Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0Cc0007;cc-rep-3
[1,0]=>[1]=>[1]=>[[1]]=>[1]
[1,0,1,0]=>[1,2]=>[1,2]=>[[1,2]]=>[2]
[1,1,0,0]=>[2,1]=>[2,1]=>[[1],[2]]=>[1,1]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[[1,2,3]]=>[3]
[1,0,1,1,0,0]=>[1,3,2]=>[3,1,2]=>[[1,2],[3]]=>[2,1]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[1,3],[2]]=>[1,2]
[1,1,0,1,0,0]=>[2,3,1]=>[2,3,1]=>[[1,3],[2]]=>[1,2]
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[[1],[2],[3]]=>[1,1,1]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[[1,2,3,4]]=>[4]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[4,1,2,3]=>[[1,2,3],[4]]=>[3,1]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,1,2,4]=>[[1,2,4],[3]]=>[2,2]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[3,1,4,2]=>[[1,2],[3,4]]=>[2,2]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[4,3,1,2]=>[[1,2],[3],[4]]=>[2,1,1]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[1,3,4],[2]]=>[1,3]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[4,2,1,3]=>[[1,3],[2],[4]]=>[1,2,1]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[2,3,1,4]=>[[1,3,4],[2]]=>[1,3]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[2,3,4,1]=>[[1,3,4],[2]]=>[1,3]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[[1,3],[2],[4]]=>[1,2,1]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[[1,4],[2],[3]]=>[1,1,2]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[3,2,4,1]=>[[1,4],[2],[3]]=>[1,1,2]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[3,4,2,1]=>[[1,4],[2],[3]]=>[1,1,2]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[[1],[2],[3],[4]]=>[1,1,1,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[[1,2,3,4,5]]=>[5]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[5,1,2,3,4]=>[[1,2,3,4],[5]]=>[4,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[4,1,2,3,5]=>[[1,2,3,5],[4]]=>[3,2]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[4,1,2,5,3]=>[[1,2,3],[4,5]]=>[3,2]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[[1,2,3],[4],[5]]=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[3,1,2,4,5]=>[[1,2,4,5],[3]]=>[2,3]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[5,3,1,2,4]=>[[1,2,4],[3],[5]]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[3,1,4,2,5]=>[[1,2,5],[3,4]]=>[2,3]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[3,1,4,5,2]=>[[1,2,5],[3,4]]=>[2,3]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[5,3,1,4,2]=>[[1,2],[3,4],[5]]=>[2,2,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[4,3,1,2,5]=>[[1,2,5],[3],[4]]=>[2,1,2]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[4,3,1,5,2]=>[[1,2],[3,5],[4]]=>[2,1,2]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[4,5,1,3,2]=>[[1,2],[3,5],[4]]=>[2,1,2]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[5,4,3,1,2]=>[[1,2],[3],[4],[5]]=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]=>[1,4]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[5,2,1,3,4]=>[[1,3,4],[2],[5]]=>[1,3,1]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[4,2,1,3,5]=>[[1,3,5],[2],[4]]=>[1,2,2]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[4,2,1,5,3]=>[[1,3],[2,5],[4]]=>[1,2,2]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[5,4,2,1,3]=>[[1,3],[2],[4],[5]]=>[1,2,1,1]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[2,3,1,4,5]=>[[1,3,4,5],[2]]=>[1,4]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[5,2,3,1,4]=>[[1,3,4],[2],[5]]=>[1,3,1]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[2,3,4,1,5]=>[[1,3,4,5],[2]]=>[1,4]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[[1,3,4,5],[2]]=>[1,4]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[[1,3,4],[2],[5]]=>[1,3,1]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[[1,3,5],[2],[4]]=>[1,2,2]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[4,2,3,5,1]=>[[1,3,5],[2],[4]]=>[1,2,2]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[4,2,5,3,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,2,3,1]=>[[1,3],[2],[4],[5]]=>[1,2,1,1]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]]=>[1,1,3]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[5,3,2,1,4]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[3,2,4,1,5]=>[[1,4,5],[2],[3]]=>[1,1,3]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[3,2,4,5,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[3,4,2,1,5]=>[[1,4,5],[2],[3]]=>[1,1,3]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,3,4,2,1]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[4,5,3,2,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]=>[6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>[[1,2,3,4,5],[6]]=>[5,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>[[1,2,3,4,6],[5]]=>[4,2]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>[[1,2,3,4],[5,6]]=>[4,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>[[1,2,3,5],[4],[6]]=>[3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>[[1,2,3,6],[4,5]]=>[3,3]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>[[1,2,3],[4,5],[6]]=>[3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>[[1,2,3,6],[4],[5]]=>[3,1,2]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>[[1,2,4,5],[3],[6]]=>[2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>[[1,2,4],[3,6],[5]]=>[2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>[[1,2,5],[3,4],[6]]=>[2,3,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>[[1,2,5,6],[3,4]]=>[2,4]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>[[1,2,5],[3,4],[6]]=>[2,3,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>[[1,2,6],[3,4],[5]]=>[2,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>[[1,2,6],[3,4],[5]]=>[2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>[[1,2],[3,4],[5],[6]]=>[2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>[[1,2,5,6],[3],[4]]=>[2,1,3]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6]]=>[2,1,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5]]=>[2,1,1,2]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>[[1,3],[2,5],[4],[6]]=>[1,2,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>[[1,3,6],[2],[4],[5]]=>[1,2,1,2]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>[[1,3],[2,4],[5,6]]=>[1,2,1,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[[1,3,4,5,6],[2]]=>[1,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>[[1,3],[2,5],[4],[6]]=>[1,2,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>[[1,3,6],[2],[4],[5]]=>[1,2,1,2]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>[[1,3,6],[2],[4],[5]]=>[1,2,1,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>[4,1,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,1,3]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>[[1,2,3,6],[4],[5],[7]]=>[3,1,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>[[1,2,3],[4,6,7],[5]]=>[3,1,3]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,1,1,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,1,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>[2,2,1,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,1,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,1,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,1,2]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,1,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,1,4]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>[[1,2,5,6],[3],[4],[7]]=>[2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,1,2,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5],[7]]=>[2,1,1,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[5,6,7,1,4,3,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[7,5,6,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>[2,1,1,1,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[6,5,7,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[6,7,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>[[1,3,4],[2,5],[6,7]]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>[[1,3],[2,5],[4],[6],[7]]=>[1,2,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>[[1,3,7],[2,4],[5,6]]=>[1,2,1,3]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>[[1,3,7],[2,4],[5,6]]=>[1,2,1,3]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>[[1,3,7],[2,4],[5,6]]=>[1,2,1,3]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>[1,2,1,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>[[1,3,7],[2],[4],[5],[6]]=>[1,2,1,1,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>[[1,3],[2,4],[5,7],[6]]=>[1,2,1,1,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>[[1,3],[2,4],[5,7],[6]]=>[1,2,1,1,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[7,2,3,1,4,5,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>[[1,3,4],[2,5],[6,7]]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[6,2,3,4,7,5,1]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,5,2,3,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[5,2,3,6,4,7,1]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[5,2,3,6,7,4,1]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,5,2,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[6,5,2,3,7,4,1]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[6,7,2,3,5,4,1]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,4,2,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[6,4,2,3,5,7,1]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[6,4,2,3,7,5,1]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,6,4,2,3,5,1]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[4,2,5,3,6,7,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,4,2,5,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[4,2,5,6,3,7,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[6,4,2,5,3,7,1]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>[1,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,5,4,2,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[5,4,2,6,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[5,6,2,4,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[5,6,2,7,4,3,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,5,6,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[1,2,1,1,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>[[1,3,7],[2],[4],[5],[6]]=>[1,2,1,1,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[6,5,7,2,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[6,7,5,2,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>[[1,4],[2,5],[3,7],[6]]=>[1,1,2,1,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[6,3,2,4,5,7,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[6,3,2,4,7,5,1]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[5,3,2,4,6,7,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[5,3,2,6,4,7,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[5,3,2,6,7,4,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,5,3,2,6,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[6,5,3,2,4,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[6,5,3,2,7,4,1]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[6,7,3,2,5,4,1]=>[[1,4],[2,5],[3,7],[6]]=>[1,1,2,1,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,3,4,2,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[6,3,4,2,5,7,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[6,3,4,2,7,5,1]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,3,4,5,2,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[5,3,6,4,2,7,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[6,4,3,2,5,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[6,4,3,2,7,5,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,4,3,5,2,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,4,5,3,2,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]=>[8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[7,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[6,1,2,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[8,6,1,2,3,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[7,6,1,2,3,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[7,8,1,2,3,4,6,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[7,5,1,2,3,4,6,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[8,7,5,1,2,3,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[5,1,2,3,6,7,4,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[5,1,2,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[8,5,1,2,3,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,1,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,1,1,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[7,6,5,1,2,3,8,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[7,6,8,1,2,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[8,6,4,1,2,3,5,7]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[8,6,4,1,2,3,7,5]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[7,6,4,1,2,3,8,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,1,2]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6,8,7]=>[8,4,1,2,5,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[8,7,4,1,2,5,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[4,1,2,5,6,3,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>[4,1,2,5,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[4,1,2,5,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>[8,7,4,1,2,5,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,4,6,5,7,8,3]=>[6,4,1,2,5,7,8,3]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>[8,6,4,1,2,5,7,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,5,8,3]=>[6,4,1,2,7,5,8,3]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>[7,6,4,1,2,5,8,3]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,1,2]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[7,8,4,1,2,6,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,1,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[5,4,1,2,6,7,8,3]=>[[1,2,3,7,8],[4,6],[5]]=>[3,1,4]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>[5,6,1,2,7,4,8,3]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[5,6,1,2,7,8,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[8,5,6,1,2,7,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>[7,5,6,1,2,4,8,3]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,1,2,2]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>[8,6,5,4,1,2,7,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,1,1,2,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[6,7,8,1,2,5,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,1,1,1,2]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,6,5,8,4,3]=>[7,6,5,8,1,2,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[7,3,1,2,4,5,6,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[7,3,1,2,4,5,8,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[6,3,1,2,4,7,8,5]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[8,6,3,1,2,4,7,5]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[7,6,3,1,2,4,8,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,1,2]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[7,5,3,1,2,4,6,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[8,7,5,3,1,2,4,6]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[5,3,1,2,6,7,8,4]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[7,5,3,1,2,8,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[6,5,3,1,2,7,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,1,3]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[6,5,3,1,2,7,8,4]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,1,3]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,2,7,8,6,5,4]=>[7,8,6,3,1,2,5,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,1,1,2]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>[8,7,3,1,4,2,5,6]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[6,3,1,4,2,7,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[6,3,1,4,2,7,8,5]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[8,6,3,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,7,6,5,8]=>[7,6,3,1,4,2,5,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,1,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[7,6,3,1,4,2,8,5]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,1,2]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>[7,8,3,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,1,2]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[8,7,6,3,1,4,2,5]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>[7,3,1,4,5,2,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[7,3,1,4,5,2,8,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[3,1,4,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[8,3,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>[8,7,3,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,8,7,5,2]=>[8,6,3,1,4,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,7,8,6,5,2]=>[7,8,3,1,4,6,5,2]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,1,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,4,6,7,8,2]=>[5,3,1,4,6,7,8,2]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[5,3,1,6,4,2,7,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[5,3,1,6,7,8,4,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,6,4,8,2]=>[7,5,3,1,6,4,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[7,5,3,1,8,6,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>[8,7,5,3,1,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>[6,7,3,1,5,8,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,1,3]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>[6,7,3,1,8,5,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,1,3]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[8,7,6,5,3,1,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[7,4,3,1,2,5,6,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,1,3,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,3,2,6,5,7,8]=>[6,4,3,1,2,5,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>[6,4,3,1,2,7,5,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[6,4,3,1,2,7,8,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[7,6,4,3,1,2,8,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,1,2,1,2]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3,5,2,8,7,6]=>[8,7,4,3,1,5,2,6]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,1,3,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>[7,4,3,1,5,8,6,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,1,3,2]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>[8,7,4,3,1,5,6,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,1,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[6,4,3,1,5,2,7,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>[6,4,3,1,5,7,2,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>[6,4,3,1,5,7,8,2]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[8,6,4,3,1,5,7,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,1,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>[6,4,3,1,7,8,5,2]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[4,5,1,3,6,7,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,3,2,7,8]=>[4,5,1,6,3,2,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[4,5,1,6,7,3,2,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[4,5,1,6,7,3,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>[4,5,1,6,7,8,3,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>[6,4,7,1,5,3,8,2]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>[6,4,7,1,5,8,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,1,2,3]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[8,7,6,4,5,1,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[8,7,5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>[5,4,3,1,6,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[8,5,4,3,1,6,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>[8,7,5,4,3,1,6,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,4,6,3,2,7,8]=>[5,4,6,1,3,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[5,4,6,1,3,7,2,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[5,6,7,1,8,4,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,5,6,8,7,4,3,2]=>[8,5,6,7,1,4,3,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,6,8,4,3,2]=>[7,5,6,8,1,4,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,5,7,8,6,4,3,2]=>[7,5,8,6,1,4,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,1,1,2,2]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[8,7,5,6,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[8,6,5,4,3,1,7,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,5,7,4,3,8,2]=>[6,5,7,4,1,3,8,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>[6,5,7,8,1,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,5,8,7,4,3,2]=>[8,6,5,7,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>[6,7,5,8,1,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[6,7,8,5,1,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[8,6,7,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[7,6,5,8,4,1,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[6,2,1,3,4,7,8,5]=>[[1,3,4,5,8],[2,7],[6]]=>[1,4,3]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[8,7,5,2,1,3,4,6]=>[[1,3,4,6],[2],[5],[7],[8]]=>[1,3,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[5,2,1,3,6,7,8,4]=>[[1,3,4,7,8],[2,6],[5]]=>[1,3,4]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,3,5,7,8,6,4]=>[7,5,2,1,3,8,6,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[1,3,2,2]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,3,5,8,7,6,4]=>[8,7,5,2,1,3,6,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>[8,6,5,2,1,3,4,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>[1,3,1,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>[6,7,2,1,3,8,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>[1,3,1,3]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,7,6,5,4,8]=>[7,6,5,2,1,3,4,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,3,7,6,8,5,4]=>[7,6,8,2,1,3,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[1,3,1,1,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>[7,8,6,2,1,3,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[1,3,1,1,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[8,4,2,1,3,5,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>[1,2,4,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[6,4,2,1,3,5,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[1,2,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[8,6,4,2,1,3,5,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[6,4,2,1,3,7,8,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[1,2,2,3]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[8,6,4,2,1,3,7,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[7,6,4,2,1,3,8,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[1,2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[7,8,4,2,1,3,6,5]=>[[1,3,5],[2,6],[4,8],[7]]=>[1,2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[8,7,6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[8,4,2,1,5,3,6,7]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[8,4,2,1,5,6,3,7]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[4,2,1,5,6,7,8,3]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>[8,4,2,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[7,4,2,1,5,8,6,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[1,2,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>[6,4,2,1,5,3,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[1,2,2,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[8,6,4,2,1,5,3,7]=>[[1,3,7],[2,5],[4],[6],[8]]=>[1,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>[6,4,2,1,7,5,8,3]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[8,6,4,2,1,7,5,3]=>[[1,3],[2,5],[4,7],[6],[8]]=>[1,2,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[7,6,4,2,1,5,8,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>[1,2,2,1,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[7,8,4,2,1,6,5,3]=>[[1,3],[2,5],[4,6],[7,8]]=>[1,2,2,1,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[8,5,4,2,1,3,6,7]=>[[1,3,6,7],[2],[4],[5],[8]]=>[1,2,1,3,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,4,6,7,8,3]=>[5,4,2,1,6,7,8,3]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>[8,5,4,2,1,6,7,3]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>[7,5,4,2,1,8,6,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>[1,2,1,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>[5,6,2,1,4,3,7,8]=>[[1,3,7,8],[2,4],[5,6]]=>[1,2,1,4]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[8,5,6,2,1,4,3,7]=>[[1,3,7],[2,4],[5,6],[8]]=>[1,2,1,3,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[5,6,2,1,7,8,4,3]=>[[1,3,7,8],[2,4],[5,6]]=>[1,2,1,4]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[7,5,6,2,1,8,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>[1,2,1,2,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[7,5,8,2,1,6,4,3]=>[[1,3],[2,4],[5,6],[7,8]]=>[1,2,1,2,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,7,6,4,3]=>[8,7,5,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>[1,2,1,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[6,5,7,2,1,4,8,3]=>[[1,3,8],[2,4],[5,7],[6]]=>[1,2,1,1,3]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[8,6,5,7,2,1,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>[1,2,1,1,2,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[6,7,5,2,1,8,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>[1,2,1,1,3]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[6,7,8,2,1,5,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>[1,2,1,1,3]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,7,5,4,3]=>[8,6,7,5,2,1,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>[1,2,1,1,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[7,6,5,8,2,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[1,2,1,1,1,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[7,6,8,5,2,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[1,2,1,1,1,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>[7,8,6,5,2,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[1,2,1,1,1,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[7,2,3,1,4,5,8,6]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[8,7,6,2,3,1,4,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,6,4,8,7]=>[8,5,2,3,1,6,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[5,2,3,1,6,7,8,4]=>[[1,3,4,7,8],[2,6],[5]]=>[1,3,4]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,1,5,6,8,7,4]=>[8,5,2,3,1,6,7,4]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>[8,6,5,2,3,1,4,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>[1,3,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,5,7,8,4]=>[6,5,2,3,1,7,8,4]=>[[1,3,4,8],[2,7],[5],[6]]=>[1,3,1,3]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[8,6,5,2,3,1,7,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>[6,7,2,3,1,5,8,4]=>[[1,3,4,8],[2,5],[6,7]]=>[1,3,1,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>[8,6,7,2,3,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[1,3,1,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,7,6,5,4,8]=>[7,6,5,2,3,1,4,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>[7,6,8,2,3,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[1,3,1,1,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[8,7,6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[8,6,2,3,4,1,7,5]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[7,6,2,3,4,1,5,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[1,4,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[7,6,2,3,4,1,8,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[7,8,2,3,4,1,6,5]=>[[1,3,4,5],[2,6],[7,8]]=>[1,4,1,2]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[8,7,6,2,3,4,1,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,8]=>[7,2,3,4,5,1,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[7,2,3,4,5,1,8,6]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[7,6,2,3,4,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[1,4,1,2]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[8,7,6,2,3,4,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,4,1,7,6,8]=>[7,5,2,3,4,1,6,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[1,3,2,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[5,2,3,4,6,7,8,1]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[7,5,2,3,4,6,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>[1,3,2,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[5,2,3,6,7,8,4,1]=>[[1,3,4,7,8],[2,6],[5]]=>[1,3,4]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[8,5,2,3,6,7,4,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[8,6,5,2,3,4,1,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>[1,3,1,2,1]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,7,5,4,1]=>[8,6,7,2,3,5,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[7,6,5,2,3,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[7,6,5,2,3,4,8,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[8,7,6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[8,6,4,2,3,1,5,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[8,6,4,2,3,1,7,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[8,7,6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[1,2,5]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[7,4,2,3,5,1,6,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[1,2,3,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[8,6,4,2,3,5,1,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>[6,4,2,3,5,7,1,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[1,2,2,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[8,6,4,2,3,5,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[7,6,4,2,3,5,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>[1,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>[4,2,5,3,1,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>[8,4,2,5,3,1,6,7]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[8,7,4,2,5,3,1,6]=>[[1,3,6],[2,5],[4],[7],[8]]=>[1,2,3,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[4,2,5,3,6,7,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]=>[8,7,4,2,5,3,6,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[1,2,3,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[4,2,5,6,7,8,3,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,4,5,7,6,3,1,8]=>[7,4,2,5,6,3,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[1,2,3,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,6,3,8,1]=>[7,4,2,5,6,3,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>[1,2,3,2]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>[7,4,2,5,8,6,3,1]=>[[1,3,6],[2,5],[4,8],[7]]=>[1,2,3,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>[6,4,2,5,3,1,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[1,2,2,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>[6,4,2,7,5,3,1,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,4,7,6,5,3,1,8]=>[7,6,4,2,5,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[1,2,2,1,2]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>[7,6,4,2,5,8,3,1]=>[[1,3,8],[2,5],[4],[6],[7]]=>[1,2,2,1,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[7,8,4,2,6,5,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>[1,2,2,1,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[1,2,1,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[7,5,4,2,3,1,8,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[1,2,1,2,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[5,4,2,3,6,7,8,1]=>[[1,3,6,7,8],[2],[4],[5]]=>[1,2,1,4]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[8,5,4,2,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[1,2,1,3,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>[5,4,2,6,3,7,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[7,5,4,2,6,3,8,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,5,6,7,4,3,1,8]=>[5,6,2,7,4,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[5,6,2,7,8,4,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,5,6,8,7,4,3,1]=>[8,5,6,2,7,4,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,5,7,6,4,3,8,1]=>[7,5,6,2,4,3,8,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>[8,6,5,4,2,3,1,7]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,5,4,8,3,1]=>[6,7,5,2,4,8,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>[6,7,8,2,5,4,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,6,5,8,4,3,1]=>[7,6,5,8,2,4,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[8,7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[8,3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>[7,3,2,1,4,5,8,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[8,7,3,2,1,4,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,2,1,4,6,5,8,7]=>[8,6,3,2,1,4,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,2,1,4,6,7,5,8]=>[6,3,2,1,4,7,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[6,3,2,1,4,7,8,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>[8,6,3,2,1,4,7,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[7,6,3,2,1,4,5,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[7,8,3,2,1,4,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[1,1,3,1,2]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,5,4,6,8,7]=>[8,5,3,2,1,4,6,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[7,5,3,2,1,4,6,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,1,5,4,8,7,6]=>[8,7,5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[5,3,2,1,6,4,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,5,6,4,8,7]=>[8,5,3,2,1,6,4,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[8,5,3,2,1,6,7,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[7,5,3,2,1,8,6,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[8,7,5,3,2,1,6,4]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>[8,6,5,3,2,1,4,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[8,6,5,3,2,1,7,4]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[7,6,8,3,2,1,5,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>[1,1,2,1,1,2]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[8,7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[8,7,3,2,4,1,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[8,6,3,2,4,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[8,6,3,2,4,1,7,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[7,8,3,2,4,1,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[1,1,3,1,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[8,7,6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,5,1,7,8,6]=>[7,3,2,4,5,1,8,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>[7,5,3,2,4,1,8,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>[1,1,2,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[8,7,5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,5,8,7,6,4,1]=>[8,7,5,3,2,6,4,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>[6,5,3,2,4,7,1,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[6,7,3,2,5,4,1,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[1,1,2,1,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[6,7,3,2,5,4,8,1]=>[[1,4,8],[2,5],[3,7],[6]]=>[1,1,2,1,3]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[8,7,6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,2,1,5,8,7,6]=>[8,7,3,4,2,1,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[8,6,3,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[6,3,4,2,1,7,8,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[7,6,3,4,2,1,8,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[7,8,3,4,2,1,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[1,1,3,1,2]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[8,7,6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[3,4,2,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[8,7,6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[3,4,5,6,2,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[7,3,4,5,8,6,2,1]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[8,7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>[6,3,4,5,2,7,1,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[1,1,3,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[8,7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[8,7,5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>[7,5,3,4,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[7,5,3,4,6,8,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,5,6,4,2,1,7,8]=>[5,3,6,4,2,1,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[5,3,6,7,4,2,8,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[5,3,6,7,8,4,2,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[7,5,3,6,4,2,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[1,1,2,2,2]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[8,7,5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[8,6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[6,5,3,4,7,2,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,5,4,8,2,1]=>[6,7,3,5,4,8,2,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[7,8,6,3,5,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[8,7,6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[8,4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[7,4,3,2,1,5,6,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[7,4,3,2,1,5,8,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[1,1,1,3,2]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[8,7,4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[6,4,3,2,1,5,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[8,6,4,3,2,1,5,7]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[6,4,3,2,1,7,5,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[6,4,3,2,1,7,8,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[8,6,4,3,2,1,7,5]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[7,6,4,3,2,1,5,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[7,6,4,3,2,1,8,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[7,8,4,3,2,1,6,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>[1,1,1,2,1,2]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[8,7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[8,7,4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[4,3,2,5,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[4,3,5,2,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[8,6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,3,6,8,7,5,2,1]=>[8,6,4,3,7,5,2,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,7,6,8,5,2,1]=>[7,6,4,3,8,5,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[7,8,4,3,6,5,2,1]=>[[1,5],[2,6],[3,8],[4],[7]]=>[1,1,1,2,1,2]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>[8,7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[4,5,3,2,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[8,4,5,3,2,1,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[7,4,5,3,2,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,3,2,7,8,6,1]=>[7,4,5,3,2,8,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>[1,1,1,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[8,4,5,3,6,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[4,5,3,6,2,7,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>[4,5,6,3,2,1,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[8,4,5,6,3,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[4,5,6,3,7,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[4,5,6,7,3,2,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[4,5,6,7,3,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[4,5,6,7,3,8,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,8,3,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,5,7,6,3,2,8,1]=>[7,4,5,6,3,2,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,6,3,8,2,1]=>[7,4,5,6,3,8,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>[7,4,5,6,8,3,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>[6,4,5,3,7,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,5,7,3,8,2,1]=>[6,4,5,7,3,8,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>[6,4,5,7,8,3,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[8,6,4,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>[6,4,7,5,8,3,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[8,6,4,7,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[7,6,4,5,3,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[7,6,4,5,8,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[8,7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[7,5,4,3,2,8,6,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>[5,4,3,6,2,7,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,4,3,7,6,8,2,1]=>[7,5,4,3,6,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,8,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[5,4,6,7,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>[7,5,4,6,8,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[5,6,4,3,2,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>[8,5,6,4,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>[5,6,4,7,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[5,6,4,7,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[5,6,7,4,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[8,5,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[7,5,6,4,3,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[7,5,6,4,3,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>[7,5,6,4,8,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[7,5,6,8,4,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[7,5,8,6,4,3,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[8,7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[8,6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[8,6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>[6,5,4,3,7,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[6,5,4,3,7,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[6,5,4,7,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[6,5,7,8,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[8,6,5,7,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[6,7,5,4,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>[6,7,5,4,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[6,7,5,8,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[6,7,8,5,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[8,6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,8,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,8,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[7,6,5,8,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[7,6,8,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[7,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[6,7,8,9,10,5,4,3,2,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
Map
to 312-avoiding permutation
Description
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
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