Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
=>
Cc0007;cc-rep-0Cc0005;cc-rep-4
[[1]]=>[1]=>[1]=>[1]=>[1,0]
[[1,2]]=>[1,2]=>[1,2]=>[1,2]=>[1,0,1,0]
[[1],[2]]=>[2,1]=>[2,1]=>[2,1]=>[1,1,0,0]
[[1,2,3]]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>[1,0,1,0,1,0]
[[1,3],[2]]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>[1,1,0,0,1,0]
[[1,2],[3]]=>[3,1,2]=>[3,1,2]=>[3,2,1]=>[1,1,1,0,0,0]
[[1],[2],[3]]=>[3,2,1]=>[2,3,1]=>[3,1,2]=>[1,1,1,0,0,0]
[[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]
[[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]
[[1,2,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]
[[1,2,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]
[[1,3],[2,4]]=>[2,4,1,3]=>[4,2,1,3]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]
[[1,2],[3,4]]=>[3,4,1,2]=>[4,1,3,2]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]
[[1,4],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]
[[1,3],[2],[4]]=>[4,2,1,3]=>[2,4,1,3]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]
[[1,2],[3],[4]]=>[4,3,1,2]=>[3,1,4,2]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]
[[1],[2],[3],[4]]=>[4,3,2,1]=>[2,3,4,1]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0]
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[5,3,6,1,2,4]=>[6,4,1,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[6,2,1,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>[6,3,1,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,3,1,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[2,5,4,3,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[3,5,4,2,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,5,3,2,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[2,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[3,6,5,4,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[4,6,5,3,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[2,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[3,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[4,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[5,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[2,4,6,5,3,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[3,4,6,5,2,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[2,5,6,4,3,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[3,5,6,4,2,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,5,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[2,4,7,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[3,4,7,6,5,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[2,5,7,6,4,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[3,5,7,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[4,5,7,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[2,6,7,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[3,6,7,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[4,6,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>[3,2,5,4,1,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]=>[4,2,5,3,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[4,3,5,2,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[4,5,1,2,3,6,7]=>[5,3,1,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[5,2,1,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>[3,2,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[6,4,1,2,3,5,7]=>[4,2,6,5,3,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>[4,3,6,5,2,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[6,5,1,3,2,4,7]=>[5,2,6,4,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]=>[5,3,6,4,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[5,4,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[4,6,1,2,3,5,7]=>[6,5,3,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[6,5,2,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[5,6,1,3,2,4,7]=>[6,4,3,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,1,6,2,3,4,7]=>[6,4,2,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[6,3,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>[3,2,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]=>[4,2,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>[4,3,7,6,5,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[7,5,1,3,2,4,6]=>[5,2,7,6,4,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]=>[5,3,7,6,4,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[7,1,2,5,4,3,6]=>[5,4,7,6,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[7,6,1,3,4,2,5]=>[6,2,7,5,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[7,1,6,2,4,3,5]=>[6,3,7,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>[6,4,7,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[6,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[4,7,1,2,3,5,6]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[5,7,1,3,2,4,6]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[5,1,7,2,3,4,6]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[6,7,1,3,4,2,5]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[6,1,7,2,4,3,5]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[6,1,2,7,3,4,5]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,5,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[6,5,3,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[6,4,3,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>[3,2,5,7,6,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[7,4,1,2,5,3,6]=>[4,2,5,7,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[7,1,4,3,5,2,6]=>[4,3,5,7,6,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[7,5,1,2,4,3,6]=>[5,4,2,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[7,1,5,3,4,2,6]=>[5,4,3,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[7,3,2,1,4,6,5]=>[3,2,6,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[7,4,1,2,3,6,5]=>[4,2,6,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[7,1,4,3,2,6,5]=>[4,3,6,7,5,2,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[7,5,1,3,2,6,4]=>[5,2,6,7,4,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[7,1,5,2,3,6,4]=>[5,3,6,7,4,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[5,4,6,7,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[7,6,1,2,3,4,5]=>[6,4,2,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]=>[6,4,3,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[7,6,1,3,2,5,4]=>[6,5,2,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[7,1,6,2,3,5,4]=>[6,5,3,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[6,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[6,7,1,2,3,4,5]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[6,1,7,3,2,4,5]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[6,7,1,3,2,5,4]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[6,1,7,2,3,5,4]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[5,6,3,1,2,4,7]=>[3,6,4,1,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[5,6,1,4,2,3,7]=>[4,6,3,1,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[5,1,6,4,3,2,7]=>[4,6,2,1,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[4,6,1,2,5,3,7]=>[5,6,3,1,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[5,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[5,7,3,1,2,4,6]=>[3,7,6,4,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[5,7,1,4,2,3,6]=>[4,7,6,3,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[5,1,7,4,3,2,6]=>[4,7,6,2,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[4,7,1,2,5,3,6]=>[5,7,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[4,1,7,3,5,2,6]=>[5,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[6,7,3,1,4,2,5]=>[3,7,5,4,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[6,7,1,4,3,2,5]=>[4,7,5,3,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[6,1,7,4,2,3,5]=>[4,7,5,2,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[6,7,1,3,5,2,4]=>[5,7,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[6,1,7,2,5,3,4]=>[5,7,4,2,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[6,1,2,7,5,4,3]=>[5,7,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[4,7,1,2,3,6,5]=>[6,7,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[6,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[5,7,1,3,2,6,4]=>[6,7,4,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[5,1,7,2,3,6,4]=>[6,7,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[6,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[6,3,4,2,1,5,7]=>[4,2,3,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[6,3,5,1,2,4,7]=>[5,2,3,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[6,4,1,5,2,3,7]=>[5,2,4,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[5,3,4,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[5,3,6,1,2,4,7]=>[6,4,1,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[5,4,1,6,2,3,7]=>[6,3,1,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[6,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[4,5,1,2,6,3,7]=>[6,3,1,4,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[7,3,4,2,1,5,6]=>[4,2,3,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[7,3,5,1,2,4,6]=>[5,2,3,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[7,4,1,5,2,3,6]=>[5,2,4,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[7,1,4,5,3,2,6]=>[5,3,4,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[7,3,6,1,4,2,5]=>[6,2,3,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[7,4,1,6,3,2,5]=>[6,2,4,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[7,1,4,6,2,3,5]=>[6,3,4,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[7,5,1,3,6,2,4]=>[6,2,5,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[7,1,5,2,6,3,4]=>[6,3,5,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[6,4,5,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[5,3,7,1,2,4,6]=>[7,6,4,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[5,4,1,7,2,3,6]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[7,6,2,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[4,5,1,2,7,3,6]=>[7,6,3,1,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[6,3,7,1,4,2,5]=>[7,5,4,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[6,4,1,7,3,2,5]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[6,1,4,7,2,3,5]=>[7,5,2,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[6,5,1,3,7,2,4]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[6,1,5,2,7,3,4]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[7,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[4,6,1,2,3,7,5]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[5,6,1,3,2,7,4]=>[7,4,3,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[5,1,6,2,3,7,4]=>[7,4,2,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[7,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[6,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[6,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[6,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[6,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[7,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[7,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[6,7,4,3,1,2,5]=>[4,3,7,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[6,7,5,1,3,2,4]=>[5,3,7,4,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[6,7,1,5,4,2,3]=>[5,4,7,3,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[6,1,7,5,4,3,2]=>[5,4,7,2,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[5,7,6,1,2,3,4]=>[6,3,7,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[5,7,1,6,2,4,3]=>[6,4,7,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[5,1,7,6,3,4,2]=>[6,4,7,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[4,7,1,2,6,5,3]=>[6,5,7,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[6,5,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[5,6,7,1,2,3,4]=>[7,4,1,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[5,6,1,7,2,4,3]=>[7,3,1,5,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[5,1,6,7,3,4,2]=>[7,2,1,5,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[4,6,1,2,7,5,3]=>[7,3,1,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[7,3,4,5,2,1,6]=>[5,2,3,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[7,3,4,6,1,2,5]=>[6,2,3,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[7,3,5,1,6,2,4]=>[6,2,3,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[7,4,1,5,6,2,3]=>[6,2,4,5,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[6,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[6,3,4,7,1,2,5]=>[7,5,1,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[6,3,5,1,7,2,4]=>[7,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[6,4,1,5,7,2,3]=>[7,3,1,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[7,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[5,3,6,1,2,7,4]=>[7,4,1,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[5,4,1,6,2,7,3]=>[7,3,1,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[7,2,1,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[4,5,1,2,6,7,3]=>[7,3,1,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[7,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[7,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[2,5,4,3,1,6,7,8]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]=>[3,5,4,2,1,6,7,8]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,5,3,2,1,6,7,8]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[5,6,4,3,2,1,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>[4,7,6,5,3,2,1,8]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>[5,7,6,4,3,2,1,8]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[4,8,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,7]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[3,5,7,6,4,2,1,8]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[5,6,7,4,3,2,1,8]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>[3,5,8,7,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[8,1,2,4,5,3,6,7]=>[4,5,8,7,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[4,6,8,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[8,1,2,3,5,6,4,7]=>[5,6,8,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]=>[5,7,8,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,7,8,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[5,3,2,1,4,6,7,8]=>[3,2,5,4,1,6,7,8]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[1,3,6,7,8],[2,4],[5]]=>[5,2,4,1,3,6,7,8]=>[4,5,1,2,3,6,7,8]=>[5,3,1,4,2,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>[4,1,5,3,2,6,7,8]=>[5,2,1,4,3,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[5,1,6,2,3,4,7,8]=>[6,4,2,1,5,3,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[6,5,7,4,3,2,1,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]=>[7,6,5,2,1,4,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,4,6,8],[2,5],[7]]=>[7,2,5,1,3,4,6,8]=>[5,7,1,3,2,4,6,8]=>[7,6,4,3,1,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,1,7,2,3,4,6,8]=>[7,6,4,2,1,5,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[7,4,3,2,1,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>[3,2,8,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[1,3,5,6,7],[2,8],[4]]=>[4,2,8,1,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>[4,2,8,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[1,3,4,6,7],[2,8],[5]]=>[5,2,8,1,3,4,6,7]=>[8,5,1,3,2,4,6,7]=>[5,2,8,7,6,4,3,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[8,1,5,2,3,4,6,7]=>[5,3,8,7,6,4,2,1]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[8,6,1,3,4,2,5,7]=>[6,2,8,7,5,4,3,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[8,1,2,3,6,5,4,7]=>[6,5,8,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[8,7,1,3,4,5,2,6]=>[7,2,8,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[8,1,2,3,7,4,5,6]=>[7,5,8,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[7,6,8,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[1,3,5,6,7],[2,4],[8]]=>[8,2,4,1,3,5,6,7]=>[4,8,1,2,3,5,6,7]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[6,1,2,8,3,4,5,7]=>[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,4,5,6],[2,7],[8]]=>[8,2,7,1,3,4,5,6]=>[7,8,1,3,4,5,2,6]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,5,6],[4,7],[8]]=>[8,4,7,1,2,3,5,6]=>[7,1,2,8,3,5,4,6]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[7,1,2,3,8,4,5,6]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[1,2,5,6,8],[3],[4],[7]]=>[7,4,3,1,2,5,6,8]=>[3,1,4,7,2,5,6,8]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,3,6,8],[4],[5],[7]]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5,6,7],[3],[4],[8]]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[2,5,1,3,8,4,6,7]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[2,4,6,8,7,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[8,1,3,2,5,6,4,7]=>[3,5,6,8,7,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[4,5,6,8,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[3,5,7,8,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[8,1,2,4,5,3,7,6]=>[4,5,7,8,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[5,6,7,8,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[1,2,6,8],[3,5,7],[4]]=>[4,3,5,7,1,2,6,8]=>[7,1,4,3,5,2,6,8]=>[4,3,5,7,6,2,1,8]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[1,4,5,8],[2,6,7],[3]]=>[3,2,6,7,1,4,5,8]=>[7,3,2,1,4,6,5,8]=>[3,2,6,7,5,4,1,8]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[7,5,1,3,2,6,4,8]=>[5,2,6,7,4,3,1,8]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[1,3,5,8],[2,4,7],[6]]=>[6,2,4,7,1,3,5,8]=>[7,6,1,2,3,4,5,8]=>[6,4,2,7,5,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[1,3,4,8],[2,5,7],[6]]=>[6,2,5,7,1,3,4,8]=>[7,6,1,3,2,5,4,8]=>[6,5,2,7,4,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[1,2,3,8],[4,5,7],[6]]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>[6,5,4,7,3,2,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[1,3,5,8],[2,4,6],[7]]=>[7,2,4,6,1,3,5,8]=>[6,7,1,2,3,4,5,8]=>[7,5,3,1,6,4,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,4,8],[2,5,6],[7]]=>[7,2,5,6,1,3,4,8]=>[6,7,1,3,2,5,4,8]=>[7,4,3,1,6,5,2,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[8,4,1,2,5,3,6,7]=>[4,2,5,8,7,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[8,3,2,1,4,6,5,7]=>[3,2,6,8,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[8,4,1,2,3,6,5,7]=>[4,2,6,8,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[8,6,1,2,3,4,5,7]=>[6,4,2,8,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[6,5,7,8,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>[8,7,1,2,3,5,4,6]=>[7,4,2,8,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,2,4,5],[3,6,8],[7]]=>[7,3,6,8,1,2,4,5]=>[8,1,7,2,4,3,6,5]=>[7,6,3,8,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[7,6,5,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,3,5,7],[2,4,6],[8]]=>[8,2,4,6,1,3,5,7]=>[6,8,1,2,3,4,5,7]=>[8,7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5,6],[3,4,7],[8]]=>[8,3,4,7,1,2,5,6]=>[7,1,8,3,2,5,4,6]=>[8,6,5,2,1,7,4,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[7,1,8,2,3,4,5,6]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[7,8,1,3,4,2,6,5]=>[8,5,4,3,1,7,6,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,5],[3,6,7],[8]]=>[8,3,6,7,1,2,4,5]=>[7,1,8,2,4,3,6,5]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[5,6,1,4,2,3,7,8]=>[4,6,3,1,5,2,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[5,1,6,4,3,2,7,8]=>[4,6,2,1,5,3,7,8]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[4,6,1,2,5,3,7,8]=>[5,6,3,1,4,2,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[5,6,2,1,4,3,7,8]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[5,7,3,1,2,4,6,8]=>[3,7,6,4,1,5,2,8]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[5,8,1,4,2,3,6,7]=>[4,8,7,6,3,1,5,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,6,7],[2,4],[5,8]]=>[5,8,2,4,1,3,6,7]=>[4,8,1,2,5,3,6,7]=>[5,8,7,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[4,1,8,3,5,2,6,7]=>[5,8,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,7],[4,6],[5,8]]=>[5,8,4,6,1,2,3,7]=>[6,1,2,8,5,4,3,7]=>[5,8,7,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,2,5,7],[3,4],[6,8]]=>[6,8,3,4,1,2,5,7]=>[4,1,8,3,2,6,5,7]=>[6,8,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2,3,7],[4,5],[6,8]]=>[6,8,4,5,1,2,3,7]=>[5,1,2,8,4,6,3,7]=>[6,8,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[7,8,1,3,5,4,2,6]=>[5,8,6,4,3,1,7,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[7,1,8,2,5,4,3,6]=>[5,8,6,4,2,1,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[7,1,2,8,5,3,4,6]=>[5,8,6,3,2,1,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[7,8,1,3,4,6,2,5]=>[6,8,5,4,3,1,7,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[7,1,8,2,4,6,3,5]=>[6,8,5,4,2,1,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[7,1,2,3,8,6,5,4]=>[6,8,4,3,2,1,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[6,1,2,8,3,4,7,5]=>[7,8,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[7,8,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[6,3,4,2,1,5,7,8]=>[4,2,3,6,5,1,7,8]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[1,2,6,8],[3,7],[4],[5]]=>[5,4,3,7,1,2,6,8]=>[7,1,4,5,3,2,6,8]=>[5,3,4,7,6,2,1,8]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[1,3,5,8],[2,7],[4],[6]]=>[6,4,2,7,1,3,5,8]=>[7,4,1,6,3,2,5,8]=>[6,2,4,7,5,3,1,8]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[5,4,1,7,2,3,6,8]=>[7,6,3,1,5,2,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,6,8],[2,4],[5],[7]]=>[7,5,2,4,1,3,6,8]=>[4,5,1,2,7,3,6,8]=>[7,6,3,1,4,2,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[8,3,4,2,1,5,6,7]=>[4,2,3,8,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[1,3,5,7],[2,8],[4],[6]]=>[6,4,2,8,1,3,5,7]=>[8,4,1,6,3,2,5,7]=>[6,2,4,8,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[8,1,2,6,3,7,4,5]=>[7,4,6,8,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[7,5,6,8,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,4,6,7],[2,5],[3],[8]]=>[8,3,2,5,1,4,6,7]=>[5,3,8,1,2,4,6,7]=>[8,7,6,4,1,5,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,6,7],[2,4],[5],[8]]=>[8,5,2,4,1,3,6,7]=>[4,5,1,2,8,3,6,7]=>[8,7,6,3,1,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[8,7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[6,3,8,1,4,2,5,7]=>[8,7,5,4,1,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>[5,6,1,3,2,8,4,7]=>[8,7,4,3,1,5,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,7],[3,5],[6],[8]]=>[8,6,3,5,1,2,4,7]=>[5,1,6,2,3,8,4,7]=>[8,7,4,2,1,5,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,4,5],[2,7],[6],[8]]=>[8,6,2,7,1,3,4,5]=>[7,6,1,3,4,8,2,5]=>[8,5,4,3,1,7,2,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[8,4,3,2,1,7,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[5,1,7,2,3,4,8,6]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[6,1,2,7,3,4,8,5]=>[8,5,3,2,1,6,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[8,4,3,2,1,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]=>[6,5,1,2,3,4,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[7,6,5,1,2,3,4,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[7,5,3,1,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[2,5,1,3,6,7,4,8]=>[7,4,3,1,2,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5,7],[3],[4],[6],[8]]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5,6],[3],[4],[7],[8]]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,6],[4],[5],[7],[8]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,7],[2,5,8],[4,6]]=>[4,6,2,5,8,1,3,7]=>[8,6,1,4,2,5,3,7]=>[4,6,5,2,8,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[1,3,6],[2,5,8],[4,7]]=>[4,7,2,5,8,1,3,6]=>[8,7,1,4,2,3,5,6]=>[4,7,5,2,8,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,6],[3,4,8],[5,7]]=>[5,7,3,4,8,1,2,6]=>[8,1,7,3,5,2,4,6]=>[5,7,4,3,8,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[8,1,7,4,2,3,6,5]=>[4,7,6,3,8,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[8,1,2,7,5,4,6,3]=>[5,7,6,4,8,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[1,3,5],[2,4,8],[6,7]]=>[6,7,2,4,8,1,3,5]=>[8,7,1,2,3,6,4,5]=>[6,7,4,2,8,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[8,1,7,2,3,6,5,4]=>[6,7,5,3,8,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[6,7,5,4,8,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[7,8,3,1,2,4,5,6]=>[3,8,6,4,1,7,5,2]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[7,8,1,2,5,3,4,6]=>[5,8,6,3,1,7,4,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,3,5],[2,6,7],[4,8]]=>[4,8,2,6,7,1,3,5]=>[7,8,1,4,3,2,6,5]=>[4,8,5,3,1,7,6,2]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[1,3,4],[2,6,7],[5,8]]=>[5,8,2,6,7,1,3,4]=>[7,8,1,3,5,2,6,4]=>[5,8,4,3,1,7,6,2]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,2,3],[4,6,7],[5,8]]=>[5,8,4,6,7,1,2,3]=>[7,1,2,8,5,4,6,3]=>[5,8,3,2,1,7,6,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,3,5],[2,4,7],[6,8]]=>[6,8,2,4,7,1,3,5]=>[7,8,1,2,3,6,4,5]=>[6,8,5,3,1,7,4,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[7,8,1,3,2,6,5,4]=>[6,8,4,3,1,7,5,2]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2,4],[3,5,7],[6,8]]=>[6,8,3,5,7,1,2,4]=>[7,1,8,2,3,6,5,4]=>[6,8,4,2,1,7,5,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[6,8,1,2,3,4,7,5]=>[7,8,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[6,1,8,3,2,4,7,5]=>[7,8,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[6,1,8,2,3,5,7,4]=>[7,8,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[7,8,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[8,3,4,2,1,6,5,7]=>[4,2,3,6,8,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[8,1,4,6,3,5,2,7]=>[6,5,3,4,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[8,5,1,2,6,4,3,7]=>[6,4,2,5,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[1,2,7],[3,4,8],[5],[6]]=>[6,5,3,4,8,1,2,7]=>[8,1,5,3,6,4,2,7]=>[6,4,3,5,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[8,4,1,5,2,3,7,6]=>[5,2,4,7,8,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>[8,4,1,6,3,2,7,5]=>[6,2,4,7,8,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[8,1,4,6,2,3,7,5]=>[6,3,4,7,8,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[1,2,4],[3,7,8],[5],[6]]=>[6,5,3,7,8,1,2,4]=>[8,1,5,2,6,3,7,4]=>[6,3,5,7,8,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[8,1,2,5,6,4,7,3]=>[6,4,5,7,8,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[8,4,1,7,2,3,5,6]=>[7,5,2,4,8,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,3,6],[2,4,8],[5],[7]]=>[7,5,2,4,8,1,3,6]=>[8,5,1,2,7,3,4,6]=>[7,4,2,5,8,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,2,6],[3,4,8],[5],[7]]=>[7,5,3,4,8,1,2,6]=>[8,1,5,3,7,2,4,6]=>[7,4,3,5,8,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,4,5],[2,6,8],[3],[7]]=>[7,3,2,6,8,1,4,5]=>[8,3,7,1,4,2,6,5]=>[7,6,2,3,8,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>[7,6,4,5,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>[7,5,4,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[7,4,1,8,2,3,5,6]=>[8,6,3,1,7,5,2,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[7,5,1,2,8,3,4,6]=>[8,6,3,1,7,4,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,5],[2,6,7],[3],[8]]=>[8,3,2,6,7,1,4,5]=>[7,3,8,1,4,2,6,5]=>[8,5,4,1,7,6,2,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[7,5,1,3,8,2,6,4]=>[8,4,3,1,7,6,2,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[7,1,5,2,8,3,6,4]=>[8,4,2,1,7,6,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3],[4,6,7],[5],[8]]=>[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>[8,3,2,1,7,6,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[6,7,1,2,3,4,8,5]=>[8,5,3,1,6,4,2,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[6,1,7,3,2,4,8,5]=>[8,5,2,1,6,4,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4],[3,5,6],[7],[8]]=>[8,7,3,5,6,1,2,4]=>[6,1,7,2,3,5,8,4]=>[8,4,2,1,6,5,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[8,3,2,1,6,5,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[6,7,4,3,1,2,5,8]=>[4,3,7,5,1,6,2,8]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[5,7,6,1,2,3,4,8]=>[6,3,7,4,1,5,2,8]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>[5,6,7,1,2,3,4,8]=>[7,4,1,5,2,6,3,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,8],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3,8]=>[4,6,1,2,7,5,3,8]=>[7,3,1,4,2,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,2,8],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[7,2,1,4,3,6,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[6,8,4,3,1,2,5,7]=>[4,3,8,7,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[1,4,7],[2,5],[3,8],[6]]=>[6,3,8,2,5,1,4,7]=>[5,8,6,1,2,3,4,7]=>[6,3,8,7,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[5,1,8,6,3,4,2,7]=>[6,4,8,7,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,3,7],[2,4],[5,8],[6]]=>[6,5,8,2,4,1,3,7]=>[4,8,1,2,6,5,3,7]=>[6,5,8,7,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[4,1,8,3,6,5,2,7]=>[6,5,8,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[7,8,1,6,3,4,2,5]=>[6,4,8,5,3,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,3,4],[2,7],[5,8],[6]]=>[6,5,8,2,7,1,3,4]=>[7,8,1,3,6,5,2,4]=>[6,5,8,4,3,1,7,2]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[4,8,1,2,7,3,5,6]=>[7,5,8,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[1,2,5],[3,6],[4,8],[7]]=>[7,4,8,3,6,1,2,5]=>[6,1,8,7,2,3,4,5]=>[7,4,8,5,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[6,1,2,8,7,4,5,3]=>[7,5,8,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[5,6,8,1,2,3,4,7]=>[8,7,4,1,5,2,6,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[8,7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[5,7,8,1,2,4,3,6]=>[8,6,4,1,5,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[4,7,1,2,8,3,5,6]=>[8,6,3,1,4,2,7,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[6,7,8,1,4,2,3,5]=>[8,5,4,1,6,2,7,3]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[6,1,7,8,2,3,4,5]=>[8,5,2,1,6,3,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[5,1,7,2,3,8,6,4]=>[8,4,2,1,5,3,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[5,1,2,7,4,8,6,3]=>[8,3,2,1,5,4,7,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[7,3,5,1,6,2,4,8]=>[6,2,3,5,7,4,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[7,4,1,5,6,2,3,8]=>[6,2,4,5,7,3,1,8]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>[6,3,5,1,7,2,4,8]=>[7,4,1,6,2,3,5,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,3,8],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3,8]=>[5,4,1,6,2,7,3,8]=>[7,3,1,5,2,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[8,3,4,5,2,1,6,7]=>[5,2,3,4,8,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[1,3,7],[2,8],[4],[5],[6]]=>[6,5,4,2,8,1,3,7]=>[8,4,1,5,6,2,3,7]=>[6,2,4,5,8,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[8,1,4,5,6,3,2,7]=>[6,3,4,5,8,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[1,5,6],[2,8],[3],[4],[7]]=>[7,4,3,2,8,1,5,6]=>[8,3,4,7,1,5,2,6]=>[7,2,3,4,8,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,4,5],[2,8],[3],[6],[7]]=>[7,6,3,2,8,1,4,5]=>[8,3,6,1,4,7,2,5]=>[7,2,3,6,8,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[8,1,5,2,6,7,3,4]=>[7,3,5,6,8,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[7,4,5,6,8,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[6,3,5,1,8,2,4,7]=>[8,7,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,7],[2,5],[3],[6],[8]]=>[8,6,3,2,5,1,4,7]=>[5,3,6,1,2,8,4,7]=>[8,7,4,1,5,2,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[5,4,1,6,2,8,3,7]=>[8,7,3,1,5,2,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[4,5,1,2,6,8,3,7]=>[8,7,3,1,4,2,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[7,3,5,1,8,4,2,6]=>[8,6,4,1,7,2,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,6],[2,7],[4],[5],[8]]=>[8,5,4,2,7,1,3,6]=>[7,4,1,5,8,3,2,6]=>[8,6,3,1,7,2,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,5],[3,7],[4],[6],[8]]=>[8,6,4,3,7,1,2,5]=>[7,1,4,6,2,8,3,5]=>[8,5,2,1,7,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4],[3,7],[5],[6],[8]]=>[8,6,5,3,7,1,2,4]=>[7,1,5,2,6,8,3,4]=>[8,4,2,1,7,3,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[7,1,2,5,6,8,4,3]=>[8,3,2,1,7,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[5,3,7,1,2,4,8,6]=>[8,6,4,1,5,2,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,6],[2,5],[4],[7],[8]]=>[8,7,4,2,5,1,3,6]=>[5,4,1,7,2,3,8,6]=>[8,6,3,1,5,2,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,6],[3,5],[4],[7],[8]]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>[8,6,2,1,5,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[8,6,2,1,4,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[6,1,5,2,7,3,8,4]=>[8,4,2,1,6,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[5,1,6,2,3,7,8,4]=>[8,4,2,1,5,3,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>[7,5,1,2,3,4,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[8,7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[8,7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]=>[8,7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[8,6,5,1,2,3,4,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[8,6,4,1,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[8,5,3,1,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[8,4,2,1,3,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[8,3,2,1,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[6,7,8,1,5,2,3,4]=>[5,8,4,1,6,2,7,3]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[6,7,1,8,5,2,4,3]=>[5,8,3,1,6,2,7,4]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[5,7,8,1,2,6,3,4]=>[6,8,4,1,5,2,7,3]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[5,7,1,8,2,6,4,3]=>[6,8,3,1,5,2,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[5,1,7,8,3,6,4,2]=>[6,8,2,1,5,3,7,4]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[4,7,1,2,8,6,5,3]=>[6,8,3,1,4,2,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[4,1,7,3,8,6,5,2]=>[6,8,2,1,4,3,7,5]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[5,1,6,8,3,4,7,2]=>[7,8,2,1,5,3,6,4]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[4,6,1,2,8,5,7,3]=>[7,8,3,1,4,2,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[7,8,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[7,8,4,6,1,3,2,5]=>[6,3,4,8,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[1,3],[2,7],[4,8],[5],[6]]=>[6,5,4,8,2,7,1,3]=>[7,8,1,5,6,4,2,3]=>[6,4,5,8,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[6,8,4,7,1,2,3,5]=>[7,3,4,8,5,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[6,8,5,1,7,2,3,4]=>[7,3,5,8,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>[7,5,6,8,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[6,7,4,8,1,2,3,5]=>[8,5,1,6,2,7,3,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[6,7,5,1,8,2,3,4]=>[8,4,1,6,2,7,3,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[5,7,6,1,2,8,3,4]=>[8,4,1,5,2,7,3,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[5,7,1,6,2,8,4,3]=>[8,3,1,5,2,7,4,6]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[5,6,7,1,2,3,8,4]=>[8,4,1,5,2,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[4,6,1,2,7,5,8,3]=>[8,3,1,4,2,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[8,2,1,4,3,6,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[8,3,4,5,7,1,2,6]=>[7,2,3,4,5,8,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[1,5],[2,8],[3],[4],[6],[7]]=>[7,6,4,3,2,8,1,5]=>[8,3,4,6,1,7,2,5]=>[7,2,3,4,6,8,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[7,3,4,5,8,1,2,6]=>[8,6,1,7,2,3,4,5]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[6,3,5,1,7,2,8,4]=>[8,4,1,6,2,3,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[6,4,1,5,7,2,8,3]=>[8,3,1,6,2,4,5,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[5,4,1,6,2,7,8,3]=>[8,3,1,5,2,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>[8,5,1,2,3,4,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[8,3,1,2,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
left-to-right-maxima to Dyck path
searching the database
Sorry, this map was not found in the database.