Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Images
=>
Cc0005;cc-rep-0Cc0007;cc-rep-2Cc0007;cc-rep-3
[1,0]=>[1]=>[[1]]=>[[1]]
[1,0,1,0]=>[2,1]=>[[1],[2]]=>[[1],[2]]
[1,1,0,0]=>[1,2]=>[[1,2]]=>[[1,2]]
[1,0,1,0,1,0]=>[2,3,1]=>[[1,3],[2]]=>[[1,2],[3]]
[1,0,1,1,0,0]=>[2,1,3]=>[[1,3],[2]]=>[[1,2],[3]]
[1,1,0,0,1,0]=>[1,3,2]=>[[1,2],[3]]=>[[1,3],[2]]
[1,1,0,1,0,0]=>[3,1,2]=>[[1,2],[3]]=>[[1,3],[2]]
[1,1,1,0,0,0]=>[1,2,3]=>[[1,2,3]]=>[[1,2,3]]
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[[1,3,4],[2]]=>[[1,2,3],[4]]
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[[1,3,4],[2]]=>[[1,2,3],[4]]
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[[1,3],[2,4]]=>[[1,3],[2,4]]
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>[[1,3],[2,4]]=>[[1,3],[2,4]]
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[[1,3,4],[2]]=>[[1,2,3],[4]]
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[[1,2,4],[3]]=>[[1,2,4],[3]]
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[[1,2,4],[3]]=>[[1,2,4],[3]]
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>[[1,2],[3,4]]=>[[1,2],[3,4]]
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>[[1,2],[3,4]]=>[[1,2],[3,4]]
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>[[1,2,4],[3]]=>[[1,2,4],[3]]
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[[1,2,3],[4]]=>[[1,3,4],[2]]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[[1,2,3],[4]]=>[[1,3,4],[2]]
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>[[1,2,3],[4]]=>[[1,3,4],[2]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[[1,2,3,4]]=>[[1,2,3,4]]
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[[1,2,3,4,5]]=>[[1,2,3,4,5]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>[[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>[[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>[[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>[[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>[[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>[[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>[[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>[[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>[[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>[[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[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]]=>[[1,2,3,4,5,6,7]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,8,1,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,7,1,8,6]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,1,6]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,1,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,8,1,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,6,1,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,1,5]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,7,1,5,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,8,1,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,1,7,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,1,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,4,1,7,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,4,7,1,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,4,7,1,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,1,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,4,1,5,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,6,4,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,5,1,6,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,7,1,4,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,6,1,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,8,1,4,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,7,4,8,6]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,7,8,1,4,6]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,5,1,4,8,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,8]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,1,6,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,7,8,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,1,7,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,6,7,1,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,1,4,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,6,1,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,1,4,7,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,7,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,7,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,1,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,1,4,8,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,3,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,6,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,6,3,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,6,3,7,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,6,7,8,3,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,8,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,6,3,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,7,3,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,4,7,8,3,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,3,5,8,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,5,6,7,3,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,4,1,5,6,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,5,6,3,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,5,3,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,3,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,5,8,3,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,5,1,6,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,5,1,6,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,6,1,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,6,1,7,3,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,1,3]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,1,3,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,6,1,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,6,1,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,6,8,1,3,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,5,1,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,5,1,7,8,3,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,7,8,1,3,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,1,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,6,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,8,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,6,3,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,6,1,3,7,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,1,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,1,3,5]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,6,1,3,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,3,5,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,7,3,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,7,8,3,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,8,1,3,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,5,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,1,5,3,6,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,5,3,6,8,4,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,6,3,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,1,5,6,3,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,5,6,7,3,4,8]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,1,5,6,8,3,4,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,7,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,5,3,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,1,5,3,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,1,5,8,3,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,5,3,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,5,1,3,6,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,6,8,4,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,1,3,6,4,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,5,1,6,3,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,6,3,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,1,6,7,3,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,5,1,6,7,3,4,8]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,5,1,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,5,1,6,8,3,4,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,5,6,1,3,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,5,6,1,3,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,5,6,1,7,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,7,1,3,8,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,7,1,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,1,3,4]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,5,6,1,3,8,4,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,7,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,7,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,7,8,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,5,7,1,3,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,5,7,1,8,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,5,1,3,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,5,1,8,3,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,6,7,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,1,3,6,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,6,3,7,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,1,6,3,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,1,6,8,3,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,1,3,4,7,8,5]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,7,5,8]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,6,1,3,7,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,1,3,7,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,6,1,7,3,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,6,1,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,6,1,7,3,4,5,8]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,6,7,1,3,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,6,7,1,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,1,3,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,1,3,4,7,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,1,3,7,4,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,1,3,7,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,7,3,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,1,7,3,4,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,1,7,3,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,7,1,3,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,1,3,4,8,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,2,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,8,2,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,7,8,2,6]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,2,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,5,8,2,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,6,2,7,5,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,6,7,2,8,5]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,7,2,5,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,8,2,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,2,7,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,4,2,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,4,7,8,2,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,4,2,5,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,5,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,5,2,6,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,6,8,4,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,7,2,8,4]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,7,2,4,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,5,6,2,4,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,5,6,2,8,4,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,8,2,4,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,7,4,8,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,7,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,7,2,4,8,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,7,2,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,7,8,2,4,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,5,2,4,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,5,2,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,2,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,2,6,7,4,8,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,7,8,4,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,2,6,7,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,6,8,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,2,7,4,8,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,6,2,7,8,4,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,7,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,2,4,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,6,2,4,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,4,7,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,7,2,4,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,7,2,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,2,4,8,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,6,8,2,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,5,2,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,7,2,8,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4,5,7,8,2,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4,5,8,2,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,2,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,6,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,6,2,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,7,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,4,6,7,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,8,2,5,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,4,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,4,2,7,5,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,7,2,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,2,5,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,4,2,8,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,5,6,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,5,6,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,5,6,8,2,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,5,6,2,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,4,1,5,7,2,8,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,5,8,2,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,5,2,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,5,1,6,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,1,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,1,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,1,8,2]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,1,2,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,1,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,6,1,8,2,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,6,8,1,2,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,5,1,7,8,2,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,5,7,1,2,8,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,7,8,1,2,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,5,1,2,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,5,1,2,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,6,5,7,8]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,6,2,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,6,2,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,6,7,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,6,7,2,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,8,2,5,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,6,1,2,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,6,1,2,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,6,1,7,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,1,7,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,6,7,1,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,6,7,1,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,6,7,8,1,2,5]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,7,1,2,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,4,1,2,5,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,4,1,2,7,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,1,2,7,5,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,4,7,1,2,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1,2,5,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,2,5,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1,2,8,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,4]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,5,6,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,5,6,8,4,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,5,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,6,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,6,2,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,5,6,8,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,5,6,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,7,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,7,8,2,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,5,2,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,6,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,6,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,5,1,6,2,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,6,2,7,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,5,1,6,7,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,5,1,6,7,2,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,1,6,8,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,5,1,6,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,5,6,1,2,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,5,6,1,2,7,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,5,6,1,7,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,7,1,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,7,1,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,1,2,4]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,5,6,1,2,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,5,6,1,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,7,8,6]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,7,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,7,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,7,1,2,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,5,1,2,4,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,5,1,2,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,5,1,2,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,6,7,8,5]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,7,5,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,2,6,4,7,8,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,1,2,6,4,7,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,6,7,8,4,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,1,2,6,8,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,1,6,7,2,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,7,8,5]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,6,1,2,7,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,6,1,2,7,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,6,1,7,2,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,6,7,1,2,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,8,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,6,1,2,4,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,2,4,5,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,2,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,1,2,4,7,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,2,7,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,2,7,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,2,7,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,7,2,4,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,7,2,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,7,1,2,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,7,1,2,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,7,1,8,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,2,4,8,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,7,3,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,6,3,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,6,8,3,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,7,3,8,6]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,7,8,3,6]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,4,5,3,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,4,5,8,3,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,3,7,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,4,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,7,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,4,7,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,4,7,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,3,5,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,5,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,5,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,5,3,6,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,5,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,5,2,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,5,2,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,5,2,6,3,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,5,2,6,8,3,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,2,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,6,2,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,2,8,3]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,2,3]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,6,8,2,3,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,7,8,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,5,2,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,7,8,3,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,4,5,7,2,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,7,8,2,3,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,5,2,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,6,7,8,5]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,6,7,5,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,6,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,6,2,3,7,8,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,6,2,7,8,3,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,6,7,2,8,3,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,6,7,8,2,3,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,6,2,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,2,3,5,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,2,3,7,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,2,7,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,2,7,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,7,2,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,7,2,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,7,8,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,4,2,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,2,3,8,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,5,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,5,6,8,3,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,5,3,7,8,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,5,7,8,3,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,5,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,5,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,5,2,6,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,5,2,6,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,5,6,2,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,5,6,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,5,7,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,5,2,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,5,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,6,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,6,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,6,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,1,6,2,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,6,2,7,3,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,1,6,7,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,5,1,6,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,5,1,6,8,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,1,6,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,1,2,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,1,2,7,3,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,1,7,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,1,7,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,6,1,7,2,3,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,1,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,1,2,3]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,6,1,2,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,7,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,5,1,7,2,3,8,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,5,1,2,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,5,1,2,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,5,1,8,2,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,6,7,8,5]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,6,7,5,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,6,3,7,8,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,7,3,8,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,6,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,6,2,3,7,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,6,2,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,6,7,2,3,8,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,6,7,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,6,7,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,6,2,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,6,1,2,7,8,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,6,1,7,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,6,7,1,2,3,8,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,6,7,1,2,8,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,6,7,1,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,6,1,2,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,1,2,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,3,7,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,1,2,7,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,1,2,7,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,7,2,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,7,2,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,1,7,2,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,7,8,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,7,1,2,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[4,7,1,2,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,7,1,2,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,1,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,2,3,5,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,8,4,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,7,4,8,6]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,7,8,4,6]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,5,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,5,3,6,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,2,5,6,3,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,2,5,6,3,7,4,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,2,5,6,7,3,8,4]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,3,4]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,2,5,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,5,6,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,2,5,7,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,2,5,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,2,5,7,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,2,5,3,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,5,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,6,7,4,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,6,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,6,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,2,6,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,2,6,7,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,5,2,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,2,6,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,6,2,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,6,2,7,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,5,6,7,2,3,8,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,6,7,2,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,6,2,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,5,6,2,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,7,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,7,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,5,7,2,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,2,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,5,2,3,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,5,2,3,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2,3,6,7,4,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,6,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,6,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,6,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,1,2,6,3,7,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,6,7,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,6,7,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,6,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,1,2,6,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,1,6,2,3,7,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,1,6,2,7,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,2,8,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[5,1,6,2,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,1,6,2,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[5,1,6,2,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1,2,7,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,1,2,7,8,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,6,1,7,2,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,6,1,7,8,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,1,7,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,1,2,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,1,2,8,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,6,1,2,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,6,1,8,2,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,7,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,7,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,7,2,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,7,2,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,7,2,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,7,8,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[5,7,1,2,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,7,1,8,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,1,2,3,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[5,1,8,2,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,6,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,6,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,3,6,7,4,8,5]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,4,5]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,6,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,6,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,2,6,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,2,6,3,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,2,6,3,7,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,2,6,3,7,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,2,6,3,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,2,6,7,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,3,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,6,2,3,7,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,3,7,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,2,3,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,6,2,7,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,6,2,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,6,7,2,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,7,2,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,7,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[6,1,2,3,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,1,2,7,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,1,2,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[6,1,2,7,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,7,2,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,1,7,2,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,7,2,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,1,2,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,7,1,2,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,7,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,7,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,7,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,7,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,2,7,3,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,7,2,3,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[7,1,2,3,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,8,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[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]]=>[[1,2,3,4,5,6,7,8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[1,3,4,5,6,7,8,9,10,11],[2]]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[[1,2,3,4,5,6,7,8,9],[10,11]]=>[[1,2,5,6,7,8,9,10,11],[3,4]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[[1,3,5,6,7,8,9,10],[2,4]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[1,2,8,3,4,5,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,8,1,2,3,4,5,9,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,1,10,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>[[1,2,3,4,5,6,7,8,9,10],[11,12]]=>[[1,2,5,6,7,8,9,10,11,12],[3,4]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[1,2,9,3,4,5,6,7,10,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,9,1,2,3,4,5,6,10,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,2,3,7,8,9,10],[4,5,6]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,4,8,5,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,1,3,4,5,9,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,8,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,8,1,2,3,4,9,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,4,5,6,7,8,9],[3]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,9,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,4,5,9,6,7,10,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]=>[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,4,5,6,7,8,9],[3]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,3,4,8,5,9,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,1,2,3,4,5,8,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,6,7,8,9],[4,5]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,6,9,7,10,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,6,7,8,9],[4,5]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,7,10,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,9,10,8]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,2,3,4,5,9,6,10,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,2,3,7,8,9,10],[4,5,6]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,1,9,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[]=>[]=>[]=>[]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,1,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,9,1,2,4,6,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,9,1,2,4,5]=>[[1,2,4,5,9],[3,6,7,8]]=>[[1,2,3,4,7],[5,6,8,9]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[3,8,1,2,4,5,9,6,7]=>[[1,2,4,5,6,7],[3,8,9]]=>[[1,2,5,6,7,9],[3,4,8]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,6,9,7,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,1,2,9,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,9,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,9,1,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,9,2,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,6,1,7,8,9,2,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,8,1,9,2,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,8,3,9,5,7]=>[[1,2,3,5,7],[4,6,8,9]]=>[[1,2,4,6,9],[3,5,7,8]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,8,3,5,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[[1,2,4,6,8,9],[3,5,7]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,7,8,9,2,3,4,6]=>[[1,2,3,4,6],[5,7,8,9]]=>[[1,2,3,5,9],[4,6,7,8]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,8,2,9,3,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,9,2,3,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,6,1,7,8,9,2,3,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,7,1,8,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,8,1,9,2,3,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,6,1,2,3,4,9,7,8]=>[[1,2,3,4,7,8],[5,6,9]]=>[[1,3,4,5,8,9],[2,6,7]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,1,2,3,4,6]=>[[1,2,3,4,6],[5,7,8,9]]=>[[1,2,3,5,9],[4,6,7,8]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,6,7,8,2,9,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,9,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,7,2,8,3,9,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[6,1,7,8,9,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,8,1,9,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,8,9,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8,9]]=>[[1,2,4,7,8,9],[3,5,6]]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,8,1,9,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8,9]]=>[[1,2,4,7,8,9],[3,5,6]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,8,9,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8,9]]=>[[1,2,4,7,8,9],[3,5,6]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7,9]=>[[1,2,3,4,5,7,9],[6,8]]=>[[1,2,4,6,7,8,9],[3,5]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,4,7,8,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,6,7,8,9],[4,5]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,4,7,9,5,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,7,8,9,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8,9]=>[[1,2,3,4,5,6,8,9],[7]]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[7,1,8,2,3,9,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[7,1,8,2,9,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[7,1,8,9,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,6,7,8,9],[4,5]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[7,8,1,9,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,6,7,8,9],[4,5]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,9,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[7,1,9,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,9,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[[1,2,3,4,5,6,8,9],[7]]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,4,8,5,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,2,3,8,4,5,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,8,2,9,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,4,5,6,7,8,9],[3]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,9,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[8,1,2,3,9,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[8,1,2,9,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,9,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,4,5,6,7,8,9],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,9,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[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]]=>[[1,2,3,4,5,6,7,8,9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,9,1,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,1,6]=>[[1,3,4,5,6,8,9],[2,7]]=>[[1,2,3,5,6,7,8],[4,9]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,1,5]=>[[1,3,4,5,7,8,9],[2,6]]=>[[1,2,3,4,6,7,8],[5,9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,1,4]=>[[1,3,4,6,7,8,9],[2,5]]=>[[1,2,3,4,5,7,8],[6,9]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,1,3]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,6,1,9,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[[1,3,4,5,6,7,8,10],[2,9]]=>[[1,2,4,5,6,7,8,9],[3,10]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[[1,3,4,5,6,7,9,10],[2,8]]=>[[1,2,3,5,6,7,8,9],[4,10]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[[1,3,4,5,6,8,9,10],[2,7]]=>[[1,2,3,4,6,7,8,9],[5,10]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[[1,3,4,5,7,8,9,10],[2,6]]=>[[1,2,3,4,5,7,8,9],[6,10]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,9,3,4]=>[[1,3,4,7,8,9],[2,5,6]]=>[[1,2,3,4,5,8],[6,7,9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[[1,3,4,6,7,8,9,10],[2,5]]=>[[1,2,3,4,5,6,8,9],[7,10]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[[1,2,3,4,5,6,7,9],[8,10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[1,3,4,5,6,7,8,9,10,11],[2]]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[1,3,4,5,6,7,8,9,10,11],[2]]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,9,1,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,9,1,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,6,10,1,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,7,8,1,9,3,4]=>[[1,3,4,7,8,9],[2,5,6]]=>[[1,2,3,4,5,8],[6,7,9]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,5,6,1,7,8,9,10,2,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[[1,2,3,4,5,6,7],[8,9,10]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,9,1,3,4]=>[[1,3,4,7,8,9],[2,5,6]]=>[[1,2,3,4,5,8],[6,7,9]]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,9,1,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,10,1,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,9,10,1,3,4]=>[[1,3,4,7,8,9,10],[2,5,6]]=>[[1,2,3,4,5,6,9],[7,8,10]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,8,9,1,10,2,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[[1,2,3,4,5,6,7],[8,9,10]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,5,6,1,2,3,9,10,7,8]=>[[1,2,3,7,8],[4,5,6,9,10]]=>[[1,2,5,6,7],[3,4,8,9,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,6]=>[[1,3,4,5,6,8,9],[2,7]]=>[[1,2,3,5,6,7,8],[4,9]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,7,6,8,9]=>[[1,3,4,5,6,8,9],[2,7]]=>[[1,2,3,5,6,7,8],[4,9]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,5,1,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,5]=>[[1,3,4,5,7,8,9],[2,6]]=>[[1,2,3,4,6,7,8],[5,9]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,6,5,7,8,9]=>[[1,3,4,5,7,8,9],[2,6]]=>[[1,2,3,4,6,7,8],[5,9]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,4]=>[[1,3,4,6,7,8,9],[2,5]]=>[[1,2,3,4,5,7,8],[6,9]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[[1,3,4,6,8],[2,5,7,9]]=>[[1,3,5,7,8],[2,4,6,9]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[[1,3,4,6,7,8,9],[2,5]]=>[[1,2,3,4,5,7,8],[6,9]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,8,3,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,5,3,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,9,5]=>[[1,3,5,7,8,9],[2,4,6]]=>[[1,2,3,4,6,8],[5,7,9]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,9,4]=>[[1,3,4,6,7,8,9],[2,5]]=>[[1,2,3,4,5,7,8],[6,9]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,2,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,7,2,9,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,7,2,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,2,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]]=>[[1,2,3,4,5,7,9],[6,8]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]=>[[1,2,3,5,6,7,8,9],[4]]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,5,3,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[[1,2,4,6,8,9],[3,5,7]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[[1,3,5,7,8,9],[2,4,6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,6]=>[[1,2,3,4,5,6,8,9],[7]]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,8,6,9]=>[[1,2,3,4,5,6,8,9],[7]]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[[1,2,3,4,5,6,8,9],[7]]=>[[1,2,3,5,6,7,8,9],[4]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,9,10,8]=>[[1,3,4,5,6,7,8,10],[2,9]]=>[[1,2,4,5,6,7,8,9],[3,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8,10]=>[[1,3,4,5,6,7,8,10],[2,9]]=>[[1,2,4,5,6,7,8,9],[3,10]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,10,7]=>[[1,3,4,5,6,7,9,10],[2,8]]=>[[1,2,3,5,6,7,8,9],[4,10]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,10,6]=>[[1,3,4,5,6,8,9,10],[2,7]]=>[[1,2,3,4,6,7,8,9],[5,10]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,9,8,10]=>[[1,3,4,5,6,8,10],[2,7,9]]=>[[1,2,4,6,7,8,9],[3,5,10]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,10,5]=>[[1,3,4,5,7,8,9,10],[2,6]]=>[[1,2,3,4,5,7,8,9],[6,10]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,10,4]=>[[1,3,4,6,7,8,9,10],[2,5]]=>[[1,2,3,4,5,6,8,9],[7,10]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[[1,3,4,6,8,10],[2,5,7,9]]=>[[1,2,4,6,8,9],[3,5,7,10]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,10,3]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[[1,2,3,4,5,6,7,9],[8,10]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,7,8,3,10,9]=>[[1,3,5,6,7,8,9],[2,4,10]]=>[[1,3,4,5,6,7,9],[2,8,10]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,9,10,5]=>[[1,3,5,7,8,9,10],[2,4,6]]=>[[1,2,3,4,5,7,9],[6,8,10]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,9,10,7]=>[[1,3,5,7,9,10],[2,4,6,8]]=>[[1,2,3,5,7,9],[4,6,8,10]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,8,9,10,7]=>[[1,3,5,6,7,9,10],[2,4,8]]=>[[1,2,3,5,6,7,9],[4,8,10]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,7,8,9,10,6]=>[[1,3,4,5,6,8,9,10],[2,7]]=>[[1,2,3,4,6,7,8,9],[5,10]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,6,7,9,10,8]=>[[1,3,4,5,6,7,8,10],[2,9]]=>[[1,2,4,5,6,7,8,9],[3,10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,9,2,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,8,6,10,9]=>[[1,2,4,6,8,9],[3,5,7,10]]=>[[1,3,4,6,8,10],[2,5,7,9]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,9,10,8]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,8,9,10,7]=>[[1,2,4,6,7,9,10],[3,5,8]]=>[[1,2,3,5,6,8,10],[4,7,9]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,10,3]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,10,4]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[[1,2,4,6,8,9,10],[3,5,7]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,10,5]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,10,6]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,8,9,6,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,8,6,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,10,7]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,9,7,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,5,6,7,8,9,10],[4]]
[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]]=>[[1,2,3,4,5,6,7,8,9,10]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,1,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,9,4]=>[[1,2,4,6,7,8,9],[3,5]]=>[[1,2,3,4,5,7,9],[6,8]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,9,5]=>[[1,2,5,7,8,9],[3,4,6]]=>[[1,2,3,4,6,7],[5,8,9]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,8,1,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,1,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,7,8,9,10,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4,10]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[[1,2,3,4,5,6],[7,8,9,10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,9,2,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[[1,2,3,4,5,6,7,10],[8,9]]=>[[1,2,3,6,7,8,9,10],[4,5]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,8,10,2,9]=>[[1,2,4,5,6,7,8,9],[3,10]]=>[[1,3,4,5,6,7,8,10],[2,9]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,6,7,9,3,8]=>[[1,3,5,6,7,8],[2,4,9]]=>[[1,3,4,5,6,8],[2,7,9]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,8,2,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,8,1,2,9,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,7,1,2,8,9,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,5,6,1,2,7,8,9,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,5,1,2,6,7,8,9,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,10,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,4,7,5,8,9,6]=>[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,6,7,8,9],[4,5]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,3,6,4,7,8,9,5]=>[[1,2,3,4,5,8,9],[6,7]]=>[[1,2,3,4,7,8,9],[5,6]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,9,4]=>[[1,2,3,4,7,8,9],[5,6]]=>[[1,2,3,4,5,8,9],[6,7]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,7,1,2,8,3,9]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,4,7,8,9]=>[[1,2,3,4,7,8,9],[5,6]]=>[[1,2,3,4,5,8,9],[6,7]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,5,8,9]=>[[1,2,3,4,5,8,9],[6,7]]=>[[1,2,3,4,7,8,9],[5,6]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,9,3]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,9,4]=>[[1,3,4,6,7,8,9],[2,5]]=>[[1,2,3,4,5,7,8],[6,9]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,8,1,9,10,7]=>[[1,3,4,5,6,7,9,10],[2,8]]=>[[1,2,3,5,6,7,8,9],[4,10]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,8,9,1,10,7]=>[[1,3,4,5,6,7,9,10],[2,8]]=>[[1,2,3,5,6,7,8,9],[4,10]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,8,2,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,5,2,6,7,8,9,4]=>[[1,2,4,6,7,8,9],[3,5]]=>[[1,2,3,4,5,7,9],[6,8]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,6,1,7,8,9,10,2,5]=>[[1,2,5,7,8,9,10],[3,4,6]]=>[[1,2,3,4,5,7,8],[6,9,10]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2,3,4,9],[5,6,7,8,10]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,8,1,3,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,6,1,7,2,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,7,8,1,2,9,10]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,1,6,2,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[[1,2,3,4,5,6],[7,8,9,10]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,2,4,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]]=>[[1,2,3,4,5,7,9],[6,8]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,9,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,4,7,5,8,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[[1,2,3,6,7,8,9],[4,5]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,7,8,1,9,6]=>[[1,3,4,5,6,8,9],[2,7]]=>[[1,2,3,5,6,7,8],[4,9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,7,1,8,9,6]=>[[1,3,4,5,6,8,9],[2,7]]=>[[1,2,3,5,6,7,8],[4,9]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,9,10,4]=>[[1,3,4,6,7,8,9,10],[2,5]]=>[[1,2,3,4,5,6,8,9],[7,10]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,11,8,9]=>[[1,2,3,4,5,6,7,8,9],[10,11]]=>[[1,2,5,6,7,8,9,10,11],[3,4]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7,9]=>[[1,2,4,7,9],[3,5,6,8]]=>[[1,2,4,5,7],[3,6,8,9]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7,9]=>[[1,2,5,7,9],[3,4,6,8]]=>[[1,2,4,6,7],[3,5,8,9]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,9,6,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[[1,3,5,7,8],[2,4,6,9,10]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[[1,2,3,4,5,6,7],[8,9,10]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,2,3,4,5],[6,7,8,9,10]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,8,9,1,2,10,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[[1,2,3,4,5,6,7],[8,9,10]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,10,1,2,3,4,5,6,7,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[[1,3,5,6,7,8,9,10],[2,4]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,10,1,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3,10]]=>[[1,3,4,5,6,7,8,10],[2,9]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[[1,2,3,4,5,6,7,8,9,10,11],[12]]=>[[1,3,4,5,6,7,8,9,10,11,12],[2]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[[1,2,4,5,6,7,8,9,10,11,12],[3]]=>[[1,2,3,4,5,6,7,8,9,10,12],[11]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,4,6,7,8,9]=>[[1,3,4,6,7,8,9],[2,5]]=>[[1,2,3,4,5,7,8],[6,9]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,5,7,8,9]=>[[1,3,4,5,7,8,9],[2,6]]=>[[1,2,3,4,6,7,8],[5,9]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,6,8,9]=>[[1,3,4,5,6,8,9],[2,7]]=>[[1,2,3,5,6,7,8],[4,9]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,2,3,4,5],[6,7,8,9,10]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,8,9,10,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,2,3,7,8,9,10],[4,5,6]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,10,1,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,10,1,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,7,8,9,5]=>[[1,2,3,4,5,8,9],[6,7]]=>[[1,2,3,4,7,8,9],[5,6]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,9,4]=>[[1,2,3,4,7,8,9],[5,6]]=>[[1,2,3,4,5,8,9],[6,7]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[5,10,1,2,3,4,6,7,8,9]=>[[1,2,3,4,6,7,8,9],[5,10]]=>[[1,3,4,5,6,8,9,10],[2,7]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,9,3]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10,11]]=>[[1,2,5,6,7,8,9,10,11],[3,4]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,9,1,10,8]=>[[1,3,4,5,6,7,8,10],[2,9]]=>[[1,2,4,5,6,7,8,9],[3,10]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,2,3,7,8,9,10],[4,5,6]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,4,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[[1,2,4,6,8,9],[3,5,7]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3,1,2,10,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3,10]]=>[[1,3,4,5,6,7,8,10],[2,9]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,10,6,7,8,9]=>[[1,2,3,4,6,7,8,9],[5,10]]=>[[1,3,4,5,6,8,9,10],[2,7]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[7,8,9,1,10,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[7,8,1,9,10,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[7,1,8,9,10,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[1,9,2,10,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,9,1,3,5]=>[[1,3,5,7,8,9],[2,4,6]]=>[[1,2,3,4,6,8],[5,7,9]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,7,8,9,10,5]=>[[1,2,3,4,5,8,9,10],[6,7]]=>[[1,2,3,4,5,8,9,10],[6,7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,8,9,10,6]=>[[1,2,3,4,5,6,9,10],[7,8]]=>[[1,2,3,4,7,8,9,10],[5,6]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,7,8,10,1,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,3,4,5,6],[2,7,8,9,10]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,9,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4,9]]=>[[1,3,4,5,6,8],[2,7,9]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7,9]=>[[1,2,3,7,9],[4,5,6,8]]=>[[1,2,4,5,6],[3,7,8,9]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6,9,8]=>[[1,2,3,6,8],[4,5,7,9]]=>[[1,3,5,6,9],[2,4,7,8]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[7,8,9,1,2,10,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,6,1,7,8,9,5]=>[[1,3,4,5,7,8,9],[2,6]]=>[[1,2,3,4,6,7,8],[5,9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,7,1,8,9,10,6]=>[[1,3,4,5,6,8,9,10],[2,7]]=>[[1,2,3,4,6,7,8,9],[5,10]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,6,1,7,8,9,10,5]=>[[1,3,4,5,7,8,9,10],[2,6]]=>[[1,2,3,4,5,7,8,9],[6,10]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,9,10,3]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[[1,2,3,4,5,6,7,9],[8,10]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,5,6,1,7,8,9,10,3]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[[1,2,3,4,5,6,7,9],[8,10]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,6,1,7,8,9,10,4]=>[[1,3,4,6,7,8,9,10],[2,5]]=>[[1,2,3,4,5,6,8,9],[7,10]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,9,8]=>[[1,2,3,6,8],[4,5,7,9]]=>[[1,3,5,6,9],[2,4,7,8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[[1,2,4,6,8,9],[3,5,7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[[1,3,5,7,9,10],[2,4,6,8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[[1,3,5,7,9,10],[2,4,6,8]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,7,8,9,10,3,4,5,6]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2,3,4,9],[5,6,7,8,10]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[3,4,1,2,8,9,10,5,6,7]=>[[1,2,5,6,7],[3,4,8,9,10]]=>[[1,2,3,7,8],[4,5,6,9,10]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,7,8,1,2,3,4,10,9]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,3,4,5,6],[2,7,8,9,10]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,6,7,8,2,9,5]=>[[1,2,4,5,7,8,9],[3,6]]=>[[1,2,3,4,6,7,9],[5,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,7,1,8,2,9,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[[1,2,3,4,5,6],[7,8,9]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,9,10,7]=>[[1,2,3,4,5,6,7,10],[8,9]]=>[[1,2,3,6,7,8,9,10],[4,5]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,4,7,5,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,9,10,2,3,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[[1,2,3,4,5,6],[7,8,9,10]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[4,10,1,2,3,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4,10]]=>[[1,3,4,5,6,7,9,10],[2,8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,1,9,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,10,1,2,3,4,5,6,9]=>[[1,2,3,4,5,6,9],[7,8,10]]=>[[1,3,4,7,8,9,10],[2,5,6]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,4,7,6,9,8]=>[[1,3,4,6,8],[2,5,7,9]]=>[[1,3,5,7,8],[2,4,6,9]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,1,3,5,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,1,8,2,9,3,10,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,7,2,8,3,9,4,10,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,12,9,11]=>[[1,2,3,5,7,9,11],[4,6,8,10,12]]=>[[1,3,5,7,9,11,12],[2,4,6,8,10]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,7,8,9,1,10,2,3,4,6]=>[[1,2,3,4,6],[5,7,8,9,10]]=>[[1,2,3,4,6],[5,7,8,9,10]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,8,9,1,2,10,3,4,7]=>[[1,2,3,4,7],[5,6,8,9,10]]=>[[1,2,3,5,6],[4,7,8,9,10]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,9,1,2,3,10,4,8]=>[[1,2,3,4,8],[5,6,7,9,10]]=>[[1,2,4,5,6],[3,7,8,9,10]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[1,3,4,5,6,7,8,9,10,11],[2]]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,9,4]=>[[1,3,4,7,8,9],[2,5,6]]=>[[1,2,3,4,5,8],[6,7,9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,4,5,9,6,10,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[[1,2,3,4,5,6,7,8,9,10,11],[12]]=>[[1,3,4,5,6,7,8,9,10,11,12],[2]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[7,8,9,1,2,3,4,10,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[[1,3,5,6,8,10],[2,4,7,9]]=>[[1,2,4,6,7,9],[3,5,8,10]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,9,10,7,8,12,11]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,10,7,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[[1,3,5,6,7,8,9,10],[2,4]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,2,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,2,3,7,6,9,8]=>[[1,2,3,6,8],[4,5,7,9]]=>[[1,3,5,6,9],[2,4,7,8]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,4,1,7,3,8,5,6,9]=>[[1,3,5,6,9],[2,4,7,8]]=>[[1,2,3,6,8],[4,5,7,9]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[7,1,2,8,3,9,4,10,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,5,7,2,4,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,7,2,9,4,6,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,5,7,9,1,2,4,6,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,9,6,11,8,10,12]=>[[1,2,4,6,8,10,12],[3,5,7,9,11]]=>[[1,2,4,6,8,10,12],[3,5,7,9,11]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,6,3,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,9,8]=>[[1,3,5,6,8],[2,4,7,9]]=>[[1,3,5,6,8],[2,4,7,9]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,2,7,3,8,4,9,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,6,2,7,3,8,4,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[8,1,9,2,10,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,2,3,7,8,9,10],[4,5,6]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[[1,2,4,5,6,7,8,9,10,11,12],[3]]=>[[1,2,3,4,5,6,7,8,9,10,12],[11]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,5,8,7,9]=>[[1,2,5,7,9],[3,4,6,8]]=>[[1,2,4,6,7],[3,5,8,9]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,7,8,9,2,10,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,2,7,4,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,7,9,2,4,10,5,8]=>[[1,2,4,5,8],[3,6,7,9,10]]=>[[1,2,4,5,8],[3,6,7,9,10]]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion 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 insertion 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 insertion tableau.
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.
searching the database
Sorry, this map was not found in the database.