Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
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]=>[2,1]=>[2,1]=>[[1],[2]]
[1,1,0,0]=>[1,2]=>[1,2]=>[[1,2]]
[1,0,1,0,1,0]=>[2,3,1]=>[3,2,1]=>[[1],[2],[3]]
[1,0,1,1,0,0]=>[2,1,3]=>[2,1,3]=>[[1,3],[2]]
[1,1,0,0,1,0]=>[1,3,2]=>[1,3,2]=>[[1,2],[3]]
[1,1,0,1,0,0]=>[3,1,2]=>[2,3,1]=>[[1,2],[3]]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[[1,2,3]]
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[4,2,3,1]=>[[1,3],[2],[4]]
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[[1,4],[2],[3]]
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[[1,3],[2,4]]
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>[3,2,4,1]=>[[1,3],[2],[4]]
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[[1,3,4],[2]]
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[1,4,3,2]=>[[1,2],[3],[4]]
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[[1,2,4],[3]]
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>[3,4,1,2]=>[[1,2],[3,4]]
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>[2,4,3,1]=>[[1,2],[3],[4]]
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>[2,3,1,4]=>[[1,2,4],[3]]
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[1,2,4,3]=>[[1,2,3],[4]]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[1,3,4,2]=>[[1,2,3],[4]]
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>[2,3,4,1]=>[[1,2,3],[4]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[[1,2,3,4]]
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[1,3,4],[2],[5]]
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[1,3,5],[2],[4]]
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[1,4],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>[4,2,3,5,1]=>[[1,3,4],[2],[5]]
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[1,3],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[1,3,5],[2,4]]
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[1,3],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>[3,2,5,4,1]=>[[1,3],[2,4],[5]]
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>[3,2,4,1,5]=>[[1,3,5],[2],[4]]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[1,3,4],[2,5]]
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>[2,1,4,5,3]=>[[1,3,4],[2,5]]
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>[3,2,4,5,1]=>[[1,3,4],[2],[5]]
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[[1,2,4],[3],[5]]
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[[1,2,5],[3],[4]]
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[[1,2,4],[3,5]]
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>[1,4,3,5,2]=>[[1,2,4],[3],[5]]
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[[1,2,4,5],[3]]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[1,2],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[1,2,5],[3,4]]
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[1,2],[3,5],[4]]
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[[1,2,4],[3],[5]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[1,2,5],[3],[4]]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>[2,3,1,5,4]=>[[1,2,4],[3,5]]
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>[3,4,1,5,2]=>[[1,2,4],[3,5]]
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>[2,4,3,5,1]=>[[1,2,4],[3],[5]]
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[1,2,4,5],[3]]
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[[1,2,3],[4],[5]]
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[[1,2,3,5],[4]]
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[[1,2,3],[4,5]]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>[1,3,5,4,2]=>[[1,2,3],[4],[5]]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>[1,3,4,2,5]=>[[1,2,3,5],[4]]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>[2,4,5,1,3]=>[[1,2,3],[4,5]]
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>[4,3,5,1,2]=>[[1,3],[2,5],[4]]
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[1,2,3],[4],[5]]
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[1,2,3,5],[4]]
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[[1,2,3,4],[5]]
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>[1,2,4,5,3]=>[[1,2,3,4],[5]]
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>[1,3,4,5,2]=>[[1,2,3,4],[5]]
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[1,2,3,4],[5]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[[1,2,3,4,5]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[1,3,5],[2,6],[4]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>[5,2,3,4,6,1]=>[[1,3,4,5],[2],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[1,4,6],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[1,3,4],[2,6],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>[4,2,3,6,5,1]=>[[1,3,4],[2,5],[6]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[4,2,3,5,1,6]=>[[1,3,4,6],[2],[5]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[1,4,5],[2,6],[3]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>[3,2,1,5,6,4]=>[[1,4,5],[2,6],[3]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>[4,2,3,5,6,1]=>[[1,3,4,5],[2],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[1,3,5],[2,4],[6]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[1,3,6],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>[2,1,5,4,6,3]=>[[1,3,5],[2,4],[6]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[1,3,5,6],[2,4]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[1,3],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[1,3,6],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[1,3],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>[3,2,6,4,5,1]=>[[1,3,5],[2,4],[6]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[3,2,5,4,1,6]=>[[1,3,6],[2,4],[5]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>[3,2,4,1,6,5]=>[[1,3,5],[2,6],[4]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>[4,2,5,1,6,3]=>[[1,3,5],[2,6],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[[1,3,5],[2,4],[6]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>[[1,3,5,6],[2],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[1,3,4],[2,5],[6]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[1,3,4,6],[2,5]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[1,3,4],[2,5,6]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>[2,1,4,6,5,3]=>[[1,3,4],[2,5],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>[[1,3,4,6],[2,5]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>[3,2,5,6,1,4]=>[[1,3,4],[2,6],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>[5,2,4,6,1,3]=>[[1,3,4],[2,6],[5]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[[1,3,4],[2,5],[6]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>[[1,3,4,6],[2],[5]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[1,3,4,5],[2,6]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>[2,1,3,5,6,4]=>[[1,3,4,5],[2,6]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>[[1,3,4,5],[2,6]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>[[1,3,4,5],[2],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[[1,2,4,5],[3],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[[1,2,4,6],[3],[5]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[[1,2,5],[3,6],[4]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>[[1,2,4,5],[3],[6]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[[1,2,5,6],[3],[4]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[[1,2,4],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[[1,2,4,6],[3,5]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[[1,2,4],[3,6],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>[[1,2,4],[3,5],[6]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>[[1,2,4,6],[3],[5]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[[1,2,4,5],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>[[1,2,4,5],[3,6]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>[[1,2,4,5],[3],[6]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[[1,2,4,5,6],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[1,2,5],[3,4],[6]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[1,2,6],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[1,2,5],[3,4,6]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>[3,5,1,4,6,2]=>[[1,2,5],[3,4],[6]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[1,2,5,6],[3,4]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[1,2],[3,5],[4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[1,2,6],[3,5],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[1,2],[3,4],[5,6]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[[1,2,4,5],[3],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>[[1,2,4,6],[3],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>[2,4,3,1,6,5]=>[[1,2,5],[3,6],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>[4,5,3,1,6,2]=>[[1,2,5],[3,6],[4]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[[1,2,4,5],[3],[6]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[1,2,5,6],[3],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>[2,3,1,6,5,4]=>[[1,2,4],[3,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>[2,3,1,5,4,6]=>[[1,2,4,6],[3,5]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[1,2,4],[3,5,6]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>[3,4,1,6,5,2]=>[[1,2,4],[3,5],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>[3,4,1,5,2,6]=>[[1,2,4,6],[3,5]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>[2,5,3,6,1,4]=>[[1,2,4],[3,6],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>[5,4,3,6,1,2]=>[[1,4],[2,6],[3],[5]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[[1,2,4],[3,5],[6]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>[[1,2,4,6],[3],[5]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>[2,3,1,4,6,5]=>[[1,2,4,5],[3,6]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>[2,3,1,5,6,4]=>[[1,2,4,5],[3,6]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>[3,4,1,5,6,2]=>[[1,2,4,5],[3,6]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>[[1,2,4,5],[3],[6]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[1,2,4,5,6],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[[1,2,3,5],[4],[6]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[[1,2,3,6],[4],[5]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>[[1,2,3,5],[4],[6]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[[1,2,3,5,6],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[[1,2,3],[4,5],[6]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[[1,2,3,6],[4,5]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[[1,2,3],[4,6],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>[[1,2,3,5],[4],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>[[1,2,3,6],[4],[5]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>[[1,2,3,5],[4,6]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>[[1,2,3,5],[4,6]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>[[1,2,3,5],[4],[6]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>[[1,2,3,5,6],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>[2,4,6,1,5,3]=>[[1,2,3],[4,5],[6]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>[2,4,5,1,3,6]=>[[1,2,3,6],[4,5]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>[4,3,6,1,5,2]=>[[1,3],[2,5],[4,6]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>[4,3,5,1,2,6]=>[[1,3,6],[2,5],[4]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>[2,5,6,4,1,3]=>[[1,2,3],[4,6],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>[5,3,6,4,1,2]=>[[1,3],[2,4],[5,6]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[1,2,3,5],[4],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[1,2,3,6],[4],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>[2,3,4,1,6,5]=>[[1,2,3,5],[4,6]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>[2,4,5,1,6,3]=>[[1,2,3,5],[4,6]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>[4,3,5,1,6,2]=>[[1,3,5],[2,6],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>[[1,2,3,5],[4],[6]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[1,2,3,5,6],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[[1,2,3,4],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[[1,2,3,4,6],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[[1,2,3,4],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>[[1,2,3,4],[5],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>[[1,2,3,4,6],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>[[1,2,3,4],[5,6]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>[[1,2,4],[3,6],[5]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>[[1,2,3,4],[5],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>[[1,2,3,4,6],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>[2,3,5,6,1,4]=>[[1,2,3,4],[5,6]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>[2,5,4,6,1,3]=>[[1,2,4],[3,6],[5]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>[5,3,4,6,1,2]=>[[1,3,4],[2,6],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[1,2,3,4],[5],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[1,2,3,4,6],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>[[1,2,3,4,5],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>[[1,2,3,4,5],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>[[1,2,3,4,5],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[1,2,3,4,5],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>[6,2,3,4,5,7,1]=>[[1,3,4,5,6],[2],[7]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[1,3,4,5],[2,7],[6]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>[5,2,3,4,7,6,1]=>[[1,3,4,5],[2,6],[7]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>[5,2,3,4,6,1,7]=>[[1,3,4,5,7],[2],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,6,7,5]=>[[1,3,5,6],[2,7],[4]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>[5,2,3,4,6,7,1]=>[[1,3,4,5,6],[2],[7]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[1,4,6],[2,5],[3,7]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,6,5,7,4]=>[[1,4,6],[2,5],[3,7]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[1,3,4],[2,6],[5,7]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[1,3,4,7],[2,6],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[1,3,4],[2,5],[6,7]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>[4,2,3,7,5,6,1]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>[4,2,3,6,5,1,7]=>[[1,3,4,7],[2,5],[6]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>[4,2,3,5,1,7,6]=>[[1,3,4,6],[2,7],[5]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,6,1,7,4]=>[[1,3,4,6],[2,7],[5]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>[4,2,3,6,5,7,1]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>[4,2,3,5,1,6,7]=>[[1,3,4,6,7],[2],[5]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[1,4,5],[2,6],[3,7]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[1,4,5],[2,6,7],[3]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,5,7,6,4]=>[[1,4,5],[2,6],[3,7]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>[3,2,1,5,6,4,7]=>[[1,4,5,7],[2,6],[3]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>[4,2,3,6,7,1,5]=>[[1,3,4,5],[2,7],[6]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,5,7,1,4]=>[[1,3,4,5],[2,7],[6]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>[4,2,3,5,7,6,1]=>[[1,3,4,5],[2,6],[7]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>[4,2,3,5,6,1,7]=>[[1,3,4,5,7],[2],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,6,7,5]=>[[1,4,5,6],[2,7],[3]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,5,6,7,4]=>[[1,4,5,6],[2,7],[3]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>[4,2,3,5,6,7,1]=>[[1,3,4,5,6],[2],[7]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[1,3,5,6],[2,4],[7]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[1,3,5,7],[2,4],[6]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[1,3,6],[2,4,7],[5]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>[2,1,6,4,5,7,3]=>[[1,3,5,6],[2,4],[7]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[1,3,5],[2,4,6],[7]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[1,3,5],[2,4,7],[6]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>[2,1,5,4,7,6,3]=>[[1,3,5],[2,4,6],[7]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>[2,1,5,4,6,3,7]=>[[1,3,5,7],[2,4],[6]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,6,7,5]=>[[1,3,5,6],[2,4,7]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>[2,1,5,4,6,7,3]=>[[1,3,5,6],[2,4],[7]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[1,3,6],[2,5],[4,7]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[1,3,7],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[1,3,6],[2,5,7],[4]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>[4,2,6,1,5,7,3]=>[[1,3,6],[2,5],[4,7]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[1,3,6,7],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[1,3,6],[2,4],[5,7]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[1,3,7],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[1,3,5],[2,4],[6,7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>[3,2,7,4,5,6,1]=>[[1,3,5,6],[2,4],[7]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>[3,2,6,4,5,1,7]=>[[1,3,5,7],[2,4],[6]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>[3,2,5,4,1,7,6]=>[[1,3,6],[2,4,7],[5]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>[5,2,6,4,1,7,3]=>[[1,3,6],[2,4],[5,7]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>[3,2,6,4,5,7,1]=>[[1,3,5,6],[2,4],[7]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>[3,2,5,4,1,6,7]=>[[1,3,6,7],[2,4],[5]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>[3,2,4,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[3,2,4,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[1,3,5],[2,6,7],[4]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>[4,2,5,1,7,6,3]=>[[1,3,5],[2,6],[4,7]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>[4,2,5,1,6,3,7]=>[[1,3,5,7],[2,6],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>[3,2,6,4,7,1,5]=>[[1,3,5],[2,4,7],[6]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>[6,2,5,4,7,1,3]=>[[1,3,5],[2,7],[4],[6]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>[3,2,5,4,7,6,1]=>[[1,3,5],[2,4,6],[7]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>[[1,3,5,7],[2,4],[6]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>[3,2,4,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>[3,2,4,1,6,7,5]=>[[1,3,5,6],[2,7],[4]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>[4,2,5,1,6,7,3]=>[[1,3,5,6],[2,7],[4]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>[[1,3,5,6],[2,4],[7]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>[2,1,3,6,5,7,4]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[1,3,4,6,7],[2,5]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[1,3,4],[2,5,6],[7]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[1,3,4,7],[2,5,6]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[1,3,4],[2,5,7],[6]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>[2,1,4,7,5,6,3]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>[2,1,4,6,5,3,7]=>[[1,3,4,7],[2,5],[6]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>[2,1,4,5,3,7,6]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>[2,1,5,6,3,7,4]=>[[1,3,4,6],[2,5,7]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>[2,1,4,6,5,7,3]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>[2,1,4,5,3,6,7]=>[[1,3,4,6,7],[2,5]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>[3,2,5,7,1,6,4]=>[[1,3,4],[2,6],[5,7]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[3,2,5,6,1,4,7]=>[[1,3,4,7],[2,6],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[1,3,4],[2,6,7],[5]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>[5,2,4,7,1,6,3]=>[[1,3,4],[2,6],[5,7]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>[5,2,4,6,1,3,7]=>[[1,3,4,7],[2,6],[5]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>[3,2,6,7,5,1,4]=>[[1,3,4],[2,5],[6,7]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>[6,2,4,7,5,1,3]=>[[1,3,4],[2,5],[6,7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>[3,2,4,7,5,6,1]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>[[1,3,4,7],[2,5],[6]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>[3,2,4,5,1,7,6]=>[[1,3,4,6],[2,7],[5]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>[3,2,5,6,1,7,4]=>[[1,3,4,6],[2,7],[5]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>[5,2,4,6,1,7,3]=>[[1,3,4,6],[2,7],[5]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>[[1,3,4,6],[2,5],[7]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[[1,3,4,6,7],[2],[5]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[1,3,4,5],[2,6],[7]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[1,3,4,5],[2,6,7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>[2,1,3,5,7,6,4]=>[[1,3,4,5],[2,6],[7]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>[2,1,3,5,6,4,7]=>[[1,3,4,5,7],[2,6]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>[2,1,4,6,7,3,5]=>[[1,3,4,5],[2,6,7]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>[2,1,6,5,7,3,4]=>[[1,3,5],[2,4,7],[6]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>[2,1,4,5,7,6,3]=>[[1,3,4,5],[2,6],[7]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>[2,1,4,5,6,3,7]=>[[1,3,4,5,7],[2,6]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>[3,2,4,6,7,1,5]=>[[1,3,4,5],[2,7],[6]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>[3,2,6,5,7,1,4]=>[[1,3,5],[2,4],[6,7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>[6,2,4,5,7,1,3]=>[[1,3,4,5],[2,7],[6]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>[[1,3,4,5],[2,6],[7]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[[1,3,4,5,7],[2],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,6,7,5]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>[2,1,3,5,6,7,4]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>[2,1,4,5,6,7,3]=>[[1,3,4,5,6],[2,7]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[[1,3,4,5,6],[2],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[[1,2,4,6],[3,7],[5]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[[1,2,4,6,7],[3],[5]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[[1,2,5,7],[3,6],[4]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[[1,2,4,5],[3,7],[6]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>[[1,2,4,5,7],[3],[6]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[[1,2,4,7],[3,6],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[[1,2,4],[3,5],[6,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>[[1,2,4,7],[3,5],[6]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>[[1,2,4,6],[3,7],[5]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>[[1,2,4,6],[3,7],[5]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>[[1,2,4,6,7],[3],[5]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[[1,2,4,5],[3,6,7]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>[[1,2,4,5,7],[3,6]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>[[1,2,4,5],[3,7],[6]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>[[1,2,4,5],[3,7],[6]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>[[1,2,4,5,7],[3],[6]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>[[1,2,4,5,6],[3,7]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>[[1,2,4,5,6],[3,7]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[1,2,5,7],[3,4],[6]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[1,2,6],[3,4,7],[5]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>[3,6,1,4,5,7,2]=>[[1,2,5,6],[3,4],[7]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[1,2,6,7],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[1,2,5],[3,4,6],[7]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[1,2,5,7],[3,4,6]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>[3,5,1,4,7,6,2]=>[[1,2,5],[3,4,6],[7]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>[3,5,1,4,6,2,7]=>[[1,2,5,7],[3,4],[6]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[1,2,5,6],[3,4,7]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,6,7,5]=>[[1,2,5,6],[3,4,7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>[3,5,1,4,6,7,2]=>[[1,2,5,6],[3,4],[7]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[1,2,6],[3,5],[4,7]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[1,2,7],[3,5],[4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[1,2,6],[3,5,7],[4]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>[4,6,3,1,5,7,2]=>[[1,2,6],[3,5],[4,7]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[1,2,6],[3,4],[5,7]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[1,2,7],[3,4],[5,6]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[1,2,5],[3,4],[6,7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>[[1,2,4,5,7],[3],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>[2,5,3,4,1,7,6]=>[[1,2,4,6],[3,7],[5]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>[5,6,3,4,1,7,2]=>[[1,2,6],[3,4],[5,7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>[2,6,3,4,5,7,1]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>[[1,2,4,6,7],[3],[5]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>[2,4,3,1,7,6,5]=>[[1,2,5],[3,6],[4,7]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[2,4,3,1,6,5,7]=>[[1,2,5,7],[3,6],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[1,2,5],[3,6,7],[4]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>[4,5,3,1,7,6,2]=>[[1,2,5],[3,6],[4,7]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>[4,5,3,1,6,2,7]=>[[1,2,5,7],[3,6],[4]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>[2,6,3,4,7,1,5]=>[[1,2,4,5],[3,7],[6]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>[6,5,3,4,7,1,2]=>[[1,4,5],[2,7],[3],[6]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>[2,5,3,4,7,6,1]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>[[1,2,4,5,7],[3],[6]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>[2,4,3,1,5,7,6]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>[2,4,3,1,6,7,5]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>[4,5,3,1,6,7,2]=>[[1,2,5,6],[3,7],[4]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[1,2,5,6,7],[3],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>[2,3,1,7,5,6,4]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>[2,3,1,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[2,3,1,5,4,7,6]=>[[1,2,4,6],[3,5,7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>[2,3,1,6,5,7,4]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>[2,3,1,5,4,6,7]=>[[1,2,4,6,7],[3,5]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[1,2,4],[3,5,6],[7]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[1,2,4,7],[3,5,6]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[1,2,4],[3,5,7],[6]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>[3,4,1,7,5,6,2]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>[3,4,1,6,5,2,7]=>[[1,2,4,7],[3,5],[6]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>[3,4,1,5,2,7,6]=>[[1,2,4,6],[3,5,7]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>[3,5,1,6,2,7,4]=>[[1,2,4,6],[3,5,7]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>[3,4,1,6,5,7,2]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>[3,4,1,5,2,6,7]=>[[1,2,4,6,7],[3,5]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>[2,5,3,7,1,6,4]=>[[1,2,4],[3,6],[5,7]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[2,5,3,6,1,4,7]=>[[1,2,4,7],[3,6],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[1,2,4],[3,6,7],[5]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>[5,4,3,7,1,6,2]=>[[1,4],[2,6],[3,7],[5]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>[5,4,3,6,1,2,7]=>[[1,4,7],[2,6],[3],[5]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>[2,6,3,7,5,1,4]=>[[1,2,4],[3,5],[6,7]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>[6,4,3,7,5,1,2]=>[[1,4],[2,5],[3,7],[6]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>[2,4,3,7,5,6,1]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>[[1,2,4,7],[3,5],[6]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>[2,4,3,5,1,7,6]=>[[1,2,4,6],[3,7],[5]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>[2,5,3,6,1,7,4]=>[[1,2,4,6],[3,7],[5]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>[5,4,3,6,1,7,2]=>[[1,4,6],[2,7],[3],[5]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>[[1,2,4,6],[3,5],[7]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>[[1,2,4,6,7],[3],[5]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>[2,3,1,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>[2,3,1,4,6,5,7]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[2,3,1,6,7,4,5]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>[2,3,1,5,7,6,4]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>[2,3,1,5,6,4,7]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>[3,4,1,6,7,2,5]=>[[1,2,4,5],[3,6,7]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>[3,6,1,5,7,2,4]=>[[1,2,5],[3,4,7],[6]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>[3,4,1,5,7,6,2]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>[3,4,1,5,6,2,7]=>[[1,2,4,5,7],[3,6]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>[2,4,3,6,7,1,5]=>[[1,2,4,5],[3,7],[6]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>[2,6,3,5,7,1,4]=>[[1,2,4,5],[3,7],[6]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>[6,4,3,5,7,1,2]=>[[1,4,5],[2,7],[3],[6]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>[[1,2,4,5],[3,6],[7]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>[[1,2,4,5,7],[3],[6]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[2,3,1,4,5,7,6]=>[[1,2,4,5,6],[3,7]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>[2,3,1,4,6,7,5]=>[[1,2,4,5,6],[3,7]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>[2,3,1,5,6,7,4]=>[[1,2,4,5,6],[3,7]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>[3,4,1,5,6,7,2]=>[[1,2,4,5,6],[3,7]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>[[1,2,4,5,6],[3],[7]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[1,2,4,5,6,7],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[[1,2,3,5,7],[4],[6]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[[1,2,3,6],[4,7],[5]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[[1,2,3,5],[4,7],[6]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>[[1,2,3,5,7],[4],[6]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[[1,2,3,6],[4,5,7]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>[[1,2,3,6],[4,5],[7]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[[1,2,3,6,7],[4,5]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[[1,2,3],[4,6],[5,7]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[[1,2,3,7],[4,6],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>[[1,2,3,5,7],[4],[6]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>[[1,2,3,6],[4,7],[5]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>[[1,2,3,6],[4,7],[5]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>[[1,2,3,6,7],[4],[5]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>[[1,2,3,5,7],[4,6]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[[1,2,3,5],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>[[1,2,3,5,7],[4,6]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>[[1,2,3,5],[4,7],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>[[1,2,5],[3,7],[4],[6]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>[[1,2,3,5,7],[4],[6]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>[[1,2,3,5,6,7],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>[2,4,7,1,5,6,3]=>[[1,2,3,6],[4,5],[7]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>[2,4,6,1,5,3,7]=>[[1,2,3,7],[4,5],[6]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[2,4,5,1,3,7,6]=>[[1,2,3,6],[4,5,7]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>[2,4,6,1,5,7,3]=>[[1,2,3,6],[4,5],[7]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>[2,4,5,1,3,6,7]=>[[1,2,3,6,7],[4,5]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[1,2,3],[4,5,6],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[1,2,3],[4,5,7],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>[4,3,7,1,5,6,2]=>[[1,3,6],[2,5],[4,7]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>[4,3,6,1,5,2,7]=>[[1,3,7],[2,5],[4,6]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>[4,3,5,1,2,7,6]=>[[1,3,6],[2,5,7],[4]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>[4,5,6,1,2,7,3]=>[[1,2,3,6],[4,5,7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>[4,3,6,1,5,7,2]=>[[1,3,6],[2,5],[4,7]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>[4,3,5,1,2,6,7]=>[[1,3,6,7],[2,5],[4]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>[2,5,7,4,1,6,3]=>[[1,2,3],[4,6],[5,7]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[2,5,6,4,1,3,7]=>[[1,2,3,7],[4,6],[5]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>[5,3,7,4,1,6,2]=>[[1,3,6],[2,4],[5,7]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>[5,3,6,4,1,2,7]=>[[1,3,7],[2,4],[5,6]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>[2,6,7,4,5,1,3]=>[[1,2,3],[4,5],[6,7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>[6,3,7,4,5,1,2]=>[[1,3,5],[2,4],[6,7]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[1,2,3,5,7],[4],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>[2,3,5,4,1,7,6]=>[[1,2,3,6],[4,7],[5]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>[2,5,6,4,1,7,3]=>[[1,2,3,6],[4,7],[5]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>[5,3,6,4,1,7,2]=>[[1,3,6],[2,4],[5,7]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[1,2,3,6,7],[4],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>[2,3,4,1,7,6,5]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>[2,3,4,1,6,5,7]=>[[1,2,3,5,7],[4,6]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[2,4,6,1,7,3,5]=>[[1,2,3,5],[4,6,7]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>[2,4,5,1,7,6,3]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>[2,4,5,1,6,3,7]=>[[1,2,3,5,7],[4,6]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>[4,3,6,1,7,2,5]=>[[1,3,5],[2,6,7],[4]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>[4,6,5,1,7,2,3]=>[[1,2,5],[3,6,7],[4]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>[4,3,5,1,7,6,2]=>[[1,3,5],[2,6],[4,7]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>[4,3,5,1,6,2,7]=>[[1,3,5,7],[2,6],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>[2,3,6,4,7,1,5]=>[[1,2,3,5],[4,7],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>[2,6,5,4,7,1,3]=>[[1,2,5],[3,7],[4],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>[6,3,5,4,7,1,2]=>[[1,3,5],[2,7],[4],[6]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>[[1,2,3,5],[4,6],[7]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>[[1,2,3,5,7],[4],[6]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[2,3,4,1,5,7,6]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>[2,3,4,1,6,7,5]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>[2,4,5,1,6,7,3]=>[[1,2,3,5,6],[4,7]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>[4,3,5,1,6,7,2]=>[[1,3,5,6],[2,7],[4]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>[[1,2,3,5,6],[4],[7]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[1,2,3,5,6,7],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[[1,2,3,4,7],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[[1,2,3,4],[5,6],[7]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[[1,2,3,4,7],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[[1,2,3,4],[5,7],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>[[1,2,3,4,7],[5],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>[[1,2,3,4,6],[5,7]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>[[1,2,3,4,6],[5,7]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>[[1,2,3,4,6,7],[5]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>[[1,2,3,4],[5,6],[7]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>[[1,2,3,4,7],[5,6]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>[[1,2,4],[3,6],[5,7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>[[1,2,4,7],[3,6],[5]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>[[1,2,3,4],[5,7],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>[[1,2,4],[3,5],[6,7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>[[1,2,3,4,7],[5],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>[[1,2,3,4,6],[5,7]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>[[1,2,3,4,6],[5,7]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>[[1,2,4,6],[3,7],[5]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>[[1,2,3,4,6,7],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>[2,3,5,7,1,6,4]=>[[1,2,3,4],[5,6],[7]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>[2,3,5,6,1,4,7]=>[[1,2,3,4,7],[5,6]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[2,5,6,7,1,3,4]=>[[1,2,3,4],[5,6,7]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>[2,5,4,7,1,6,3]=>[[1,2,4],[3,6],[5,7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>[2,5,4,6,1,3,7]=>[[1,2,4,7],[3,6],[5]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>[5,3,6,7,1,2,4]=>[[1,3,4],[2,6,7],[5]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>[5,6,4,7,1,2,3]=>[[1,2,4],[3,6,7],[5]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>[5,3,4,7,1,6,2]=>[[1,3,4],[2,6],[5,7]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>[5,3,4,6,1,2,7]=>[[1,3,4,7],[2,6],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>[2,3,6,7,5,1,4]=>[[1,2,3,4],[5,7],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>[2,6,4,7,5,1,3]=>[[1,2,4],[3,5],[6,7]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>[6,3,4,7,5,1,2]=>[[1,3,4],[2,5],[6,7]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[1,2,3,4,7],[5],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[2,3,4,5,1,7,6]=>[[1,2,3,4,6],[5,7]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>[2,3,5,6,1,7,4]=>[[1,2,3,4,6],[5,7]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>[2,5,4,6,1,7,3]=>[[1,2,4,6],[3,7],[5]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>[5,3,4,6,1,7,2]=>[[1,3,4,6],[2,7],[5]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>[[1,2,3,4,6],[5],[7]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[1,2,3,4,6,7],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[[1,2,3,4,5],[6,7]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>[[1,2,3,4,5],[6],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>[[1,2,3,4,5,7],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>[[1,2,3,4,5],[6,7]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>[[1,2,3,5],[4,7],[6]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>[[1,2,3,4,5],[6],[7]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>[[1,2,3,4,5,7],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>[[1,2,3,4,5],[6,7]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>[[1,2,3,5],[4,7],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>[[1,2,4,5],[3,7],[6]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>[[1,2,3,4,5],[6],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>[[1,2,3,4,5,7],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[2,3,4,6,7,1,5]=>[[1,2,3,4,5],[6,7]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>[2,3,6,5,7,1,4]=>[[1,2,3,5],[4,7],[6]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>[2,6,4,5,7,1,3]=>[[1,2,4,5],[3,7],[6]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>[6,3,4,5,7,1,2]=>[[1,3,4,5],[2,7],[6]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[1,2,3,4,5],[6],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[[1,2,3,4,5,7],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>[[1,2,3,4,5,6],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>[[1,2,3,4,5,6],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>[[1,2,3,4,5,6],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>[[1,2,3,4,5,6],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[1,2,3,4,5,6],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,8,1,7]=>[7,2,3,4,5,6,8,1]=>[[1,3,4,5,6,7],[2],[8]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,7,1,8,6]=>[7,2,3,4,5,8,1,6]=>[[1,3,4,5,6],[2,8],[7]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,1,6]=>[6,2,3,4,5,8,7,1]=>[[1,3,4,5,6],[2,7],[8]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6,8]=>[6,2,3,4,5,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,7,8,6]=>[[1,3,4,6,7],[2,8],[5]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,8,1,6,7]=>[6,2,3,4,5,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]=>[4,2,3,1,7,6,8,5]=>[[1,3,5,7],[2,6],[4,8]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,6,7,1,8,5]=>[7,2,3,4,8,6,1,5]=>[[1,3,4,5],[2,6],[7,8]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,1,5]=>[5,2,3,4,8,6,7,1]=>[[1,3,4,5,7],[2,6],[8]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,7,1,5,8]=>[5,2,3,4,7,6,1,8]=>[[1,3,4,5,8],[2,6],[7]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,8,7]=>[5,2,3,4,6,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[5,2,3,4,6,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,6,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,4,7,1,8,5,6]=>[7,2,3,4,6,8,1,5]=>[[1,3,4,5,6],[2,8],[7]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[5,2,3,4,6,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,6,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[5,2,3,4,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]=>[[1,4,7],[2,5,8],[3,6]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[3,2,1,7,5,6,8,4]=>[[1,4,6,7],[2,5],[3,8]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[3,2,1,6,5,8,7,4]=>[[1,4,6],[2,5,7],[3,8]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,5,8,4,6,7]=>[3,2,1,6,5,7,8,4]=>[[1,4,6,7],[2,5],[3,8]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[1,3,4,7],[2,6],[5,8]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[[1,3,4,7],[2,6,8],[5]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,5,1,6,8,4,7]=>[5,2,3,7,1,6,8,4]=>[[1,3,4,7],[2,6],[5,8]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,4,7,8]=>[5,2,3,6,1,4,7,8]=>[[1,3,4,7,8],[2,6],[5]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>[6,2,3,8,5,1,7,4]=>[[1,3,4,7],[2,5],[6,8]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,5,6,1,7,4,8]=>[6,2,3,7,5,1,4,8]=>[[1,3,4,8],[2,5],[6,7]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,7,1,8,4]=>[7,2,3,8,5,6,1,4]=>[[1,3,4,6],[2,5],[7,8]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]=>[4,2,3,8,5,6,7,1]=>[[1,3,4,6,7],[2,5],[8]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,7,1,4,8]=>[4,2,3,7,5,6,1,8]=>[[1,3,4,6,8],[2,5],[7]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,8,1,4,7]=>[4,2,3,7,5,6,8,1]=>[[1,3,4,6,7],[2,5],[8]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,7,8,6]=>[4,2,3,5,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,7,8,1,4,6]=>[4,2,3,6,5,8,7,1]=>[[1,3,4,6],[2,5,7],[8]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,5,1,4,8,6,7]=>[4,2,3,5,1,7,8,6]=>[[1,3,4,6,7],[2,8],[5]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[5,2,3,6,1,7,8,4]=>[[1,3,4,6,7],[2,8],[5]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[[1,4,5,8],[2,6],[3,7]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,1,4,6,8,5,7]=>[3,2,1,4,7,6,8,5]=>[[1,4,5,7],[2,6],[3,8]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,8]=>[3,2,1,6,7,4,5,8]=>[[1,4,5,8],[2,6,7],[3]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,6,7,4,8,5]=>[3,2,1,7,8,6,4,5]=>[[1,4,5],[2,6,8],[3,7]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[3,2,1,5,8,6,7,4]=>[[1,4,5,7],[2,6],[3,8]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,6,7,4,5,8]=>[3,2,1,5,7,6,4,8]=>[[1,4,5,8],[2,6],[3,7]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[3,2,1,6,7,4,8,5]=>[[1,4,5,7],[2,6,8],[3]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,8,4,5,7]=>[3,2,1,5,7,6,8,4]=>[[1,4,5,7],[2,6],[3,8]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,1,6,4,5,7,8]=>[3,2,1,5,6,4,7,8]=>[[1,4,5,7,8],[2,6],[3]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,6,1,7,4,8,5]=>[6,2,3,7,8,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,1,7,8,4,5]=>[6,2,3,5,8,1,7,4]=>[[1,3,4,5],[2,7],[6,8]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,6,7,1,4,8,5]=>[4,2,3,7,8,6,1,5]=>[[1,3,4,5],[2,6],[7,8]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]=>[4,2,3,5,6,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,6,1,4,5,7,8]=>[4,2,3,5,6,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,6,8,7,5]=>[[1,4,5,6],[2,7],[3,8]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,7,4,5,8,6]=>[3,2,1,5,7,8,4,6]=>[[1,4,5,6],[2,7,8],[3]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[3,2,1,7,6,8,4,5]=>[[1,4,6],[2,5,8],[3,7]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,7,8,4,5,6]=>[3,2,1,5,6,8,7,4]=>[[1,4,5,6],[2,7],[3,8]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[4,2,3,5,6,8,7,1]=>[[1,3,4,5,6],[2,7],[8]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6,8]=>[4,2,3,5,6,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[3,2,1,4,5,7,8,6]=>[[1,4,5,6,7],[2,8],[3]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,6,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[3,2,1,5,6,7,8,4]=>[[1,4,5,6,7],[2,8],[3]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[4,2,3,5,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[[1,3,5,6],[2,4,8],[7]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,7,8,3,6]=>[2,1,6,4,5,8,7,3]=>[[1,3,5,6],[2,4,7],[8]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]=>[2,1,6,4,5,7,8,3]=>[[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,7,6,8,5]=>[[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[2,1,7,4,8,6,3,5]=>[[1,3,5],[2,4,6],[7,8]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,6,7,8,3,5]=>[2,1,5,4,8,6,7,3]=>[[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[2,1,5,4,6,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]=>[2,1,6,4,7,3,8,5]=>[[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,8,3,5,7]=>[2,1,5,4,7,6,8,3]=>[[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,6,8,7,5]=>[[1,3,5,6],[2,4,7],[8]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,4,7,3,8,5,6]=>[2,1,7,4,6,8,3,5]=>[[1,3,5,6],[2,4,8],[7]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,4,7,8,3,5,6]=>[2,1,5,4,6,8,7,3]=>[[1,3,5,6],[2,4,7],[8]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,7,8,6]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,6,7,8,5]=>[[1,3,5,6,7],[2,4,8]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[2,1,5,4,6,7,8,3]=>[[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,5,6,7,3,8]=>[4,2,7,1,5,6,3,8]=>[[1,3,6,8],[2,5],[4,7]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[4,2,7,1,5,6,8,3]=>[[1,3,6,7],[2,5],[4,8]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[[1,3,7,8],[2,5],[4,6]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[[1,3,6,8],[2,5,7],[4]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,3,6,8,7]=>[4,2,5,1,3,6,8,7]=>[[1,3,6,7],[2,5,8],[4]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[4,2,5,1,3,7,8,6]=>[[1,3,6,7],[2,5,8],[4]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,5,8,3,6,7]=>[4,2,6,1,5,7,8,3]=>[[1,3,6,7],[2,5],[4,8]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,3]=>[5,2,8,4,1,6,7,3]=>[[1,3,6,7],[2,4],[5,8]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,5,1,6,7,3,8]=>[5,2,7,4,1,6,3,8]=>[[1,3,6,8],[2,4],[5,7]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,5,1,6,3,8,7]=>[5,2,6,4,1,3,8,7]=>[[1,3,7],[2,4,8],[5,6]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,5,1,6,8,3,7]=>[5,2,7,4,1,6,8,3]=>[[1,3,6,7],[2,4],[5,8]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[[1,3,7,8],[2,4],[5,6]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,6,1,7,8,3]=>[6,2,8,4,5,1,7,3]=>[[1,3,5,7],[2,4],[6,8]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,6,1,7,3,8]=>[6,2,7,4,5,1,3,8]=>[[1,3,5,8],[2,4],[6,7]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>[7,2,8,4,5,6,1,3]=>[[1,3,5,6],[2,4],[7,8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,1,3]=>[3,2,8,4,5,6,7,1]=>[[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,1,3,8]=>[3,2,7,4,5,6,1,8]=>[[1,3,5,6,8],[2,4],[7]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,6,1,3,8,7]=>[3,2,6,4,5,1,8,7]=>[[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,6,1,8,3,7]=>[6,2,7,4,5,1,8,3]=>[[1,3,5,7],[2,4],[6,8]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,7,8,6]=>[3,2,5,4,1,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6,8]=>[3,2,5,4,1,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,5,1,7,3,8,6]=>[5,2,7,4,1,8,3,6]=>[[1,3,6],[2,4,8],[5,7]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,5,1,7,8,3,6]=>[5,2,6,4,1,8,7,3]=>[[1,3,6],[2,4,7],[5,8]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[5,2,6,4,1,7,3,8]=>[[1,3,6,8],[2,4],[5,7]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,7,1,3,8,6]=>[3,2,7,4,5,8,1,6]=>[[1,3,5,6],[2,4,8],[7]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,7,1,8,3,6]=>[7,2,6,4,5,8,1,3]=>[[1,3,5,6],[2,8],[4],[7]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[5,2,6,4,1,7,8,3]=>[[1,3,6,7],[2,4],[5,8]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,1,3,6,7,8]=>[3,2,5,4,1,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,7,5,8]=>[3,2,4,1,7,6,5,8]=>[[1,3,5,8],[2,6],[4,7]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,8,5,7]=>[3,2,4,1,7,6,8,5]=>[[1,3,5,7],[2,6],[4,8]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]=>[4,2,6,1,8,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[[1,3,5,8],[2,6,7],[4]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]=>[4,2,7,1,8,6,3,5]=>[[1,3,5],[2,6,8],[4,7]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[4,2,5,1,8,6,7,3]=>[[1,3,5,7],[2,6],[4,8]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,8,7]=>[4,2,5,1,6,3,8,7]=>[[1,3,5,7],[2,6,8],[4]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[4,2,6,1,7,3,8,5]=>[[1,3,5,7],[2,6,8],[4]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,8,3,5,7]=>[4,2,5,1,7,6,8,3]=>[[1,3,5,7],[2,6],[4,8]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,6,3,5,7,8]=>[4,2,5,1,6,3,7,8]=>[[1,3,5,7,8],[2,6],[4]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,6,1,3,7,8,5]=>[3,2,6,4,8,1,7,5]=>[[1,3,5],[2,4,7],[6,8]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,6,1,3,7,5,8]=>[3,2,6,4,7,1,5,8]=>[[1,3,5,8],[2,4,7],[6]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>[6,2,7,4,8,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,1,3,8,5]=>[3,2,7,4,8,6,1,5]=>[[1,3,5],[2,4,6],[7,8]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,6,7,1,8,3,5]=>[7,2,5,4,8,6,1,3]=>[[1,3,5],[2,6],[4,8],[7]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,1,3,5]=>[3,2,5,4,8,6,7,1]=>[[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[3,2,5,4,7,6,1,8]=>[[1,3,5,8],[2,4,6],[7]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]=>[3,2,5,4,6,1,8,7]=>[[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]=>[3,2,6,4,7,1,8,5]=>[[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[6,2,5,4,7,1,8,3]=>[[1,3,5,7],[2,8],[4],[6]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[3,2,5,4,7,6,8,1]=>[[1,3,5,7],[2,4,6],[8]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,3,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>[3,2,4,1,7,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,3,7,8,5,6]=>[3,2,4,1,6,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,1,3,7,5,6,8]=>[3,2,4,1,6,7,5,8]=>[[1,3,5,6,8],[2,7],[4]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,7,3,5,8,6]=>[4,2,5,1,7,8,3,6]=>[[1,3,5,6],[2,7,8],[4]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[4,2,7,1,6,8,3,5]=>[[1,3,6],[2,5,8],[4,7]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,7,8,3,5,6]=>[4,2,5,1,6,8,7,3]=>[[1,3,5,6],[2,7],[4,8]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,7,1,3,5,8,6]=>[3,2,5,4,7,8,1,6]=>[[1,3,5,6],[2,4,8],[7]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,7,1,3,8,5,6]=>[3,2,7,4,6,8,1,5]=>[[1,3,5,6],[2,4],[7,8]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[3,2,5,4,6,8,7,1]=>[[1,3,5,6],[2,4,7],[8]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,3,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>[[1,3,5,6,7],[2,8],[4]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,3,5,8,6,7]=>[3,2,4,1,5,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]=>[3,2,4,1,6,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[4,2,5,1,6,7,8,3]=>[[1,3,5,6,7],[2,8],[4]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,8,1,3,5,6,7]=>[3,2,5,4,6,7,8,1]=>[[1,3,5,6,7],[2,4],[8]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,7,4,8,6]=>[2,1,3,7,5,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,7,8,4,6]=>[2,1,3,6,5,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,5,4,8,6,7]=>[2,1,3,5,4,7,8,6]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[[1,3,4,7],[2,5,6],[8]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,5,3,6,8,4,7]=>[2,1,5,7,3,6,8,4]=>[[1,3,4,7],[2,5,6],[8]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,6,4,7,8]=>[2,1,5,6,3,4,7,8]=>[[1,3,4,7,8],[2,5,6]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]=>[2,1,4,8,5,6,7,3]=>[[1,3,4,6,7],[2,5],[8]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[2,1,4,6,5,3,8,7]=>[[1,3,4,7],[2,5,8],[6]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,1,5,6,3,4,7,8]=>[2,1,4,6,5,3,7,8]=>[[1,3,4,7,8],[2,5],[6]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[1,3,4,6],[2,5,7,8]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,7,8,4,6]=>[2,1,5,6,3,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6,8]=>[2,1,5,6,3,7,4,8]=>[[1,3,4,6,8],[2,5,7]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>[2,1,7,6,5,8,3,4]=>[[1,3,6],[2,4,8],[5],[7]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]=>[2,1,4,6,5,8,7,3]=>[[1,3,4,6],[2,5,7],[8]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,5,3,4,6,8,7]=>[2,1,4,5,3,6,8,7]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,1,5,3,8,4,6,7]=>[2,1,5,6,3,7,8,4]=>[[1,3,4,6,7],[2,5,8]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,5,3,4,6,7,8]=>[2,1,4,5,3,6,7,8]=>[[1,3,4,6,7,8],[2,5]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,4]=>[3,2,5,8,1,6,7,4]=>[[1,3,4,7],[2,6],[5,8]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,7,4,8]=>[3,2,5,7,1,6,4,8]=>[[1,3,4,8],[2,6],[5,7]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,6,8,4,7]=>[3,2,5,7,1,6,8,4]=>[[1,3,4,7],[2,6],[5,8]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,1,3,6,4,7,8]=>[3,2,5,6,1,4,7,8]=>[[1,3,4,7,8],[2,6],[5]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,5,1,6,3,7,8,4]=>[5,2,6,8,1,3,7,4]=>[[1,3,4],[2,6,7],[5,8]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[[1,3,4,8],[2,6,7],[5]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,1,6,7,3,8,4]=>[5,2,7,8,1,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[5,2,4,8,1,6,7,3]=>[[1,3,4,7],[2,6],[5,8]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,5,1,6,3,4,8,7]=>[5,2,4,6,1,3,8,7]=>[[1,3,4,7],[2,6,8],[5]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,5,6,1,3,7,8,4]=>[3,2,6,8,5,1,7,4]=>[[1,3,4],[2,5,7],[6,8]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,5,6,1,3,7,4,8]=>[3,2,6,7,5,1,4,8]=>[[1,3,4,8],[2,5],[6,7]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,5,6,1,7,3,8,4]=>[6,2,7,8,5,1,3,4]=>[[1,3,4],[2,5,8],[6,7]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,7,1,3,8,4]=>[3,2,7,8,5,6,1,4]=>[[1,3,4],[2,5,6],[7,8]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,1,3,4]=>[3,2,4,8,5,6,7,1]=>[[1,3,4,6,7],[2,5],[8]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[3,2,4,7,5,6,8,1]=>[[1,3,4,6,7],[2,5],[8]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,7,8,6]=>[3,2,4,5,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,7,4,8,6]=>[3,2,5,7,1,8,4,6]=>[[1,3,4,6],[2,7,8],[5]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,7,8,4,6]=>[3,2,5,6,1,8,7,4]=>[[1,3,4,6],[2,7],[5,8]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>[5,2,4,7,1,8,3,6]=>[[1,3,4,6],[2,7,8],[5]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,5,7,1,3,4,8,6]=>[3,2,4,7,5,8,1,6]=>[[1,3,4,6],[2,5,8],[7]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,5,7,1,3,8,4,6]=>[3,2,7,6,5,8,1,4]=>[[1,3,6],[2,4],[5,8],[7]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[3,2,4,6,5,8,7,1]=>[[1,3,4,6],[2,5,7],[8]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,5,1,3,8,4,6,7]=>[3,2,5,6,1,7,8,4]=>[[1,3,4,6,7],[2,8],[5]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[2,1,3,7,8,6,4,5]=>[[1,3,4,5],[2,6,8],[7]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,6,7,8,4,5]=>[2,1,3,5,8,6,7,4]=>[[1,3,4,5,7],[2,6],[8]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[2,1,3,5,6,4,8,7]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,1,3,6,4,8,5,7]=>[2,1,3,6,7,4,8,5]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[2,1,4,6,8,3,7,5]=>[[1,3,4,5],[2,6,7],[8]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,6,3,7,8,4,5]=>[2,1,6,5,8,3,7,4]=>[[1,3,5],[2,4,7],[6,8]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[2,1,4,7,8,6,3,5]=>[[1,3,4,5],[2,6,8],[7]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,1,6,7,3,8,4,5]=>[2,1,7,5,8,6,3,4]=>[[1,3,5],[2,4,6],[7,8]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>[2,1,4,5,8,6,7,3]=>[[1,3,4,5,7],[2,6],[8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,8,7]=>[2,1,4,5,6,3,8,7]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]=>[2,1,4,6,7,3,8,5]=>[[1,3,4,5,7],[2,6,8]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,1,6,3,8,4,5,7]=>[2,1,6,5,7,3,8,4]=>[[1,3,5,7],[2,4,8],[6]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,6,1,3,7,4,8,5]=>[3,2,6,7,8,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,1,3,7,8,4,5]=>[3,2,6,5,8,1,7,4]=>[[1,3,5],[2,4,7],[6,8]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,6,1,3,7,4,5,8]=>[3,2,6,5,7,1,4,8]=>[[1,3,5,8],[2,4],[6,7]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,6,1,7,3,4,8,5]=>[6,2,4,7,8,1,3,5]=>[[1,3,4,5],[2,7,8],[6]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>[3,2,4,7,8,6,1,5]=>[[1,3,4,5],[2,6],[7,8]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,6,7,1,3,8,4,5]=>[3,2,7,5,8,6,1,4]=>[[1,3,5],[2,4,6],[7,8]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[3,2,4,5,8,6,7,1]=>[[1,3,4,5,7],[2,6],[8]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,8,4,5,7]=>[3,2,6,5,7,1,8,4]=>[[1,3,5,7],[2,4],[6,8]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>[6,2,4,5,7,1,8,3]=>[[1,3,4,5,7],[2,8],[6]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]=>[3,2,4,5,7,6,8,1]=>[[1,3,4,5,7],[2,6],[8]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[2,1,3,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,7,3,4,5,8,6]=>[2,1,4,5,7,8,3,6]=>[[1,3,4,5,6],[2,7,8]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,1,7,3,8,4,5,6]=>[2,1,7,5,6,8,3,4]=>[[1,3,5,6],[2,4,8],[7]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>[2,1,4,5,6,8,7,3]=>[[1,3,4,5,6],[2,7],[8]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6,8]=>[2,1,4,5,6,7,3,8]=>[[1,3,4,5,6,8],[2,7]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,8,6]=>[3,2,4,5,7,8,1,6]=>[[1,3,4,5,6],[2,8],[7]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>[7,2,4,5,6,8,1,3]=>[[1,3,4,5,6],[2,8],[7]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>[3,2,4,5,6,8,7,1]=>[[1,3,4,5,6],[2,7],[8]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[2,1,3,5,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[2,1,4,5,6,7,8,3]=>[[1,3,4,5,6,7],[2,8]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[[1,2,4,5,6,8],[3],[7]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,6,8,2]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[[1,2,4,5,7,8],[3],[6]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,7,8,2,6]=>[1,6,3,4,5,8,7,2]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,2,8,6,7]=>[1,5,3,4,2,7,8,6]=>[[1,2,4,6,7],[3,8],[5]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,6,2,7,8,5]=>[1,6,3,4,8,2,7,5]=>[[1,2,4,5],[3,7],[6,8]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>[[1,2,4,5],[3,6],[7,8]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,6,7,8,2,5]=>[1,5,3,4,8,6,7,2]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,8,7]=>[1,5,3,4,6,2,8,7]=>[[1,2,4,5,7],[3,8],[6]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>[[1,2,5,6],[3,7,8],[4]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,4,2,7,8,5,6]=>[1,4,3,2,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>[[1,2,5,6,8],[3,7],[4]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,4,7,2,5,8,6]=>[1,5,3,4,7,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[1,5,3,4,6,7,2,8]=>[[1,2,4,5,6,8],[3],[7]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,5,6,8,4,7]=>[1,3,2,7,5,6,8,4]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,7,4,8,6]=>[1,3,2,7,5,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[1,3,2,6,5,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6,8]=>[1,3,2,6,5,7,4,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>[[1,2,4,6,7],[3,5,8]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,5,2,6,7,8,4]=>[1,5,3,8,2,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,5,6,2,7,8,4]=>[1,6,3,8,5,2,7,4]=>[[1,2,4,7],[3,5],[6,8]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>[[1,2,4,8],[3,5],[6,7]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,7,2,8,4]=>[1,7,3,8,5,6,2,4]=>[[1,2,4,6],[3,5],[7,8]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]=>[1,4,3,8,5,6,7,2]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[1,4,3,6,5,2,7,8]=>[[1,2,4,7,8],[3,5],[6]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,8]=>[1,4,3,5,2,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,7,8,4,6]=>[1,5,3,6,2,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[1,5,3,6,2,7,4,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>[[1,2,4,6],[3,8],[5],[7]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,7,8,2,4,6]=>[1,4,3,6,5,8,7,2]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>[[1,2,4,6,7],[3,8],[5]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,7,6,8,5]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>[[1,2,4,5,8],[3,6,7]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,2,6,7,4,5,8]=>[1,3,2,5,7,6,4,8]=>[[1,2,4,5,8],[3,6],[7]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>[[1,2,4,5,7],[3,6,8]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,2,7,4,8,5]=>[1,6,3,7,8,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,6,7,2,4,8,5]=>[1,4,3,7,8,6,2,5]=>[[1,2,4,5],[3,6],[7,8]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,6,7,2,8,4,5]=>[1,7,3,5,8,6,2,4]=>[[1,2,4,5],[3,6],[7,8]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,2,4,5]=>[1,4,3,5,8,6,7,2]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]=>[1,4,3,5,7,6,2,8]=>[[1,2,4,5,8],[3,6],[7]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>[[1,2,4,5,7],[3,8],[6]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>[[1,2,4,5,7],[3,8],[6]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>[[1,2,4,5,7,8],[3],[6]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,6,8,7,5]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,7,8,4,5,6]=>[1,3,2,5,6,8,7,4]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>[[1,2,4,6],[3,5],[7,8]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,2,8]=>[3,7,1,4,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,6,8,2,7]=>[3,7,1,4,5,6,8,2]=>[[1,2,5,6,7],[3,4],[8]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,6,2,7,8]=>[3,6,1,4,5,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,5,2,7,8,6]=>[3,5,1,4,2,8,7,6]=>[[1,2,6],[3,4,7],[5,8]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,2,6,7,8]=>[3,5,1,4,2,6,7,8]=>[[1,2,6,7,8],[3,4],[5]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,6,7,5,8]=>[3,4,1,2,7,6,5,8]=>[[1,2,5,8],[3,4,6],[7]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>[3,4,1,2,7,6,8,5]=>[[1,2,5,7],[3,4,6],[8]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[[1,2,5,7,8],[3,4,6]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,1,4,6,2,7,5,8]=>[3,6,1,4,7,2,5,8]=>[[1,2,5,8],[3,4,7],[6]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[3,5,1,4,6,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,8,5,7]=>[3,6,1,4,7,2,8,5]=>[[1,2,5,7],[3,4,8],[6]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,8,2,5,7]=>[3,5,1,4,7,6,8,2]=>[[1,2,5,7],[3,4,6],[8]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,4,2,7,8,5,6]=>[3,4,1,2,6,8,7,5]=>[[1,2,5,6],[3,4,7],[8]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,4,2,7,5,6,8]=>[3,4,1,2,6,7,5,8]=>[[1,2,5,6,8],[3,4,7]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,4,7,2,8,5,6]=>[3,7,1,4,6,8,2,5]=>[[1,2,5,6],[3,4,8],[7]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,1,4,7,2,5,6,8]=>[3,5,1,4,6,7,2,8]=>[[1,2,5,6,8],[3,4],[7]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,2,5,6,8,7]=>[3,4,1,2,5,6,8,7]=>[[1,2,5,6,7],[3,4,8]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,2,5,8,6,7]=>[3,4,1,2,5,7,8,6]=>[[1,2,5,6,7],[3,4,8]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,4,2,8,5,6,7]=>[3,4,1,2,6,7,8,5]=>[[1,2,5,6,7],[3,4,8]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[3,5,1,4,6,7,8,2]=>[[1,2,5,6,7],[3,4],[8]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,2]=>[4,8,3,1,5,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,5,6,7,2,8]=>[4,7,3,1,5,6,2,8]=>[[1,2,6,8],[3,5],[4,7]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,5,6,2,8,7]=>[4,6,3,1,5,2,8,7]=>[[1,2,7],[3,5,8],[4,6]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[[1,2,7,8],[3,5],[4,6]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,4,1,5,2,7,8,6]=>[4,5,3,1,2,8,7,6]=>[[1,2,6],[3,5,7],[4,8]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[4,6,3,1,5,8,7,2]=>[[1,2,6],[3,5,7],[4,8]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,4,1,5,2,6,8,7]=>[4,5,3,1,2,6,8,7]=>[[1,2,6,7],[3,5,8],[4]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,2]=>[5,8,3,4,1,6,7,2]=>[[1,2,6,7],[3,4],[5,8]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,2,8]=>[5,7,3,4,1,6,2,8]=>[[1,2,6,8],[3,4],[5,7]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[[1,2,7,8],[3,4],[5,6]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,1,7,8,2]=>[6,8,3,4,5,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,1,7,2,8]=>[6,7,3,4,5,1,2,8]=>[[1,2,5,8],[3,4],[6,7]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>[2,8,3,4,5,6,7,1]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,1,2,8]=>[2,7,3,4,5,6,1,8]=>[[1,2,4,5,6,8],[3],[7]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[2,6,3,4,5,1,7,8]=>[[1,2,4,5,7,8],[3],[6]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,7,8,6]=>[2,5,3,4,1,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,5,1,7,2,8,6]=>[5,7,3,4,1,8,2,6]=>[[1,2,6],[3,4,8],[5,7]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6,8]=>[5,6,3,4,1,7,2,8]=>[[1,2,6,8],[3,4],[5,7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,5,7,1,2,8,6]=>[2,7,3,4,5,8,1,6]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,5,7,1,8,2,6]=>[7,6,3,4,5,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,7,8,1,2,6]=>[2,6,3,4,5,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,8,2,6,7]=>[5,6,3,4,1,7,8,2]=>[[1,2,6,7],[3,4],[5,8]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[2,6,3,4,5,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[2,5,3,4,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,8,5,7]=>[2,4,3,1,7,6,8,5]=>[[1,2,5,7],[3,6],[4,8]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,6,5,7,8]=>[2,4,3,1,6,5,7,8]=>[[1,2,5,7,8],[3,6],[4]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,6,2,7,8,5]=>[4,6,3,1,8,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[[1,2,5,8],[3,6,7],[4]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,6,7,2,8,5]=>[4,7,3,1,8,6,2,5]=>[[1,2,5],[3,6,8],[4,7]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[4,5,3,1,8,6,7,2]=>[[1,2,5,7],[3,6],[4,8]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,6,7,2,5,8]=>[4,5,3,1,7,6,2,8]=>[[1,2,5,8],[3,6],[4,7]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[4,6,3,1,7,2,8,5]=>[[1,2,5,7],[3,6,8],[4]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,8,2,5,7]=>[4,5,3,1,7,6,8,2]=>[[1,2,5,7],[3,6],[4,8]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,6,1,2,7,5,8]=>[2,6,3,4,7,1,5,8]=>[[1,2,4,5,8],[3,7],[6]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,6,1,7,2,8,5]=>[6,7,3,4,8,1,2,5]=>[[1,2,5],[3,4,8],[6,7]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,1,7,8,2,5]=>[6,5,3,4,8,1,7,2]=>[[1,4,5],[2,7],[3,8],[6]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,6,7,8,1,2,5]=>[2,5,3,4,8,6,7,1]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[2,5,3,4,7,6,8,1]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,4,1,2,5,7,8,6]=>[2,4,3,1,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,4,1,2,7,5,8,6]=>[2,4,3,1,7,8,5,6]=>[[1,2,5,6],[3,7,8],[4]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>[2,4,3,1,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,4,1,7,2,5,8,6]=>[4,5,3,1,7,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,7,2,8,5,6]=>[4,7,3,1,6,8,2,5]=>[[1,2,6],[3,5,8],[4,7]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,1,7,8,2,5,6]=>[4,5,3,1,6,8,7,2]=>[[1,2,5,6],[3,7],[4,8]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[7,5,3,4,6,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[2,5,3,4,6,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6,8]=>[2,5,3,4,6,7,1,8]=>[[1,2,4,5,6,8],[3],[7]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1,2,8,5,6,7]=>[2,4,3,1,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[4,5,3,1,6,7,8,2]=>[[1,2,5,6,7],[3,8],[4]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>[2,5,3,4,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,5,6,7,4,8]=>[2,3,1,7,5,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[2,3,1,7,5,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,7,8,4,6]=>[2,3,1,6,5,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6,8]=>[2,3,1,6,5,7,4,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,6,8,4,7]=>[3,5,1,7,2,6,8,4]=>[[1,2,4,7],[3,5,6],[8]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,4,7,8]=>[3,5,1,6,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,6,2,7,8,4]=>[3,6,1,8,5,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,5,6,2,7,4,8]=>[3,6,1,7,5,2,4,8]=>[[1,2,4,8],[3,5,7],[6]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[3,7,1,8,5,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,8,2,4]=>[3,4,1,8,5,6,7,2]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,5,6,7,2,4,8]=>[3,4,1,7,5,6,2,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>[3,6,1,7,5,2,8,4]=>[[1,2,4,7],[3,5,8],[6]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,5,6,8,2,4,7]=>[3,4,1,7,5,6,8,2]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]=>[3,4,1,5,2,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,8]=>[3,4,1,5,2,7,6,8]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,7,8,4,6]=>[3,5,1,6,2,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]=>[3,5,1,6,2,7,4,8]=>[[1,2,4,6,8],[3,5,7]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[3,4,1,7,5,8,2,6]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]=>[3,7,1,6,5,8,2,4]=>[[1,2,6],[3,4,8],[5],[7]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,7,8,2,4,6]=>[3,4,1,6,5,8,7,2]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6,8]=>[3,4,1,6,5,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,8,4,6,7]=>[3,5,1,6,2,7,8,4]=>[[1,2,4,6,7],[3,5,8]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>[3,4,1,6,5,7,8,2]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,5,2,4,6,7,8]=>[3,4,1,5,2,6,7,8]=>[[1,2,4,6,7,8],[3,5]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,4]=>[2,5,3,8,1,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[2,5,3,7,1,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,6,8,4,7]=>[2,5,3,7,1,6,8,4]=>[[1,2,4,7],[3,6],[5,8]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,6,4,7,8]=>[2,5,3,6,1,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,5,1,6,2,7,8,4]=>[5,6,3,8,1,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[[1,2,4,8],[3,6,7],[5]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[5,4,3,8,1,6,7,2]=>[[1,4,7],[2,6],[3,8],[5]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>[5,4,3,6,1,2,8,7]=>[[1,4,7],[2,6,8],[3],[5]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,1,6,8,2,4,7]=>[5,4,3,7,1,6,8,2]=>[[1,4,7],[2,6],[3,8],[5]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,5,1,6,2,4,7,8]=>[5,4,3,6,1,2,7,8]=>[[1,4,7,8],[2,6],[3],[5]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,5,6,1,2,7,8,4]=>[2,6,3,8,5,1,7,4]=>[[1,2,4,7],[3,5],[6,8]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,5,6,1,7,2,8,4]=>[6,7,3,8,5,1,2,4]=>[[1,2,4],[3,5,8],[6,7]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]=>[6,4,3,8,5,1,7,2]=>[[1,4,7],[2,5],[3,8],[6]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[6,4,3,7,5,1,2,8]=>[[1,4,8],[2,5],[3,7],[6]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,7,1,2,8,4]=>[2,7,3,8,5,6,1,4]=>[[1,2,4,6],[3,5],[7,8]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,1,2,4]=>[2,4,3,8,5,6,7,1]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,8,7]=>[2,4,3,6,5,1,8,7]=>[[1,2,4,7],[3,5,8],[6]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,5,6,1,2,8,4,7]=>[2,6,3,7,5,1,8,4]=>[[1,2,4,7],[3,5],[6,8]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[6,4,3,7,5,1,8,2]=>[[1,4,7],[2,5],[3,8],[6]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[2,4,3,7,5,6,8,1]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,5,6,1,2,4,7,8]=>[2,4,3,6,5,1,7,8]=>[[1,2,4,7,8],[3,5],[6]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,7,8,6]=>[2,4,3,5,1,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[2,4,3,5,1,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,7,4,8,6]=>[2,5,3,7,1,8,4,6]=>[[1,2,4,6],[3,7,8],[5]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,7,8,4,6]=>[2,5,3,6,1,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6,8]=>[2,5,3,6,1,7,4,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,7,2,4,8,6]=>[5,4,3,7,1,8,2,6]=>[[1,4,6],[2,7,8],[3],[5]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[5,7,3,6,1,8,2,4]=>[[1,2,6],[3,4,8],[5,7]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]=>[5,4,3,6,1,8,7,2]=>[[1,4,6],[2,7],[3,8],[5]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6,8]=>[5,4,3,6,1,7,2,8]=>[[1,4,6,8],[2,7],[3],[5]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,7,1,2,4,8,6]=>[2,4,3,7,5,8,1,6]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,7,1,2,8,4,6]=>[2,7,3,6,5,8,1,4]=>[[1,2,4,6],[3,8],[5],[7]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,7,1,8,2,4,6]=>[7,4,3,6,5,8,1,2]=>[[1,4,6],[2,5],[3,8],[7]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[2,4,3,6,5,8,7,1]=>[[1,2,4,6],[3,5,7],[8]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6,8]=>[2,4,3,6,5,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,5,1,2,4,6,8,7]=>[2,4,3,5,1,6,8,7]=>[[1,2,4,6,7],[3,8],[5]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,5,1,2,4,8,6,7]=>[2,4,3,5,1,7,8,6]=>[[1,2,4,6,7],[3,8],[5]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>[5,4,3,6,1,7,8,2]=>[[1,4,6,7],[2,8],[3],[5]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,5,8,1,2,4,6,7]=>[2,4,3,6,5,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8]=>[2,4,3,5,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[2,3,1,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,2,4,6,8,5,7]=>[2,3,1,4,7,6,8,5]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,2,6,4,7,8,5]=>[2,3,1,6,8,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[2,3,1,7,8,6,4,5]=>[[1,2,4,5],[3,6,8],[7]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,1,2,6,8,4,5,7]=>[2,3,1,5,7,6,8,4]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,6,4,5,7,8]=>[2,3,1,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,6,2,4,7,5,8]=>[3,4,1,6,7,2,5,8]=>[[1,2,4,5,8],[3,6,7]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[[1,2,4,5],[3,6,7,8]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]=>[3,4,1,5,7,6,2,8]=>[[1,2,4,5,8],[3,6],[7]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,8,7]=>[3,4,1,5,6,2,8,7]=>[[1,2,4,5,7],[3,6,8]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,8,5,7]=>[3,4,1,6,7,2,8,5]=>[[1,2,4,5,7],[3,6,8]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[3,4,1,5,7,6,8,2]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,6,2,4,5,7,8]=>[3,4,1,5,6,2,7,8]=>[[1,2,4,5,7,8],[3,6]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,7,8,5]=>[2,4,3,6,8,1,7,5]=>[[1,2,4,5],[3,7],[6,8]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[2,4,3,6,7,1,5,8]=>[[1,2,4,5,8],[3,7],[6]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,6,1,2,7,4,8,5]=>[2,6,3,7,8,1,4,5]=>[[1,2,4,5],[3,7,8],[6]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,6,1,2,7,8,4,5]=>[2,6,3,5,8,1,7,4]=>[[1,2,4,5],[3,7],[6,8]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,6,1,2,7,4,5,8]=>[2,6,3,5,7,1,4,8]=>[[1,2,4,5,8],[3,7],[6]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,6,1,7,2,4,8,5]=>[6,4,3,7,8,1,2,5]=>[[1,4,5],[2,7,8],[3],[6]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[6,7,3,5,8,1,2,4]=>[[1,2,5],[3,4,8],[6,7]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>[6,4,3,5,8,1,7,2]=>[[1,4,5],[2,7],[3,8],[6]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,6,7,1,2,4,8,5]=>[2,4,3,7,8,6,1,5]=>[[1,2,4,5],[3,6],[7,8]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>[2,7,3,5,8,6,1,4]=>[[1,2,4,5],[3,6],[7,8]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[2,4,3,5,8,6,7,1]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,8,7]=>[2,4,3,5,6,1,8,7]=>[[1,2,4,5,7],[3,8],[6]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>[6,4,3,5,7,1,8,2]=>[[1,4,5,7],[2,8],[3],[6]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[2,4,3,5,7,6,8,1]=>[[1,2,4,5,7],[3,6],[8]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,2,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[2,3,1,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,1,2,4,7,5,6,8]=>[2,3,1,4,6,7,5,8]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,7,4,5,8,6]=>[2,3,1,5,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,2,7,4,8,5,6]=>[2,3,1,7,6,8,4,5]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,2,7,4,5,6,8]=>[2,3,1,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,7,2,4,5,8,6]=>[3,4,1,5,7,8,2,6]=>[[1,2,4,5,6],[3,7,8]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,7,2,4,8,5,6]=>[3,4,1,7,6,8,2,5]=>[[1,2,4,6],[3,5,8],[7]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,7,2,8,4,5,6]=>[3,7,1,5,6,8,2,4]=>[[1,2,5,6],[3,4,8],[7]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>[3,4,1,5,6,8,7,2]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6,8]=>[3,4,1,5,6,7,2,8]=>[[1,2,4,5,6,8],[3,7]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,8,6]=>[2,4,3,5,7,8,1,6]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]=>[2,4,3,5,6,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>[2,3,1,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,2,4,8,5,6,7]=>[2,3,1,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[2,3,1,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[3,4,1,5,6,7,8,2]=>[[1,2,4,5,6,7],[3,8]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]=>[2,4,3,5,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,6,8,3,7]=>[1,2,7,4,5,6,8,3]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[[1,2,3,5,7,8],[4],[6]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>[[1,2,3,5,8],[4,7],[6]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,6,7,8,3,5]=>[1,2,5,4,8,6,7,3]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>[[1,2,3,5,7],[4,8],[6]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,7,3,5,8,6]=>[1,2,5,4,7,8,3,6]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,4,7,8,3,5,6]=>[1,2,5,4,6,8,7,3]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>[[1,2,3,5,6,8],[4],[7]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>[[1,2,3,6,8],[4,5],[7]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[1,4,7,2,5,6,8,3]=>[[1,2,3,6,7],[4,5],[8]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,5,6,3,7,8]=>[1,4,6,2,5,3,7,8]=>[[1,2,3,7,8],[4,5],[6]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>[[1,2,3,6,7],[4,5,8]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,5,2,6,7,8,3]=>[1,5,8,4,2,6,7,3]=>[[1,2,3,7],[4,6],[5,8]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,5,2,6,8,3,7]=>[1,5,7,4,2,6,8,3]=>[[1,2,3,7],[4,6],[5,8]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>[[1,2,3,7,8],[4,6],[5]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,2,7,8,3]=>[1,6,8,4,5,2,7,3]=>[[1,2,3,7],[4,5],[6,8]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>[[1,2,3,8],[4,5],[6,7]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,2,8,3]=>[1,7,8,4,5,6,2,3]=>[[1,2,3,6],[4,5],[7,8]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,2,3]=>[1,3,8,4,5,6,7,2]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>[1,3,7,4,5,6,2,8]=>[[1,2,3,5,6,8],[4],[7]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,6,2,3,8,7]=>[1,3,6,4,5,2,8,7]=>[[1,2,3,5,7],[4,8],[6]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,6,2,8,3,7]=>[1,6,7,4,5,2,8,3]=>[[1,2,3,7],[4,5],[6,8]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,6,8,2,3,7]=>[1,3,7,4,5,6,8,2]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6,8]=>[1,3,5,4,2,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,5,2,7,3,8,6]=>[1,5,7,4,2,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>[[1,2,3,6],[4,7],[5,8]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,7,8,2,3,6]=>[1,3,6,4,5,8,7,2]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[1,3,6,4,5,7,2,8]=>[[1,2,3,5,6,8],[4],[7]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,8,5,7]=>[1,3,4,2,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[1,4,5,2,8,6,7,3]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>[[1,2,3,5,7],[4,6,8]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>[[1,2,3,5,7],[4,6,8]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,6,2,3,7,8,5]=>[1,3,6,4,8,2,7,5]=>[[1,2,3,5],[4,7],[6,8]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>[[1,2,3,5,8],[4,7],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]=>[1,6,7,4,8,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,6,2,7,8,3,5]=>[1,6,5,4,8,2,7,3]=>[[1,2,5],[3,7],[4,8],[6]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[1,6,5,4,7,2,3,8]=>[[1,2,5,8],[3,7],[4],[6]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,6,7,2,3,8,5]=>[1,3,7,4,8,6,2,5]=>[[1,2,3,5],[4,6],[7,8]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>[[1,2,5],[3,6],[4,8],[7]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[1,3,5,4,7,6,2,8]=>[[1,2,3,5,8],[4,6],[7]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>[[1,2,3,5,7],[4,8],[6]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>[[1,2,3,5,6],[4,7,8]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>[[1,2,3,6],[4,5,8],[7]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>[[1,2,3,5,6,8],[4,7]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,7,2,3,5,8,6]=>[1,3,5,4,7,8,2,6]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,3]=>[2,4,8,1,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[2,4,6,1,5,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,5,6,8,3,7]=>[2,4,7,1,5,6,8,3]=>[[1,2,3,6,7],[4,5],[8]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3,7,8]=>[2,4,6,1,5,3,7,8]=>[[1,2,3,7,8],[4,5],[6]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,5,3,7,8,6]=>[2,4,5,1,3,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6,8]=>[2,4,5,1,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,5,7,8,3,6]=>[2,4,6,1,5,8,7,3]=>[[1,2,3,6],[4,5,7],[8]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,5,3,8,6,7]=>[2,4,5,1,3,7,8,6]=>[[1,2,3,6,7],[4,5,8]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[4,5,8,1,2,6,7,3]=>[[1,2,3,7],[4,5,6],[8]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,5,2,6,7,3,8]=>[4,5,7,1,2,6,3,8]=>[[1,2,3,8],[4,5,6],[7]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,5,2,6,8,3,7]=>[4,5,7,1,2,6,8,3]=>[[1,2,3,7],[4,5,6],[8]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,5,2,6,3,7,8]=>[4,5,6,1,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,5,6,2,7,3,8]=>[4,6,7,1,5,2,3,8]=>[[1,2,3,8],[4,5,7],[6]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[4,7,8,1,5,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,2,3]=>[4,3,8,1,5,6,7,2]=>[[1,3,6,7],[2,5],[4,8]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[4,3,6,1,5,2,8,7]=>[[1,3,7],[2,5,8],[4,6]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>[4,3,7,1,5,6,8,2]=>[[1,3,6,7],[2,5],[4,8]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,5,6,2,3,7,8]=>[4,3,6,1,5,2,7,8]=>[[1,3,7,8],[2,5],[4,6]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[4,3,5,1,2,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6,8]=>[4,3,5,1,2,7,6,8]=>[[1,3,6,8],[2,5,7],[4]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]=>[4,5,6,1,2,8,7,3]=>[[1,2,3,6],[4,5,7],[8]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6,8]=>[4,5,6,1,2,7,3,8]=>[[1,2,3,6,8],[4,5,7]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,5,7,2,3,8,6]=>[4,3,7,1,5,8,2,6]=>[[1,3,6],[2,5,8],[4,7]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,1,5,7,8,2,3,6]=>[4,3,6,1,5,8,7,2]=>[[1,3,6],[2,5,7],[4,8]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6,8]=>[4,3,6,1,5,7,2,8]=>[[1,3,6,8],[2,5],[4,7]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,8,3,6,7]=>[4,5,6,1,2,7,8,3]=>[[1,2,3,6,7],[4,5,8]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,5,2,3,6,7,8]=>[4,3,5,1,2,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[2,5,7,4,1,6,3,8]=>[[1,2,3,8],[4,6],[5,7]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,6,3,8,7]=>[2,5,6,4,1,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,6,8,3,7]=>[2,5,7,4,1,6,8,3]=>[[1,2,3,7],[4,6],[5,8]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,1,6,2,7,8,3]=>[5,6,8,4,1,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[[1,2,3,8],[4,6,7],[5]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[[1,2,3],[4,6,8],[5,7]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[5,3,8,4,1,6,7,2]=>[[1,3,6,7],[2,4],[5,8]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,5,1,6,7,2,3,8]=>[5,3,7,4,1,6,2,8]=>[[1,3,6,8],[2,4],[5,7]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,5,1,6,2,3,8,7]=>[5,3,6,4,1,2,8,7]=>[[1,3,7],[2,4,8],[5,6]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>[5,6,7,4,1,2,8,3]=>[[1,2,3,7],[4,6,8],[5]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,5,1,6,8,2,3,7]=>[5,3,7,4,1,6,8,2]=>[[1,3,6,7],[2,4],[5,8]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,1,6,2,3,7,8]=>[5,3,6,4,1,2,7,8]=>[[1,3,7,8],[2,4],[5,6]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,1,2,7,8,3]=>[2,6,8,4,5,1,7,3]=>[[1,2,3,7],[4,5],[6,8]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,1,2,7,3,8]=>[2,6,7,4,5,1,3,8]=>[[1,2,3,8],[4,5],[6,7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,1,7,2,8,3]=>[6,7,8,4,5,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,1,7,8,2,3]=>[6,3,8,4,5,1,7,2]=>[[1,3,5,7],[2,4],[6,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,3]=>[7,3,8,4,5,6,1,2]=>[[1,3,5,6],[2,4],[7,8]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,1,2,3]=>[2,3,8,4,5,6,7,1]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>[2,3,6,4,5,1,8,7]=>[[1,2,3,5,7],[4,8],[6]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,6,1,2,8,3,7]=>[2,6,7,4,5,1,8,3]=>[[1,2,3,7],[4,5],[6,8]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[6,3,7,4,5,1,8,2]=>[[1,3,5,7],[2,4],[6,8]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[2,3,7,4,5,6,8,1]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[2,3,6,4,5,1,7,8]=>[[1,2,3,5,7,8],[4],[6]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,7,8,6]=>[2,3,5,4,1,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>[2,3,5,4,1,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,7,3,8,6]=>[2,5,7,4,1,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6,8]=>[2,5,6,4,1,7,3,8]=>[[1,2,3,6,8],[4,7],[5]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[5,7,6,4,1,8,2,3]=>[[1,2,6],[3,7,8],[4],[5]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>[5,3,6,4,1,8,7,2]=>[[1,3,6],[2,4,7],[5,8]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6,8]=>[5,3,6,4,1,7,2,8]=>[[1,3,6,8],[2,4],[5,7]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>[2,7,6,4,5,8,1,3]=>[[1,2,5,6],[3,8],[4],[7]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[2,3,6,4,5,8,7,1]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,5,1,2,3,6,8,7]=>[2,3,5,4,1,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,5,1,2,8,3,6,7]=>[2,5,6,4,1,7,8,3]=>[[1,2,3,6,7],[4,8],[5]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[2,3,6,4,5,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[2,3,5,4,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[[1,2,3,5,8],[4,6],[7]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,8,5,7]=>[2,3,4,1,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,6,3,7,8,5]=>[2,4,6,1,8,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,6,7,3,5,8]=>[2,4,5,1,7,6,3,8]=>[[1,2,3,5,8],[4,6],[7]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[2,4,5,1,6,3,8,7]=>[[1,2,3,5,7],[4,6,8]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]=>[2,4,6,1,7,3,8,5]=>[[1,2,3,5,7],[4,6,8]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,6,3,5,7,8]=>[2,4,5,1,6,3,7,8]=>[[1,2,3,5,7,8],[4,6]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[4,3,6,1,8,2,7,5]=>[[1,3,5],[2,6,7],[4,8]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,6,2,3,7,5,8]=>[4,3,6,1,7,2,5,8]=>[[1,3,5,8],[2,6,7],[4]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,6,7,8,2,3,5]=>[4,3,5,1,8,6,7,2]=>[[1,3,5,7],[2,6],[4,8]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,8,7]=>[4,3,5,1,6,2,8,7]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,8,5,7]=>[4,3,6,1,7,2,8,5]=>[[1,3,5,7],[2,6,8],[4]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[4,3,5,1,7,6,8,2]=>[[1,3,5,7],[2,6],[4,8]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,6,2,3,5,7,8]=>[4,3,5,1,6,2,7,8]=>[[1,3,5,7,8],[2,6],[4]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[2,3,6,4,7,1,5,8]=>[[1,2,3,5,8],[4,7],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,6,1,2,7,3,8,5]=>[2,6,7,4,8,1,3,5]=>[[1,2,3,5],[4,7,8],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,6,1,2,7,8,3,5]=>[2,6,5,4,8,1,7,3]=>[[1,2,5],[3,7],[4,8],[6]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,6,1,2,7,3,5,8]=>[2,6,5,4,7,1,3,8]=>[[1,2,5,8],[3,7],[4],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,6,1,7,2,3,8,5]=>[6,3,7,4,8,1,2,5]=>[[1,3,5],[2,4,8],[6,7]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[6,7,5,4,8,1,2,3]=>[[1,2,5],[3,7,8],[4],[6]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,6,1,7,8,2,3,5]=>[6,3,5,4,8,1,7,2]=>[[1,3,5],[2,7],[4,8],[6]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]=>[6,3,5,4,7,1,2,8]=>[[1,3,5,8],[2,7],[4],[6]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,6,7,1,2,8,3,5]=>[2,7,5,4,8,6,1,3]=>[[1,2,5],[3,6],[4,8],[7]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[7,3,5,4,8,6,1,2]=>[[1,3,5],[2,6],[4,8],[7]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[2,3,5,4,8,6,7,1]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,8,3,5,7]=>[2,6,5,4,7,1,8,3]=>[[1,2,5,7],[3,8],[4],[6]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[6,3,5,4,7,1,8,2]=>[[1,3,5,7],[2,8],[4],[6]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[2,3,5,4,7,6,8,1]=>[[1,2,3,5,7],[4,6],[8]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,6,1,2,3,5,7,8]=>[2,3,5,4,6,1,7,8]=>[[1,2,3,5,7,8],[4],[6]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,1,2,3,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[2,3,4,1,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,3,7,8,5,6]=>[2,3,4,1,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,3,7,5,6,8]=>[2,3,4,1,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[2,4,5,1,7,8,3,6]=>[[1,2,3,5,6],[4,7,8]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[4,1,2,7,3,8,5,6]=>[2,4,7,1,6,8,3,5]=>[[1,2,3,6],[4,5,8],[7]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,1,2,7,8,3,5,6]=>[2,4,5,1,6,8,7,3]=>[[1,2,3,5,6],[4,7],[8]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,7,2,3,5,8,6]=>[4,3,5,1,7,8,2,6]=>[[1,3,5,6],[2,7,8],[4]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,7,2,3,8,5,6]=>[4,3,7,1,6,8,2,5]=>[[1,3,6],[2,5,8],[4,7]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,1,7,2,8,3,5,6]=>[4,7,5,1,6,8,2,3]=>[[1,2,5,6],[3,7,8],[4]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,7,8,2,3,5,6]=>[4,3,5,1,6,8,7,2]=>[[1,3,5,6],[2,7],[4,8]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[7,3,5,4,6,8,1,2]=>[[1,3,5,6],[2,8],[4],[7]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6,8]=>[2,3,5,4,6,7,1,8]=>[[1,2,3,5,6,8],[4],[7]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,2,3,5,8,6,7]=>[2,3,4,1,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>[2,3,4,1,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[2,4,5,1,6,7,8,3]=>[[1,2,3,5,6,7],[4,8]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[4,3,5,1,6,7,8,2]=>[[1,3,5,6,7],[2,8],[4]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[2,3,5,4,6,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[[1,2,3,4,7],[5,8],[6]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[[1,2,3,4,6],[5,8],[7]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6,8]=>[1,2,3,6,5,7,4,8]=>[[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,2,5,3,6,7,4,8]=>[1,2,5,7,3,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,5,3,6,4,8,7]=>[1,2,5,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,2,5,3,6,8,4,7]=>[1,2,5,7,3,6,8,4]=>[[1,2,3,4,7],[5,6],[8]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>[[1,2,3,4,7],[5,8],[6]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,2,5,6,8,3,4,7]=>[1,2,4,7,5,6,8,3]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>[[1,2,3,4,7,8],[5],[6]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,7,8,6]=>[1,2,4,5,3,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6,8]=>[1,2,4,5,3,7,6,8]=>[[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,7,8,4,6]=>[1,2,5,6,3,8,7,4]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>[[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>[[1,2,3,6],[4,8],[5],[7]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,6,7,4,8]=>[1,3,5,7,2,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>[[1,2,3,4,7],[5,6,8]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,5,2,6,7,3,8,4]=>[1,5,7,8,2,6,3,4]=>[[1,2,3,4],[5,6,8],[7]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[1,5,4,8,2,6,7,3]=>[[1,2,4,7],[3,6],[5,8]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,2,6,7,3,4,8]=>[1,5,4,7,2,6,3,8]=>[[1,2,4,8],[3,6],[5,7]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>[[1,2,3,4,7],[5,6,8]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,2,6,8,3,4,7]=>[1,5,4,7,2,6,8,3]=>[[1,2,4,7],[3,6],[5,8]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>[[1,2,4,7,8],[3,6],[5]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,6,2,3,7,8,4]=>[1,3,6,8,5,2,7,4]=>[[1,2,3,4],[5,7],[6,8]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,5,6,2,3,7,4,8]=>[1,3,6,7,5,2,4,8]=>[[1,2,3,4,8],[5,7],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,6,2,7,8,3,4]=>[1,6,4,8,5,2,7,3]=>[[1,2,4,7],[3,5],[6,8]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,7,3,4,8]=>[1,6,4,7,5,2,3,8]=>[[1,2,4,8],[3,5],[6,7]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,5,6,7,2,3,8,4]=>[1,3,7,8,5,6,2,4]=>[[1,2,3,4],[5,6],[7,8]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,6,7,2,8,3,4]=>[1,7,4,8,5,6,2,3]=>[[1,2,4,6],[3,5],[7,8]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>[[1,2,3,4,7],[5,8],[6]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,7,8,6]=>[1,3,4,5,2,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>[[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>[[1,2,3,4,6],[5,7,8]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>[[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>[[1,2,4,6],[3,7,8],[5]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>[[1,2,3,6],[4,7,8],[5]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>[[1,2,3,4,6],[5,8],[7]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>[[1,2,3,6],[4,8],[5],[7]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>[[1,2,4,6],[3,8],[5],[7]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>[[1,2,4,6,7],[3,8],[5]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]=>[2,3,5,8,1,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,3,6,4,8,7]=>[2,3,5,6,1,4,8,7]=>[[1,2,3,4,7],[5,6,8]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,6,4,7,8]=>[2,3,5,6,1,4,7,8]=>[[1,2,3,4,7,8],[5,6]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,6,3,7,8,4]=>[2,5,6,8,1,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[2,5,7,8,1,6,3,4]=>[[1,2,3,4],[5,6,8],[7]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,6,3,8,4,7]=>[2,5,6,7,1,3,8,4]=>[[1,2,3,4,7],[5,6,8]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,6,3,4,7,8]=>[2,5,4,6,1,3,7,8]=>[[1,2,4,7,8],[3,6],[5]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[5,3,6,8,1,2,7,4]=>[[1,3,4],[2,6,7],[5,8]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,6,2,7,8,3,4]=>[5,6,4,8,1,2,7,3]=>[[1,2,4],[3,6,7],[5,8]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[5,3,7,8,1,6,2,4]=>[[1,3,4],[2,6,8],[5,7]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,2,8,3,4]=>[5,7,4,8,1,6,2,3]=>[[1,2,4],[3,6,8],[5,7]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,2,3,4]=>[5,3,4,8,1,6,7,2]=>[[1,3,4,7],[2,6],[5,8]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[5,1,6,2,3,8,4,7]=>[5,3,6,7,1,2,8,4]=>[[1,3,4,7],[2,6,8],[5]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,1,6,2,8,3,4,7]=>[5,6,4,7,1,2,8,3]=>[[1,2,4,7],[3,6,8],[5]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,7,8,4]=>[2,3,6,8,5,1,7,4]=>[[1,2,3,4],[5,7],[6,8]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1,2,7,3,8,4]=>[2,6,7,8,5,1,3,4]=>[[1,2,3,4],[5,7,8],[6]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,1,2,7,8,3,4]=>[2,6,4,8,5,1,7,3]=>[[1,2,4,7],[3,5],[6,8]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,6,1,7,2,3,8,4]=>[6,3,7,8,5,1,2,4]=>[[1,3,4],[2,5,8],[6,7]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[5,6,1,7,2,8,3,4]=>[6,7,4,8,5,1,2,3]=>[[1,2,4],[3,5,8],[6,7]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,6,1,7,8,2,3,4]=>[6,3,4,8,5,1,7,2]=>[[1,3,4,7],[2,5],[6,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,1,2,3,8,4]=>[2,3,7,8,5,6,1,4]=>[[1,2,3,4],[5,6],[7,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,1,2,8,3,4]=>[2,7,4,8,5,6,1,3]=>[[1,2,4,6],[3,5],[7,8]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[7,3,4,8,5,6,1,2]=>[[1,3,4,6],[2,5],[7,8]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[2,3,4,8,5,6,7,1]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[2,3,4,7,5,6,1,8]=>[[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,8,4,7]=>[2,3,6,7,5,1,8,4]=>[[1,2,3,4,7],[5,8],[6]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[2,3,4,7,5,6,8,1]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[2,3,4,6,5,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,7,8,6]=>[2,3,4,5,1,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6,8]=>[2,3,4,5,1,7,6,8]=>[[1,2,3,4,6,8],[5,7]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[2,3,5,7,1,8,4,6]=>[[1,2,3,4,6],[5,7,8]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[2,5,4,7,1,8,3,6]=>[[1,2,4,6],[3,7,8],[5]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6,8]=>[2,5,4,6,1,7,3,8]=>[[1,2,4,6,8],[3,7],[5]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,7,2,8,3,4,6]=>[5,7,4,6,1,8,2,3]=>[[1,2,6],[3,4,8],[5,7]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,8,6]=>[2,3,4,7,5,8,1,6]=>[[1,2,3,4,6],[5,8],[7]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[5,7,1,2,3,8,4,6]=>[2,3,7,6,5,8,1,4]=>[[1,2,3,6],[4,8],[5],[7]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]=>[2,7,4,6,5,8,1,3]=>[[1,2,4,6],[3,8],[5],[7]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[2,3,4,6,5,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]=>[2,3,4,6,5,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[2,3,4,5,1,6,8,7]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,1,2,3,4,8,6,7]=>[2,3,4,5,1,7,8,6]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,8,4,6,7]=>[2,3,5,6,1,7,8,4]=>[[1,2,3,4,6,7],[5,8]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[2,5,4,6,1,7,8,3]=>[[1,2,4,6,7],[3,8],[5]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[2,3,4,6,5,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[1,2,3,4,6,7,8],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[[1,2,3,4,5],[6,8],[7]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>[[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>[[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>[[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,2,6,3,4,7,8,5]=>[1,2,4,6,8,3,7,5]=>[[1,2,3,4,5],[6,7],[8]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>[[1,2,3,5],[4,7],[6,8]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,2,6,7,3,4,8,5]=>[1,2,4,7,8,6,3,5]=>[[1,2,3,4,5],[6,8],[7]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,2,6,7,3,8,4,5]=>[1,2,7,5,8,6,3,4]=>[[1,2,3,5],[4,6],[7,8]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>[[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>[[1,2,3,5,7],[4,8],[6]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>[[1,2,3,5,8],[4,7],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>[[1,2,4,5],[3,7,8],[6]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>[[1,2,3,5],[4,7,8],[6]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>[[1,2,4,5,8],[3,7],[6]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>[[1,2,3,5],[4,6],[7,8]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>[[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>[[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>[[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>[[1,2,4,5,7],[3,8],[6]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,7,8,5]=>[2,3,4,6,8,1,7,5]=>[[1,2,3,4,5],[6,7],[8]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,7,5,8]=>[2,3,4,6,7,1,5,8]=>[[1,2,3,4,5,8],[6,7]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[2,3,6,7,8,1,4,5]=>[[1,2,3,4,5],[6,7,8]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,1,2,7,3,8,4,5]=>[2,6,7,5,8,1,3,4]=>[[1,2,3,5],[4,7,8],[6]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,1,2,7,8,3,4,5]=>[2,6,4,5,8,1,7,3]=>[[1,2,4,5],[3,7],[6,8]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[6,1,2,7,3,4,5,8]=>[2,6,4,5,7,1,3,8]=>[[1,2,4,5,8],[3,7],[6]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,7,2,8,3,4,5]=>[6,7,4,5,8,1,2,3]=>[[1,2,5],[3,4,8],[6,7]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[6,3,4,5,8,1,7,2]=>[[1,3,4,5],[2,7],[6,8]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]=>[6,3,4,5,7,1,2,8]=>[[1,3,4,5,8],[2,7],[6]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,8,5]=>[2,3,4,7,8,6,1,5]=>[[1,2,3,4,5],[6,8],[7]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,1,2,3,8,4,5]=>[2,3,7,5,8,6,1,4]=>[[1,2,3,5],[4,6],[7,8]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[7,3,4,5,8,6,1,2]=>[[1,3,4,5],[2,6],[7,8]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[2,3,4,5,8,6,7,1]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]=>[2,3,4,5,7,6,1,8]=>[[1,2,3,4,5,8],[6],[7]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[2,3,4,5,6,1,8,7]=>[[1,2,3,4,5,7],[6,8]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[2,6,4,5,7,1,8,3]=>[[1,2,4,5,7],[3,8],[6]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[6,3,4,5,7,1,8,2]=>[[1,3,4,5,7],[2,8],[6]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]=>[2,3,4,5,7,6,8,1]=>[[1,2,3,4,5,7],[6],[8]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[[1,2,3,4,5,7,8],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[[1,2,3,4,5,6],[7,8]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>[[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>[[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>[[1,2,3,4,5,6],[7,8]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>[[1,2,3,4,6],[5,8],[7]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>[[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>[[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>[[1,2,3,4,5,6],[7,8]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>[[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>[[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>[[1,2,3,4,5,6],[7,8]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>[[1,2,3,4,6],[5,8],[7]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>[[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>[[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[2,3,4,5,7,8,1,6]=>[[1,2,3,4,5,6],[7,8]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,8,5,6]=>[2,3,4,7,6,8,1,5]=>[[1,2,3,4,6],[5,8],[7]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[7,1,2,3,8,4,5,6]=>[2,3,7,5,6,8,1,4]=>[[1,2,3,5,6],[4,8],[7]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>[2,7,4,5,6,8,1,3]=>[[1,2,4,5,6],[3,8],[7]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[7,3,4,5,6,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[2,3,4,5,6,8,7,1]=>[[1,2,3,4,5,6],[7],[8]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[[1,2,3,4,5,6,8],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>[[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>[[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>[[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>[[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>[[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[[1,2,3,4,5,6,7],[8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[[1,2,3,4,5,6,7,8],[9]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[2,3,4,5,6,8,9,1,7]=>[[1,2,3,4,5,6,7],[8,9]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8],[2],[9]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[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]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[2,3,4,5,6,7,9,10,1,8]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,9,7]=>[1,3,4,5,6,8,9,2,7]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[2,3,4,5,6,7,1,9,8]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>[2,1,4,5,6,7,8,9,3]=>[[1,3,4,5,6,7,8],[2,9]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[[1,3,4,5,6,7,9],[2],[8]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[2,3,4,5,6,7,8,10,11,1,9]=>[[1,2,3,4,5,6,7,8,9],[10,11]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[2,3,4,5,6,7,8,1,10,9]=>[[1,2,3,4,5,6,7,9],[8,10]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,4,5,6,7,8,9,10,3]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[3,2,4,5,6,7,8,9,10,11,1]=>[[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,11,10]=>[2,3,4,5,6,7,8,9,1,11,10]=>[[1,2,3,4,5,6,7,8,10],[9,11]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,9,8]=>[1,3,4,5,6,7,2,9,8]=>[[1,2,3,4,5,6,8],[7,9]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7,9]=>[2,1,4,5,6,7,8,3,9]=>[[1,3,4,5,6,7,9],[2,8]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,9,10,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,10,9,1]=>[[1,3,4,5,6,7,8],[2,9],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,9,8]=>[2,3,1,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[[1,2,3,4,5,6,7,9],[8]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,9,7,8]=>[2,1,3,4,5,6,8,9,7]=>[[1,3,4,5,6,7,8],[2,9]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,3,4,8,5,9,6]=>[2,3,4,7,8,9,1,5,6]=>[[1,2,3,4,5,6],[7,8,9]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[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]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[1,4,3,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8],[3],[9]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,6,9,7,10,8]=>[1,2,3,4,5,6,9,10,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[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]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[2,3,4,5,7,9,1,8,6]=>[[1,2,3,4,5,6],[7,8],[9]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,7,10,8,9]=>[2,1,3,4,5,6,7,9,10,8]=>[[1,3,4,5,6,7,8,9],[2,10]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7,9]=>[2,3,4,5,6,1,8,7,9]=>[[1,2,3,4,5,7,9],[6,8]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8],[2],[9]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>[[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]=>[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]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,2,3,4,5,9,6,10,7]=>[2,3,4,5,8,9,10,1,6,7]=>[[1,2,3,4,5,6,7],[8,9,10]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[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]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,5,8,9,7]=>[2,3,4,5,6,1,9,8,7]=>[[1,2,3,4,5,7],[6,8],[9]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,1,9,4,5,6,7,8]=>[3,2,1,5,6,7,8,9,4]=>[[1,4,5,6,7,8],[2,9],[3]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[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]=>[3,4,5,6,7,8,9,1,2]=>[2,9,3,4,5,6,7,8,1]=>[[1,2,4,5,6,7,8],[3],[9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[2,8,3,4,5,6,7,1,9]=>[[1,2,4,5,6,7,9],[3],[8]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,6,9,7,8]=>[2,3,1,4,5,6,8,9,7]=>[[1,2,4,5,6,7,8],[3,9]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,1,2,9,4,5,6,7,8]=>[2,3,1,5,6,7,8,9,4]=>[[1,2,4,5,6,7,8],[3,9]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,9,2,4,5,6,7,8]=>[3,4,1,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8],[3,9]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,9,1,2,4,5,6,7,8]=>[2,4,3,5,6,7,8,9,1]=>[[1,2,4,5,6,7,8],[3],[9]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,2,3]=>[1,3,9,4,5,6,7,8,2]=>[[1,2,3,5,6,7,8],[4],[9]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[2,3,9,4,5,6,7,8,1]=>[[1,2,3,5,6,7,8],[4],[9]]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[2,3,6,4,5,1,7,8,9]=>[[1,2,3,5,7,8,9],[4],[6]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[1,2,3,6,7,8,9],[4],[5]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,1,2,3,9,5,6,7,8]=>[2,3,4,1,6,7,8,9,5]=>[[1,2,3,5,6,7,8],[4,9]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8,9]=>[1,3,4,5,2,6,7,8,9]=>[[1,2,3,4,6,7,8,9],[5]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[2,3,4,9,5,6,7,8,1]=>[[1,2,3,4,6,7,8],[5],[9]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[2,3,4,8,5,6,7,1,9]=>[[1,2,3,4,6,7,9],[5],[8]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,6,1,2,3,4,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>[[1,2,3,4,7,8,9],[5],[6]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,9,6,7,8]=>[2,3,4,5,1,7,8,9,6]=>[[1,2,3,4,6,7,8],[5,9]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,9,1,2,3,4,6,7,8]=>[2,3,4,6,5,7,8,9,1]=>[[1,2,3,4,6,7,8],[5],[9]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[1,2,3,4,6,7,8,9],[5]]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,6,3,4,5,7,8,9]=>[1,2,4,5,6,3,7,8,9]=>[[1,2,3,4,5,7,8,9],[6]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[2,3,4,5,9,6,7,8,1]=>[[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,7,9,1,2,3,4,5,8]=>[2,3,4,5,8,6,7,9,1]=>[[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7,9]=>[2,3,4,5,7,6,8,1,9]=>[[1,2,3,4,5,7,9],[6],[8]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,9,7,8]=>[2,3,4,5,6,1,8,9,7]=>[[1,2,3,4,5,7,8],[6,9]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[6,9,1,2,3,4,5,7,8]=>[2,3,4,5,7,6,8,9,1]=>[[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[1,2,3,4,5,7,8,9],[6]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[1,3,4,5,6,8,7,9,2]=>[[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8,9]=>[1,3,4,5,6,7,2,8,9]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6,9]=>[7,3,4,5,6,8,1,2,9]=>[[1,3,4,5,6,9],[2,8],[7]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[2,3,4,5,6,9,7,8,1]=>[[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[2,3,4,5,6,8,7,1,9]=>[[1,2,3,4,5,6,9],[7],[8]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,9,6,8]=>[2,3,4,5,7,8,1,9,6]=>[[1,2,3,4,5,6,8],[7,9]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,9,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,7,9,1]=>[[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[1,2,3,4,5,6,8,9],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,7,9,8,6]=>[[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,7,8,6,9]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,6,7,9,8,5]=>[[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7,9]=>[1,2,3,5,6,7,8,4,9]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,8,2,9,3,4,5,6,7]=>[1,8,4,5,6,7,9,2,3]=>[[1,2,4,5,6,7],[3,9],[8]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>[[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[8,1,2,3,9,4,5,6,7]=>[2,3,8,5,6,7,9,1,4]=>[[1,2,3,5,6,7],[4,9],[8]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,9,8,1]=>[[1,2,3,4,5,6,7],[8],[9]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[[1,2,3,4,5,6,7,9],[8]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,7,8,9,6]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,6,7,8,9,5]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,5,6,7,8,9,4]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[1,2,4,5,6,7,8,9,3]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>[[1,2,3,4,5,6,7,8],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[1,3,4,5,6,7,9],[2],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,9,1,8]=>[8,2,3,4,5,6,7,9,1]=>[[1,3,4,5,6,7,8],[2],[9]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,1,7]=>[7,2,3,4,5,6,9,8,1]=>[[1,3,4,5,6,7],[2,8],[9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,1,6]=>[6,2,3,4,5,9,7,8,1]=>[[1,3,4,5,6,8],[2,7],[9]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,1,5]=>[5,2,3,4,9,6,7,8,1]=>[[1,3,4,5,7,8],[2,6],[9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,1,4]=>[4,2,3,9,5,6,7,8,1]=>[[1,3,4,6,7,8],[2,5],[9]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,1,3]=>[3,2,9,4,5,6,7,8,1]=>[[1,3,5,6,7,8],[2,4],[9]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[1,3,4,5,6,8,9],[2],[7]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[9,2,3,4,5,6,7,8,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,6,1,9,7,8]=>[6,2,3,4,5,1,8,9,7]=>[[1,3,4,5,7,8],[2,9],[6]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[8,2,3,4,5,6,7,10,9,1]=>[[1,3,4,5,6,7,8],[2,9],[10]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,1,8,9,6,7]=>[5,2,3,4,1,7,9,8,6]=>[[1,3,4,6,7],[2,8],[5,9]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[7,2,3,4,5,6,10,8,9,1]=>[[1,3,4,5,6,7,9],[2,8],[10]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,1,7,8,9,5,6]=>[4,2,3,1,6,9,7,8,5]=>[[1,3,5,6,8],[2,7],[4,9]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[6,2,3,4,5,10,7,8,9,1]=>[[1,3,4,5,6,8,9],[2,7],[10]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,9,4,5]=>[3,2,1,5,9,6,7,8,4]=>[[1,4,5,7,8],[2,6],[3,9]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[5,2,3,4,10,6,7,8,9,1]=>[[1,3,4,5,7,8,9],[2,6],[10]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,9,3,4]=>[2,1,4,9,5,6,7,8,3]=>[[1,3,4,6,7,8],[2,5],[9]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[4,2,3,10,5,6,7,8,9,1]=>[[1,3,4,6,7,8,9],[2,5],[10]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[3,2,10,4,5,6,7,8,9,1]=>[[1,3,5,6,7,8,9],[2,4],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[2,10,3,4,5,6,7,8,9,1]=>[[1,2,4,5,6,7,8,9],[3],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[10,2,3,4,5,6,7,8,9,11,1]=>[[1,3,4,5,6,7,8,9,10],[2],[11]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[1,3,4,5,7,8,9],[2],[6]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[1,3,4,6,7,8,9],[2],[5]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,10,1,6,7,8,9]=>[6,2,3,4,5,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,5,6,1,2,3,9,10,7,8]=>[2,3,6,4,5,1,8,10,9,7]=>[[1,2,3,5,7,8],[4,9],[6,10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>[[1,3,4,5,6,8],[2,9],[7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[[1,4,6,8],[2,5,7,9],[3]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>[[1,4,6,7,8,9],[2,5],[3]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>[[1,3,5,6,7,8],[2,4],[9]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[[1,3,5,7,8,9],[2,4,6]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[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]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8],[3,9]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[[1,2,3,5,6,7,8],[4],[9]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[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]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[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]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[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]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[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]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[[1,2,3,4,5,6,8,9],[7]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[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]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[[1,3,5,7,9,10],[2,4,6,8]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[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]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8,9],[3],[10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[[1,2,4,6,8],[3,5,7,9],[10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[[1,2,3,5,6,7,8,9],[4],[10]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[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]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[[1,2,3,4,5,7,8,9],[6],[10]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>[[1,2,3,4,5,7,9],[6,8,10]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[[1,2,3,4,5,6,8,9],[7],[10]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[[1,2,3,4,5,6,7,9],[8],[10]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[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]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[3,9,1,4,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4],[9]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,2]=>[6,9,3,4,5,1,7,8,2]=>[[1,2,5,7,8],[3,4],[6,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,2]=>[7,9,3,4,5,6,1,8,2]=>[[1,2,5,6,8],[3,4],[7,9]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,1,9,2]=>[8,9,3,4,5,6,7,1,2]=>[[1,2,5,6,7],[3,4],[8,9]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[3,10,1,4,5,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,8,1,9,10,2]=>[8,10,3,4,5,6,7,1,9,2]=>[[1,2,5,6,7,9],[3,4],[8,10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,1,10,2]=>[9,10,3,4,5,6,7,8,1,2]=>[[1,2,5,6,7,8],[3,4],[9,10]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,9,2,8]=>[1,8,3,4,5,6,7,9,2]=>[[1,2,4,5,6,7,8],[3],[9]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[1,2,3,4,5,6,7,8,9,11],[10]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[2,3,4,5,6,7,9,8,1,10]=>[[1,2,3,4,5,6,7,10],[8],[9]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,10,9,2]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,8,2,9]=>[3,8,1,4,5,6,7,2,9]=>[[1,2,5,6,7,9],[3,4],[8]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,9,10,8]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,10,11,9]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,7,9,5,8,6]=>[[1,2,3,4,5,6],[7,8],[9]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,3,6,4,7,8,9,5]=>[1,2,3,6,9,4,7,8,5]=>[[1,2,3,4,5,8],[6,7],[9]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,9,4]=>[1,2,5,9,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6],[9]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,9,3]=>[1,4,9,2,5,6,7,8,3]=>[[1,2,3,6,7,8],[4,5],[9]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[1,2,3,4,5,6,7,8,9,10],[11]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>[3,2,4,5,6,10,7,8,9,1]=>[[1,3,4,5,6,8,9],[2,7],[10]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,1,6,2,7,8,9]=>[5,6,3,4,1,2,7,8,9]=>[[1,2,7,8,9],[3,4],[5,6]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,1,4,8,9,2,5,6,7]=>[3,5,1,4,6,7,9,8,2]=>[[1,2,5,6,7],[3,4,8],[9]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[2,3,4,10,5,6,7,8,9,1]=>[[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,4,7,6,8,9]=>[2,3,4,5,1,7,6,8,9]=>[[1,2,3,4,6,8,9],[5,7]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[1,2,3,6,5,7,8,9,4]=>[[1,2,3,4,6,7,8],[5],[9]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,8,7,9,6]=>[[1,2,3,4,5,6,8],[7],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,8,9,10,7]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,7,6,8,9,5]=>[[1,2,3,4,5,7,8],[6],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,7,8,9,10,6]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,6,7,8,9,10,5]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[1,2,5,4,6,7,8,9,3]=>[[1,2,3,5,6,7,8],[4],[9]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,5,6,7,8,9,10,4]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,4,5,6,7,8,9,10,3]=>[[1,2,3,4,5,6,7,8,9],[10]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,4,7,5,8,6,9]=>[1,2,3,4,7,8,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[3,4,1,5,2,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7,9]=>[3,5,1,6,2,4,8,7,9]=>[[1,2,4,7,9],[3,5,6,8]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7,9]=>[3,4,1,2,6,5,8,7,9]=>[[1,2,5,7,9],[3,4,6,8]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[2,4,3,1,5,6,7,8,9,10]=>[[1,2,5,6,7,8,9,10],[3],[4]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[2,3,10,4,5,6,7,8,9,1]=>[[1,2,3,5,6,7,8,9],[4],[10]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[1,3,4,5,6,7,8,9,2,10]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,8,4,5,6,7,9,10]=>[1,2,3,5,6,7,8,4,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[3,2,5,4,7,6,9,8,10,1]=>[[1,3,5,7,9],[2,4,6,8],[10]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[6,7,8,9,10,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[[1,3,5,7,9,11],[2,4,6,8,10],[12]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[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]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[1,2,4,5,6,7,8,9,10,11],[3]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,10,7,9]=>[2,3,4,5,6,8,9,1,10,7]=>[[1,2,3,4,5,6,7,9],[8,10]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,10,2,4,5,6,7,8,9]=>[3,4,1,5,6,7,8,9,10,2]=>[[1,2,4,5,6,7,8,9],[3,10]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[3,11,1,4,5,6,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4],[11]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[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]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[2,3,4,5,10,6,7,8,9,1]=>[[1,2,3,4,5,7,8,9],[6],[10]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[9,3,4,5,6,7,8,10,1,2]=>[[1,3,4,5,6,7,8],[2,10],[9]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,9,10,1,2,4,5,6]=>[2,4,3,5,6,10,7,8,9,1]=>[[1,2,4,5,6,8,9],[3,7],[10]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,10,1,4,5,6,7,8,9]=>[4,2,3,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,7,8,9,5]=>[2,3,4,6,9,1,7,8,5]=>[[1,2,3,4,5,8],[6,7],[9]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,4,5,8,6,7,9,10]=>[1,2,3,4,5,7,8,6,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[5,10,1,2,3,4,6,7,8,9]=>[2,3,4,6,5,7,8,9,10,1]=>[[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,10,9,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[1,2,3,4,5,6,7,8,9],[10],[11]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,8,1,9,7]=>[8,2,3,4,5,6,9,1,7]=>[[1,3,4,5,6,7],[2,9],[8]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,9,1,10,8]=>[9,2,3,4,5,6,7,10,1,8]=>[[1,3,4,5,6,7,8],[2,10],[9]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[2,3,4,5,6,10,7,8,9,1]=>[[1,2,3,4,5,6,8,9],[7],[10]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,10,8,9,1]=>[[1,2,3,4,5,6,7,9],[8],[10]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,10,1,11,2]=>[10,11,3,4,5,6,7,8,9,1,2]=>[[1,2,5,6,7,8,9],[3,4],[10,11]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7,9]=>[2,3,4,1,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,1,9,3]=>[8,2,9,4,5,6,7,1,3]=>[[1,3,5,6,7],[2,4],[8,9]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[2,3,4,8,5,6,7,1,9,10]=>[[1,2,3,4,6,7,9,10],[5],[8]]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[2,3,6,4,5,1,7,8,9,10]=>[[1,2,3,5,7,8,9,10],[4],[6]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,5,6,9,7,8,10]=>[1,2,3,4,5,6,8,9,7,10]=>[[1,2,3,4,5,6,7,8,10],[9]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9,10]=>[1,3,4,2,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3,1,2,10,4,5,6,7,8,9]=>[2,3,1,5,6,7,8,9,10,4]=>[[1,2,4,5,6,7,8,9],[3,10]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,10,6,7,8,9]=>[2,3,4,5,1,7,8,9,10,6]=>[[1,2,3,4,6,7,8,9],[5,10]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,10,1,2,3,4,6]=>[2,3,4,6,5,10,7,8,9,1]=>[[1,2,3,4,6,8,9],[5,7],[10]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,9,10,1,2,3,5,6]=>[2,3,5,4,6,10,7,8,9,1]=>[[1,2,3,5,6,8,9],[4,7],[10]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>[10,2,3,4,5,6,7,8,11,1,9]=>[[1,3,4,5,6,7,8,9],[2,11],[10]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,7,8,10,1,2,3,4,9]=>[2,3,4,9,5,6,7,8,10,1]=>[[1,2,3,4,6,7,8,9],[5],[10]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[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]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,9,1,10,3]=>[9,2,10,4,5,6,7,8,1,3]=>[[1,3,5,6,7,8],[2,4],[9,10]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,9,8]=>[1,4,5,2,3,7,6,9,8]=>[[1,2,3,6,8],[4,5,7,9]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7,9]=>[1,3,4,2,6,5,8,7,9]=>[[1,2,3,5,7,9],[4,6,8]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7,10,9]=>[1,3,4,2,6,5,8,7,10,9]=>[[1,2,3,5,7,9],[4,6,8,10]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,9]=>[3,2,4,1,6,5,8,7,9]=>[[1,3,5,7,9],[2,6,8],[4]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,7,8,9,10,3,4,5,6]=>[2,1,4,5,6,10,7,8,9,3]=>[[1,3,4,5,6,8,9],[2,7],[10]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[3,4,1,2,8,9,10,5,6,7]=>[2,4,3,1,6,7,10,8,9,5]=>[[1,2,5,6,7,9],[3,8],[4,10]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,7,8,1,2,3,4,10,9]=>[2,3,4,8,5,6,7,1,10,9]=>[[1,2,3,4,6,7,9],[5,10],[8]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,7,1,8,2,9,3]=>[7,8,9,4,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7,8,9]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,9,10,7]=>[2,3,4,5,6,8,10,1,9,7]=>[[1,2,3,4,5,6,7],[8,9],[10]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[1,2,3,4,5,6,8,10,9,7]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[1,3,2,5,4,7,6,9,10,8]=>[[1,2,4,6,8,9],[3,5,7,10]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[4,2,6,1,8,3,9,5,10,7]=>[[1,3,5,7,9],[2,6,8,10],[4]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,5,8,10,7,9]=>[2,1,4,3,6,5,9,8,10,7]=>[[1,3,5,7,9],[2,4,6,8],[10]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,4,6,8,10,1,2,5,7,9]=>[2,5,3,4,7,6,9,8,10,1]=>[[1,2,4,5,7,9],[3,6,8],[10]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,6,2,7,3,8,4,9,5,10]=>[1,6,7,8,9,2,3,4,5,10]=>[[1,2,3,4,5,10],[6,7,8,9]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,12,10,11]=>[1,3,2,5,4,7,6,9,8,11,12,10]=>[[1,2,4,6,8,10,11],[3,5,7,9,12]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[[1,2,3,4,5,6,7,8,9,10,11],[12]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[[1,2,3,4,5,6,7,8,9,10,11],[12]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[4,2,5,1,3,7,6,9,8,10]=>[[1,3,6,8,10],[2,5,7,9],[4]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,9,10,7,8,12,11]=>[2,1,4,6,5,3,8,10,9,7,12,11]=>[[1,3,4,7,8,11],[2,5,9,12],[6,10]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7,9]=>[4,2,6,1,7,3,8,5,9]=>[[1,3,5,7,9],[2,6,8],[4]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,5,6,9,10,1,2,3,7,8]=>[2,3,7,4,5,6,8,10,9,1]=>[[1,2,3,5,6,7,8],[4,9],[10]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,5,8,9,10,1,2,3,6,7]=>[2,3,6,4,5,7,10,8,9,1]=>[[1,2,3,5,6,7,9],[4,8],[10]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,6,3,5,8,7,9]=>[4,2,5,1,6,3,8,7,9]=>[[1,3,5,7,9],[2,6,8],[4]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,9,8]=>[4,2,5,1,3,7,6,9,8]=>[[1,3,6,8],[2,5,7,9],[4]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7,10,9]=>[3,2,4,1,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,6,8,10],[4]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[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]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,8,9,10,1,3,4,5,7]=>[3,2,4,5,7,6,10,8,9,1]=>[[1,3,4,5,7,9],[2,6,8],[10]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>[3,2,4,5,6,7,12,8,9,10,11,1]=>[[1,3,4,5,6,7,9,10,11],[2,8],[12]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,2,7,3,8,4,9,5]=>[1,6,7,8,9,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,6,2,7,3,8,4,9]=>[5,6,7,8,1,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,10,11,1,12,2]=>[11,12,3,4,5,6,7,8,9,10,1,2]=>[[1,2,5,6,7,8,9,10],[3,4],[11,12]]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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.