Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Images
=>
Cc0005;cc-rep-0Cc0007;cc-rep-3
[1,0]=>[1]=>[1]=>[[1]]
[1,0,1,0]=>[1,2]=>[1,2]=>[[1,2]]
[1,1,0,0]=>[2,1]=>[2,1]=>[[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]=>[1,3,2]=>[[1,2],[3]]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[1,3],[2]]
[1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>[[1],[2],[3]]
[1,1,1,0,0,0]=>[3,2,1]=>[3,1,2]=>[[1,3],[2]]
[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]=>[1,2,4,3]=>[[1,2,3],[4]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[[1,2,4],[3]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[[1,2],[3],[4]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,4,2,3]=>[[1,2,4],[3]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[1,3,4],[2]]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[[1,3],[2,4]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>[[1,4],[2],[3]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[1,3],[2],[4]]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,1,3]=>[[1,4],[2],[3]]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,1,2,4]=>[[1,3,4],[2]]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,3,2,1]=>[[1],[2],[3],[4]]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,1,3,2]=>[[1,3],[2],[4]]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,1,2,3]=>[[1,3,4],[2]]
[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]=>[1,2,3,5,4]=>[[1,2,3,4],[5]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[[1,2,3,5],[4]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[[1,2,3],[4],[5]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,5,3,4]=>[[1,2,3,5],[4]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[[1,2,4,5],[3]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[[1,2,4],[3,5]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[[1,2,5],[3],[4]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[[1,2,4],[3],[5]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,5,3,2,4]=>[[1,2,5],[3],[4]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,4,2,3,5]=>[[1,2,4,5],[3]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[[1,2],[3],[4],[5]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,5,2,4,3]=>[[1,2,4],[3],[5]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,5,2,3,4]=>[[1,2,4,5],[3]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[1,3,4],[2,5]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[1,3,5],[2,4]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[1,3],[2,4],[5]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,5,3,4]=>[[1,3,5],[2,4]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[1,4],[2,5],[3]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[1,3,5],[2],[4]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[1,3,4],[2],[5]]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,1,4]=>[[1,3,5],[2],[4]]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,1,3,5]=>[[1,4,5],[2],[3]]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[[1,3],[2],[4],[5]]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,2,1,4,3]=>[[1,4],[2,5],[3]]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,2,1,3,4]=>[[1,4,5],[2],[3]]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[[1,3,4,5],[2]]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,1,2,5,4]=>[[1,3,4],[2,5]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[1,4],[2],[3],[5]]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,1,4]=>[[1,5],[2],[3],[4]]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[[1,3,5],[2],[4]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,1,3,4,2]=>[[1,3,4],[2],[5]]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,1,3,2,4]=>[[1,3,5],[2],[4]]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[[1,3,4,5],[2]]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,4,2,3,1]=>[[1,4],[2],[3],[5]]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,1,4,3,2]=>[[1,3],[2],[4],[5]]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,1,2,4,3]=>[[1,3,4],[2],[5]]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[[1,3,4,5],[2]]
[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]=>[1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[[1,2,3,4,6],[5]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[[1,2,3,4],[5],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>[[1,2,3,4,6],[5]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[[1,2,3,5,6],[4]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[[1,2,3,6],[4],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[[1,2,3,5],[4],[6]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,6,4,3,5]=>[[1,2,3,6],[4],[5]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,5,3,4,6]=>[[1,2,3,5,6],[4]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>[[1,2,3,5],[4],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>[[1,2,3,5,6],[4]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[[1,2,4,5,6],[3]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[[1,2,4,5],[3,6]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[[1,2,4,6],[3,5]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[[1,2,4],[3,5],[6]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>[[1,2,4,6],[3,5]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[[1,2,5,6],[3],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[[1,2,5],[3,6],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[[1,2,4,6],[3],[5]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[[1,2,4,5],[3],[6]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,6,3,4,2,5]=>[[1,2,4,6],[3],[5]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,5,3,2,4,6]=>[[1,2,5,6],[3],[4]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[[1,2,4],[3],[5],[6]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,6,3,2,5,4]=>[[1,2,5],[3,6],[4]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,6,3,2,4,5]=>[[1,2,5,6],[3],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,4,2,3,5,6]=>[[1,2,4,5,6],[3]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,4,2,3,6,5]=>[[1,2,4,5],[3,6]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[[1,2,6],[3],[4],[5]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[[1,2,5],[3],[4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,6,4,3,2,5]=>[[1,2,6],[3],[4],[5]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>[[1,2,4,6],[3],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,6,2,4,5,3]=>[[1,2,4,5],[3],[6]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,6,2,4,3,5]=>[[1,2,4,6],[3],[5]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,5,2,3,4,6]=>[[1,2,4,5,6],[3]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,5,3,4,2]=>[[1,2,5],[3],[4],[6]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,6,2,5,4,3]=>[[1,2,4],[3],[5],[6]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,6,2,3,5,4]=>[[1,2,4,5],[3],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>[[1,2,4,5,6],[3]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[1,3,4,5],[2,6]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[1,3,4,6],[2,5]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[1,3,4],[2,5],[6]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,6,4,5]=>[[1,3,4,6],[2,5]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[1,3,5,6],[2,4]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[1,3,6],[2,4],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[1,3,5],[2,4],[6]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,6,4,3,5]=>[[1,3,6],[2,4],[5]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,5,3,4,6]=>[[1,3,5,6],[2,4]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>[[1,3,5],[2,4],[6]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,6,3,4,5]=>[[1,3,5,6],[2,4]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[1,4,5],[2,6],[3]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[1,4,6],[2,5],[3]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,2,1,6,4,5]=>[[1,4,6],[2,5],[3]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[1,3,5],[2,6],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,1,5]=>[[1,3,4,6],[2],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,1,4,6]=>[[1,3,5,6],[2],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[[1,3,4],[2],[5],[6]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,2,3,1,5,4]=>[[1,3,5],[2,6],[4]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,2,3,1,4,5]=>[[1,3,5,6],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,1,3,5,6]=>[[1,4,5,6],[2],[3]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[4,2,1,3,6,5]=>[[1,4,5],[2,6],[3]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[[1,3,6],[2],[4],[5]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[[1,3,5],[2],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,2,4,3,1,5]=>[[1,3,6],[2],[4],[5]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,2,1,4,3,6]=>[[1,4,6],[2,5],[3]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[[1,3],[2],[4],[5],[6]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,2,1,4,5,3]=>[[1,4,5],[2,6],[3]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,2,1,4,3,5]=>[[1,4,6],[2,5],[3]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,2,1,3,4,6]=>[[1,4,5,6],[2],[3]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,2,5,3,4,1]=>[[1,3,5],[2],[4],[6]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,2,1,5,4,3]=>[[1,4],[2,5],[3],[6]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,2,1,3,5,4]=>[[1,4,5],[2,6],[3]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,2,1,3,4,5]=>[[1,4,5,6],[2],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>[[1,3,4,5,6],[2]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,1,2,4,6,5]=>[[1,3,4,5],[2,6]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,1,2,5,4,6]=>[[1,3,4,6],[2,5]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,1,2,6,5,4]=>[[1,3,4],[2,5],[6]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,1,2,6,4,5]=>[[1,3,4,6],[2,5]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,1,5]=>[[1,4,6],[2],[3],[5]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,1,4,6]=>[[1,5,6],[2],[3],[4]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[[1,4],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,3,2,1,5,4]=>[[1,5],[2,6],[3],[4]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,3,2,1,4,5]=>[[1,5,6],[2],[3],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>[[1,3,5,6],[2],[4]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>[[1,3,5],[2,6],[4]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,4,3,2,1,5]=>[[1,6],[2],[3],[4],[5]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>[[1,3,4,6],[2],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>[[1,3,4,5],[2],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,1,3,4,2,5]=>[[1,3,4,6],[2],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,1,3,2,4,6]=>[[1,3,5,6],[2],[4]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,5,3,2,4,1]=>[[1,5],[2],[3],[4],[6]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,1,3,5,4,2]=>[[1,3,4],[2],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,1,3,2,5,4]=>[[1,3,5],[2,6],[4]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,1,3,2,4,5]=>[[1,3,5,6],[2],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>[[1,3,4,5,6],[2]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,1,2,3,6,5]=>[[1,3,4,5],[2,6]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>[[1,4,6],[2],[3],[5]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>[[1,4,5],[2],[3],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,2,3,1,5]=>[[1,4,6],[2],[3],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>[[1,3,6],[2],[4],[5]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>[[1,3,5],[2],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,1,4,3,2,5]=>[[1,3,6],[2],[4],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>[[1,3,4,6],[2],[5]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>[[1,4],[2],[3],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>[[1,3],[2],[4],[5],[6]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>[[1,3,4,5],[2],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,1,2,4,3,5]=>[[1,3,4,6],[2],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>[[1,3,4,5,6],[2]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>[[1,4,5],[2],[3],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>[[1,3,5],[2],[4],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>[[1,3,4],[2],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>[[1,3,4,5],[2],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[[1,3,4,5,6],[2]]
[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]=>[1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,5,6]=>[[1,2,3,4,5,7],[6]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[[1,2,3,4,7],[5],[6]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[[1,2,3,4,6],[5],[7]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,7,5,4,6]=>[[1,2,3,4,7],[5],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,6,4,5,7]=>[[1,2,3,4,6,7],[5]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,7,4,6,5]=>[[1,2,3,4,6],[5],[7]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6]=>[[1,2,3,4,6,7],[5]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,5,6]=>[[1,2,3,5,7],[4,6]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[[1,2,3,6],[4,7],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[[1,2,3,5,7],[4],[6]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[[1,2,3,5,6],[4],[7]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,7,4,5,3,6]=>[[1,2,3,5,7],[4],[6]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,6,4,3,5,7]=>[[1,2,3,6,7],[4],[5]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[[1,2,3,5],[4],[6],[7]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,7,4,3,6,5]=>[[1,2,3,6],[4,7],[5]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,7,4,3,5,6]=>[[1,2,3,6,7],[4],[5]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,5,3,4,6,7]=>[[1,2,3,5,6,7],[4]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,5,3,4,7,6]=>[[1,2,3,5,6],[4,7]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[[1,2,3,7],[4],[5],[6]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[[1,2,3,6],[4],[5],[7]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,7,5,4,3,6]=>[[1,2,3,7],[4],[5],[6]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,6,3,5,4,7]=>[[1,2,3,5,7],[4],[6]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,7,3,5,6,4]=>[[1,2,3,5,6],[4],[7]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,7,3,5,4,6]=>[[1,2,3,5,7],[4],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,6,3,4,5,7]=>[[1,2,3,5,6,7],[4]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,7,6,4,5,3]=>[[1,2,3,6],[4],[5],[7]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,7,3,6,5,4]=>[[1,2,3,5],[4],[6],[7]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,7,3,4,6,5]=>[[1,2,3,5,6],[4],[7]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,7,3,4,5,6]=>[[1,2,3,5,6,7],[4]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[[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]=>[1,3,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,5,6]=>[[1,2,4,5,7],[3,6]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[[1,2,4,6],[3,5],[7]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,7,5,4,6]=>[[1,2,4,7],[3,5],[6]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,6,4,5,7]=>[[1,2,4,6,7],[3,5]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,7,4,6,5]=>[[1,2,4,6],[3,5],[7]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6]=>[[1,2,4,6,7],[3,5]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[[1,2,5,7],[3,6],[4]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,3,2,7,5,6]=>[[1,2,5,7],[3,6],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[[1,2,4,6],[3,7],[5]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,7,3,4,5,2,6]=>[[1,2,4,5,7],[3],[6]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,6,3,4,2,5,7]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[[1,2,4,5],[3],[6],[7]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,7,3,4,2,6,5]=>[[1,2,4,6],[3,7],[5]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,7,3,4,2,5,6]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,5,3,2,4,6,7]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,5,3,2,4,7,6]=>[[1,2,5,6],[3,7],[4]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[[1,2,4,7],[3],[5],[6]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[[1,2,4,6],[3],[5],[7]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,7,3,5,4,2,6]=>[[1,2,4,7],[3],[5],[6]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,6,3,2,5,4,7]=>[[1,2,5,7],[3,6],[4]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,7,3,2,5,6,4]=>[[1,2,5,6],[3,7],[4]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,7,3,2,5,4,6]=>[[1,2,5,7],[3,6],[4]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,6,3,2,4,5,7]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,3,6,4,5,2]=>[[1,2,4,6],[3],[5],[7]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,7,3,2,6,5,4]=>[[1,2,5],[3,6],[4],[7]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,7,3,2,4,6,5]=>[[1,2,5,6],[3,7],[4]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,7,3,2,4,5,6]=>[[1,2,5,6,7],[3],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,4,2,3,5,6,7]=>[[1,2,4,5,6,7],[3]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,4,2,3,5,7,6]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,4,2,3,6,5,7]=>[[1,2,4,5,7],[3,6]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,4,2,3,7,6,5]=>[[1,2,4,5],[3,6],[7]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,4,2,3,7,5,6]=>[[1,2,4,5,7],[3,6]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[[1,2,6],[3,7],[4],[5]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[[1,2,5,7],[3],[4],[6]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[[1,2,5,6],[3],[4],[7]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,7,4,3,5,2,6]=>[[1,2,5,7],[3],[4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,6,4,3,2,5,7]=>[[1,2,6,7],[3],[4],[5]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,7,4,3,2,6,5]=>[[1,2,6],[3,7],[4],[5]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,7,4,3,2,5,6]=>[[1,2,6,7],[3],[4],[5]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,5,2,4,3,6,7]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,5,2,4,3,7,6]=>[[1,2,4,6],[3,7],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[[1,2,6],[3],[4],[5],[7]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,7,5,4,3,2,6]=>[[1,2,7],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,6,2,4,5,3,7]=>[[1,2,4,5,7],[3],[6]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,7,2,4,5,6,3]=>[[1,2,4,5,6],[3],[7]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,7,2,4,5,3,6]=>[[1,2,4,5,7],[3],[6]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,6,2,4,3,5,7]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,7,6,4,3,5,2]=>[[1,2,6],[3],[4],[5],[7]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,7,2,4,6,5,3]=>[[1,2,4,5],[3],[6],[7]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,7,2,4,3,6,5]=>[[1,2,4,6],[3,7],[5]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,7,2,4,3,5,6]=>[[1,2,4,6,7],[3],[5]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,5,2,3,4,6,7]=>[[1,2,4,5,6,7],[3]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,5,2,3,4,7,6]=>[[1,2,4,5,6],[3,7]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,6,5,3,4,2,7]=>[[1,2,5,7],[3],[4],[6]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,5,3,4,6,2]=>[[1,2,5,6],[3],[4],[7]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,7,5,3,4,2,6]=>[[1,2,5,7],[3],[4],[6]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,6,2,5,4,3,7]=>[[1,2,4,7],[3],[5],[6]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,7,2,5,4,6,3]=>[[1,2,4,6],[3],[5],[7]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,7,2,5,4,3,6]=>[[1,2,4,7],[3],[5],[6]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,6,2,3,5,4,7]=>[[1,2,4,5,7],[3],[6]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,7,6,3,5,4,2]=>[[1,2,5],[3],[4],[6],[7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,7,2,6,5,4,3]=>[[1,2,4],[3],[5],[6],[7]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,7,2,3,5,6,4]=>[[1,2,4,5,6],[3],[7]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,7,2,3,5,4,6]=>[[1,2,4,5,7],[3],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,6,2,3,4,5,7]=>[[1,2,4,5,6,7],[3]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,6,3,4,5,2]=>[[1,2,5,6],[3],[4],[7]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,7,2,6,4,5,3]=>[[1,2,4,6],[3],[5],[7]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,7,2,3,6,5,4]=>[[1,2,4,5],[3],[6],[7]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,7,2,3,4,6,5]=>[[1,2,4,5,6],[3],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[[1,2,4,5,6,7],[3]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[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]=>[2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[1,3,4,5],[2,6],[7]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,5,6]=>[[1,3,4,5,7],[2,6]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[1,3,4,6,7],[2,5]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[1,3,4,6],[2,5,7]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[1,3,4,6],[2,5],[7]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,7,5,4,6]=>[[1,3,4,7],[2,5],[6]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,6,4,5,7]=>[[1,3,4,6,7],[2,5]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,7,4,6,5]=>[[1,3,4,6],[2,5],[7]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,7,4,5,6]=>[[1,3,4,6,7],[2,5]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[1,3,5],[2,4,6],[7]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,5,6]=>[[1,3,5,7],[2,4,6]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[1,3,6],[2,4,7],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[1,3,5,7],[2,4],[6]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[1,3,5,6],[2,4],[7]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,7,4,5,3,6]=>[[1,3,5,7],[2,4],[6]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,6,4,3,5,7]=>[[1,3,6,7],[2,4],[5]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[[1,3,5],[2,4],[6],[7]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,7,4,3,6,5]=>[[1,3,6],[2,4,7],[5]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,7,4,3,5,6]=>[[1,3,6,7],[2,4],[5]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,5,3,4,6,7]=>[[1,3,5,6,7],[2,4]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,5,3,4,7,6]=>[[1,3,5,6],[2,4,7]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[[1,3,7],[2,4],[5],[6]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[[1,3,6],[2,4],[5],[7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,7,5,4,3,6]=>[[1,3,7],[2,4],[5],[6]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,6,3,5,4,7]=>[[1,3,5,7],[2,4],[6]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,7,3,5,6,4]=>[[1,3,5,6],[2,4],[7]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,7,3,5,4,6]=>[[1,3,5,7],[2,4],[6]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,6,3,4,5,7]=>[[1,3,5,6,7],[2,4]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,6,4,5,3]=>[[1,3,6],[2,4],[5],[7]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,7,3,6,5,4]=>[[1,3,5],[2,4],[6],[7]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,7,3,4,6,5]=>[[1,3,5,6],[2,4],[7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,7,3,4,5,6]=>[[1,3,5,6,7],[2,4]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[1,4,5],[2,6],[3,7]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,2,1,4,7,5,6]=>[[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]=>[3,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[1,4,6],[2,5],[3,7]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,2,1,7,5,4,6]=>[[1,4,7],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,2,1,6,4,5,7]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,2,1,7,4,6,5]=>[[1,4,6],[2,5],[3,7]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,2,1,7,4,5,6]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,2,3,1,7,5,6]=>[[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,1,6]=>[[1,3,4,5,7],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,1,5,7]=>[[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[[1,3,4,5],[2],[6],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,2,3,4,1,6,5]=>[[1,3,4,6],[2,7],[5]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,2,3,4,1,5,6]=>[[1,3,4,6,7],[2],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,1,4,6,7]=>[[1,3,5,6,7],[2],[4]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[5,2,3,1,4,7,6]=>[[1,3,5,6],[2,7],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[[1,3,4,7],[2],[5],[6]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[[1,3,4,6],[2],[5],[7]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,2,3,5,4,1,6]=>[[1,3,4,7],[2],[5],[6]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,2,3,1,5,4,7]=>[[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,2,3,1,5,6,4]=>[[1,3,5,6],[2,7],[4]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,2,3,1,5,4,6]=>[[1,3,5,7],[2,6],[4]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,2,3,1,4,5,7]=>[[1,3,5,6,7],[2],[4]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,2,3,6,4,5,1]=>[[1,3,4,6],[2],[5],[7]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,2,3,1,6,5,4]=>[[1,3,5],[2,6],[4],[7]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,2,3,1,4,6,5]=>[[1,3,5,6],[2,7],[4]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,2,3,1,4,5,6]=>[[1,3,5,6,7],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[4,2,1,3,5,7,6]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[4,2,1,3,6,5,7]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[4,2,1,3,7,6,5]=>[[1,4,5],[2,6],[3,7]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[4,2,1,3,7,5,6]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[[1,3,6],[2,7],[4],[5]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,2,4,3,5,1,6]=>[[1,3,5,7],[2],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,2,4,3,1,5,7]=>[[1,3,6,7],[2],[4],[5]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,2,4,3,1,6,5]=>[[1,3,6],[2,7],[4],[5]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,2,4,3,1,5,6]=>[[1,3,6,7],[2],[4],[5]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,2,1,4,3,6,7]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[5,2,1,4,3,7,6]=>[[1,4,6],[2,5,7],[3]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,2,5,4,3,1,6]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,2,1,4,5,3,7]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,2,1,4,5,6,3]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,2,1,4,5,3,6]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,2,1,4,3,5,7]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,2,6,4,3,5,1]=>[[1,3,6],[2],[4],[5],[7]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,2,1,4,6,5,3]=>[[1,4,5],[2,6],[3],[7]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,2,1,4,3,6,5]=>[[1,4,6],[2,5,7],[3]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,2,1,4,3,5,6]=>[[1,4,6,7],[2,5],[3]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,2,1,3,4,6,7]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[5,2,1,3,4,7,6]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,2,5,3,4,1,7]=>[[1,3,5,7],[2],[4],[6]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,2,5,3,4,6,1]=>[[1,3,5,6],[2],[4],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,2,5,3,4,1,6]=>[[1,3,5,7],[2],[4],[6]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,2,1,5,4,3,7]=>[[1,4,7],[2,5],[3],[6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,2,1,5,4,6,3]=>[[1,4,6],[2,5],[3],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,2,1,5,4,3,6]=>[[1,4,7],[2,5],[3],[6]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,2,1,3,5,4,7]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,2,6,3,5,4,1]=>[[1,3,5],[2],[4],[6],[7]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,2,1,6,5,4,3]=>[[1,4],[2,5],[3],[6],[7]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,2,1,3,5,6,4]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,2,1,3,5,4,6]=>[[1,4,5,7],[2,6],[3]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,2,1,3,4,5,7]=>[[1,4,5,6,7],[2],[3]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,2,6,3,4,5,1]=>[[1,3,5,6],[2],[4],[7]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,2,1,6,4,5,3]=>[[1,4,6],[2,5],[3],[7]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,2,1,3,6,5,4]=>[[1,4,5],[2,6],[3],[7]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,2,1,3,4,6,5]=>[[1,4,5,6],[2,7],[3]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,2,1,3,4,5,6]=>[[1,4,5,6,7],[2],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[1,3,4,5,6,7],[2]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[[1,3,4,5,6],[2,7]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[[1,3,4,5,7],[2,6]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,1,2,4,7,6,5]=>[[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]=>[3,1,2,4,7,5,6]=>[[1,3,4,5,7],[2,6]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[[1,3,4,6],[2,5,7]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,1,2,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,1,2,7,5,6,4]=>[[1,3,4,6],[2,5],[7]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,1,2,7,5,4,6]=>[[1,3,4,7],[2,5],[6]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,1,2,6,4,5,7]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,1,2,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[3,1,2,7,4,6,5]=>[[1,3,4,6],[2,5],[7]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[3,1,2,7,4,5,6]=>[[1,3,4,6,7],[2,5]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[[1,5,7],[2,6],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[[1,5],[2,6],[3,7],[4]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,3,2,1,7,5,6]=>[[1,5,7],[2,6],[3],[4]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[[1,4,6],[2,7],[3],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[[1,4,5,6],[2],[3],[7]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,1,6]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,1,5,7]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[[1,4,5],[2,6],[3],[7]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,3,2,4,1,6,5]=>[[1,4,6],[2,7],[3],[5]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,3,2,4,1,5,6]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,1,4,6,7]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[5,3,2,1,4,7,6]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[[1,4,7],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[[1,4,6],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,3,2,5,4,1,6]=>[[1,4,7],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,3,2,1,5,4,7]=>[[1,5,7],[2,6],[3],[4]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,3,2,1,5,6,4]=>[[1,5,6],[2,7],[3],[4]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,3,2,1,5,4,6]=>[[1,5,7],[2,6],[3],[4]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,3,2,1,4,5,7]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,3,2,6,4,5,1]=>[[1,4,6],[2,5],[3],[7]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,3,2,1,6,5,4]=>[[1,5],[2,6],[3,7],[4]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,3,2,1,4,6,5]=>[[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]=>[7,3,2,1,4,5,6]=>[[1,5,6,7],[2],[3],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>[[1,3,5,6,7],[2],[4]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[4,1,3,2,5,7,6]=>[[1,3,5,6],[2,7],[4]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[4,1,3,2,6,5,7]=>[[1,3,5,7],[2,6],[4]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[4,1,3,2,7,6,5]=>[[1,3,5],[2,6],[4,7]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[4,1,3,2,7,5,6]=>[[1,3,5,7],[2,6],[4]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[[1,6],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,4,3,2,5,1,6]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,4,3,2,1,5,7]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[[1,5],[2,6],[3],[4],[7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,4,3,2,1,6,5]=>[[1,6],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,4,3,2,1,5,6]=>[[1,6,7],[2],[3],[4],[5]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,1,3,4,2,6,7]=>[[1,3,4,6,7],[2],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[5,1,3,4,2,7,6]=>[[1,3,4,6],[2,7],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,5,3,4,2,1,6]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,1,3,4,5,2,7]=>[[1,3,4,5,7],[2],[6]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,1,3,4,5,6,2]=>[[1,3,4,5,6],[2],[7]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,1,3,4,5,2,6]=>[[1,3,4,5,7],[2],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,1,3,4,2,5,7]=>[[1,3,4,6,7],[2],[5]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,6,3,4,2,5,1]=>[[1,4,6],[2],[3],[5],[7]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,1,3,4,6,5,2]=>[[1,3,4,5],[2],[6],[7]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,1,3,4,2,6,5]=>[[1,3,4,6],[2,7],[5]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,1,3,4,2,5,6]=>[[1,3,4,6,7],[2],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,1,3,2,4,6,7]=>[[1,3,5,6,7],[2],[4]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[5,1,3,2,4,7,6]=>[[1,3,5,6],[2,7],[4]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,5,3,2,4,1,7]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,5,3,2,4,6,1]=>[[1,5,6],[2],[3],[4],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,2,4,1,6]=>[[1,5,7],[2],[3],[4],[6]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,1,3,5,4,2,7]=>[[1,3,4,7],[2],[5],[6]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,1,3,5,4,6,2]=>[[1,3,4,6],[2],[5],[7]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,1,3,5,4,2,6]=>[[1,3,4,7],[2],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,1,3,2,5,4,7]=>[[1,3,5,7],[2,6],[4]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,6,3,2,5,4,1]=>[[1,5],[2,6],[3],[4],[7]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,1,3,6,5,4,2]=>[[1,3,4],[2],[5],[6],[7]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,1,3,2,5,6,4]=>[[1,3,5,6],[2,7],[4]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,1,3,2,5,4,6]=>[[1,3,5,7],[2,6],[4]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,1,3,2,4,5,7]=>[[1,3,5,6,7],[2],[4]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,6,3,2,4,5,1]=>[[1,5,6],[2],[3],[4],[7]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,1,3,6,4,5,2]=>[[1,3,4,6],[2],[5],[7]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,1,3,2,6,5,4]=>[[1,3,5],[2,6],[4],[7]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,1,3,2,4,6,5]=>[[1,3,5,6],[2,7],[4]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,1,3,2,4,5,6]=>[[1,3,5,6,7],[2],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,1,2,3,5,7,6]=>[[1,3,4,5,6],[2,7]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,1,2,3,6,5,7]=>[[1,3,4,5,7],[2,6]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,1,2,3,7,6,5]=>[[1,3,4,5],[2,6],[7]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,1,2,3,7,5,6]=>[[1,3,4,5,7],[2,6]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,4,2,3,1,7,6]=>[[1,4,6],[2,7],[3],[5]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,4,2,3,5,1,7]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,4,2,3,5,6,1]=>[[1,4,5,6],[2],[3],[7]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,2,3,5,1,6]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,2,3,1,5,7]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,4,2,3,6,5,1]=>[[1,4,5],[2,6],[3],[7]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,4,2,3,1,6,5]=>[[1,4,6],[2,7],[3],[5]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,4,2,3,1,5,6]=>[[1,4,6,7],[2],[3],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,1,4,3,2,6,7]=>[[1,3,6,7],[2],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[5,1,4,3,2,7,6]=>[[1,3,6],[2,7],[4],[5]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,5,4,3,2,1,6]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,1,4,3,5,2,7]=>[[1,3,5,7],[2],[4],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,1,4,3,5,6,2]=>[[1,3,5,6],[2],[4],[7]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,1,4,3,5,2,6]=>[[1,3,5,7],[2],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,1,4,3,2,5,7]=>[[1,3,6,7],[2],[4],[5]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,6,4,3,2,5,1]=>[[1,6],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,1,4,3,6,5,2]=>[[1,3,5],[2,6],[4],[7]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,1,4,3,2,6,5]=>[[1,3,6],[2,7],[4],[5]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,1,4,3,2,5,6]=>[[1,3,6,7],[2],[4],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,1,2,4,3,6,7]=>[[1,3,4,6,7],[2],[5]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[5,1,2,4,3,7,6]=>[[1,3,4,6],[2,7],[5]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,5,2,4,3,1,7]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,5,2,4,3,6,1]=>[[1,4,6],[2],[3],[5],[7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,5,2,4,3,1,6]=>[[1,4,7],[2],[3],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,1,5,4,3,2,7]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,1,5,4,3,6,2]=>[[1,3,6],[2],[4],[5],[7]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,1,5,4,3,2,6]=>[[1,3,7],[2],[4],[5],[6]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,1,2,4,5,3,7]=>[[1,3,4,5,7],[2],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,6,2,4,5,3,1]=>[[1,4,5],[2],[3],[6],[7]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,1,6,4,5,3,2]=>[[1,3,5],[2],[4],[6],[7]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,1,2,4,5,6,3]=>[[1,3,4,5,6],[2],[7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,1,2,4,5,3,6]=>[[1,3,4,5,7],[2],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,1,2,4,3,5,7]=>[[1,3,4,6,7],[2],[5]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,6,2,4,3,5,1]=>[[1,4,6],[2],[3],[5],[7]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,1,6,4,3,5,2]=>[[1,3,6],[2],[4],[5],[7]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,1,2,4,6,5,3]=>[[1,3,4,5],[2],[6],[7]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,1,2,4,3,6,5]=>[[1,3,4,6],[2,7],[5]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,1,2,4,3,5,6]=>[[1,3,4,6,7],[2],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,1,2,3,4,7,6]=>[[1,3,4,5,6],[2,7]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,5,2,3,4,1,7]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,5,2,3,4,6,1]=>[[1,4,5,6],[2],[3],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,2,3,4,1,6]=>[[1,4,5,7],[2],[3],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,1,5,3,4,2,7]=>[[1,3,5,7],[2],[4],[6]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,6,5,3,4,2,1]=>[[1,5],[2],[3],[4],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,1,5,3,4,6,2]=>[[1,3,5,6],[2],[4],[7]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,1,5,3,4,2,6]=>[[1,3,5,7],[2],[4],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,1,2,5,4,3,7]=>[[1,3,4,7],[2],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,6,2,5,4,3,1]=>[[1,4],[2],[3],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,1,6,5,4,3,2]=>[[1,3],[2],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,1,2,5,4,6,3]=>[[1,3,4,6],[2],[5],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,1,2,5,4,3,6]=>[[1,3,4,7],[2],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,1,2,3,5,4,7]=>[[1,3,4,5,7],[2],[6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,6,2,3,5,4,1]=>[[1,4,5],[2],[3],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,1,6,3,5,4,2]=>[[1,3,5],[2],[4],[6],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,1,2,6,5,4,3]=>[[1,3,4],[2],[5],[6],[7]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,1,2,3,5,6,4]=>[[1,3,4,5,6],[2],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,1,2,3,5,4,6]=>[[1,3,4,5,7],[2],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>[[1,3,4,5,6,7],[2]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,6,2,3,4,5,1]=>[[1,4,5,6],[2],[3],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,1,6,3,4,5,2]=>[[1,3,5,6],[2],[4],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,1,2,6,4,5,3]=>[[1,3,4,6],[2],[5],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,1,2,3,6,5,4]=>[[1,3,4,5],[2],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,6,5]=>[[1,3,4,5,6],[2],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>[[1,3,4,5,6,7],[2]]
[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]=>[1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[[1,2,3,4,5,6,8],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[[1,2,3,4,5,6],[7],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,6,7]=>[[1,2,3,4,5,6,8],[7]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[[1,2,3,4,5,7,8],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,8,6,5,7]=>[[1,2,3,4,5,8],[6],[7]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,7,5,6,8]=>[[1,2,3,4,5,7,8],[6]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,5,7,6]=>[[1,2,3,4,5,7],[6],[8]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,5,6,7]=>[[1,2,3,4,5,7,8],[6]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[[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]=>[1,2,3,5,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,8,6,7]=>[[1,2,3,4,6,8],[5,7]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[[1,2,3,4,7],[5,8],[6]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[[1,2,3,4,6,8],[5],[7]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,5,6,4,7]=>[[1,2,3,4,6,8],[5],[7]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>[1,2,3,7,5,4,6,8]=>[[1,2,3,4,7,8],[5],[6]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>[[1,2,3,4,6],[5],[7],[8]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,5,4,7,6]=>[[1,2,3,4,7],[5,8],[6]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,5,4,6,7]=>[[1,2,3,4,7,8],[5],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[1,2,3,6,4,5,7,8]=>[[1,2,3,4,6,7,8],[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]=>[1,2,3,6,4,5,8,7]=>[[1,2,3,4,6,7],[5,8]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>[[1,2,3,4,8],[5],[6],[7]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>[[1,2,3,4,7],[5],[6],[8]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,6,5,4,7]=>[[1,2,3,4,8],[5],[6],[7]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>[1,2,3,7,4,6,5,8]=>[[1,2,3,4,6,8],[5],[7]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,4,6,7,5]=>[[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,4,6,5,7]=>[[1,2,3,4,6,8],[5],[7]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[1,2,3,7,4,5,6,8]=>[[1,2,3,4,6,7,8],[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]=>[1,2,3,8,7,5,6,4]=>[[1,2,3,4,7],[5],[6],[8]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,4,7,6,5]=>[[1,2,3,4,6],[5],[7],[8]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,4,5,7,6]=>[[1,2,3,4,6,7],[5],[8]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,4,5,6,7]=>[[1,2,3,4,6,7,8],[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]=>[1,2,4,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,8,6,7]=>[[1,2,3,5,6,8],[4,7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[[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]=>[1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,7,5,6,8]=>[[1,2,3,5,7,8],[4,6]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,8,5,7,6]=>[[1,2,3,5,7],[4,6],[8]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,5,6,7]=>[[1,2,3,5,7,8],[4,6]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[[1,2,3,6,7],[4,8],[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]=>[1,2,5,4,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,8,6,7]=>[[1,2,3,6,8],[4,7],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[[1,2,3,5,7,8],[4],[6]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>[1,2,8,4,5,6,3,7]=>[[1,2,3,5,6,8],[4],[7]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,6,3]=>[1,2,8,4,5,3,7,6]=>[[1,2,3,5,7],[4,8],[6]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>[1,2,6,4,3,5,7,8]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,5,8,3]=>[1,2,8,4,7,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[1,2,8,4,3,6,7,5]=>[[1,2,3,6,7],[4,8],[5]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>[1,2,8,4,3,6,5,7]=>[[1,2,3,6,8],[4,7],[5]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,4,7,6,5,3,8]=>[1,2,7,4,3,5,6,8]=>[[1,2,3,6,7,8],[4],[5]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,6,8,5,3]=>[1,2,8,4,3,7,6,5]=>[[1,2,3,6],[4,7],[5],[8]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[1,2,8,4,3,5,7,6]=>[[1,2,3,6,7],[4,8],[5]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[1,2,8,4,3,5,6,7]=>[[1,2,3,6,7,8],[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]=>[1,2,5,3,4,6,7,8]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>[1,2,5,3,4,6,8,7]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,5,4,3,7,6,8]=>[1,2,5,3,4,7,6,8]=>[[1,2,3,5,6,8],[4,7]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[1,2,5,3,4,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[1,2,5,3,4,8,6,7]=>[[1,2,3,5,6,8],[4,7]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,5,4,6,3,7,8]=>[1,2,6,5,4,3,7,8]=>[[1,2,3,7,8],[4],[5],[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]=>[1,2,7,5,4,6,3,8]=>[[1,2,3,6,8],[4],[5],[7]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>[[1,2,3,6,7],[4],[5],[8]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,4,7,6,8,3]=>[1,2,8,5,4,7,6,3]=>[[1,2,3,6],[4,7],[5],[8]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>[1,2,8,5,4,3,6,7]=>[[1,2,3,7,8],[4],[5],[6]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>[1,2,6,3,5,4,7,8]=>[[1,2,3,5,7,8],[4],[6]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[1,2,8,6,5,4,7,3]=>[[1,2,3,7],[4],[5],[6],[8]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,5,6,4,8,7,3]=>[1,2,8,6,5,4,3,7]=>[[1,2,3,8],[4],[5],[6],[7]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[1,2,8,3,5,6,7,4]=>[[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[1,2,8,3,5,6,4,7]=>[[1,2,3,5,6,8],[4],[7]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,6,4,3,8]=>[1,2,7,3,5,4,6,8]=>[[1,2,3,5,7,8],[4],[6]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>[1,2,8,7,5,4,6,3]=>[[1,2,3,7],[4],[5],[6],[8]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>[1,2,8,3,5,7,6,4]=>[[1,2,3,5,6],[4],[7],[8]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,8,6,4,3]=>[1,2,8,3,5,4,7,6]=>[[1,2,3,5,7],[4,8],[6]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,7,6,4,3]=>[1,2,8,3,5,4,6,7]=>[[1,2,3,5,7,8],[4],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[1,2,6,3,4,5,7,8]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,5,4,3,8,7]=>[1,2,6,3,4,5,8,7]=>[[1,2,3,5,6,7],[4,8]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[1,2,8,6,4,5,7,3]=>[[1,2,3,6,7],[4],[5],[8]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>[1,2,8,6,4,5,3,7]=>[[1,2,3,6,8],[4],[5],[7]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,5,7,4,8,3]=>[1,2,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>[1,2,8,3,6,5,7,4]=>[[1,2,3,5,7],[4],[6],[8]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,5,8,7,4,3]=>[1,2,8,3,6,5,4,7]=>[[1,2,3,5,8],[4],[6],[7]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,5,4,3,8]=>[1,2,7,3,4,6,5,8]=>[[1,2,3,5,6,8],[4],[7]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,6,7,5,4,8,3]=>[1,2,8,7,4,6,5,3]=>[[1,2,3,6],[4],[5],[7],[8]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,6,7,5,8,4,3]=>[1,2,8,3,7,6,5,4]=>[[1,2,3,5],[4],[6],[7],[8]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[1,2,8,3,4,6,7,5]=>[[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,6,8,7,5,4,3]=>[1,2,8,3,4,6,5,7]=>[[1,2,3,5,6,8],[4],[7]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[1,2,7,3,4,5,6,8]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>[1,2,8,7,4,5,6,3]=>[[1,2,3,6,7],[4],[5],[8]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>[1,2,8,3,4,7,6,5]=>[[1,2,3,5,6],[4],[7],[8]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>[1,2,8,3,4,5,7,6]=>[[1,2,3,5,6,7],[4],[8]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[1,2,8,3,4,5,6,7]=>[[1,2,3,5,6,7,8],[4]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[[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]=>[1,3,2,4,5,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[[1,2,4,5,8],[3,6],[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]=>[1,3,2,4,8,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,8,6,5,7]=>[[1,2,4,5,8],[3,6],[7]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,2,4,7,8,6,5]=>[1,3,2,4,8,5,7,6]=>[[1,2,4,5,7],[3,6],[8]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[[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]=>[1,3,2,5,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,8,6,7]=>[[1,2,4,6,8],[3,5,7]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,7,4]=>[1,3,2,8,5,6,4,7]=>[[1,2,4,6,8],[3,5],[7]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[1,3,2,7,5,4,6,8]=>[[1,2,4,7,8],[3,5],[6]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]=>[[1,2,4,6],[3,5],[7],[8]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[1,3,2,8,5,4,7,6]=>[[1,2,4,7],[3,5,8],[6]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,7,6,4]=>[1,3,2,8,5,4,6,7]=>[[1,2,4,7,8],[3,5],[6]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>[1,3,2,6,4,5,7,8]=>[[1,2,4,6,7,8],[3,5]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>[1,3,2,8,6,5,4,7]=>[[1,2,4,8],[3,5],[6],[7]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,5,4,8]=>[1,3,2,7,4,6,5,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,2,6,7,8,5,4]=>[1,3,2,8,4,6,7,5]=>[[1,2,4,6,7],[3,5],[8]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,7,5,4]=>[1,3,2,8,4,6,5,7]=>[[1,2,4,6,8],[3,5],[7]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[1,3,2,7,4,5,6,8]=>[[1,2,4,6,7,8],[3,5]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,2,7,8,6,5,4]=>[1,3,2,8,4,5,7,6]=>[[1,2,4,6,7],[3,5],[8]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,4,5,6,7]=>[[1,2,4,6,7,8],[3,5]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,8,6,7]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,8,5,6,7]=>[[1,2,5,7,8],[3,6],[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]=>[1,5,3,4,2,6,7,8]=>[[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]=>[1,5,3,4,2,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[[1,2,4,5,7,8],[3],[6]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[[1,2,4,5,6,8],[3],[7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[1,8,3,4,5,6,2,7]=>[[1,2,4,5,6,8],[3],[7]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[1,8,3,4,5,2,7,6]=>[[1,2,4,5,7],[3,8],[6]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>[1,8,3,4,5,2,6,7]=>[[1,2,4,5,7,8],[3],[6]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,4,6,5,2,7,8]=>[1,6,3,4,2,5,7,8]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,4,6,5,2,8,7]=>[1,6,3,4,2,5,8,7]=>[[1,2,4,6,7],[3,8],[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]=>[1,7,3,4,2,6,5,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>[1,8,3,4,2,6,7,5]=>[[1,2,4,6,7],[3,8],[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]=>[1,8,3,4,2,7,6,5]=>[[1,2,4,6],[3,7],[5],[8]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,8,3,4,2,5,6,7]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>[1,5,3,2,4,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>[1,5,3,2,4,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>[1,5,3,2,4,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>[1,5,3,2,4,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,5,4,2,8,7,6]=>[1,5,3,2,4,8,6,7]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,4,6,2,7,8]=>[1,6,3,5,4,2,7,8]=>[[1,2,4,7,8],[3],[5],[6]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,4,6,7,2,8]=>[1,7,3,5,4,6,2,8]=>[[1,2,4,6,8],[3],[5],[7]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,4,6,7,8,2]=>[1,8,3,5,4,6,7,2]=>[[1,2,4,6,7],[3],[5],[8]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>[1,7,3,5,4,2,6,8]=>[[1,2,4,7,8],[3],[5],[6]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>[1,8,3,5,4,2,7,6]=>[[1,2,4,7],[3,8],[5],[6]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[1,6,3,2,5,4,7,8]=>[[1,2,5,7,8],[3,6],[4]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>[1,7,3,6,5,4,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,4,7,8,2]=>[1,8,3,6,5,4,7,2]=>[[1,2,4,7],[3],[5],[6],[8]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,4,2,8]=>[1,7,3,2,5,6,4,8]=>[[1,2,5,6,8],[3,7],[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]=>[1,8,3,7,5,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[1,8,3,2,5,6,7,4]=>[[1,2,5,6,7],[3,8],[4]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,8,7,4,2]=>[1,8,3,2,5,6,4,7]=>[[1,2,5,6,8],[3,7],[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]=>[1,7,3,2,5,4,6,8]=>[[1,2,5,7,8],[3,6],[4]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[1,8,3,2,5,4,7,6]=>[[1,2,5,7],[3,6,8],[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]=>[1,8,3,2,5,4,6,7]=>[[1,2,5,7,8],[3,6],[4]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,6,5,4,2,7,8]=>[1,6,3,2,4,5,7,8]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>[1,8,3,6,4,5,2,7]=>[[1,2,4,6,8],[3],[5],[7]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,5,7,4,8,2]=>[1,8,3,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,5,4,2,8]=>[1,7,3,2,4,6,5,8]=>[[1,2,5,6,8],[3,7],[4]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>[1,8,3,2,7,6,5,4]=>[[1,2,5],[3,6],[4],[7],[8]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,6,5,4,2,8]=>[1,7,3,2,4,5,6,8]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,7,6,5,8,4,2]=>[1,8,3,2,7,5,6,4]=>[[1,2,5,7],[3,6],[4],[8]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,6,5,4,2]=>[1,8,3,2,4,5,7,6]=>[[1,2,5,6,7],[3,8],[4]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[1,8,3,2,4,5,6,7]=>[[1,2,5,6,7,8],[3],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,3,2,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[1,4,2,3,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,3,2,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,3,2,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,3,2,6,8,7,5]=>[1,4,2,3,8,6,5,7]=>[[1,2,4,5,8],[3,6],[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]=>[1,4,2,3,7,5,6,8]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[1,4,2,3,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,4,3,2,7,8,6,5]=>[1,4,2,3,8,5,7,6]=>[[1,2,4,5,7],[3,6],[8]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,4,2,3,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,3,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,3,5,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,3,5,7,6,8,2]=>[1,8,4,3,5,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>[1,8,4,3,5,2,7,6]=>[[1,2,5,7],[3,8],[4],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[1,6,4,3,2,5,7,8]=>[[1,2,6,7,8],[3],[4],[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]=>[1,8,4,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[1,8,4,3,6,5,2,7]=>[[1,2,5,8],[3,6],[4],[7]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>[1,8,4,3,2,6,7,5]=>[[1,2,6,7],[3,8],[4],[5]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,3,7,6,5,2,8]=>[1,7,4,3,2,5,6,8]=>[[1,2,6,7,8],[3],[4],[5]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>[1,8,4,3,2,7,6,5]=>[[1,2,6],[3,7],[4,8],[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]=>[1,8,4,3,2,5,7,6]=>[[1,2,6,7],[3,8],[4],[5]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,8,4,3,2,5,6,7]=>[[1,2,6,7,8],[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]=>[1,5,2,4,3,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,3,2,6,8,7]=>[1,5,2,4,3,6,8,7]=>[[1,2,4,6,7],[3,8],[5]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,3,2,7,6,8]=>[1,5,2,4,3,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,3,2,7,8,6]=>[1,5,2,4,3,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,3,2,8,7,6]=>[1,5,2,4,3,8,6,7]=>[[1,2,4,6,8],[3,7],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,3,6,2,7,8]=>[1,6,5,4,3,2,7,8]=>[[1,2,7,8],[3],[4],[5],[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]=>[1,7,5,4,3,6,2,8]=>[[1,2,6,8],[3],[4],[5],[7]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,3,6,8,7,2]=>[1,8,5,4,3,6,2,7]=>[[1,2,6,8],[3],[4],[5],[7]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,5,3,7,6,2,8]=>[1,7,5,4,3,2,6,8]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,3,7,8,6,2]=>[1,8,5,4,3,2,7,6]=>[[1,2,7],[3,8],[4],[5],[6]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,3,8,7,6,2]=>[1,8,5,4,3,2,6,7]=>[[1,2,7,8],[3],[4],[5],[6]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,3,2,7,8]=>[1,6,2,4,5,3,7,8]=>[[1,2,4,5,7,8],[3],[6]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,3,7,2,8]=>[1,7,6,4,5,3,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,6,3,7,8,2]=>[1,8,6,4,5,3,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[1,7,2,4,5,6,3,8]=>[[1,2,4,5,6,8],[3],[7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[1,8,7,4,5,6,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>[1,8,2,4,5,6,7,3]=>[[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,4,5,7,6,3,2,8]=>[1,7,2,4,5,3,6,8]=>[[1,2,4,5,7,8],[3],[6]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,5,7,6,3,8,2]=>[1,8,7,4,5,3,6,2]=>[[1,2,5,7],[3],[4],[6],[8]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,7,6,8,3,2]=>[1,8,2,4,5,7,6,3]=>[[1,2,4,5,6],[3],[7],[8]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,5,3,2,7,8]=>[1,6,2,4,3,5,7,8]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,6,5,3,7,8,2]=>[1,8,6,4,3,5,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,5,7,3,2,8]=>[1,7,2,4,6,5,3,8]=>[[1,2,4,5,8],[3],[6],[7]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,5,8,7,3,2]=>[1,8,2,4,6,5,3,7]=>[[1,2,4,5,8],[3],[6],[7]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>[1,8,7,4,3,6,5,2]=>[[1,2,6],[3,7],[4],[5],[8]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>[1,8,2,4,7,6,5,3]=>[[1,2,4,5],[3],[6],[7],[8]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>[1,8,2,4,3,6,5,7]=>[[1,2,4,6,8],[3,7],[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]=>[1,7,2,4,3,5,6,8]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,7,6,5,3,8,2]=>[1,8,7,4,3,5,6,2]=>[[1,2,6,7],[3],[4],[5],[8]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,6,5,8,3,2]=>[1,8,2,4,7,5,6,3]=>[[1,2,4,5,7],[3],[6],[8]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,4,7,6,8,5,3,2]=>[1,8,2,4,3,7,6,5]=>[[1,2,4,6],[3,7],[5],[8]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[1,8,2,4,3,5,6,7]=>[[1,2,4,6,7,8],[3],[5]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,4,3,2,6,8,7]=>[1,5,2,3,4,6,8,7]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[1,5,2,3,4,7,6,8]=>[[1,2,4,5,6,8],[3,7]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,4,3,2,7,8,6]=>[1,5,2,3,4,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[1,5,2,3,4,8,6,7]=>[[1,2,4,5,6,8],[3,7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[1,8,5,3,4,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[1,8,5,3,4,6,2,7]=>[[1,2,5,6,8],[3],[4],[7]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,4,3,7,6,8,2]=>[1,8,5,3,4,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[1,7,6,5,4,3,2,8]=>[[1,2,8],[3],[4],[5],[6],[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]=>[1,8,6,5,4,3,7,2]=>[[1,2,7],[3],[4],[5],[6],[8]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,4,6,3,8,7,2]=>[1,8,6,5,4,3,2,7]=>[[1,2,8],[3],[4],[5],[6],[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]=>[1,7,2,5,4,6,3,8]=>[[1,2,4,6,8],[3],[5],[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]=>[1,8,7,5,4,6,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>[1,8,2,5,4,6,7,3]=>[[1,2,4,6,7],[3],[5],[8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,4,7,6,3,2,8]=>[1,7,2,5,4,3,6,8]=>[[1,2,4,7,8],[3],[5],[6]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,4,7,6,3,8,2]=>[1,8,7,5,4,3,6,2]=>[[1,2,7],[3],[4],[5],[6],[8]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,4,7,6,8,3,2]=>[1,8,2,5,4,7,6,3]=>[[1,2,4,6],[3,7],[5],[8]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,5,6,4,3,7,2,8]=>[1,7,6,3,5,4,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>[1,8,6,3,5,4,2,7]=>[[1,2,5,8],[3],[4],[6],[7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,5,6,4,7,3,2,8]=>[1,7,2,6,5,4,3,8]=>[[1,2,4,8],[3],[5],[6],[7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[1,8,2,3,5,6,7,4]=>[[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,5,6,8,7,4,3,2]=>[1,8,2,3,5,6,4,7]=>[[1,2,4,5,6,8],[3],[7]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,5,7,6,4,3,2,8]=>[1,7,2,3,5,4,6,8]=>[[1,2,4,5,7,8],[3],[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]=>[1,8,2,3,5,4,6,7]=>[[1,2,4,5,7,8],[3],[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]=>[1,6,2,3,4,5,7,8]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[1,6,2,3,4,5,8,7]=>[[1,2,4,5,6,7],[3,8]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,5,4,3,7,2,8]=>[1,7,6,3,4,5,2,8]=>[[1,2,5,6,8],[3],[4],[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]=>[1,8,6,3,4,5,2,7]=>[[1,2,5,6,8],[3],[4],[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]=>[1,8,7,3,6,5,4,2]=>[[1,2,5],[3],[4],[6],[7],[8]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,5,7,4,8,3,2]=>[1,8,2,7,6,5,4,3]=>[[1,2,4],[3],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>[1,8,2,3,6,5,7,4]=>[[1,2,4,5,7],[3],[6],[8]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,5,8,7,4,3,2]=>[1,8,2,3,6,5,4,7]=>[[1,2,4,5,8],[3],[6],[7]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,5,4,3,2,8]=>[1,7,2,3,4,6,5,8]=>[[1,2,4,5,6,8],[3],[7]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,5,4,3,8,2]=>[1,8,7,3,4,6,5,2]=>[[1,2,5,6],[3],[4],[7],[8]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,6,7,5,4,8,3,2]=>[1,8,2,7,4,6,5,3]=>[[1,2,4,6],[3],[5],[7],[8]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>[1,8,2,3,7,6,5,4]=>[[1,2,4,5],[3],[6],[7],[8]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[1,8,2,3,4,6,7,5]=>[[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[1,8,2,3,4,6,5,7]=>[[1,2,4,5,6,8],[3],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[1,7,2,3,4,5,6,8]=>[[1,2,4,5,6,7,8],[3]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>[1,8,7,3,4,5,6,2]=>[[1,2,5,6,7],[3],[4],[8]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>[1,8,2,7,4,5,6,3]=>[[1,2,4,6,7],[3],[5],[8]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[1,8,2,3,7,5,6,4]=>[[1,2,4,5,7],[3],[6],[8]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[1,8,2,3,4,7,6,5]=>[[1,2,4,5,6],[3],[7],[8]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[1,8,2,3,4,5,7,6]=>[[1,2,4,5,6,7],[3],[8]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[[1,2,4,5,6,7,8],[3]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[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]=>[2,1,3,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[[1,3,4,5,6],[2,7],[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]=>[2,1,3,4,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,4,6,8,7,5]=>[2,1,3,4,8,6,5,7]=>[[1,3,4,5,8],[2,6],[7]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,5,7,6]=>[[1,3,4,5,7],[2,6],[8]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[[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]=>[2,1,3,5,4,8,7,6]=>[[1,3,4,6],[2,5,7],[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]=>[2,1,3,8,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]=>[[1,3,4,6],[2,5],[7],[8]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,3,5,7,8,6,4]=>[2,1,3,8,5,4,7,6]=>[[1,3,4,7],[2,5,8],[6]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,3,5,8,7,6,4]=>[2,1,3,8,5,4,6,7]=>[[1,3,4,7,8],[2,5],[6]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,6,5,4,7,8]=>[2,1,3,6,4,5,7,8]=>[[1,3,4,6,7,8],[2,5]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>[2,1,3,6,4,5,8,7]=>[[1,3,4,6,7],[2,5,8]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,6,5,7,8,4]=>[2,1,3,8,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[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]=>[2,1,3,8,6,5,4,7]=>[[1,3,4,8],[2,5],[6],[7]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>[2,1,3,8,4,6,7,5]=>[[1,3,4,6,7],[2,5],[8]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,7,5,4]=>[2,1,3,8,4,6,5,7]=>[[1,3,4,6,8],[2,5],[7]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,7,6,5,8,4]=>[2,1,3,8,7,5,6,4]=>[[1,3,4,7],[2,5],[6],[8]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,3,7,6,8,5,4]=>[2,1,3,8,4,7,6,5]=>[[1,3,4,6],[2,5],[7],[8]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>[2,1,3,8,4,5,7,6]=>[[1,3,4,6,7],[2,5],[8]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,4,5,6,7]=>[[1,3,4,6,7,8],[2,5]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[[1,3,5,6],[2,4,7],[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]=>[2,1,4,3,5,8,6,7]=>[[1,3,5,6,8],[2,4,7]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[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]=>[2,1,4,3,8,6,7,5]=>[[1,3,5,7],[2,4,6],[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]=>[2,1,4,3,8,6,5,7]=>[[1,3,5,8],[2,4,6],[7]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,5,7,6]=>[[1,3,5,7],[2,4,6],[8]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,5,6,7]=>[[1,3,5,7,8],[2,4,6]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,6,8,3]=>[2,1,8,4,5,7,6,3]=>[[1,3,5,6],[2,4],[7],[8]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[2,1,8,4,5,3,7,6]=>[[1,3,5,7],[2,4,8],[6]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>[2,1,6,4,3,5,7,8]=>[[1,3,6,7,8],[2,4],[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]=>[2,1,6,4,3,5,8,7]=>[[1,3,6,7],[2,4,8],[5]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,5,7,8,3]=>[2,1,8,4,6,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[2,1,8,4,3,6,5,7]=>[[1,3,6,8],[2,4,7],[5]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[2,1,8,4,7,5,6,3]=>[[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,6,8,5,3]=>[2,1,8,4,3,7,6,5]=>[[1,3,6],[2,4,7],[5],[8]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[2,1,8,4,3,5,7,6]=>[[1,3,6,7],[2,4,8],[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]=>[2,1,5,3,4,6,7,8]=>[[1,3,5,6,7,8],[2,4]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,5,3,4,6,8,7]=>[[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[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]=>[2,1,8,5,4,6,7,3]=>[[1,3,6,7],[2,4],[5],[8]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>[2,1,8,5,4,6,3,7]=>[[1,3,6,8],[2,4],[5],[7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>[2,1,8,5,4,3,7,6]=>[[1,3,7],[2,4,8],[5],[6]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,4,8,7,6,3]=>[2,1,8,5,4,3,6,7]=>[[1,3,7,8],[2,4],[5],[6]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[2,1,6,3,5,4,8,7]=>[[1,3,5,7],[2,4,8],[6]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,5,6,4,7,3,8]=>[2,1,7,6,5,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]=>[[1,3,7],[2,4],[5],[6],[8]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,4,8,7,3]=>[2,1,8,6,5,4,3,7]=>[[1,3,8],[2,4],[5],[6],[7]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[2,1,8,3,5,6,7,4]=>[[1,3,5,6,7],[2,4],[8]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>[2,1,8,7,5,4,6,3]=>[[1,3,7],[2,4],[5],[6],[8]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[2,1,8,3,5,7,6,4]=>[[1,3,5,6],[2,4],[7],[8]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[2,1,8,3,5,4,7,6]=>[[1,3,5,7],[2,4,8],[6]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,6,3,4,5,8,7]=>[[1,3,5,6,7],[2,4,8]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,5,4,7,8,3]=>[2,1,8,6,4,5,7,3]=>[[1,3,6,7],[2,4],[5],[8]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[2,1,8,3,6,5,7,4]=>[[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>[2,1,8,7,4,6,5,3]=>[[1,3,6],[2,4],[5],[7],[8]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[2,1,8,3,7,6,5,4]=>[[1,3,5],[2,4],[6],[7],[8]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[2,1,8,3,4,6,7,5]=>[[1,3,5,6,7],[2,4],[8]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[2,1,7,3,4,5,6,8]=>[[1,3,5,6,7,8],[2,4]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[2,1,8,3,7,5,6,4]=>[[1,3,5,7],[2,4],[6],[8]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[2,1,8,3,4,7,6,5]=>[[1,3,5,6],[2,4],[7],[8]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,8,3,4,5,6,7]=>[[1,3,5,6,7,8],[2,4]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[[1,4,5,8],[2,6],[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]=>[3,2,1,4,8,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,8,5,7,6]=>[[1,4,5,7],[2,6],[3,8]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,8,5,6,7]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]=>[[1,4,7],[2,5,8],[3,6]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,1,5,6,8,7,4]=>[3,2,1,8,5,6,4,7]=>[[1,4,6,8],[2,5],[3,7]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,6,4]=>[3,2,1,8,5,4,7,6]=>[[1,4,7],[2,5,8],[3,6]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,1,5,8,7,6,4]=>[3,2,1,8,5,4,6,7]=>[[1,4,7,8],[2,5],[3,6]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>[3,2,1,6,4,5,7,8]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]=>[[1,4,8],[2,5],[3,6],[7]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,5,7,8,4]=>[3,2,1,8,6,5,7,4]=>[[1,4,7],[2,5],[3,6],[8]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[3,2,1,8,6,5,4,7]=>[[1,4,8],[2,5],[3,6],[7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,5,4,8]=>[3,2,1,7,4,6,5,8]=>[[1,4,6,8],[2,5],[3,7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>[3,2,1,8,4,6,7,5]=>[[1,4,6,7],[2,5],[3,8]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>[3,2,1,8,4,6,5,7]=>[[1,4,6,8],[2,5],[3,7]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,7,6,5,4,8]=>[3,2,1,7,4,5,6,8]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,7,5,6,4]=>[[1,4,7],[2,5],[3,6],[8]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>[3,2,1,8,4,7,6,5]=>[[1,4,6],[2,5],[3,7],[8]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,6,5,4]=>[3,2,1,8,4,5,7,6]=>[[1,4,6,7],[2,5],[3,8]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[3,2,1,8,4,5,6,7]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,8,5,7,6]=>[[1,3,5,7],[2,6],[4,8]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,8,5,6,7]=>[[1,3,5,7,8],[2,6],[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]=>[5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[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]=>[5,2,3,4,1,6,8,7]=>[[1,3,4,6,7],[2,8],[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]=>[5,2,3,4,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,8,6,7]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,6,1,7]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[7,2,3,4,5,1,6,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[8,2,3,4,5,1,7,6]=>[[1,3,4,5,7],[2,8],[6]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[8,2,3,4,5,1,6,7]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,6,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,5,1,8]=>[7,2,3,4,1,6,5,8]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[8,2,3,4,1,6,7,5]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[7,2,3,4,1,5,6,8]=>[[1,3,4,6,7,8],[2],[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]=>[8,2,3,4,1,5,7,6]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[8,2,3,4,1,5,6,7]=>[[1,3,4,6,7,8],[2],[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]=>[5,2,3,1,4,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[5,2,3,1,4,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>[[1,3,4,7,8],[2],[5],[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]=>[7,2,3,5,4,6,1,8]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[8,2,3,5,4,6,7,1]=>[[1,3,4,6,7],[2],[5],[8]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,5,4,7,6,1,8]=>[7,2,3,5,4,1,6,8]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>[8,2,3,5,4,1,7,6]=>[[1,3,4,7],[2,8],[5],[6]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,4,1,7,8]=>[6,2,3,1,5,4,7,8]=>[[1,3,5,7,8],[2,6],[4]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[8,2,3,6,5,4,7,1]=>[[1,3,4,7],[2],[5],[6],[8]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,4,1,8]=>[7,2,3,1,5,6,4,8]=>[[1,3,5,6,8],[2,7],[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]=>[8,2,3,7,5,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[8,2,3,1,5,6,7,4]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[8,2,3,1,5,6,4,7]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>[8,2,3,1,5,7,6,4]=>[[1,3,5,6],[2,7],[4],[8]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[8,2,3,1,5,4,7,6]=>[[1,3,5,7],[2,6,8],[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]=>[6,2,3,1,4,5,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,4,1]=>[8,2,3,1,6,5,7,4]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>[8,2,3,1,6,5,4,7]=>[[1,3,5,8],[2,6],[4],[7]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,5,4,1,8]=>[7,2,3,1,4,6,5,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,5,8,4,1]=>[8,2,3,1,7,6,5,4]=>[[1,3,5],[2,6],[4],[7],[8]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,7,5,4,1]=>[8,2,3,1,4,6,5,7]=>[[1,3,5,6,8],[2,7],[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]=>[7,2,3,1,4,5,6,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[8,2,3,7,4,5,6,1]=>[[1,3,4,6,7],[2],[5],[8]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>[8,2,3,1,7,5,6,4]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,6,5,4,1]=>[8,2,3,1,4,5,7,6]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[8,2,3,1,4,5,6,7]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,4,3,1,5,7,8,6]=>[4,2,1,3,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,3,1,5,8,7,6]=>[4,2,1,3,5,8,6,7]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,3,1,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[[1,4,5,7],[2,6,8],[3]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[4,2,1,3,8,6,5,7]=>[[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]=>[4,2,1,3,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[4,2,1,3,8,5,7,6]=>[[1,4,5,7],[2,6],[3,8]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[4,2,1,3,8,5,6,7]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,3,5,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[[1,3,6,8],[2,7],[4],[5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,3,5,6,1,8,7]=>[6,2,4,3,5,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,7,8,6,1]=>[8,2,4,3,5,1,7,6]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,6,5,1,7,8]=>[6,2,4,3,1,5,7,8]=>[[1,3,6,7,8],[2],[4],[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]=>[6,2,4,3,1,5,8,7]=>[[1,3,6,7],[2,8],[4],[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]=>[7,2,4,3,6,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[8,2,4,3,6,5,1,7]=>[[1,3,5,8],[2,6],[4],[7]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[8,2,4,3,7,5,6,1]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>[5,2,1,4,3,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[5,2,1,4,3,8,6,7]=>[[1,4,6,8],[2,5,7],[3]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,4,5,3,6,7,1,8]=>[7,2,5,4,3,6,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[8,2,5,4,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,3,7,6,8,1]=>[8,2,5,4,3,7,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>[6,2,1,4,5,3,7,8]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,6,3,7,1,8]=>[7,2,6,4,5,3,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]=>[8,2,6,4,5,3,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,3,1,8]=>[7,2,1,4,5,6,3,8]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[8,2,1,4,5,6,7,3]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,4,5,7,6,3,1,8]=>[7,2,1,4,5,3,6,8]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,6,3,8,1]=>[8,2,7,4,5,3,6,1]=>[[1,3,5,7],[2],[4],[6],[8]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>[6,2,1,4,3,5,7,8]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>[6,2,1,4,3,5,8,7]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>[8,2,6,4,3,5,1,7]=>[[1,3,6,8],[2],[4],[5],[7]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>[8,2,1,4,6,5,7,3]=>[[1,4,5,7],[2,6],[3],[8]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>[7,2,1,4,3,6,5,8]=>[[1,4,6,8],[2,5,7],[3]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[8,2,1,4,3,6,5,7]=>[[1,4,6,8],[2,5,7],[3]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,4,7,6,5,3,1,8]=>[7,2,1,4,3,5,6,8]=>[[1,4,6,7,8],[2,5],[3]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[8,2,1,4,3,5,7,6]=>[[1,4,6,7],[2,5,8],[3]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[5,2,1,3,4,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,4,3,6,1,8,7]=>[6,2,5,3,4,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>[7,2,5,3,4,6,1,8]=>[[1,3,5,6,8],[2],[4],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,5,4,3,7,6,1,8]=>[7,2,5,3,4,1,6,8]=>[[1,3,5,7,8],[2],[4],[6]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[8,2,5,3,4,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[8,2,5,3,4,1,7,6]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,5,4,6,3,1,7,8]=>[6,2,1,5,4,3,7,8]=>[[1,4,7,8],[2,5],[3],[6]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,5,4,6,3,1,8,7]=>[6,2,1,5,4,3,8,7]=>[[1,4,7],[2,5,8],[3],[6]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,4,6,7,3,1,8]=>[7,2,1,5,4,6,3,8]=>[[1,4,6,8],[2,5],[3],[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]=>[8,2,7,5,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,5,4,7,6,3,1,8]=>[7,2,1,5,4,3,6,8]=>[[1,4,7,8],[2,5],[3],[6]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[8,2,7,5,4,3,6,1]=>[[1,3,7],[2],[4],[5],[6],[8]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[8,2,1,5,4,3,7,6]=>[[1,4,7],[2,5,8],[3],[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]=>[7,2,1,6,5,4,3,8]=>[[1,4,8],[2,5],[3],[6],[7]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,5,6,4,7,3,8,1]=>[8,2,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]=>[8,2,1,6,5,4,7,3]=>[[1,4,7],[2,5],[3],[6],[8]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]=>[8,2,1,7,5,6,4,3]=>[[1,4,6],[2,5],[3],[7],[8]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[8,2,1,3,5,6,7,4]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,5,7,6,4,3,1,8]=>[7,2,1,3,5,4,6,8]=>[[1,4,5,7,8],[2,6],[3]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,6,5,4,3,7,1,8]=>[7,2,6,3,4,5,1,8]=>[[1,3,5,6,8],[2],[4],[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]=>[8,2,6,3,4,5,7,1]=>[[1,3,5,6,7],[2],[4],[8]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,5,4,3,8,7,1]=>[8,2,6,3,4,5,1,7]=>[[1,3,5,6,8],[2],[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]=>[8,2,7,3,6,5,4,1]=>[[1,3,5],[2],[4],[6],[7],[8]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,5,7,4,8,3,1]=>[8,2,1,7,6,5,4,3]=>[[1,4],[2,5],[3],[6],[7],[8]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,4,3,1]=>[8,2,1,3,6,5,7,4]=>[[1,4,5,7],[2,6],[3],[8]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,6,5,8,7,4,3,1]=>[8,2,1,3,6,5,4,7]=>[[1,4,5,8],[2,6],[3],[7]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>[8,2,1,3,7,6,5,4]=>[[1,4,5],[2,6],[3],[7],[8]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[8,2,1,3,4,6,5,7]=>[[1,4,5,6,8],[2,7],[3]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>[7,2,1,3,4,5,6,8]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[8,2,7,3,4,5,6,1]=>[[1,3,5,6,7],[2],[4],[8]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[8,2,1,3,4,5,7,6]=>[[1,4,5,6,7],[2,8],[3]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[8,2,1,3,4,5,6,7]=>[[1,4,5,6,7,8],[2],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[3,1,2,4,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,2,1,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>[[1,3,4,5,7],[2,6],[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]=>[3,1,2,4,8,6,5,7]=>[[1,3,4,5,8],[2,6],[7]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[3,1,2,4,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[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]=>[3,1,2,4,8,5,7,6]=>[[1,3,4,5,7],[2,6],[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]=>[3,1,2,4,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[[1,3,4,6,8],[2,5,7]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[3,1,2,8,5,6,7,4]=>[[1,3,4,6,7],[2,5],[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]=>[3,1,2,8,5,6,4,7]=>[[1,3,4,6,8],[2,5],[7]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[3,1,2,7,5,4,6,8]=>[[1,3,4,7,8],[2,5],[6]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[3,1,2,8,5,4,7,6]=>[[1,3,4,7],[2,5,8],[6]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>[3,1,2,6,4,5,8,7]=>[[1,3,4,6,7],[2,5,8]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[3,1,2,8,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[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]=>[3,1,2,8,6,5,4,7]=>[[1,3,4,8],[2,5],[6],[7]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[3,1,2,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[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]=>[3,1,2,8,4,6,7,5]=>[[1,3,4,6,7],[2,5],[8]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[3,1,2,7,4,5,6,8]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[3,1,2,8,7,5,6,4]=>[[1,3,4,7],[2,5],[6],[8]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[3,1,2,8,4,5,7,6]=>[[1,3,4,6,7],[2,5],[8]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[3,1,2,8,4,5,6,7]=>[[1,3,4,6,7,8],[2,5]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,8,6,7]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[[1,5,7],[2,6,8],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[[1,5,8],[2,6],[3,7],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[[1,5,7],[2,6],[3,8],[4]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,8,6,5,7]=>[[1,5,8],[2,6],[3,7],[4]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,7,5,6,8]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[[1,5],[2,6],[3,7],[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]=>[4,3,2,1,8,5,7,6]=>[[1,5,7],[2,6],[3,8],[4]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,8,5,6,7]=>[[1,5,7,8],[2,6],[3],[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]=>[5,3,2,4,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[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]=>[8,3,2,4,5,6,1,7]=>[[1,4,5,6,8],[2],[3],[7]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,2,4,6,5,8,7,1]=>[8,3,2,4,6,5,1,7]=>[[1,4,5,8],[2,6],[3],[7]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>[5,3,2,1,4,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>[5,3,2,1,4,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>[5,3,2,1,4,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[5,3,2,1,4,8,6,7]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,5,4,6,1,7,8]=>[6,3,2,5,4,1,7,8]=>[[1,4,7,8],[2,5],[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]=>[6,3,2,5,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,5,4,6,7,1,8]=>[7,3,2,5,4,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[7,3,2,5,4,1,6,8]=>[[1,4,7,8],[2,5],[3],[6]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>[6,3,2,1,5,4,8,7]=>[[1,5,7],[2,6,8],[3],[4]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,5,6,7,4,1,8]=>[7,3,2,1,5,6,4,8]=>[[1,5,6,8],[2,7],[3],[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]=>[8,3,2,7,5,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[8,3,2,1,5,6,7,4]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,5,6,8,7,4,1]=>[8,3,2,1,5,6,4,7]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,5,7,6,4,1,8]=>[7,3,2,1,5,4,6,8]=>[[1,5,7,8],[2,6],[3],[4]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>[8,3,2,1,5,4,7,6]=>[[1,5,7],[2,6,8],[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]=>[6,3,2,1,4,5,8,7]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[8,3,2,6,4,5,1,7]=>[[1,4,6,8],[2,5],[3],[7]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,6,5,7,8,4,1]=>[8,3,2,1,6,5,7,4]=>[[1,5,7],[2,6],[3,8],[4]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,2,6,5,8,7,4,1]=>[8,3,2,1,6,5,4,7]=>[[1,5,8],[2,6],[3,7],[4]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[7,3,2,1,4,6,5,8]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[8,3,2,7,4,6,5,1]=>[[1,4,6],[2,5],[3],[7],[8]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,6,7,5,8,4,1]=>[8,3,2,1,7,6,5,4]=>[[1,5],[2,6],[3,7],[4],[8]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>[8,3,2,1,4,6,5,7]=>[[1,5,6,8],[2,7],[3],[4]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[7,3,2,1,4,5,6,8]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,2,7,6,8,5,4,1]=>[8,3,2,1,4,7,6,5]=>[[1,5,6],[2,7],[3,8],[4]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[8,3,2,1,4,5,7,6]=>[[1,5,6,7],[2,8],[3],[4]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[8,3,2,1,4,5,6,7]=>[[1,5,6,7,8],[2],[3],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,4,2,1,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[4,1,3,2,8,6,5,7]=>[[1,3,5,8],[2,6],[4,7]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[4,1,3,2,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[4,1,3,2,8,5,7,6]=>[[1,3,5,7],[2,6],[4,8]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[4,1,3,2,8,5,6,7]=>[[1,3,5,7,8],[2,6],[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]=>[5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[[1,6],[2,7],[3,8],[4],[5]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,8,6,7]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[8,4,3,2,5,1,7,6]=>[[1,5,7],[2,8],[3],[4],[6]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,4,2,6,5,1,7,8]=>[6,4,3,2,1,5,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>[6,4,3,2,1,5,8,7]=>[[1,6,7],[2,8],[3],[4],[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]=>[7,4,3,2,1,6,5,8]=>[[1,6,8],[2,7],[3],[4],[5]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[8,4,3,2,7,6,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,2,6,7,8,5,1]=>[8,4,3,2,1,6,7,5]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,2,7,6,5,1,8]=>[7,4,3,2,1,5,6,8]=>[[1,6,7,8],[2],[3],[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]=>[8,4,3,2,7,5,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>[8,4,3,2,1,5,7,6]=>[[1,6,7],[2,8],[3],[4],[5]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[8,4,3,2,1,5,6,7]=>[[1,6,7,8],[2],[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]=>[5,1,3,4,2,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,2,1,6,8,7]=>[5,1,3,4,2,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,2,1,7,6,8]=>[5,1,3,4,2,7,6,8]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[5,1,3,4,2,8,6,7]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[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]=>[6,5,3,4,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[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]=>[7,5,3,4,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[8,5,3,4,2,7,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>[6,1,3,4,5,2,7,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>[7,1,3,4,5,6,2,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[8,1,3,4,5,6,7,2]=>[[1,3,4,5,6,7],[2],[8]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[8,1,3,4,5,7,6,2]=>[[1,3,4,5,6],[2],[7],[8]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[8,1,3,4,5,2,6,7]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,5,2,1,8,7]=>[6,1,3,4,2,5,8,7]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[8,7,3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,4,6,5,8,7,2,1]=>[8,1,3,4,6,5,2,7]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]=>[8,7,3,4,2,6,5,1]=>[[1,4,6],[2,7],[3],[5],[8]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>[8,1,3,4,2,6,7,5]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,6,8,7,5,2,1]=>[8,1,3,4,2,6,5,7]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,6,8,5,2,1]=>[8,1,3,4,2,7,6,5]=>[[1,3,4,6],[2,7],[5],[8]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>[5,1,3,2,4,6,8,7]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,4,2,1,7,6,8]=>[5,1,3,2,4,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[5,1,3,2,4,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,4,2,6,1,8,7]=>[6,5,3,2,4,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[7,5,3,2,4,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,5,4,2,6,8,7,1]=>[8,5,3,2,4,6,1,7]=>[[1,5,6,8],[2],[3],[4],[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]=>[7,5,3,2,4,1,6,8]=>[[1,5,7,8],[2],[3],[4],[6]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,4,2,7,8,6,1]=>[8,5,3,2,4,1,7,6]=>[[1,5,7],[2,8],[3],[4],[6]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,5,4,6,2,1,7,8]=>[6,1,3,5,4,2,7,8]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[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]=>[8,7,3,5,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,5,4,6,8,7,2,1]=>[8,1,3,5,4,6,2,7]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>[8,7,3,5,4,2,6,1]=>[[1,4,7],[2],[3],[5],[6],[8]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[8,1,3,5,4,7,6,2]=>[[1,3,4,6],[2,7],[5],[8]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,5,4,8,7,6,2,1]=>[8,1,3,5,4,2,6,7]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>[6,1,3,2,5,4,8,7]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,4,2,7,1,8]=>[7,6,3,2,5,4,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]=>[8,6,3,2,5,4,7,1]=>[[1,5,7],[2,6],[3],[4],[8]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,4,7,2,1,8]=>[7,1,3,6,5,4,2,8]=>[[1,3,4,8],[2],[5],[6],[7]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,4,8,7,2,1]=>[8,1,3,6,5,4,2,7]=>[[1,3,4,8],[2],[5],[6],[7]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,4,2,1,8]=>[7,1,3,2,5,6,4,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[8,7,3,2,5,6,4,1]=>[[1,5,6],[2,7],[3],[4],[8]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>[8,1,3,7,5,6,4,2]=>[[1,3,4,6],[2],[5],[7],[8]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[8,1,3,2,5,6,7,4]=>[[1,3,5,6,7],[2,8],[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]=>[8,1,3,2,5,6,4,7]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[7,1,3,2,5,4,6,8]=>[[1,3,5,7,8],[2,6],[4]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>[8,7,3,2,5,4,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[8,1,3,2,5,4,7,6]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[8,1,3,2,5,4,6,7]=>[[1,3,5,7,8],[2,6],[4]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,5,4,2,7,1,8]=>[7,6,3,2,4,5,1,8]=>[[1,5,6,8],[2],[3],[4],[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]=>[8,6,3,2,4,5,1,7]=>[[1,5,6,8],[2],[3],[4],[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]=>[7,1,3,6,4,5,2,8]=>[[1,3,4,6,8],[2],[5],[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]=>[8,7,3,6,4,5,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]=>[8,1,3,6,4,5,2,7]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,5,7,4,8,2,1]=>[8,1,3,7,6,5,4,2]=>[[1,3,4],[2],[5],[6],[7],[8]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,5,7,8,4,2,1]=>[8,1,3,2,6,5,7,4]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,5,8,7,4,2,1]=>[8,1,3,2,6,5,4,7]=>[[1,3,5,8],[2,6],[4],[7]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,6,7,5,4,2,8,1]=>[8,7,3,2,4,6,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,5,4,8,2,1]=>[8,1,3,7,4,6,5,2]=>[[1,3,4,6],[2],[5],[7],[8]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]=>[8,1,3,2,7,6,5,4]=>[[1,3,5],[2,6],[4],[7],[8]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,5,4,2,1]=>[8,1,3,2,4,6,7,5]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>[8,1,3,2,4,6,5,7]=>[[1,3,5,6,8],[2,7],[4]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,7,6,5,4,2,1,8]=>[7,1,3,2,4,5,6,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>[8,1,3,7,4,5,6,2]=>[[1,3,4,6,7],[2],[5],[8]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>[8,1,3,2,7,5,6,4]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[8,1,3,2,4,7,6,5]=>[[1,3,5,6],[2,7],[4],[8]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[8,1,3,2,4,5,7,6]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[8,1,3,2,4,5,6,7]=>[[1,3,5,6,7,8],[2],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[[1,3,4,5,6],[2,7],[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]=>[4,1,2,3,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[[1,3,4,5,8],[2,6],[7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[[1,3,4,5,7],[2,6],[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]=>[4,1,2,3,8,6,5,7]=>[[1,3,4,5,8],[2,6],[7]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[4,1,2,3,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>[[1,3,4,5],[2,6],[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]=>[4,1,2,3,8,5,7,6]=>[[1,3,4,5,7],[2,6],[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]=>[4,1,2,3,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,3,2,5,1,6,8,7]=>[5,4,2,3,1,6,8,7]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,3,2,5,1,7,8,6]=>[5,4,2,3,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[5,4,2,3,1,8,6,7]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[6,4,2,3,5,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>[[1,4,5,6,8],[2],[3],[7]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[8,4,2,3,5,6,7,1]=>[[1,4,5,6,7],[2],[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]=>[7,4,2,3,5,1,6,8]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>[8,4,2,3,5,7,6,1]=>[[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]=>[8,4,2,3,5,1,6,7]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>[8,4,2,3,6,5,7,1]=>[[1,4,5,7],[2,6],[3],[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]=>[8,4,2,3,7,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,6,7,8,5,1]=>[8,4,2,3,1,6,7,5]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>[8,4,2,3,1,6,5,7]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[8,4,2,3,7,5,6,1]=>[[1,4,5,7],[2,6],[3],[8]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]=>[8,4,2,3,1,5,7,6]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[8,4,2,3,1,5,6,7]=>[[1,4,6,7,8],[2],[3],[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]=>[5,1,4,3,2,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,3,5,2,1,6,8,7]=>[5,1,4,3,2,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,3,5,2,1,7,8,6]=>[5,1,4,3,2,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[1,7],[2,8],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,3,5,2,6,8,7,1]=>[8,5,4,3,2,6,1,7]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,3,5,2,7,6,1,8]=>[7,5,4,3,2,1,6,8]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[[1,6],[2,7],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>[8,5,4,3,2,1,6,7]=>[[1,7,8],[2],[3],[4],[5],[6]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[6,1,4,3,5,2,8,7]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[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]=>[8,7,4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4],[7],[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]=>[8,1,4,3,5,6,7,2]=>[[1,3,5,6,7],[2],[4],[8]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>[8,1,4,3,5,6,2,7]=>[[1,3,5,6,8],[2],[4],[7]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,3,5,7,6,2,8,1]=>[8,7,4,3,5,2,6,1]=>[[1,5,7],[2],[3],[4],[6],[8]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>[8,1,4,3,5,7,6,2]=>[[1,3,5,6],[2,7],[4],[8]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>[8,1,4,3,5,2,7,6]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,3,5,8,7,6,2,1]=>[8,1,4,3,5,2,6,7]=>[[1,3,5,7,8],[2],[4],[6]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,3,6,5,2,7,1,8]=>[7,6,4,3,2,5,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,3,6,5,2,7,8,1]=>[8,6,4,3,2,5,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[8,1,4,3,6,5,7,2]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[8,1,4,3,6,5,2,7]=>[[1,3,5,8],[2,6],[4],[7]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,3,6,7,5,8,2,1]=>[8,1,4,3,7,6,5,2]=>[[1,3,5],[2,6],[4],[7],[8]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>[8,1,4,3,2,6,7,5]=>[[1,3,6,7],[2,8],[4],[5]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,3,6,8,7,5,2,1]=>[8,1,4,3,2,6,5,7]=>[[1,3,6,8],[2,7],[4],[5]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,7,6,5,2,1,8]=>[7,1,4,3,2,5,6,8]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]=>[8,7,4,3,2,5,6,1]=>[[1,6,7],[2],[3],[4],[5],[8]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]=>[8,1,4,3,7,5,6,2]=>[[1,3,5,7],[2,6],[4],[8]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,7,6,8,5,2,1]=>[8,1,4,3,2,7,6,5]=>[[1,3,6],[2,7],[4,8],[5]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[8,1,4,3,2,5,7,6]=>[[1,3,6,7],[2,8],[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]=>[8,1,4,3,2,5,6,7]=>[[1,3,6,7,8],[2],[4],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[5,1,2,4,3,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,8,7,1]=>[8,5,2,4,3,6,1,7]=>[[1,4,6,8],[2],[3],[5],[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]=>[7,5,2,4,3,1,6,8]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,3,2,7,8,6,1]=>[8,5,2,4,3,1,7,6]=>[[1,4,7],[2,8],[3],[5],[6]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>[8,5,2,4,3,1,6,7]=>[[1,4,7,8],[2],[3],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[6,1,5,4,3,2,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[8,6,5,4,3,2,1,7]=>[[1,8],[2],[3],[4],[5],[6],[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]=>[8,7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,3,6,7,8,2,1]=>[8,1,5,4,3,6,7,2]=>[[1,3,6,7],[2],[4],[5],[8]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>[8,1,5,4,3,6,2,7]=>[[1,3,6,8],[2],[4],[5],[7]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,3,7,6,2,8,1]=>[8,7,5,4,3,2,6,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>[8,1,5,4,3,7,6,2]=>[[1,3,6],[2,7],[4],[5],[8]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>[8,1,5,4,3,2,7,6]=>[[1,3,7],[2,8],[4],[5],[6]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,3,8,7,6,2,1]=>[8,1,5,4,3,2,6,7]=>[[1,3,7,8],[2],[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]=>[6,1,2,4,5,3,8,7]=>[[1,3,4,5,7],[2,8],[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]=>[8,6,2,4,5,3,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>[8,6,2,4,5,3,1,7]=>[[1,4,5,8],[2],[3],[6],[7]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>[8,1,6,4,5,3,2,7]=>[[1,3,5,8],[2],[4],[6],[7]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[7,1,2,4,5,6,3,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[8,7,2,4,5,6,3,1]=>[[1,4,5,6],[2],[3],[7],[8]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,1,2,4,5,6,7,3]=>[[1,3,4,5,6,7],[2],[8]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>[8,1,2,4,5,6,3,7]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,5,7,6,3,2,8,1]=>[8,7,2,4,5,3,6,1]=>[[1,4,5,7],[2],[3],[6],[8]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>[8,1,2,4,5,3,7,6]=>[[1,3,4,5,7],[2,8],[6]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[8,1,2,4,5,3,6,7]=>[[1,3,4,5,7,8],[2],[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]=>[6,1,2,4,3,5,8,7]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]=>[8,6,2,4,3,5,1,7]=>[[1,4,6,8],[2],[3],[5],[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]=>[8,7,6,4,3,5,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,6,5,3,7,8,2,1]=>[8,1,6,4,3,5,7,2]=>[[1,3,6,7],[2],[4],[5],[8]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,5,3,8,7,2,1]=>[8,1,6,4,3,5,2,7]=>[[1,3,6,8],[2],[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]=>[8,7,2,4,6,5,3,1]=>[[1,4,5],[2],[3],[6],[7],[8]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,5,7,3,8,2,1]=>[8,1,7,4,6,5,3,2]=>[[1,3,5],[2],[4],[6],[7],[8]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>[8,1,2,4,6,5,7,3]=>[[1,3,4,5,7],[2],[6],[8]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[8,1,2,4,6,5,3,7]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]=>[8,7,2,4,3,6,5,1]=>[[1,4,6],[2,7],[3],[5],[8]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,5,3,8,2,1]=>[8,1,7,4,3,6,5,2]=>[[1,3,6],[2,7],[4],[5],[8]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>[8,1,2,4,7,6,5,3]=>[[1,3,4,5],[2],[6],[7],[8]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[8,1,2,4,3,6,5,7]=>[[1,3,4,6,8],[2,7],[5]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[7,1,2,4,3,5,6,8]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>[8,7,2,4,3,5,6,1]=>[[1,4,6,7],[2],[3],[5],[8]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>[8,1,7,4,3,5,6,2]=>[[1,3,6,7],[2],[4],[5],[8]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[8,1,2,4,7,5,6,3]=>[[1,3,4,5,7],[2],[6],[8]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>[8,1,2,4,3,7,6,5]=>[[1,3,4,6],[2,7],[5],[8]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>[8,1,2,4,3,5,7,6]=>[[1,3,4,6,7],[2,8],[5]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[8,1,2,4,3,5,6,7]=>[[1,3,4,6,7,8],[2],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[5,1,2,3,4,6,8,7]=>[[1,3,4,5,6,7],[2,8]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[5,1,2,3,4,8,7,6]=>[[1,3,4,5,6],[2,7],[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]=>[5,1,2,3,4,8,6,7]=>[[1,3,4,5,6,8],[2,7]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[8,5,2,3,4,6,1,7]=>[[1,4,5,6,8],[2],[3],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[7,5,2,3,4,1,6,8]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[8,5,2,3,4,1,6,7]=>[[1,4,5,7,8],[2],[3],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>[6,1,5,3,4,2,8,7]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>[8,6,5,3,4,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[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]=>[8,6,5,3,4,2,1,7]=>[[1,5,8],[2],[3],[4],[6],[7]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]=>[8,7,5,3,4,6,2,1]=>[[1,5,6],[2],[3],[4],[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]=>[8,1,5,3,4,6,2,7]=>[[1,3,5,6,8],[2],[4],[7]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,3,7,6,2,8,1]=>[8,7,5,3,4,2,6,1]=>[[1,5,7],[2],[3],[4],[6],[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]=>[8,1,5,3,4,2,7,6]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>[8,1,5,3,4,2,6,7]=>[[1,3,5,7,8],[2],[4],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>[6,1,2,5,4,3,8,7]=>[[1,3,4,7],[2,8],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>[7,6,2,5,4,3,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>[8,6,2,5,4,3,7,1]=>[[1,4,7],[2],[3],[5],[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]=>[7,1,6,5,4,3,2,8]=>[[1,3,8],[2],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,4,6,3,8,7,2,1]=>[8,1,6,5,4,3,2,7]=>[[1,3,8],[2],[4],[5],[6],[7]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,4,6,7,3,2,1,8]=>[7,1,2,5,4,6,3,8]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,8,7,3,2,1]=>[8,1,2,5,4,6,3,7]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,4,7,6,3,2,8,1]=>[8,7,2,5,4,3,6,1]=>[[1,4,7],[2],[3],[5],[6],[8]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,4,8,7,6,3,2,1]=>[8,1,2,5,4,3,6,7]=>[[1,3,4,7,8],[2],[5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[6,1,2,3,5,4,7,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,4,3,2,7,1,8]=>[7,6,2,3,5,4,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,4,3,2,8,7,1]=>[8,6,2,3,5,4,1,7]=>[[1,4,5,8],[2],[3],[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]=>[7,1,6,3,5,4,2,8]=>[[1,3,5,8],[2],[4],[6],[7]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,4,3,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,4,3,7,8,2,1]=>[8,1,6,3,5,4,7,2]=>[[1,3,5,7],[2],[4],[6],[8]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>[7,1,2,6,5,4,3,8]=>[[1,3,4,8],[2],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,4,7,3,8,2,1]=>[8,1,7,6,5,4,3,2]=>[[1,3],[2],[4],[5],[6],[7],[8]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>[8,1,2,6,5,4,3,7]=>[[1,3,4,8],[2],[5],[6],[7]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[7,1,2,3,5,6,4,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]=>[8,1,7,3,5,6,4,2]=>[[1,3,5,6],[2],[4],[7],[8]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,1,2,3,5,6,7,4]=>[[1,3,4,5,6,7],[2],[8]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[8,1,2,3,5,6,4,7]=>[[1,3,4,5,6,8],[2],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[7,1,2,3,5,4,6,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>[8,7,2,3,5,4,6,1]=>[[1,4,5,7],[2],[3],[6],[8]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[8,1,7,3,5,4,6,2]=>[[1,3,5,7],[2],[4],[6],[8]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[8,1,2,3,5,7,6,4]=>[[1,3,4,5,6],[2],[7],[8]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[8,1,2,3,5,4,7,6]=>[[1,3,4,5,7],[2,8],[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]=>[8,1,2,3,5,4,6,7]=>[[1,3,4,5,7,8],[2],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[6,1,2,3,4,5,7,8]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[6,1,2,3,4,5,8,7]=>[[1,3,4,5,6,7],[2,8]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,5,4,3,2,7,1,8]=>[7,6,2,3,4,5,1,8]=>[[1,4,5,6,8],[2],[3],[7]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[8,6,2,3,4,5,7,1]=>[[1,4,5,6,7],[2],[3],[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]=>[8,7,6,3,4,5,2,1]=>[[1,5,6],[2],[3],[4],[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]=>[8,1,6,3,4,5,7,2]=>[[1,3,5,6,7],[2],[4],[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]=>[8,1,6,3,4,5,2,7]=>[[1,3,5,6,8],[2],[4],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[7,1,2,6,4,5,3,8]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>[8,7,2,6,4,5,3,1]=>[[1,4,6],[2],[3],[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]=>[8,1,7,6,4,5,3,2]=>[[1,3,6],[2],[4],[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]=>[8,1,2,6,4,5,7,3]=>[[1,3,4,6,7],[2],[5],[8]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>[8,1,2,6,4,5,3,7]=>[[1,3,4,6,8],[2],[5],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[7,1,2,3,6,5,4,8]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[8,7,2,3,6,5,4,1]=>[[1,4,5],[2],[3],[6],[7],[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]=>[8,1,7,3,6,5,4,2]=>[[1,3,5],[2],[4],[6],[7],[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]=>[8,1,2,7,6,5,4,3]=>[[1,3,4],[2],[5],[6],[7],[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]=>[8,1,2,3,6,5,7,4]=>[[1,3,4,5,7],[2],[6],[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]=>[8,1,2,3,6,5,4,7]=>[[1,3,4,5,8],[2],[6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[7,1,2,3,4,6,5,8]=>[[1,3,4,5,6,8],[2],[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]=>[8,1,2,7,4,6,5,3]=>[[1,3,4,6],[2],[5],[7],[8]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[8,1,2,3,7,6,5,4]=>[[1,3,4,5],[2],[6],[7],[8]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,1,2,3,4,6,7,5]=>[[1,3,4,5,6,7],[2],[8]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[8,1,2,3,4,6,5,7]=>[[1,3,4,5,6,8],[2],[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]=>[7,1,2,3,4,5,6,8]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,7,2,3,4,5,6,1]=>[[1,4,5,6,7],[2],[3],[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]=>[8,1,7,3,4,5,6,2]=>[[1,3,5,6,7],[2],[4],[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]=>[8,1,2,7,4,5,6,3]=>[[1,3,4,6,7],[2],[5],[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]=>[8,1,2,3,7,5,6,4]=>[[1,3,4,5,7],[2],[6],[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]=>[8,1,2,3,4,7,6,5]=>[[1,3,4,5,6],[2],[7],[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]=>[8,1,2,3,4,5,7,6]=>[[1,3,4,5,6,7],[2],[8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7]=>[[1,3,4,5,6,7,8],[2]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,6,7,9]=>[[1,3,4,5,6,7,8,9],[2]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[[1,2,4,5,6,7,8,9],[3]]
[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]=>[9,1,2,3,4,5,6,7,8,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,7,6,9]=>[[1,3,4,5,6,7,9],[2],[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]=>[1,9,2,3,4,5,6,8,7]=>[[1,2,4,5,6,7,8],[3],[9]]
[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]=>[1,10,2,3,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>[9,1,2,3,4,5,6,8,7,10]=>[[1,3,4,5,6,7,8,10],[2],[9]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,5,4,3,2,1,9]=>[8,1,2,3,4,7,6,5,9]=>[[1,3,4,5,6,9],[2],[7],[8]]
[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]=>[8,1,2,3,4,6,5,7,9]=>[[1,3,4,5,6,8,9],[2],[7]]
[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]=>[1,9,2,3,4,5,8,7,6]=>[[1,2,4,5,6,7],[3],[8],[9]]
[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]=>[1,9,2,3,4,5,7,6,8]=>[[1,2,4,5,6,7,9],[3],[8]]
[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]=>[1,10,2,3,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8,9],[3],[10]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10,11],[3]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,10,11,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,10,9]=>[[1,2,4,5,6,7,8,9,10],[3],[11]]
[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]=>[8,2,1,3,4,5,6,7,9]=>[[1,4,5,6,7,8,9],[2],[3]]
[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]=>[7,1,2,3,4,5,6,9,8]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,3,4,5,6,7,8]=>[[1,3,5,6,7,8,9],[2,4]]
[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]=>[1,9,3,2,4,5,6,7,8]=>[[1,2,5,6,7,8,9],[3],[4]]
[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]=>[7,1,2,3,4,5,6,8,9]=>[[1,3,4,5,6,7,8,9],[2]]
[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]=>[1,8,2,3,4,5,6,7,9]=>[[1,2,4,5,6,7,8,9],[3]]
[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]=>[1,2,9,3,4,5,6,7,8]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,9,8,7,6,5,4,3,1,10]=>[9,2,1,3,4,5,6,7,8,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[8,1,2,3,4,5,6,7,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,8,9,7,6,5,4,3]=>[1,2,9,3,4,5,6,8,7]=>[[1,2,3,5,6,7,8],[4],[9]]
[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]=>[2,1,10,3,4,5,6,7,8,9]=>[[1,3,5,6,7,8,9,10],[2,4]]
[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]=>[8,1,2,3,4,5,6,7,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[1,9,2,3,4,5,6,7,8,10]=>[[1,2,4,5,6,7,8,9,10],[3]]
[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]=>[1,2,10,3,4,5,6,7,8,9]=>[[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]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2],[9]]
[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]=>[9,2,3,4,5,6,7,1,8]=>[[1,3,4,5,6,7,9],[2],[8]]
[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]=>[9,2,3,4,5,6,1,7,8]=>[[1,3,4,5,6,8,9],[2],[7]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,9,8,7,6,1]=>[9,2,3,4,5,1,6,7,8]=>[[1,3,4,5,7,8,9],[2],[6]]
[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]=>[9,2,3,1,4,5,6,7,8]=>[[1,3,5,6,7,8,9],[2],[4]]
[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]=>[9,2,1,3,4,5,6,7,8]=>[[1,4,5,6,7,8,9],[2],[3]]
[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]=>[9,3,2,4,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3],[9]]
[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]=>[9,4,3,2,5,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4],[9]]
[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]=>[9,1,3,4,5,6,7,8,2]=>[[1,3,4,5,6,7,8],[2],[9]]
[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]=>[9,1,3,2,4,5,6,7,8]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,4,7,3,8,2,9,1]=>[9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,6,9,8,7,4,3,2,1]=>[9,1,2,3,5,6,4,7,8]=>[[1,3,4,5,6,8,9],[2],[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]=>[9,1,2,3,5,4,6,7,8]=>[[1,3,4,5,7,8,9],[2],[6]]
[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]=>[9,1,2,3,4,5,7,8,6]=>[[1,3,4,5,6,7,8],[2],[9]]
[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]=>[9,1,2,3,4,5,7,6,8]=>[[1,3,4,5,6,7,9],[2],[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]=>[9,8,2,3,4,5,6,7,1]=>[[1,4,5,6,7,8],[2],[3],[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]=>[9,1,8,3,4,5,6,7,2]=>[[1,3,5,6,7,8],[2],[4],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>[9,1,2,8,4,5,6,7,3]=>[[1,3,4,6,7,8],[2],[5],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[9,1,2,3,8,5,6,7,4]=>[[1,3,4,5,7,8],[2],[6],[9]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>[9,1,2,3,4,8,6,7,5]=>[[1,3,4,5,6,8],[2],[7],[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]=>[9,1,2,3,4,5,8,7,6]=>[[1,3,4,5,6,7],[2],[8],[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]=>[9,1,2,3,4,5,6,8,7]=>[[1,3,4,5,6,7,8],[2],[9]]
[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]=>[9,1,2,3,4,5,6,7,8]=>[[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]=>[1,2,3,4,5,6,7,8,9]=>[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]=>[1,2,3,4,5,6,7,9,8]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9]]
[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]=>[1,2,3,4,5,9,7,8,6]=>[[1,2,3,4,5,6,8],[7],[9]]
[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]=>[1,2,3,4,9,6,7,8,5]=>[[1,2,3,4,5,7,8],[6],[9]]
[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]=>[1,2,3,9,5,6,7,8,4]=>[[1,2,3,4,6,7,8],[5],[9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[[1,2,3,5,6,7,8],[4],[9]]
[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]=>[1,9,3,4,5,6,7,8,2]=>[[1,2,4,5,6,7,8],[3],[9]]
[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]=>[1,2,3,4,5,6,7,8,10,9]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,7,8]=>[[1,2,3,4,5,6,7,9],[8]]
[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]=>[1,2,3,4,5,6,7,10,9,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[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]=>[1,2,3,4,5,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[[1,2,3,4,5,6,7,9],[8],[10]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,9,7,6,8,5]=>[[1,2,3,4,5,8],[6],[7],[9]]
[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]=>[1,2,3,4,5,10,7,8,9,6]=>[[1,2,3,4,5,6,8,9],[7],[10]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,9,4]=>[1,2,3,9,6,5,7,8,4]=>[[1,2,3,4,7,8],[5],[6],[9]]
[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]=>[1,2,3,4,10,6,7,8,9,5]=>[[1,2,3,4,5,7,8,9],[6],[10]]
[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]=>[1,2,9,5,4,6,7,8,3]=>[[1,2,3,6,7,8],[4],[5],[9]]
[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]=>[1,2,3,10,5,6,7,8,9,4]=>[[1,2,3,4,6,7,8,9],[5],[10]]
[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]=>[1,9,4,3,5,6,7,8,2]=>[[1,2,5,6,7,8],[3],[4],[9]]
[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]=>[1,2,10,4,5,6,7,8,9,3]=>[[1,2,3,5,6,7,8,9],[4],[10]]
[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]=>[1,10,3,4,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8,9],[3],[10]]
[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]=>[10,2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[[1,2,3,4,5,6,7,8,9,10,11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,10,8,9]=>[[1,2,3,4,5,6,7,8,10],[9]]
[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]=>[1,2,3,4,5,6,7,8,11,10,9]=>[[1,2,3,4,5,6,7,8,9],[10],[11]]
[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]=>[1,2,3,4,5,9,6,8,7]=>[[1,2,3,4,5,6,8],[7],[9]]
[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]=>[1,2,3,4,5,9,6,7,8]=>[[1,2,3,4,5,6,8,9],[7]]
[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]=>[10,3,2,4,5,6,7,8,9,1]=>[[1,4,5,6,7,8,9],[2],[3],[10]]
[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]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9,10],[2],[11]]
[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]=>[1,2,3,4,5,6,7,8,11,9,10]=>[[1,2,3,4,5,6,7,8,9,11],[10]]
[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]=>[1,2,3,4,5,6,10,7,8,9]=>[[1,2,3,4,5,6,7,9,10],[8]]
[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]=>[1,2,3,4,9,5,6,7,8]=>[[1,2,3,4,5,7,8,9],[6]]
[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]=>[1,2,3,4,5,10,6,7,8,9]=>[[1,2,3,4,5,6,8,9,10],[7]]
[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]=>[1,9,8,4,5,6,7,3,2]=>[[1,2,5,6,7],[3],[4],[8],[9]]
[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]=>[1,2,3,9,4,5,6,7,8]=>[[1,2,3,4,6,7,8,9],[5]]
[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]=>[1,2,3,4,10,5,6,7,8,9]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[[1,2,3,4,5,6,7,9],[8]]
[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]=>[1,2,3,4,5,7,6,8,9]=>[[1,2,3,4,5,6,8,9],[7]]
[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]=>[1,2,3,4,5,7,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[[1,2,3,4,5,7,8,9],[6]]
[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]=>[1,2,3,4,6,5,8,7,9]=>[[1,2,3,4,5,7,9],[6,8]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[[1,2,3,4,6,7,8,9],[5]]
[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]=>[1,2,3,5,4,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]
[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]=>[1,2,4,3,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]
[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]=>[1,2,4,3,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]
[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]=>[1,3,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]
[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]=>[1,3,2,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,9,7,8]=>[[1,2,4,5,6,7,9],[3,8]]
[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]=>[1,3,2,5,4,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]]
[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]=>[1,3,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]
[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]=>[1,4,2,3,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,7,6,5,4,3,2,8,9]=>[1,7,2,3,4,5,6,8,9]=>[[1,2,4,5,6,7,8,9],[3]]
[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]=>[1,7,2,3,4,5,6,9,8]=>[[1,2,4,5,6,7,8],[3,9]]
[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]=>[2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]
[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]=>[2,1,3,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[[1,3,4,5,6,7,9],[2,8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,9,8,7]=>[2,1,3,4,5,6,9,7,8]=>[[1,3,4,5,6,7,9],[2,8]]
[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]=>[2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]
[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]=>[2,1,4,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,7,6,5,4,3,9]=>[2,1,8,3,4,5,6,7,9]=>[[1,3,5,6,7,8,9],[2,4]]
[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]=>[3,1,2,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,7,9,8]=>[3,1,2,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]
[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]=>[3,1,2,5,4,7,6,9,8]=>[[1,3,4,6,8],[2,5,7,9]]
[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]=>[3,1,2,9,4,5,6,7,8]=>[[1,3,4,6,7,8,9],[2,5]]
[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]=>[4,1,2,3,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]
[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]=>[4,1,2,3,6,5,8,7,9]=>[[1,3,4,5,7,9],[2,6,8]]
[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]=>[4,1,2,3,9,5,6,7,8]=>[[1,3,4,5,7,8,9],[2,6]]
[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]=>[5,1,2,3,4,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]
[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]=>[5,1,2,3,4,7,6,8,9]=>[[1,3,4,5,6,8,9],[2,7]]
[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]=>[5,1,2,3,4,9,6,7,8]=>[[1,3,4,5,6,8,9],[2,7]]
[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]=>[6,1,2,3,4,5,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]
[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]=>[6,1,2,3,4,5,9,7,8]=>[[1,3,4,5,6,7,9],[2,8]]
[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]=>[1,2,3,4,5,6,7,9,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]
[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]=>[1,2,3,4,5,6,8,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]
[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]=>[1,2,3,4,5,6,8,7,10,9]=>[[1,2,3,4,5,6,7,9],[8,10]]
[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]=>[1,2,3,4,5,7,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]
[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]=>[1,2,3,4,6,5,7,8,9,10]=>[[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]=>[1,2,3,5,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]
[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]=>[1,2,3,5,4,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]
[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]=>[1,2,3,10,4,5,6,7,8,9]=>[[1,2,3,4,6,7,8,9,10],[5]]
[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]=>[1,2,4,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]
[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]=>[1,2,4,3,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]
[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]=>[1,3,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]
[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]=>[1,3,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]
[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]=>[2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[2,1,3,4,5,6,7,8,10,9]=>[[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]=>[2,1,4,3,5,6,7,8,9,10]=>[[1,3,5,6,7,8,9,10],[2,4]]
[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]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]
[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]=>[2,1,6,3,4,5,10,7,8,9]=>[[1,3,5,6,7,9,10],[2,4,8]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,8,3,4,5,6,7,10,9]=>[[1,3,5,6,7,8,9],[2,4,10]]
[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]=>[3,1,2,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[3,1,2,5,4,7,6,9,8,10]=>[[1,3,4,6,8,10],[2,5,7,9]]
[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]=>[3,1,2,10,4,5,6,7,8,9]=>[[1,3,4,6,7,8,9,10],[2,5]]
[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]=>[4,1,2,3,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[4,1,2,3,6,5,8,7,10,9]=>[[1,3,4,5,7,9],[2,6,8,10]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>[4,1,2,3,6,5,10,7,8,9]=>[[1,3,4,5,7,9,10],[2,6,8]]
[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]=>[4,1,2,3,8,5,6,7,10,9]=>[[1,3,4,5,7,8,9],[2,6,10]]
[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]=>[4,1,2,3,10,5,6,7,8,9]=>[[1,3,4,5,7,8,9,10],[2,6]]
[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]=>[5,1,2,3,4,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[5,1,2,3,4,10,6,7,8,9]=>[[1,3,4,5,6,8,9,10],[2,7]]
[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]=>[6,1,2,3,4,5,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[6,1,2,3,4,5,10,7,8,9]=>[[1,3,4,5,6,7,9,10],[2,8]]
[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]=>[7,1,2,3,4,5,6,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[7,1,2,3,4,5,6,10,8,9]=>[[1,3,4,5,6,7,8,10],[2,9]]
[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]=>[10,1,2,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9,10],[2]]
[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]=>[3,2,1,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]
[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]=>[4,2,3,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[1,3,4,6,7,8,9],[2],[5]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[1,3,4,5,7,8,9],[2],[6]]
[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]=>[7,2,3,4,5,6,1,8,9]=>[[1,3,4,5,6,8,9],[2],[7]]
[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]=>[8,2,3,4,5,6,7,1,9]=>[[1,3,4,5,6,7,9],[2],[8]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[1,3,4,5,6,7,8,10],[2],[9]]
[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]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>[10,2,3,4,5,6,7,8,1,9]=>[[1,3,4,5,6,7,8,10],[2],[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]=>[10,1,2,3,4,5,6,9,8,7]=>[[1,3,4,5,6,7,8],[2],[9],[10]]
[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]=>[1,3,2,4,5,6,9,8,7]=>[[1,2,4,5,6,7],[3,8],[9]]
[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]=>[10,2,1,3,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[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]=>[10,9,2,3,4,5,6,7,8,1]=>[[1,4,5,6,7,8,9],[2],[3],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,10,2,3,4,5,6,7,8,9,1]=>[[1,4,5,6,7,8,9,10],[2],[3],[11]]
[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]=>[4,3,2,1,5,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]
[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]=>[10,1,2,3,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[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]=>[10,1,2,3,4,6,5,7,8,9]=>[[1,3,4,5,6,8,9,10],[2],[7]]
[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]=>[10,1,2,3,5,4,6,7,8,9]=>[[1,3,4,5,7,8,9,10],[2],[6]]
[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]=>[7,2,3,4,5,6,1,9,8]=>[[1,3,4,5,6,8],[2,9],[7]]
[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]=>[2,1,9,4,5,6,7,8,3]=>[[1,3,5,6,7,8],[2,4],[9]]
[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]=>[10,2,3,4,5,6,7,1,8,9]=>[[1,3,4,5,6,7,9,10],[2],[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]=>[6,1,2,3,4,5,9,8,7]=>[[1,3,4,5,6,7],[2,8],[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]=>[10,1,9,3,4,5,6,7,8,2]=>[[1,3,5,6,7,8,9],[2],[4],[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]=>[10,1,2,9,4,5,6,7,8,3]=>[[1,3,4,6,7,8,9],[2],[5],[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]=>[10,1,2,3,9,5,6,7,8,4]=>[[1,3,4,5,7,8,9],[2],[6],[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]=>[10,1,2,3,4,9,6,7,8,5]=>[[1,3,4,5,6,8,9],[2],[7],[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]=>[10,1,2,3,4,5,9,7,8,6]=>[[1,3,4,5,6,7,9],[2],[8],[10]]
[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]=>[3,2,1,5,4,6,7,8,9]=>[[1,4,6,7,8,9],[2,5],[3]]
[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]=>[3,2,1,5,4,7,6,9,8]=>[[1,4,6,8],[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]=>[3,2,1,5,4,7,6,9,8,10]=>[[1,4,6,8,10],[2,5,7,9],[3]]
[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]=>[10,1,3,4,5,6,7,8,9,2]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[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]=>[11,2,3,4,5,6,7,8,9,1,10]=>[[1,3,4,5,6,7,8,9,11],[2],[10]]
[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]=>[11,1,3,4,5,6,7,8,9,10,2]=>[[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,4,7,3,9,10,8,2]=>[1,10,7,6,5,4,3,2,9,8]=>[[1,2,9],[3,10],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,7,5,8,4,9,3,10,2]=>[1,10,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,8,6,9,5,10,4]=>[3,2,1,10,9,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8],[9],[10]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1,8,9,7,10,6]=>[5,4,3,2,1,10,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,3,6,2,7,1,9,10,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,7,8,6,9,5,10,4,11,3,12,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,8,9,7,10,6,11,5,12,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8],[9],[10],[11],[12]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,4,2,5,1,9,10,8,11,7,12,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5,10],[11],[12]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1,10,11,9,12,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[[1,8],[2,9],[3,10],[4,11],[5,12],[6],[7]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,6,4,7,3,8,2,9,1,11,12,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[1,10],[2,11],[3,12],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,9,10,8,7,6,5,4,3,1]=>[10,2,1,3,4,5,6,7,9,8]=>[[1,4,5,6,7,8,9],[2,10],[3]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,10,9,8,7,6,5,4,3,1]=>[11,2,1,3,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10,11],[2],[3]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,12,11,10,9,8,7,6,5,4,3,1]=>[12,2,1,3,4,5,6,7,8,9,10,11]=>[[1,4,5,6,7,8,9,10,11,12],[2],[3]]
[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]=>[1,2,9,4,3,5,6,7,8]=>[[1,2,3,6,7,8,9],[4],[5]]
[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]=>[1,2,3,9,5,4,6,7,8]=>[[1,2,3,4,7,8,9],[5],[6]]
[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]=>[1,2,3,4,9,6,5,7,8]=>[[1,2,3,4,5,8,9],[6],[7]]
[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]=>[1,2,3,4,5,9,7,6,8]=>[[1,2,3,4,5,6,9],[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]=>[1,4,3,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[[1,2,3,4,5,6,7,8,9,11],[10]]
[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]=>[5,4,3,2,1,6,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[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]=>[10,1,2,3,4,6,7,8,9,5]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[1,3,2,5,4,7,6,9,8,11,10]=>[[1,2,4,6,8,10],[3,5,7,9,11]]
[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]=>[4,1,3,2,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,6,8,10],[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]=>[4,3,2,1,6,5,8,7,9]=>[[1,5,7,9],[2,6,8],[3],[4]]
[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]=>[4,3,2,1,6,5,8,7,10,9]=>[[1,5,7,9],[2,6,8,10],[3],[4]]
[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]=>[2,1,4,3,6,5,10,9,8,7]=>[[1,3,5,7],[2,4,6,8],[9],[10]]
[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]=>[1,3,2,5,4,7,6,10,9,8]=>[[1,2,4,6,8],[3,5,7,9],[10]]
[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]=>[4,3,2,1,5,6,7,8,9,10]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10,11,12]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[[1,3,4,5,6,7,8,9,10,11,12],[2]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[[1,7,9],[2,8,10],[3],[4],[5],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,8,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[[1,5,9],[2,6,10],[3,7],[4,8]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,8,7,9,6,10,5]=>[2,1,4,3,10,9,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8],[9],[10]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,8,7,9,6,10,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,8,5,9,4,10,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,9,8,10,7]=>[6,5,4,3,2,1,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,9,8,10,7]=>[2,1,6,5,4,3,10,9,8,7]=>[[1,3,7],[2,4,8],[5,9],[6,10]]
[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]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,1,2,3,4,5,6,7,8,9,12,11]=>[[1,3,4,5,6,7,8,9,10,11],[2,12]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,4,6,3,7,2,8,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,5,7,4,8,3,9,2]=>[1,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,7,8,9,10,6,5,4,3]=>[2,1,10,3,4,5,7,8,9,6]=>[[1,3,5,6,7,8,9],[2,4],[10]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,6,5,9,10,8,7]=>[4,1,3,2,6,5,10,7,9,8]=>[[1,3,5,7,9],[2,6,8],[4,10]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,4,7,3,8,2,10,9,1]=>[10,8,7,6,5,4,3,2,1,9]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,3,6,2,7,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
Map
to 312-avoiding permutation
Description
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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.
searching the database
Sorry, this map was not found in the database.