,6]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,9,1,2,3,4,6,8]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4,8,9]=>[[1,3,5,6,8,9],[2,4,7]]=>[1,2,3,3]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,9,4]=>[[1,2,4,5,6,7,8],[3,9]]=>[2,6,1]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,6,7,8,9,1,2,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7,8,9]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8,9]=>[[1,2,3,4,7,8,9],[5,6]]=>[4,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3,9]=>[[1,3,4,5,6,7,9],[2,8]]=>[1,6,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[1,2,6]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,10,1,2,3,4,5,6,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[[1,2,3,4,5,6,7,8,9,10,12],[11]]=>[10,2]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[6,4]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,5,6,7,8,9,2,4]=>[[1,3,4,5,6,7],[2,8,9]]=>[1,6,2]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,6,7,8,9,2,3,5]=>[[1,3,4,5,6],[2,7,8,9]]=>[1,5,3]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[1,8,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,9,3,4,6,8]=>[[1,3,5,7,8,9],[2,4,6]]=>[1,2,2,4]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[3,1,2,9,4,5,6,7,8]=>[[1,3,4,6,7,8,9],[2,5]]=>[1,3,5]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2,10,9]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[5,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,6,7,8,9,2,3,4,5,10]=>[[1,2,3,4,5,10],[6,7,8,9]]=>[5,5]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]]=>[2,2,5]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,9,10,4]=>[[1,2,4,5,6,7,8,9],[3,10]]=>[2,7,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,10,2]=>[[1,2,3,4,5,6,8,9],[7,10]]=>[6,3,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,9,1,2,3,4,8]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,9,5]=>[[1,2,3,7,8],[4,5,6,9]]=>[3,5,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,9,5]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[[1,2,3,4,5,8,9],[6,7]]=>[5,4]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
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