Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00070: Permutations —Robinson-Schensted recording 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]=>[1,2]=>[[1,2]]=>[[1,2]]
[1,1,0,0]=>[2,1]=>[[1],[2]]=>[[1],[2]]
[1,0,1,0,1,0]=>[1,2,3]=>[[1,2,3]]=>[[1,2,3]]
[1,0,1,1,0,0]=>[1,3,2]=>[[1,2],[3]]=>[[1,3],[2]]
[1,1,0,0,1,0]=>[2,1,3]=>[[1,3],[2]]=>[[1,2],[3]]
[1,1,0,1,0,0]=>[2,3,1]=>[[1,2],[3]]=>[[1,3],[2]]
[1,1,1,0,0,0]=>[3,2,1]=>[[1],[2],[3]]=>[[1],[2],[3]]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[[1,2,3,4]]=>[[1,2,3,4]]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[[1,2,3],[4]]=>[[1,3,4],[2]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[[1,2,4],[3]]=>[[1,2,4],[3]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[[1,2,3],[4]]=>[[1,3,4],[2]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[[1,2],[3],[4]]=>[[1,4],[2],[3]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[[1,3,4],[2]]=>[[1,2,3],[4]]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[[1,3],[2,4]]=>[[1,3],[2,4]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[[1,2,4],[3]]=>[[1,2,4],[3]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[[1,2,3],[4]]=>[[1,3,4],[2]]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[[1,2],[3],[4]]=>[[1,4],[2],[3]]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[[1,4],[2],[3]]=>[[1,2],[3],[4]]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[[1,3],[2],[4]]=>[[1,3],[2],[4]]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[[1,2],[3],[4]]=>[[1,4],[2],[3]]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[[1],[2],[3],[4]]=>[[1],[2],[3],[4]]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[[1,2,3,4,5]]=>[[1,2,3,4,5]]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[[1,2,5],[3],[4]]=>[[1,2,5],[3],[4]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[[1,3],[2,4],[5]]=>[[1,4],[2,5],[3]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[[1,2,5],[3],[4]]=>[[1,2,5],[3],[4]]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[[1,4],[2,5],[3]]=>[[1,3],[2,4],[5]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[[1,3,4],[2],[5]]=>[[1,3,4],[2],[5]]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[[1,3],[2,4],[5]]=>[[1,4],[2,5],[3]]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[[1,2,5],[3],[4]]=>[[1,2,5],[3],[4]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[[1,4],[2],[3],[5]]=>[[1,3],[2],[4],[5]]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[[1,3],[2],[4],[5]]=>[[1,4],[2],[3],[5]]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]=>[[1],[2],[3],[4],[5]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[[1,2,5],[3,6],[4]]=>[[1,3,6],[2,4],[5]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[[1,2,4,6],[3],[5]]=>[[1,2,4,6],[3],[5]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[[1,2,4,5],[3],[6]]=>[[1,3,4,6],[2],[5]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[[1,3,6],[2,4],[5]]=>[[1,2,5],[3,6],[4]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[[1,3,5],[2,4],[6]]=>[[1,3,5],[2,6],[4]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6]]=>[[1,5],[2,6],[3],[4]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[[1,2,5],[3,6],[4]]=>[[1,3,6],[2,4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[[1,2,4,6],[3],[5]]=>[[1,2,4,6],[3],[5]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[[1,2,4,5],[3],[6]]=>[[1,3,4,6],[2],[5]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[[1,4,5],[2,6],[3]]=>[[1,3,4],[2,5],[6]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[[1,4,6],[2,5],[3]]=>[[1,2,4],[3,5],[6]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[[1,4,5],[2,6],[3]]=>[[1,3,4],[2,5],[6]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]]=>[[1,4],[2,5],[3,6]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[[1,3,5],[2,6],[4]]=>[[1,3,5],[2,4],[6]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[[1,3,6],[2,4],[5]]=>[[1,2,5],[3,6],[4]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[[1,3,5],[2,4],[6]]=>[[1,3,5],[2,6],[4]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[[1,3],[2,4],[5],[6]]=>[[1,5],[2,6],[3],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[[1,2,5],[3,6],[4]]=>[[1,3,6],[2,4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[[1,2,4,6],[3],[5]]=>[[1,2,4,6],[3],[5]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[[1,2,4,5],[3],[6]]=>[[1,3,4,6],[2],[5]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4]]=>[[1,3],[2,4],[5],[6]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[[1,4],[2,5],[3],[6]]=>[[1,4],[2,5],[3],[6]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[[1,3,6],[2],[4],[5]]=>[[1,2,5],[3],[4],[6]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[[1,3,5],[2],[4],[6]]=>[[1,3,5],[2],[4],[6]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[[1,3],[2,4],[5],[6]]=>[[1,5],[2,6],[3],[4]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[[1,4],[2],[3],[5],[6]]=>[[1,4],[2],[3],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[[1,3],[2],[4],[5],[6]]=>[[1,5],[2],[3],[4],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[[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]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]=>[[1,2,3,4,5,6,7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[[1,2,3,4,7],[5],[6]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>[[1,2,4,7],[3,5],[6]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>[[1,4,7],[2,5],[3,6]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[[1,2,4,6],[3,7],[5]]=>[[1,3,5,7],[2,4],[6]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[[1,2,4,5,7],[3],[6]]=>[[1,2,4,5,7],[3],[6]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[[1,2,4,5,6],[3],[7]]=>[[1,3,4,5,7],[2],[6]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[[1,2,5],[3,6],[4],[7]]=>[[1,4,7],[2,5],[3],[6]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[[1,3,5],[2,4,6],[7]]=>[[1,4,6],[2,5,7],[3]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]=>[[1,2,3,6],[4,7],[5]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[[1,3,6],[2,4,7],[5]]=>[[1,3,6],[2,4,7],[5]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[[1,3,5,7],[2,4],[6]]=>[[1,2,4,6],[3,7],[5]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[[1,3,5,6],[2,4],[7]]=>[[1,3,4,6],[2,7],[5]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[[1,3,5],[2,4,6],[7]]=>[[1,4,6],[2,5,7],[3]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>[[1,2,6],[3,7],[4],[5]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[[1,3,6],[2,4],[5],[7]]=>[[1,3,6],[2,7],[4],[5]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[[1,3,5],[2,4],[6],[7]]=>[[1,4,6],[2,7],[3],[5]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>[[1,6],[2,7],[3],[4],[5]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[[1,2,3,4,7],[5],[6]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>[[1,2,4,7],[3,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>[[1,4,7],[2,5],[3,6]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[[1,2,4,6],[3,7],[5]]=>[[1,3,5,7],[2,4],[6]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[[1,2,4,5,7],[3],[6]]=>[[1,2,4,5,7],[3],[6]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[[1,2,4,5,6],[3],[7]]=>[[1,3,4,5,7],[2],[6]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[[1,2,5],[3,6],[4],[7]]=>[[1,4,7],[2,5],[3],[6]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3]]=>[[1,3,4,5],[2,6],[7]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3]]=>[[1,2,4,5],[3,6],[7]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[[1,4,5,6],[2,7],[3]]=>[[1,3,4,5],[2,6],[7]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[[1,4,5],[2,6],[3,7]]=>[[1,4,5],[2,6],[3,7]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3]]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3]]=>[[1,3,5],[2,4,6],[7]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[[1,4,5,7],[2,6],[3]]=>[[1,2,4,5],[3,6],[7]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[[1,4,5,6],[2,7],[3]]=>[[1,3,4,5],[2,6],[7]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[[1,4,5],[2,6],[3,7]]=>[[1,4,5],[2,6],[3,7]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[[1,4,6],[2,5],[3,7]]=>[[1,3,5],[2,6],[4,7]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[[1,4,5],[2,6],[3,7]]=>[[1,4,5],[2,6],[3,7]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7]]=>[[1,5],[2,6],[3,7],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]=>[[1,3,4,6],[2,5],[7]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]=>[[1,2,4,6],[3,5],[7]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[[1,3,5,6],[2,7],[4]]=>[[1,3,4,6],[2,5],[7]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]=>[[1,4,6],[2,5],[3,7]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[[1,3,4,6],[2,7],[5]]=>[[1,3,5,6],[2,4],[7]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[[1,3,6,7],[2,4],[5]]=>[[1,2,3,6],[4,7],[5]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[[1,3,6],[2,4,7],[5]]=>[[1,3,6],[2,4,7],[5]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[[1,3,5,7],[2,4],[6]]=>[[1,2,4,6],[3,7],[5]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[[1,3,5,6],[2,4],[7]]=>[[1,3,4,6],[2,7],[5]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[[1,3,5],[2,4,6],[7]]=>[[1,4,6],[2,5,7],[3]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[[1,3,7],[2,4],[5],[6]]=>[[1,2,6],[3,7],[4],[5]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[[1,3,6],[2,4],[5],[7]]=>[[1,3,6],[2,7],[4],[5]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[[1,3,5],[2,4],[6],[7]]=>[[1,4,6],[2,7],[3],[5]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[[1,3],[2,4],[5],[6],[7]]=>[[1,6],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[[1,2,3,4,7],[5],[6]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>[[1,2,4,7],[3,5],[6]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>[[1,4,7],[2,5],[3,6]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[[1,2,4,6],[3,7],[5]]=>[[1,3,5,7],[2,4],[6]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[[1,2,4,5,7],[3],[6]]=>[[1,2,4,5,7],[3],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[[1,2,4,5,6],[3],[7]]=>[[1,3,4,5,7],[2],[6]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[[1,2,5],[3,6],[4],[7]]=>[[1,4,7],[2,5],[3],[6]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[[1,5,6],[2,7],[3],[4]]=>[[1,3,4],[2,5],[6],[7]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[[1,5,7],[2,6],[3],[4]]=>[[1,2,4],[3,5],[6],[7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[[1,5,6],[2,7],[3],[4]]=>[[1,3,4],[2,5],[6],[7]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[[1,5],[2,6],[3,7],[4]]=>[[1,4],[2,5],[3,6],[7]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[[1,4,6],[2,7],[3],[5]]=>[[1,3,5],[2,4],[6],[7]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[[1,4,5],[2,6],[3],[7]]=>[[1,4,5],[2,6],[3],[7]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[[1,4,7],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4],[7]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[[1,4,6],[2,5],[3],[7]]=>[[1,3,5],[2,6],[4],[7]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[[1,4,5],[2,6],[3],[7]]=>[[1,4,5],[2,6],[3],[7]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[[1,4],[2,5],[3,6],[7]]=>[[1,5],[2,6],[3,7],[4]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[[1,3,6],[2,7],[4],[5]]=>[[1,3,6],[2,4],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[[1,3,5],[2,6],[4],[7]]=>[[1,4,6],[2,5],[3],[7]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[[1,3,7],[2,4],[5],[6]]=>[[1,2,6],[3,7],[4],[5]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[[1,3,6],[2,4],[5],[7]]=>[[1,3,6],[2,7],[4],[5]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[[1,3,5],[2,4],[6],[7]]=>[[1,4,6],[2,7],[3],[5]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[[1,3],[2,4],[5],[6],[7]]=>[[1,6],[2,7],[3],[4],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[[1,2,5],[3,6],[4],[7]]=>[[1,4,7],[2,5],[3],[6]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[[1,6],[2,7],[3],[4],[5]]=>[[1,3],[2,4],[5],[6],[7]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[[1,5],[2,6],[3],[4],[7]]=>[[1,4],[2,5],[3],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[[1,4],[2,5],[3],[6],[7]]=>[[1,5],[2,6],[3],[4],[7]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[[1,2,6],[3],[4],[5],[7]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[[1,3,6],[2],[4],[5],[7]]=>[[1,3,6],[2],[4],[5],[7]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[[1,3],[2,4],[5],[6],[7]]=>[[1,6],[2,7],[3],[4],[5]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[[1,6],[2],[3],[4],[5],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[[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]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>[[1,3,6,7,8],[2,4],[5]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,6,3,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,6,3]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,4,6,7,5,3,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[[1,4,7,8],[2,5],[3,6]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>[[1,2,3,5,6,8],[4],[7]]=>[[1,2,4,5,7,8],[3],[6]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[[1,2,3,5,6,7],[4],[8]]=>[[1,3,4,5,7,8],[2],[6]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,4,7,6,8,3]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,5,6,7,4,3,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,6,4,3,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,7,6,4,3]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,5,8,7,4,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,5,4,3,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,6,5,8,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,7,4]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,7,6,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,6,8],[4,7],[5]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[[1,3,6,8],[2,4,7],[5]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>[[1,2,4,6,8],[3,7],[5]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[[1,2,4,6,7],[3,5],[8]]=>[[1,3,4,6,8],[2,7],[5]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,5,4,8]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,5,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,2,6,7,8,5,4]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,7,5,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,6,8],[3,7],[4],[5]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,6,8],[2,7],[4],[5]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,6,8,5,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[[1,4,6,8],[2,7],[3],[5]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,2,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,6,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,6,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,4,6,5,7,8,2]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,5,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,5,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,6,8,5,2]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[[1,2,4,7,8],[3,5],[6]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>[[1,2,3,5,8],[4,6],[7]]=>[[1,2,5,7,8],[3,6],[4]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,4,8,7,6,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,4,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,5,6,7,4,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,8,7,4,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[[1,2,4,7,8],[3],[5],[6]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,6,5,7,4,2,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,5,7,4,8,2]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,5,4,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,7,5,4,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,6,5,4,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[[1,2,3,4,5,8],[6],[7]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>[[1,3,4,5,8],[2,6],[7]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>[[1,2,4,5,8],[3,6],[7]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,3,2,5,7,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[[1,3,4,5,8],[2,6],[7]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>[[1,2,5,6,8],[3,7],[4]]=>[[1,2,4,5,8],[3,6],[7]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[[1,3,4,5,8],[2,6],[7]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,3,2,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>[[1,2,5,8],[3,6],[4,7]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[[1,2,5,7],[3,6],[4,8]]=>[[1,3,5,8],[2,6],[4,7]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>[[1,2,4,6,8],[3,5],[7]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,3,5,6,2,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[[1,2,3,5,6,8],[4],[7]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[[1,2,4,5,6,7],[3],[8]]=>[[1,3,4,5,6,8],[2],[7]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,6,8],[4,7],[5]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[[1,2,4,6,8],[3,7],[5]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>[[1,2,4,6,7],[3,5],[8]]=>[[1,3,4,6,8],[2,7],[5]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[[1,2,4,6],[3,5,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,6,8,7,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[[1,4,6,8],[2,7],[3],[5]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,3,2,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,3,2,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,3,2,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[[1,2,4,7,8],[3,5],[6]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,3,2,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,3,2,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[[1,4,7,8],[2,5],[3,6]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,3,6,2,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[[1,2,3,5,7,8],[4],[6]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,3,6,7,2,8]=>[[1,2,3,5,6,8],[4],[7]]=>[[1,2,4,5,7,8],[3],[6]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[[1,2,3,5,6,7],[4],[8]]=>[[1,3,4,5,7,8],[2],[6]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,3,6,8,7,2]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,3,7,8,6,2]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,3,8,7,6,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,3,2,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,3,8,7,2]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,7,6,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,5,3,2,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,5,3,8,7,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,5,7,3,2,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,5,7,3,8,2]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,5,8,7,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,4,6,7,5,3,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,5,3,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,4,7,6,5,3,2,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,6,5,8,3,2]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,4,8],[5],[6],[7]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[[1,2,4,8],[3,5],[6],[7]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,4,3,2,7,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,4,8],[2,5],[6],[7]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[[1,4,8],[2,5],[3,6],[7]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[[1,2,3,5,8],[4],[6],[7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,4,3,6,7,2,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[[1,2,4,5,8],[3],[6],[7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[[1,2,5,6,7],[3],[4],[8]]=>[[1,3,4,5,8],[2],[6],[7]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[[1,4,5,8],[2,6],[3],[7]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,4,6,3,2,7,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[[1,2,3,6,8],[4],[5],[7]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,4,6,3,2,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>[[1,3,6,8],[2,4],[5],[7]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[[1,2,4,6,8],[3],[5],[7]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,4,6,3,7,8,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[[1,3,4,6,8],[2],[5],[7]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,4,6,7,3,2,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[[1,2,5,6,8],[3],[4],[7]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,4,6,7,3,8,2]=>[[1,2,4,5,7],[3],[6],[8]]=>[[1,3,5,6,8],[2],[4],[7]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[[1,4,5,6,8],[2],[3],[7]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,4,7,8,6,3,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,4,3,2,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,4,3,2,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,5,6,4,7,3,2,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,4,7,3,8,2]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,5,6,4,7,8,3,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,4,3,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,4,3,8,2]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,6,8,4,3,2]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[[1,3,8],[2,4],[5],[6],[7]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[[1,4,8],[2,5],[3],[6],[7]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,5,4,7,8,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[[1,4,5,8],[2],[3],[6],[7]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,5,7,4,3,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[[1,2,6,8],[3],[4],[5],[7]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,5,7,4,3,8,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>[[1,3,6,8],[2],[4],[5],[7]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[[1,5,6,8],[2],[3],[4],[7]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,5,8,7,4,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,5,4,3,2,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,5,4,3,8,2]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,3,8],[2],[4],[5],[6],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[[1,3,4,5,7],[2,6],[8]]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,6,5,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,5,4,8]=>[[1,3,4,5,8],[2,6],[7]]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,7,5,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[[1,3,5,7],[2,4,6],[8]]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>[[1,5,7],[2,6,8],[3],[4]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,4,5,3,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[[1,2,3,6,7],[4,8],[5]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[[1,3,6,7],[2,4,8],[5]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[[1,3,4,6],[2,5,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>[[1,3,4,5,7],[2,6],[8]]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[[1,2,3,4,7],[5,8],[6]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,4,3,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>[[1,2,4,7],[3,5,8],[6]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,5,4,3,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>[[1,4,7],[2,5,8],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[[1,3,5,7],[2,4,8],[6]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,4,6,7,8,3]=>[[1,3,5,6,7],[2,4],[8]]=>[[1,3,4,5,7],[2,8],[6]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[[1,3,5,7],[2,4,6],[8]]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,4,8,7,6,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[[1,5,7],[2,6,8],[3],[4]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[[1,2,3,6,7],[4,8],[5]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[[1,3,6,7],[2,4,8],[5]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,4,7,8,3]=>[[1,3,4,6,7],[2,5],[8]]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,4,8,7,3]=>[[1,3,4,6],[2,5,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,4,3,8]=>[[1,3,4,5,8],[2,6],[7]]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>[[1,3,4,5,7],[2,6],[8]]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,5,6,8,7,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,7,6,4,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[[1,3,7],[2,4,8],[5],[6]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,5,4,8,7,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[[1,4,7],[2,5,8],[3],[6]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[[1,4,5,7],[2,8],[3],[6]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[[1,5,7],[2,6,8],[3],[4]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,5,4,3,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[[1,2,6,7],[3,8],[4],[5]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,7,5,4,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,7],[3,8],[4],[5],[6]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,6,5,4,8,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[[1,3,7],[2,8],[4],[5],[6]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[[1,4,7],[2,8],[3],[5],[6]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[[1,5,7],[2,8],[3],[4],[6]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[[1,7],[2,8],[3],[4],[5],[6]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,6,5]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,6,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,6,4]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,6,8],[4,7],[5]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[[1,3,6,8],[2,4,7],[5]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,5,4,8]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,6,5,8,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,6,8],[2,7],[4],[5]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,6,5,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>[[1,2,5,7,8],[3,6],[4]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,5,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,5,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,7,5,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,5,4,1,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,4,1,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[[1,2,4,7,8],[3,5],[6]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[[1,4,7,8],[2,5],[3,6]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,4,6,1,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[[1,2,3,5,7,8],[4],[6]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,4,6,7,1,8]=>[[1,2,3,5,6,8],[4],[7]]=>[[1,2,4,5,7,8],[3],[6]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,4,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,4,1,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>[[1,3,6,7,8],[2,4],[5]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,4,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,4,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,4,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,6,4,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,6,4,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,5,4,1,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,5,7,4,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,5,4,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[[1,2,3,4,5,8],[6],[7]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,3,1,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,3,1,6,5,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[[1,2,3,5,8],[4,6],[7]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[[1,3,5,8],[2,4,6],[7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[[1,3,4,5,8],[2,6],[7]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[[1,2,5,7],[3,6],[4,8]]=>[[1,3,5,8],[2,6],[4,7]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[[1,2,3,4,6,8],[5],[7]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,3,5,1,6,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>[[1,3,4,6,8],[2,5],[7]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[[1,3,4,6,8],[2,5],[7]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>[[1,4,6,8],[2,5],[3,7]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,3,5,6,1,8,7]=>[[1,2,4,5,7],[3,8],[6]]=>[[1,3,5,6,8],[2,4],[7]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,6,5,1,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,6,8],[4,7],[5]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[[1,3,6,8],[2,4,7],[5]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[[1,2,4,6],[3,5,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,6,7,8,5,1]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,6,8],[2,7],[4],[5]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,4,5,3,1,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[[1,2,4,7,8],[3,5],[6]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,3,1,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[[1,4,7,8],[2,5],[3,6]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,3,6,1,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>[[1,3,5,7,8],[2,4],[6]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,8,7,1]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,3,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,7,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,5,3,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,5,8,3,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,4,8],[5],[6],[7]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,4,8],[2,5],[6],[7]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,5,4,3,1,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[[1,2,4,8],[3,5],[6],[7]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,4,8],[2,5],[6],[7]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[[1,4,8],[2,5],[3,6],[7]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,4,3,6,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[[1,3,5,8],[2,4],[6],[7]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[[1,2,4,5,8],[3],[6],[7]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[[1,4,5,8],[2,6],[3],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[[1,3,5,8],[2,6],[4],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[[1,4,5,8],[2,6],[3],[7]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[[1,2,4,6,8],[3],[5],[7]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,4,6,7,3,1,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[[1,2,5,6,8],[3],[4],[7]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[[1,3,5,6,8],[2],[4],[7]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[[1,4,5,6,8],[2],[3],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,5,4,7,6,3,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,6,8],[3,7],[4],[5]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,6,8],[2,7],[4],[5]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,5,6,4,3,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,4,3,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,4,7,3,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,5,6,7,4,3,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,5,7,6,4,3,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,7,6,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[[1,3,8],[2,4],[5],[6],[7]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[[1,3,4,8],[2],[5],[6],[7]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,5,4,3,8,7,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[[1,4,8],[2,5],[3],[6],[7]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[[1,4,5,8],[2],[3],[6],[7]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,5,4,8,7,3,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[[1,5,8],[2,6],[3],[4],[7]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,5,7,4,3,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[[1,3,6,8],[2],[4],[5],[7]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,7,5,4,3,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,3,8],[2],[4],[5],[6],[7]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>[[1,3,4,5,6],[2,7],[8]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[[1,3,4,5,6],[2,7],[8]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[[1,3,4,5,6],[2,7],[8]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>[[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>[[1,2,5,6],[3,7],[4,8]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[[1,4,5,7],[2,6],[3,8]]=>[[1,3,5,6],[2,7],[4,8]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[[1,4,5,6,7],[2,8],[3]]=>[[1,3,4,5,6],[2,7],[8]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[[1,4,5,8],[2,6],[3,7]]=>[[1,2,5,6],[3,7],[4,8]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[[1,4,5,7],[2,6],[3,8]]=>[[1,3,5,6],[2,7],[4,8]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,2,1,6,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]]=>[[1,2,3,6],[4,7],[5,8]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>[[1,4,7],[2,5,8],[3,6]]=>[[1,3,6],[2,4,7],[5,8]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[[1,4,6,7],[2,5],[3,8]]=>[[1,3,4,6],[2,7],[5,8]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[[1,4,6],[2,5,7],[3,8]]=>[[1,4,6],[2,5,7],[3,8]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[[1,4,5,7],[2,6],[3,8]]=>[[1,3,5,6],[2,7],[4,8]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>[[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[[1,2,6],[3,7],[4,8],[5]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[[1,4,7],[2,5],[3,6],[8]]=>[[1,3,6],[2,7],[4,8],[5]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[[1,4,6],[2,7],[3,8],[5]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>[[1,6],[2,7],[3,8],[4],[5]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>[[1,3,4,5,7],[2,6],[8]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[[1,3,4,5,7],[2,6],[8]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>[[1,4,5,7],[2,6],[3,8]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[[1,3,5,7],[2,4,6],[8]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[[1,3,5,6,8],[2,7],[4]]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[[1,3,4,5,7],[2,6],[8]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]=>[[1,4,5,7],[2,6],[3,8]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[[1,3,5,8],[2,6],[4,7]]=>[[1,2,5,7],[3,6],[4,8]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[[1,3,5,7],[2,6],[4,8]]=>[[1,3,5,7],[2,6],[4,8]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[[1,3,5,6],[2,7],[4,8]]=>[[1,4,5,7],[2,6],[3,8]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>[[1,5,7],[2,6],[3,8],[4]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>[[1,4,6,7],[2,5],[3,8]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,6,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[[1,3,4,5,6,7],[2],[8]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[[1,3,4,5,7],[2,6],[8]]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,2,4,6,5,8,7,1]=>[[1,3,4,6],[2,5,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,2,4,6,7,5,1,8]=>[[1,3,4,5,8],[2,6],[7]]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[[1,2,3,4,7],[5,8],[6]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[[1,3,4,7],[2,5,8],[6]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>[[1,2,4,7],[3,5,8],[6]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[[1,3,4,7],[2,5,8],[6]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>[[1,4,7],[2,5,8],[3,6]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[[1,3,5,7],[2,4,8],[6]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>[[1,3,5,6,7],[2,4],[8]]=>[[1,3,4,5,7],[2,8],[6]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,5,4,6,8,7,1]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[[1,3,5,8],[2,4,6],[7]]=>[[1,2,5,7],[3,6,8],[4]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[[1,3,5,7],[2,4,6],[8]]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,7,8,6,1]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[[1,3,6,7],[2,4,8],[5]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,1]=>[[1,3,4,6,7],[2,5],[8]]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,5,6,7,4,1,8]=>[[1,3,4,5,8],[2,6],[7]]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]=>[[1,3,4,5,7],[2,6],[8]]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,5,7,6,4,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[[1,2,6,7],[3,8],[4],[5]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,5,7,6,4,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,2,6,5,4,1,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[[1,3,7],[2,4,8],[5],[6]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[[1,2,4,7],[3,8],[5],[6]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[[1,4,7],[2,5,8],[3],[6]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,2,6,5,7,4,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[[1,2,5,7],[3,8],[4],[6]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[[1,2,6,7],[3,8],[4],[5]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,7],[3,8],[4],[5],[6]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,2,7,6,5,4,8,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[[1,3,7],[2,8],[4],[5],[6]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[[1,7],[2,8],[3],[4],[5],[6]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[[1,2,3,4,5,8],[6],[7]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[[1,3,5,8],[2,4,6],[7]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[[1,3,4,5,8],[2,6],[7]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[[1,2,5,7],[3,6],[4,8]]=>[[1,3,5,8],[2,6],[4,7]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[[1,2,3,4,6,8],[5],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[[1,3,4,6,8],[2,5],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>[[1,4,6,8],[2,5],[3,7]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,2,5,6,1,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[[1,2,3,5,6,8],[4],[7]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>[[1,2,4,5,7],[3,8],[6]]=>[[1,3,5,6,8],[2,4],[7]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,7,1,8]=>[[1,2,4,5,6,8],[3],[7]]=>[[1,2,4,5,6,8],[3],[7]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,4,2,5,7,6,1,8]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,2,5,7,6,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,2,5,8,7,6,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[[1,3,6,8],[2,4,7],[5]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,4,2,6,7,5,1,8]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,2,7,6,5,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,6,8],[3,7],[4],[5]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,6,8],[2,7],[4],[5]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,2,1,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,2,1,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[[1,2,4,7,8],[3,5],[6]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[[1,4,7,8],[2,5],[3,6]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[[1,2,3,5,7,8],[4],[6]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>[[1,3,5,7,8],[2,4],[6]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,2,6,7,1,8]=>[[1,2,3,5,6,8],[4],[7]]=>[[1,2,4,5,7,8],[3],[6]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,5,2,7,6,1,8]=>[[1,2,3,5,8],[4,6],[7]]=>[[1,2,5,7,8],[3,6],[4]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,2,7,8,6,1]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,2,1,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>[[1,3,6,7,8],[2,4],[5]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,6,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,5,2,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[[1,2,4,7,8],[3],[5],[6]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,5,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,4,8],[5],[6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,4,8],[2,5],[6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,4,2,1,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[[1,2,4,8],[3,5],[6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,4,2,1,7,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,4,8],[2,5],[6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[[1,4,8],[2,5],[3,6],[7]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,5,4,2,6,1,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[[1,2,3,5,8],[4],[6],[7]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,4,2,6,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[[1,3,5,8],[2,4],[6],[7]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[[1,2,4,5,8],[3],[6],[7]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[[1,2,5,8],[3,6],[4],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,4,2,7,6,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[[1,3,5,8],[2,6],[4],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,4,2,7,8,6,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[[1,4,5,8],[2,6],[3],[7]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[[1,2,4,6,8],[3],[5],[7]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,4,6,2,7,8,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[[1,3,5,6,8],[2],[4],[7]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,2,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[[1,4,5,6,8],[2],[3],[7]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,4,7,6,2,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,6,8],[3,7],[4],[5]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,6,8],[2,7],[4],[5]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,4,2,7,1,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[[1,2,4,7,8],[3],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,4,7,2,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,4,2,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,6,4,8,2,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[[1,3,8],[2,4],[5],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,5,4,2,7,1,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>[[1,2,4,8],[3],[5],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[[1,3,4,8],[2],[5],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,5,4,2,8,7,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[[1,4,8],[2,5],[3],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,6,5,4,7,2,1,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[[1,2,5,8],[3],[4],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[[1,3,5,8],[2],[4],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,2,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[[1,4,5,8],[2],[3],[6],[7]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[[1,5,8],[2,6],[3],[4],[7]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[[1,3,4,5],[2,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[[1,2,4,5],[3,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[[1,3,4,5],[2,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>[[1,4,5],[2,6],[3,7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[[1,2,3,5],[4,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[[1,3,5],[2,4,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[[1,2,4,5],[3,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[[1,3,4,5],[2,6],[7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[[1,4,5],[2,6],[3,7],[8]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[[1,2,5],[3,6],[4,7],[8]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[[1,3,5],[2,6],[4,7],[8]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[[1,4,5],[2,6],[3,7],[8]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8]]=>[[1,5],[2,6],[3,7],[4,8]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[[1,2,3,4,6],[5],[7],[8]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,3,2,5,1,7,8,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[[1,3,4,6],[2,5],[7],[8]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>[[1,4,6],[2,5],[3,7],[8]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,3,2,5,6,1,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[[1,3,5,6],[2,4],[7],[8]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,7,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,4,5,6],[3],[7],[8]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[[1,3,4,5,6],[2],[7],[8]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[[1,4,5,6],[2,7],[3],[8]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,3,2,5,7,6,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[[1,2,5,6],[3,7],[4],[8]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[[1,3,5,6],[2,7],[4],[8]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,2,5,7,8,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[[1,4,5,6],[2,7],[3],[8]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[[1,2,3,6],[4,7],[5],[8]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,3,2,6,5,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[[1,3,6],[2,4,7],[5],[8]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,3,2,6,5,7,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[[1,2,4,6],[3,7],[5],[8]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[[1,3,4,6],[2,7],[5],[8]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[[1,4,6],[2,5,7],[3],[8]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,3,2,6,7,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[[1,2,5,6],[3,7],[4],[8]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,6,7,5,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[[1,3,5,6],[2,7],[4],[8]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[[1,3,6],[2,7],[4,8],[5]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[[1,6],[2,7],[3,8],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[[1,2,3,4,7],[5],[6],[8]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,3,5,2,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[[1,3,4,7],[2,5],[6],[8]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>[[1,4,7],[2,5],[3,6],[8]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[[1,2,3,5,7],[4],[6],[8]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[[1,3,5,7],[2,4],[6],[8]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[[1,3,4,5,7],[2],[6],[8]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,3,5,2,7,6,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[[1,2,5,7],[3,6],[4],[8]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>[[1,3,6,7],[2,4],[5],[8]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,3,5,6,2,7,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[[1,2,4,6,7],[3],[5],[8]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[[1,3,4,6,7],[2],[5],[8]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,2,8,1]=>[[1,3,4,5,7],[2],[6],[8]]=>[[1,3,5,6,7],[2],[4],[8]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[[1,4,5,6,7],[2],[3],[8]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,3,5,7,6,2,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[[1,2,6,7],[3,8],[4],[5]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,3,6,5,2,1,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[[1,2,3,7],[4,8],[5],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[[1,3,7],[2,4,8],[5],[6]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[[1,4,7],[2,5,8],[3],[6]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,3,6,5,7,2,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[[1,2,5,7],[3,8],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[[1,4,5,7],[2,8],[3],[6]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[[1,5,7],[2,6,8],[3],[4]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,7,6,5,2,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,7],[3,8],[4],[5],[6]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[[1,3,7],[2,8],[4],[5],[6]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[[1,4,7],[2,8],[3],[5],[6]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[[1,7],[2,8],[3],[4],[5],[6]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,4,8],[5],[6],[7]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,4,8],[2,5],[6],[7]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,3,2,1,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[[1,2,4,8],[3,5],[6],[7]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[[1,4,8],[2,5],[3,6],[7]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,3,2,6,1,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[[1,2,3,5,8],[4],[6],[7]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[[1,3,5,8],[2,4],[6],[7]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[[1,2,5,8],[3,6],[4],[7]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>[[1,3,6,8],[2,4],[5],[7]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[[1,2,4,6,8],[3],[5],[7]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[[1,4,6,8],[2,5],[3],[7]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[[1,3,5,6,8],[2],[4],[7]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,3,7,6,2,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,6,8],[3,7],[4],[5]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,5,7,6,3,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,5,3,2,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[[1,3,8],[2,4],[5],[6],[7]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[[1,4,8],[2,5],[3],[6],[7]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[[1,3,5,8],[2],[4],[6],[7]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,5,7,3,2,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[[1,2,6,8],[3],[4],[5],[7]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[[1,3,6,8],[2],[4],[5],[7]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[[1,5,6,8],[2],[3],[4],[7]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,6,7,5,3,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,3,8],[2],[4],[5],[6],[7]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>[[1,3,4],[2,5],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[[1,2,4],[3,5],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[[1,6,7],[2,8],[3],[4],[5]]=>[[1,3,4],[2,5],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>[[1,4],[2,5],[3,6],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>[[1,3,5],[2,4],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[[1,4,5],[2,6],[3],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[[1,2,5],[3,6],[4],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[[1,3,5],[2,6],[4],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[[1,4,5],[2,6],[3],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[[1,5],[2,6],[3,7],[4],[8]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,4,3,6,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,3,6],[4],[5],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>[[1,3,6],[2,4],[5],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[[1,3,4,6],[2],[5],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[[1,4,6],[2,5],[3],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,4,3,6,7,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[[1,2,5,6],[3],[4],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[[1,3,5,6],[2],[4],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[[1,4,5,6],[2],[3],[7],[8]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[[1,5,6],[2,7],[3],[4],[8]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,4,3,7,6,2,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[[1,2,6],[3,7],[4],[5],[8]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,3,7,6,2,8,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[[1,3,6],[2,7],[4],[5],[8]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[[1,5,6],[2,7],[3],[4],[8]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[[1,6],[2,7],[3,8],[4],[5]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,4,6,3,2,1,7,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[[1,2,3,7],[4],[5],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>[[1,3,7],[2,4],[5],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[[1,2,4,7],[3],[5],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[[1,3,4,7],[2],[5],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[[1,4,7],[2,5],[3],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,4,6,3,7,2,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[[1,2,5,7],[3],[4],[6],[8]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,4,6,7,3,2,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[[1,2,6,7],[3],[4],[5],[8]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[[1,4,6,7],[2],[3],[5],[8]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[[1,5,6,7],[2],[3],[4],[8]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,4,7,6,3,2,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,7],[3,8],[4],[5],[6]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[[1,4,7],[2,8],[3],[5],[6]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[[1,5,7],[2,8],[3],[4],[6]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[[1,3,8],[2,4],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,4,3,2,7,1,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>[[1,2,4,8],[3],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,4,3,7,2,1,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[[1,2,5,8],[3],[4],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[[1,5,8],[2,6],[3],[4],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[[1,2,6,8],[3],[4],[5],[7]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[[1,5,6,8],[2],[3],[4],[7]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,4,3,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,3,8],[2],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[[1,3],[2,4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,5,4,3,2,7,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[[1,3,4],[2],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[[1,4],[2,5],[3],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[[1,3,5],[2],[4],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[[1,4,5],[2],[3],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[[1,5],[2,6],[3],[4],[7],[8]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[[1,2,6],[3],[4],[5],[7],[8]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[[1,3,6],[2],[4],[5],[7],[8]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[[1,4,6],[2],[3],[5],[7],[8]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[[1,5,6],[2],[3],[4],[7],[8]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[[1,2,7],[3],[4],[5],[6],[8]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[[1,3,7],[2],[4],[5],[6],[8]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[[1,4,7],[2],[3],[5],[6],[8]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[[1,5,7],[2],[3],[4],[6],[8]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[[1,6,7],[2],[3],[4],[5],[8]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[[1,7],[2,8],[3],[4],[5],[6]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,8],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,3,8],[2],[4],[5],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,3],[2],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,4],[2],[3],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[[1,5],[2],[3],[4],[6],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,6],[2],[3],[4],[5],[7],[8]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[[1,7],[2],[3],[4],[5],[6],[8]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[[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]=>[8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,7,9,6,5,4,3,2]=>[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,8,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[8,7,9,6,5,4,3,2,1,10]=>[[1,3,10],[2],[4],[5],[6],[7],[8],[9]]=>[[1,2,9],[3],[4],[5],[6],[7],[8],[10]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,8,5,4,3,2,1,9]=>[[1,2,3,9],[4],[5],[6],[7],[8]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,7,8,9,6,5,4,3,2]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,8,10,7,6,5,4,3,2]=>[[1,2,4],[3],[5],[6],[7],[8],[9],[10]]=>[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,9,6,5,4,3,2,1,10]=>[[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[6,7,5,8,4,3,2,1,9]=>[[1,2,4,9],[3],[5],[6],[7],[8]]=>[[1,2,7,9],[3],[4],[5],[6],[8]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,8,7,6,5,3,2,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,10,7,6,5,4,3,2]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,9,8,7,6,4,3,2,1,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,6,5,4,3,8,2,1,9]=>[[1,6,9],[2],[3],[4],[5],[7],[8]]=>[[1,2,5],[3],[4],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[6,5,7,8,4,3,2,1,9]=>[[1,3,4,9],[2],[5],[6],[7],[8]]=>[[1,2,7,8],[3],[4],[5],[6],[9]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,6,8,9,5,4,3,2]=>[[1,2,4,5],[3],[6],[7],[8],[9]]=>[[1,6,7,9],[2],[3],[4],[5],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,6,5,4,3,2,8,1,9]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[[1,2,4],[3],[5],[6],[7],[8],[9]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,8,7,6,5,4,3,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,6,5,4,3,2,1,9,8]=>[[1,8],[2,9],[3],[4],[5],[6],[7]]=>[[1,3],[2,4],[5],[6],[7],[8],[9]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,9,5,4,3,2]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9]]=>[[1,8],[2,9],[3],[4],[5],[6],[7]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,9,8,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,7,6,5,4,3,9,2,1,10]=>[[1,7,10],[2],[3],[4],[5],[6],[8],[9]]=>[[1,2,5],[3],[4],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,7,5,4,3,2,1,9,8]=>[[1,2,8],[3,9],[4],[5],[6],[7]]=>[[1,3,9],[2,4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,7,8,9,10,6,5,4,3,2]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,7,6,5,4,3,2,9,1,10]=>[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[[1,2,4],[3],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9]=>[[1,2,8,9],[3],[4],[5],[6],[7]]=>[[1,2,3,9],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,7,8,6,5,4,3,2,9]=>[[1,2,3,9],[4],[5],[6],[7],[8]]=>[[1,2,8,9],[3],[4],[5],[6],[7]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,10,9,8,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[6,5,4,3,7,8,2,1,9]=>[[1,5,6,9],[2],[3],[4],[7],[8]]=>[[1,2,5,6],[3],[4],[7],[8],[9]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,9,4,3,2]=>[[1,2,4,5,6],[3],[7],[8],[9]]=>[[1,5,6,7,9],[2],[3],[4],[8]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
[]=>[]=>[]=>[]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,7,9,1]=>[[1,2,3,4,5,6,8],[7],[9]]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,7,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,9,8,7,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,5,7,8,6,9,1]=>[[1,2,3,4,5,6,8],[7],[9]]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,6,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,5,7,9,8,6,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,8,7,9,6,1]=>[[1,2,3,4,5,7],[6],[8],[9]]=>[[1,4,6,7,8,9],[2],[3],[5]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,7,6,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,6,5,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,5,4,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,8,7,6,5,4,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,1]=>[[1,2,4,5,6,7,8],[3],[9]]=>[[1,3,4,5,6,7,9],[2],[8]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,3,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,4,3,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,8,7,6,5,4,3,9,1]=>[[1,2,8],[3],[4],[5],[6],[7],[9]]=>[[1,3,9],[2],[4],[5],[6],[7],[8]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,8,7,9,6,5,4,3,1]=>[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8,9,7,6,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8],[2],[9]]=>[[1,3,4,5,6,7,8],[2],[9]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,9,8,1]=>[[1,3,5,7],[2,4,6,8],[9]]=>[[1,4,6,8],[2,5,7,9],[3]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,9,8,7,6,5,4,1]=>[[1,3],[2,4],[5],[6],[7],[8],[9]]=>[[1,8],[2,9],[3],[4],[5],[6],[7]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>[[1,2,4,5,6,7,8],[3],[9]]=>[[1,3,4,5,6,7,9],[2],[8]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,2,9,1]=>[[1,2,3,4,5,6,8],[7],[9]]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,9,4,2,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,7,9,8,4,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,8,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,1]=>[[1,4,5,6,7,8],[2],[3],[9]]=>[[1,3,4,5,6,7],[2],[8],[9]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,7,3,9,8,2,1]=>[[1,2,3,4,6],[5,7],[8],[9]]=>[[1,5,7,8,9],[2,6],[3],[4]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,9,8,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,9,8,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,1]=>[[1,5,6,7,8],[2],[3],[4],[9]]=>[[1,3,4,5,6],[2],[7],[8],[9]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,9,8,7,6,1]=>[[1,5],[2,6],[3,7],[4,8],[9]]=>[[1,6],[2,7],[3,8],[4,9],[5]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[[1,3,4,5,6],[2],[7],[8],[9]]=>[[1,5,6,7,8],[2],[3],[4],[9]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,9,8,3,2,1]=>[[1,3,5],[2,4,6],[7],[8],[9]]=>[[1,6,8],[2,7,9],[3],[4],[5]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,9,8,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,7,9,8,6,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,8,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,1]=>[[1,6,7,8],[2],[3],[4],[5],[9]]=>[[1,3,4,5],[2],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,5,4,9,8,7,3,2,1]=>[[1,4],[2,5],[3,6],[7],[8],[9]]=>[[1,7],[2,8],[3,9],[4],[5],[6]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8],[9]]=>[[1,6,7,8],[2],[3],[4],[5],[9]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[6,7,5,9,8,4,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8],[9]]=>[[1,7,9],[2,8],[3],[4],[5],[6]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,9,8,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,8,7,5,4,3,2,9,1]=>[[1,2,8],[3],[4],[5],[6],[7],[9]]=>[[1,3,9],[2],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,8,7,9,5,4,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,1]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]=>[[1,3],[2,4],[5],[6],[7],[8],[9]]=>[[1,8],[2,9],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,6,5,4,3,2,9,1]=>[[1,2,8],[3],[4],[5],[6],[7],[9]]=>[[1,3,9],[2],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8],[9]]=>[[1,4],[2],[3],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[[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]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,5,8,7,9,6]=>[[1,2,3,4,5,6,8],[7],[9]]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,9,3]=>[[1,2,3,5,6,7,8],[4],[9]]=>[[1,3,4,5,6,8,9],[2],[7]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8],[3],[9]]=>[[1,3,4,5,6,7,9],[2],[8]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,5,8,9,7,6]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,10,9]=>[[1,2,3,4,5,6,7,8,9],[10],[11]]=>[[1,4,5,6,7,8,9,10,11],[2],[3]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,10,1]=>[[1,4,5,6,7,8,9],[2],[3],[10]]=>[[1,3,4,5,6,7,8],[2],[9],[10]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[[1,2,3,4,5,6,7,8,9,10,11],[12]]=>[[1,3,4,5,6,7,8,9,10,11,12],[2]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,8,3,9,2]=>[[1,2,3,4,5,6,8],[7],[9]]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,10,1]=>[[1,5,6,7,8,9],[2],[3],[4],[10]]=>[[1,3,4,5,6,7],[2],[8],[9],[10]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,3,2]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,9,4,3,2]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,9,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,10,1]=>[[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[[1,3,4,5,6],[2],[7],[8],[9],[10]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,10,3,2]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,2,10,1]=>[[1,2,3,4,5,6,7,9],[8],[10]]=>[[1,3,5,6,7,8,9,10],[2],[4]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,9,10,4,3,2]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[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]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>[[1,2,3,4,5,7,9],[6,8]]=>[[1,2,4,6,7,8,9],[3,5]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,9,8,7]=>[[1,2,3,4,5,7],[6,8],[9]]=>[[1,4,6,7,8,9],[2,5],[3]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[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]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,9,8,7,6]=>[[1,2,3,4,6],[5,7],[8],[9]]=>[[1,5,7,8,9],[2,6],[3],[4]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,3,6,5,4,9,8,7]=>[[1,2,3,4,7],[5,8],[6,9]]=>[[1,4,7,8,9],[2,5],[3,6]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[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]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,9,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8],[9]]=>[[1,6,8,9],[2,7],[3],[4],[5]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,9,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8],[9]]=>[[1,7,9],[2,8],[3],[4],[5],[6]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]=>[[1,2,3,4,5,6,9],[7],[8]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2,9,8,7,6]=>[[1,2,6],[3,7],[4,8],[5,9]]=>[[1,5,9],[2,6],[3,7],[4,8]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,6,5,4,3,2,9,8]=>[[1,2,8],[3,9],[4],[5],[6],[7]]=>[[1,3,9],[2,4],[5],[6],[7],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,9,8,7]=>[[1,3,5,7],[2,4,6,8],[9]]=>[[1,4,6,8],[2,5,7,9],[3]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,9,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8],[9]]=>[[1,6,8],[2,7,9],[3],[4],[5]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9]=>[[1,4,6,7,8,9],[2,5],[3]]=>[[1,2,3,4,5,7],[6,8],[9]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6,9,8]=>[[1,4,6,8],[2,5,7,9],[3]]=>[[1,3,5,7],[2,4,6,8],[9]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,6,5,4,7,8,9]=>[[1,4,7,8,9],[2,5],[3,6]]=>[[1,2,3,4,7],[5,8],[6,9]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4,9,8,7]=>[[1,4,7],[2,5,8],[3,6,9]]=>[[1,4,7],[2,5,8],[3,6,9]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,1,9,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8],[9]]=>[[1,7],[2,8],[3,9],[4],[5],[6]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[[1,2,3,4,5,6],[7],[8],[9]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,3,2,1,6,5,7,8,9]=>[[1,5,7,8,9],[2,6],[3],[4]]=>[[1,2,3,4,6],[5,7],[8],[9]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,8,7,9]=>[[1,5,7,9],[2,6,8],[3],[4]]=>[[1,2,4,6],[3,5,7],[8],[9]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,2,1,7,6,5,8,9]=>[[1,5,8,9],[2,6],[3,7],[4]]=>[[1,2,3,6],[4,7],[5,8],[9]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2,1,7,6,5,9,8]=>[[1,5,8],[2,6,9],[3,7],[4]]=>[[1,3,6],[2,4,7],[5,8],[9]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,8,7,6,5,9]=>[[1,5,9],[2,6],[3,7],[4,8]]=>[[1,2,6],[3,7],[4,8],[5,9]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8],[9]]=>[[1,6],[2,7],[3,8],[4,9],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[[1,2,3,4,5],[6],[7],[8],[9]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,4,3,2,1,7,6,8,9]=>[[1,6,8,9],[2,7],[3],[4],[5]]=>[[1,2,3,5],[4,6],[7],[8],[9]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,4,3,2,1,8,7,6,9]=>[[1,6,9],[2,7],[3,8],[4],[5]]=>[[1,2,5],[3,6],[4,7],[8],[9]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4,3,2,1,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5]]=>[[1,5],[2,6],[3,7],[4,8],[9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[[1,2,3,4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,5,4,3,2,1,8,7,9]=>[[1,7,9],[2,8],[3],[4],[5],[6]]=>[[1,2,4],[3,5],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,5,4,3,2,1,9,8,7]=>[[1,7],[2,8],[3,9],[4],[5],[6]]=>[[1,4],[2,5],[3,6],[7],[8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[[1,3,5,6,7,8,9,10],[2,4]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[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]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[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]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[[1,3,5,7,9,10],[2,4,6,8]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3,10,9,8,7]=>[[1,2,3,7],[4,8],[5,9],[6,10]]=>[[1,5,9,10],[2,6],[3,7],[4,8]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,7,6,10,9,8]=>[[1,2,4,6,8],[3,5,7,9],[10]]=>[[1,4,6,8,10],[2,5,7,9],[3]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,10,9,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[[1,8,10],[2,9],[3],[4],[5],[6],[7]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9,10]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[[1,2,3,4,5,6,7,9],[8,10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5,10,9,8]=>[[1,3,5,8],[2,4,6,9],[7,10]]=>[[1,4,7,9],[2,5,8,10],[3,6]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[[1,3,7],[2,4,8],[5,9],[6,10]]=>[[1,5,9],[2,6,10],[3,7],[4,8]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9,10]=>[[1,4,6,7,8,9,10],[2,5],[3]]=>[[1,2,3,4,5,6,8],[7,9],[10]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,9,8,10]=>[[1,4,6,8,10],[2,5,7,9],[3]]=>[[1,2,4,6,8],[3,5,7,9],[10]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7,10,9]=>[[1,4,7,9],[2,5,8,10],[3,6]]=>[[1,3,5,8],[2,4,6,9],[7,10]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,6,5,4,10,9,8,7]=>[[1,4,7],[2,5,8],[3,6,9],[10]]=>[[1,5,8],[2,6,9],[3,7,10],[4]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,1,10,9,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[[1,2,3,4,5,6,7],[8],[9],[10]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[[1,5,7,9],[2,6,8,10],[3],[4]]=>[[1,3,5,7],[2,4,6,8],[9],[10]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5,10,9,8]=>[[1,5,8],[2,6,9],[3,7,10],[4]]=>[[1,4,7],[2,5,8],[3,6,9],[10]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,8,7,6,5,9,10]=>[[1,5,9,10],[2,6],[3,7],[4,8]]=>[[1,2,3,7],[4,8],[5,9],[6,10]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>[[1,5,9],[2,6,10],[3,7],[4,8]]=>[[1,3,7],[2,4,8],[5,9],[6,10]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,9,8,10]=>[[1,6,8,10],[2,7,9],[3],[4],[5]]=>[[1,2,4,6],[3,5,7],[8],[9],[10]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,3,2,1,9,8,7,6,10]=>[[1,6,10],[2,7],[3,8],[4,9],[5]]=>[[1,2,6],[3,7],[4,8],[5,9],[10]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,5,4,3,2,1,9,8,7,10]=>[[1,7,10],[2,8],[3,9],[4],[5],[6]]=>[[1,2,5],[3,6],[4,7],[8],[9],[10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,6,5,4,3,2,1,9,8,10]=>[[1,8,10],[2,9],[3],[4],[5],[6],[7]]=>[[1,2,4],[3,5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>[[1,4],[2,5],[3,6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[[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]=>[2,3,1,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[[1,2,3,4,5,6,8,9],[7]]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,4,5,6,7,8,9],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]=>[[1,2,3,4,5,6,9],[7],[8]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8,9]=>[[1,2,3,6,7,8,9],[4],[5]]=>[[1,2,3,4,5,8,9],[6],[7]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[[1,2,3,4,5,6,8,9,10],[7]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,10,9,4,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,4,3,2,1]=>[[1,3,4,5,6],[2],[7],[8],[9],[10]]=>[[1,6,7,8,9],[2],[3],[4],[5],[10]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,8,10,9,3,2,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,10,3,2,1]=>[[1,3,4,5,6,7],[2],[8],[9],[10]]=>[[1,5,6,7,8,9],[2],[3],[4],[10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,8,9,7]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,10,9,7,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,8,10,9,6,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[8,7,9,10,6,5,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,7,9,10,8]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,6,8,9,7]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,6,8,9,7]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8,9]=>[[1,2,3,6,7,8,9],[4],[5]]=>[[1,2,3,4,5,8,9],[6],[7]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]=>[[1,2,3,4,5,6,9],[7],[8]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[[1,2,9],[3],[4],[5],[6],[7],[8],[10]]=>[[1,3,10],[2],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[6,5,4,3,2,7,1,8,9]=>[[1,6,8,9],[2],[3],[4],[5],[7]]=>[[1,2,3,5],[4],[6],[7],[8],[9]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,2,6,1,7,8,9]=>[[1,5,7,8,9],[2],[3],[4],[6]]=>[[1,2,3,4,6],[5],[7],[8],[9]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8,9]=>[[1,4,6,7,8,9],[2],[3],[5]]=>[[1,2,3,4,5,7],[6],[8],[9]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]=>[[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,10,9,8,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,10,9,8,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,10,9,8,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,10,9,8,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,7,2,1,9,8]=>[[1,2,3,4,5,8],[6,9],[7]]=>[[1,3,6,7,8,9],[2,4],[5]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,3,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,9,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8],[9]]=>[[1,7,9],[2,8],[3],[4],[5],[6]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,2,1,9,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8],[9]]=>[[1,6,9],[2,7],[3,8],[4],[5]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,3,2,1,9,8,7,6]=>[[1,2,6],[3,7],[4,8],[5,9]]=>[[1,5,9],[2,6],[3,7],[4,8]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,6,4,3,2,1,9,8,7]=>[[1,2,7],[3,8],[4,9],[5],[6]]=>[[1,4,9],[2,5],[3,6],[7],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,9,6,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8,9]=>[[1,3,4,6,7,8,9],[2,5]]=>[[1,2,3,4,5,7,8],[6,9]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,9,10,5,4,3,2]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,9,3,2]=>[[1,2,4,5,6,7],[3],[8],[9]]=>[[1,4,5,6,7,9],[2],[3],[8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,9,8,2]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,3]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,9,8,7]=>[[1,2,3,4,5,7],[6,8],[9]]=>[[1,4,6,7,8,9],[2,5],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,10,9,8,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,9,8,7,6]=>[[1,2,3,4,6],[5,7],[8],[9]]=>[[1,5,7,8,9],[2,6],[3],[4]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,6,9,10,8,7,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,10,7,6,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,10,6,5,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,10,5,4,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,10,4,3,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,7,6,5,4,2,1,9,8]=>[[1,2,8],[3,9],[4],[5],[6],[7]]=>[[1,3,9],[2,4],[5],[6],[7],[8]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[4,6,5,3,2,1,9,8,7]=>[[1,2,7],[3,8],[4,9],[5],[6]]=>[[1,4,9],[2,5],[3,6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,7]=>[[1,7,8],[2,9],[3],[4],[5],[6]]=>[[1,3,4],[2,5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7,9]=>[[1,2,3,4,5,7,9],[6,8]]=>[[1,2,4,6,7,8,9],[3,5]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]]=>[[1,2,3,4,5,7,9],[6,8]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,6,8,10],[4]]=>[[1,3,5,7,10],[2,4,6,8],[9]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,10,9,1]=>[[1,2,4,6,8],[3,5,7,9],[10]]=>[[1,4,6,8,10],[2,5,7,9],[3]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[1,2,3,4,5,6,7,8,9],[10],[11]]=>[[1,4,5,6,7,8,9,10,11],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,6,9,8,10,7,1]=>[[1,2,3,4,5,6,8],[7],[9],[10]]=>[[1,4,6,7,8,9,10],[2],[3],[5]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[[1,2,3,4,5,6,7,8,9],[10],[11]]=>[[1,4,5,6,7,8,9,10,11],[2],[3]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,7,10,9,6,5,4,3,2,1]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,10,9,8,4,3,2,1]=>[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,10,9,8,7,2,1]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,5,7,9,10,8,6,4,2]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,9,8,7,6,5,3]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,9,8,7,6,4]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,9,8,7,5]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,9,8,6]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,9,4]=>[[1,4,5,6,7,8],[2,9],[3]]=>[[1,3,4,5,6,7],[2,8],[9]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,9,5]=>[[1,5,6,7,8],[2,9],[3],[4]]=>[[1,3,4,5,6],[2,7],[8],[9]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9]=>[[1,2,7,8,9],[3],[4],[5],[6]]=>[[1,2,3,4,9],[5],[6],[7],[8]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8,9]=>[[1,2,6,7,8,9],[3],[4],[5]]=>[[1,2,3,4,5,9],[6],[7],[8]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,10,3]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,9,4]=>[[1,2,4,5,6,7,8],[3,9]]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,1,8,9,10,7]=>[[1,2,3,4,5,7,8,9],[6,10]]=>[[1,3,4,5,7,8,9,10],[2,6]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,6,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,4,5,6,7,8,9],[3]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,7,9,8,4]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,6,8,9,7,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,7,2,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>[[1,3,5,6,7,8,9],[2,4]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8,9]=>[[1,2,4,6,7,8,9],[3],[5]]=>[[1,2,3,4,5,7,9],[6],[8]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,2,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[[1,2,4,5,6,7,8,9],[3]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,2,10,9,8,7,6,5,4,1]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,9,4]=>[[1,3,4,5,6,7,8],[2,9]]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,6,8,9,7,5]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8,9,10]=>[[1,2,3,6,7,8,9,10],[4],[5]]=>[[1,2,3,4,5,6,9,10],[7],[8]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9,10]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[[1,2,3,4,5,6,7,10],[8],[9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,10,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>[[1,3,5,6,7,8,9,10],[2,4]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9,10]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[[1,2,3,4,5,10],[6],[7],[8],[9]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,6,4,3,2,7,1,8,9]=>[[1,2,6,8,9],[3],[4],[5],[7]]=>[[1,2,3,5,9],[4],[6],[7],[8]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9,10]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[[1,2,3,4,10],[5],[6],[7],[8],[9]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,6,8,10],[4]]=>[[1,3,5,7,10],[2,4,6,8],[9]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,9,2,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,3,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,6,8,10,9,7]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,7,8,4,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,7,10,9,8,5]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,8,7,9]=>[[1,3,5,7,9],[2,6,8],[4]]=>[[1,2,4,6,8],[3,5,7],[9]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,6,8,10],[4]]=>[[1,3,5,7,9],[2,4,6,8],[10]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,10,1]=>[[1,3,5,7,9],[2,4,6,8],[10]]=>[[1,3,5,7,9],[2,6,8,10],[4]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,2,1,7,8,9,6]=>[[1,6,7,8],[2,9],[3],[4],[5]]=>[[1,3,4,5],[2,6],[7],[8],[9]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,6,8,7,9,2]=>[[1,2,3,4,5,6,8],[7],[9]]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,8,10,9,2]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[[1,3,4],[2],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,10,1]=>[[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[[1,3,4,5],[2],[6],[7],[8],[9],[10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,8,10,7]=>[[1,3,5,7,9],[2,4,6,8],[10]]=>[[1,3,5,7,9],[2,6,8,10],[4]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,9,8,10,5]=>[[1,3,5,7,9],[2,4,6,8],[10]]=>[[1,3,5,7,9],[2,6,8,10],[4]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,9,8,10,3]=>[[1,3,5,7,9],[2,4,6,8],[10]]=>[[1,3,5,7,9],[2,6,8,10],[4]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[[1,2,4,6,8,9],[3,5,7,10]]=>[[1,3,4,6,8,10],[2,5,7,9]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9,10]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[[1,2,3,4,5,6,7,10],[8],[9]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,9,5]=>[[1,3,5,6,7,8],[2,4,9]]=>[[1,3,4,5,6,8],[2,7,9]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9,10]=>[[1,3,5,6,7,8,9,10],[2],[4]]=>[[1,2,3,4,5,6,7,9],[8],[10]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,7,2,8,9]=>[[1,2,3,4,5,6,8,9],[7]]=>[[1,2,3,5,6,7,8,9],[4]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,7,9,8,6,4,2]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,6,7,9,8,5]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,9,8,3]=>[[1,2,3,5,7],[4,6,8],[9]]=>[[1,4,6,8,9],[2,5,7],[3]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,10,9,2]=>[[1,2,4,6,8],[3,5,7,9],[10]]=>[[1,4,6,8,10],[2,5,7,9],[3]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,4,5,7,8,9,10,6]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8,10]=>[[1,2,3,4,5,6,8,10],[7,9]]=>[[1,2,4,6,7,8,9,10],[3,5]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,10,9,2,1]=>[[1,3,5,7],[2,4,6,8],[9],[10]]=>[[1,5,7,9],[2,6,8,10],[3],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[[1,3,5,7,9,10],[2,4,6,8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,5,4,3,2,1,9,10,8]=>[[1,8,9],[2,10],[3],[4],[5],[6],[7]]=>[[1,3,4],[2,5],[6],[7],[8],[9],[10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,10,7]=>[[1,7,8,9],[2,10],[3],[4],[5],[6]]=>[[1,3,4,5],[2,6],[7],[8],[9],[10]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,7,8,9,10,6]=>[[1,6,7,8,9],[2,10],[3],[4],[5]]=>[[1,3,4,5,6],[2,7],[8],[9],[10]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,9,10,5]=>[[1,5,6,7,8,9],[2,10],[3],[4]]=>[[1,3,4,5,6,7],[2,8],[9],[10]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,9,10,4]=>[[1,4,5,6,7,8,9],[2,10],[3]]=>[[1,3,4,5,6,7,8],[2,9],[10]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[[1,2,4,6,8,9],[3,5,7]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,10,9,8,1]=>[[1,4,7],[2,5,8],[3,6,9],[10]]=>[[1,5,8],[2,6,9],[3,7,10],[4]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,1,9,10,8]=>[[1,2,3,4,5,6,8,9],[7,10]]=>[[1,3,4,6,7,8,9,10],[2,5]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,5,8,9,10,7]=>[[1,2,3,5,7,8,9],[4,6,10]]=>[[1,3,4,5,7,9,10],[2,6,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,6,7,8,10,9,5]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,8,10,9,6]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,9,10,5]=>[[1,3,5,6,7,8,9],[2,4,10]]=>[[1,3,4,5,6,7,9],[2,8,10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,5,8,9,10,7]=>[[1,3,5,7,8,9],[2,4,6,10]]=>[[1,3,4,5,7,9],[2,6,8,10]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]=>[[1,2,4,6,8,9],[3,5,7]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[[1,2,4,6,8,9,10],[3,5,7]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[[1,3,5,7,8,9],[2,4,6]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]=>[[1,3,5,7,8,9],[2,4,6]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[[1,2,4,6,8,9,10],[3,5,7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,5,7,9,10,8,6]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,6,8,9,7,4]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,10,9,8,7,6,5,3]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,10,9]=>[[1,2,3,4,5,7,9],[6,8,10]]=>[[1,3,5,7,8,9,10],[2,4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]=>[[1,3,5,7,9,10],[2,4,6,8]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,9,8,7,6,4,2]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5,10,9,8,7,6,4,2]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,5,7,10,9,8,6,4,2]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]
Map
to 312-avoiding permutation
Description
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
Map
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.