Identifier
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0002;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[1]
[1,0,1,0]=>[1,2]=>[1,2]=>[1,2]=>[1,1]
[1,1,0,0]=>[2,1]=>[2,1]=>[2,1]=>[2]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>[1,1,1]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[1,3,2]=>[2,1]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>[2,1]
[1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>[2,3,1]=>[3]
[1,1,1,0,0,0]=>[3,1,2]=>[3,1,2]=>[3,1,2]=>[3]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[1,1,1,1]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>[2,1,1]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>[2,1,1]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[1,3,4,2]=>[3,1]
[1,0,1,1,1,0,0,0]=>[1,4,2,3]=>[1,4,2,3]=>[1,4,2,3]=>[3,1]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,1]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>[2,2]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]=>[3,1]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[3,4,2,1]=>[4]
[1,1,0,1,1,0,0,0]=>[2,4,1,3]=>[4,2,1,3]=>[2,4,1,3]=>[4]
[1,1,1,0,0,0,1,0]=>[3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]=>[3,1]
[1,1,1,0,0,1,0,0]=>[3,1,4,2]=>[4,3,1,2]=>[3,1,4,2]=>[4]
[1,1,1,0,1,0,0,0]=>[3,4,1,2]=>[4,1,3,2]=>[4,3,1,2]=>[4]
[1,1,1,1,0,0,0,0]=>[4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[2,1,1,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[2,1,1,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[3,1,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[2,1,1,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[3,1,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[1,4,5,3,2]=>[4,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,5,3,2,4]=>[1,3,5,2,4]=>[4,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[3,1,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>[1,5,4,2,3]=>[1,4,2,5,3]=>[4,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>[1,5,2,4,3]=>[1,5,4,2,3]=>[4,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[4,1]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,1,1]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[2,2,1]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[3,2]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[3,2]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,1,1]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[3,2]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[4,1]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[5]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[4,1]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[5]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>[5,2,1,4,3]=>[2,5,4,1,3]=>[5]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[5]
[1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[3,2]
[1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[4,1]
[1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>[5,3,1,4,2]=>[3,5,4,2,1]=>[5]
[1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[5]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[4,3,1,2,5]=>[4,1]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[5]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[5,4,1,3,2]=>[5]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[5,3,1,2,4]=>[5]
[1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>[5,1,4,2,3]=>[5,4,2,1,3]=>[5]
[1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[5]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[5,1,4,2,3]=>[5]
[1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[3,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[3,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,5,6,4,3]=>[4,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>[4,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>[4,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[1,2,6,5,3,4]=>[4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[3,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,4,5,3,2,6]=>[4,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,5,6,3,4,2]=>[5,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[1,4,6,3,2,5]=>[5,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>[4,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>[1,6,3,5,2,4]=>[1,5,6,2,3,4]=>[5,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[1,3,6,5,2,4]=>[5,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>[5,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[3,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>[4,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>[1,6,4,2,5,3]=>[1,4,6,5,3,2]=>[5,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>[5,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[1,5,4,2,3,6]=>[4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>[1,6,5,4,2,3]=>[1,4,2,5,6,3]=>[5,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[1,6,5,2,4,3]=>[5,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[1,6,4,2,3,5]=>[5,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,6,2,5,3,4]=>[1,6,5,3,2,4]=>[5,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>[1,6,5,2,3,4]=>[1,5,2,3,6,4]=>[5,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[1,6,2,5,3,4]=>[5,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[5,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>[4,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>[4,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>[4,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[2,1,6,5,3,4]=>[4,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[4,2]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[3,3]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>[3,3]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>[4,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>[6,2,3,5,1,4]=>[5,6,2,1,3,4]=>[6]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[3,6,2,5,1,4]=>[6]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>[4,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[5,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>[6,2,4,1,5,3]=>[4,6,5,2,1,3]=>[6]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[6]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[2,5,4,1,3,6]=>[5,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>[6,2,5,4,1,3]=>[4,5,2,6,1,3]=>[6]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[2,6,5,1,4,3]=>[6]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[2,6,4,1,3,5]=>[6]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>[6,2,1,5,3,4]=>[2,6,5,3,1,4]=>[6]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>[6]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[2,6,1,5,3,4]=>[6]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>[3,3]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>[4,2]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[5,3,1,4,2,6]=>[3,5,4,2,1,6]=>[5,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>[6,3,1,4,5,2]=>[3,6,5,2,4,1]=>[6]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>[6,3,1,4,2,5]=>[3,6,4,2,1,5]=>[6]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>[6,3,1,5,2,4]=>[3,6,5,1,2,4]=>[6]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>[6,3,1,2,5,4]=>[3,1,6,5,2,4]=>[6]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[4,3,1,2,5,6]=>[4,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[4,3,1,2,6,5]=>[4,2]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>[6,4,3,1,5,2]=>[3,4,6,5,1,2]=>[6]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[5,4,1,3,2,6]=>[5,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[6,5,1,3,4,2]=>[6]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[6,4,1,3,2,5]=>[6]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[5,3,1,2,4,6]=>[5,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>[6,1,3,5,2,4]=>[6,5,1,2,3,4]=>[6]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[6,3,1,5,2,4]=>[6]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[6,3,1,2,4,5]=>[6]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[4,2]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[5,1,4,2,3,6]=>[5,4,2,1,3,6]=>[5,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>[6,1,4,2,5,3]=>[6,4,5,1,2,3]=>[6]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>[6,1,4,2,3,5]=>[6,4,2,1,3,5]=>[6]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>[6,4,1,2,5,3]=>[4,1,6,5,3,2]=>[6]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[5,1,4,2,3,6]=>[5,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>[6,1,5,4,2,3]=>[6,4,2,5,1,3]=>[6]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>[6,5,1,4,2,3]=>[5,4,2,1,6,3]=>[6]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[6,1,5,2,4,3]=>[6]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[6,1,4,2,3,5]=>[6]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>[6,1,2,5,3,4]=>[6,1,5,3,2,4]=>[6]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>[6,1,5,2,3,4]=>[6,5,2,3,1,4]=>[6]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[6,1,2,5,3,4]=>[6]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[1,2,3,6,7,5,4]=>[4,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>[4,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]=>[4,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[1,2,3,7,6,4,5]=>[4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[3,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[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]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[3,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[3,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[1,2,5,6,4,3,7]=>[4,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[1,2,6,7,4,5,3]=>[5,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[1,2,5,7,4,3,6]=>[5,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>[4,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>[1,2,7,4,6,3,5]=>[1,2,6,7,3,4,5]=>[5,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[1,2,4,7,6,3,5]=>[5,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]=>[5,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[3,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[3,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]=>[4,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>[1,2,7,5,3,6,4]=>[1,2,5,7,6,4,3]=>[5,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]=>[5,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[1,2,6,5,3,4,7]=>[4,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>[1,2,7,6,5,3,4]=>[1,2,5,3,6,7,4]=>[5,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[1,2,7,6,3,5,4]=>[5,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[1,2,7,5,3,4,6]=>[5,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[4,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>[1,2,7,3,6,4,5]=>[1,2,7,6,4,3,5]=>[5,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,7,6,3,4,5]=>[1,2,6,3,4,7,5]=>[5,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[1,2,7,3,6,4,5]=>[5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[5,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[3,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[3,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[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]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[3,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[1,3,2,6,7,5,4]=>[4,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]=>[4,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[3,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]=>[4,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[1,3,2,7,6,4,5]=>[4,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[4,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[3,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[3,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[3,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[3,3,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]=>[3,3,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[1,4,5,3,2,6,7]=>[4,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,4,5,3,2,7,6]=>[4,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,5,6,3,4,2,7]=>[5,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,6,7,3,4,5,2]=>[6,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[1,5,7,3,4,2,6]=>[6,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[1,4,6,3,2,5,7]=>[5,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>[1,7,3,4,6,2,5]=>[1,6,7,3,2,4,5]=>[6,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[1,4,7,3,6,2,5]=>[6,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[1,4,7,3,2,5,6]=>[6,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>[4,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]=>[4,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>[1,6,3,5,2,4,7]=>[1,5,6,2,3,4,7]=>[5,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>[1,7,3,5,2,6,4]=>[1,5,7,6,3,2,4]=>[6,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,7,3,5,2,4,6]=>[1,5,7,2,3,4,6]=>[6,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[1,3,6,5,2,4,7]=>[5,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>[1,7,3,6,5,2,4]=>[1,5,6,3,7,2,4]=>[6,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[1,3,7,6,2,5,4]=>[6,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[1,3,7,5,2,4,6]=>[6,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]=>[5,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>[1,7,3,2,6,4,5]=>[1,3,7,6,4,2,5]=>[6,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,7,3,6,2,4,5]=>[1,6,7,2,4,3,5]=>[6,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[1,3,7,2,6,4,5]=>[6,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>[6,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[3,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]=>[3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]=>[4,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]=>[4,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>[1,6,4,2,5,3,7]=>[1,4,6,5,3,2,7]=>[5,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,7,4,2,5,6,3]=>[1,4,7,6,3,5,2]=>[6,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>[1,7,4,2,5,3,6]=>[1,4,7,5,3,2,6]=>[6,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]=>[5,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,7,4,2,6,3,5]=>[1,4,7,6,2,3,5]=>[6,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>[1,7,4,2,3,6,5]=>[1,4,2,7,6,3,5]=>[6,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]=>[6,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[1,5,4,2,3,6,7]=>[4,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[1,5,4,2,3,7,6]=>[4,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>[1,6,5,4,2,3,7]=>[1,4,2,5,6,3,7]=>[5,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>[1,7,5,4,2,6,3]=>[1,4,5,7,6,2,3]=>[6,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,7,5,4,2,3,6]=>[1,4,2,5,7,3,6]=>[6,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[1,6,5,2,4,3,7]=>[5,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>[1,7,6,4,5,2,3]=>[1,5,2,6,4,7,3]=>[6,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[1,7,6,2,4,5,3]=>[6,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[1,7,5,2,4,3,6]=>[6,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[1,6,4,2,3,5,7]=>[5,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>[1,7,2,4,6,3,5]=>[1,7,6,2,3,4,5]=>[6,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,7,6,4,2,3,5]=>[1,4,2,6,3,7,5]=>[6,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[1,7,4,2,6,3,5]=>[6,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[1,7,4,2,3,5,6]=>[6,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[4,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[4,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,6,4,7]=>[1,6,2,5,3,4,7]=>[1,6,5,3,2,4,7]=>[5,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,7,2,5,3,6,4]=>[1,7,5,6,2,3,4]=>[6,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6]=>[1,7,2,5,3,4,6]=>[1,7,5,3,2,4,6]=>[6,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,6,3,4,7]=>[1,6,5,2,3,4,7]=>[1,5,2,3,6,4,7]=>[5,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,7,6,5,2,3,4]=>[1,5,2,3,6,7,4]=>[6,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,6,7,3,4]=>[1,7,5,2,3,6,4]=>[1,5,2,7,6,4,3]=>[6,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6]=>[1,7,5,2,3,4,6]=>[1,5,2,3,7,4,6]=>[6,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[1,6,2,5,3,4,7]=>[5,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,2,3,7,4]=>[1,7,2,6,5,3,4]=>[1,7,5,3,6,2,4]=>[6,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,7,6,2,5,3,4]=>[1,6,5,3,2,7,4]=>[6,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[1,7,2,6,3,5,4]=>[6,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[1,7,2,5,3,4,6]=>[6,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,7,2,3,6,4,5]=>[1,7,2,6,4,3,5]=>[6,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,7,4,5]=>[1,7,2,6,3,4,5]=>[1,7,6,3,4,2,5]=>[6,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,7,3,4,5]=>[1,7,6,2,3,4,5]=>[1,6,2,3,4,7,5]=>[6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[1,7,2,3,6,4,5]=>[6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[6,1]
[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]=>[2,1,3,4,5,6,7]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[3,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,2,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,2,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,1,3,6,7,5,4]=>[4,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]=>[4,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,4,7,5]=>[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]=>[4,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[2,1,3,7,6,4,5]=>[4,2,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[4,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[3,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,5,6,4,3,7]=>[4,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,6,7,4,5,3]=>[5,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[2,1,5,7,4,3,6]=>[5,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]=>[4,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,7,5]=>[2,1,7,4,6,3,5]=>[2,1,6,7,3,4,5]=>[5,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[2,1,4,7,6,3,5]=>[5,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]=>[5,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[3,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[3,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]=>[4,2,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,6,7,4]=>[2,1,7,5,3,6,4]=>[2,1,5,7,6,4,3]=>[5,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6]=>[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]=>[5,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[2,1,6,5,3,4,7]=>[4,2,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,3,7,4]=>[2,1,7,6,5,3,4]=>[2,1,5,3,6,7,4]=>[5,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[2,1,7,6,3,5,4]=>[5,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[2,1,7,5,3,4,6]=>[5,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[4,2,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,7,5]=>[2,1,7,3,6,4,5]=>[2,1,7,6,4,3,5]=>[5,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,7,4,5]=>[2,1,7,6,3,4,5]=>[2,1,6,3,4,7,5]=>[5,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[2,1,7,3,6,4,5]=>[5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[3,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[3,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[3,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>[3,3,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[3,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[3,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[2,3,1,6,7,5,4]=>[4,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]=>[4,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]=>[3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]=>[4,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[2,3,1,7,6,4,5]=>[4,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]=>[4,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[3,4,2,1,5,7,6]=>[4,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[3,4,2,1,6,5,7]=>[4,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[3,4,2,1,6,7,5]=>[4,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[3,4,2,1,7,5,6]=>[4,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[4,5,2,3,1,7,6]=>[5,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,7,5]=>[7,2,3,4,6,1,5]=>[6,7,2,3,1,4,5]=>[7]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[4,7,2,3,6,1,5]=>[7]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[3,5,2,1,4,7,6]=>[5,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,6,4,7]=>[6,2,3,5,1,4,7]=>[5,6,2,1,3,4,7]=>[6,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,6,7,4]=>[7,2,3,5,1,6,4]=>[5,7,2,6,3,1,4]=>[7]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6]=>[7,2,3,5,1,4,6]=>[5,7,2,1,3,4,6]=>[7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[3,6,2,5,1,4,7]=>[6,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,1,7,4]=>[7,2,3,6,5,1,4]=>[5,6,1,2,7,3,4]=>[7]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[3,7,2,6,1,5,4]=>[7]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[3,7,2,5,1,4,6]=>[7]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,7,5]=>[7,2,3,1,6,4,5]=>[3,7,2,6,4,1,5]=>[7]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[7,2,3,6,1,4,5]=>[6,7,2,1,4,3,5]=>[7]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[3,7,2,1,6,4,5]=>[7]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>[4,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>[4,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]=>[4,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>[4,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,5,3,6,7]=>[5,2,4,1,3,6,7]=>[4,5,1,2,3,6,7]=>[5,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6]=>[5,2,4,1,3,7,6]=>[4,5,1,2,3,7,6]=>[5,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,3,7]=>[6,2,4,1,5,3,7]=>[4,6,5,2,1,3,7]=>[6,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,3]=>[7,2,4,1,5,6,3]=>[4,7,6,2,1,5,3]=>[7]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6]=>[7,2,4,1,5,3,6]=>[4,7,5,2,1,3,6]=>[7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,7]=>[6,2,4,1,3,5,7]=>[4,6,1,2,3,5,7]=>[6,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,7,5]=>[7,2,4,1,6,3,5]=>[4,7,6,2,3,1,5]=>[7]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,7,3,5]=>[7,2,4,1,3,6,5]=>[4,7,1,2,6,3,5]=>[7]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,7,3,5,6]=>[7,2,4,1,3,5,6]=>[4,7,1,2,3,5,6]=>[7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[2,5,4,1,3,6,7]=>[5,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[2,5,4,1,3,7,6]=>[5,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,1,6,3,7]=>[6,2,5,4,1,3,7]=>[4,5,2,6,1,3,7]=>[6,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,1,6,7,3]=>[7,2,5,4,1,6,3]=>[4,5,7,6,3,2,1]=>[7]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6]=>[7,2,5,4,1,3,6]=>[4,5,2,7,1,3,6]=>[7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[2,6,5,1,4,3,7]=>[6,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,1,7,3]=>[7,2,6,4,5,1,3]=>[5,7,1,6,4,2,3]=>[7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[2,7,6,1,4,5,3]=>[7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[2,7,5,1,4,3,6]=>[7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[2,6,4,1,3,5,7]=>[6,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,7,5]=>[7,2,1,4,6,3,5]=>[2,7,6,1,3,4,5]=>[7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[7,2,6,4,1,3,5]=>[4,6,2,7,3,1,5]=>[7]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[2,7,4,1,6,3,5]=>[7]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]=>[7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>[5,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,6,4,7]=>[6,2,1,5,3,4,7]=>[2,6,5,3,1,4,7]=>[6,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,6,7,4]=>[7,2,1,5,3,6,4]=>[2,7,5,6,1,3,4]=>[7]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6]=>[7,2,1,5,3,4,6]=>[2,7,5,3,1,4,6]=>[7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,6,3,4,7]=>[6,2,5,1,3,4,7]=>[5,6,1,3,2,4,7]=>[6,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,6,3,7,4]=>[7,2,6,5,1,3,4]=>[5,6,2,3,7,1,4]=>[7]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,6,7,3,4]=>[7,2,5,1,3,6,4]=>[5,7,1,6,2,3,4]=>[7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6]=>[7,2,5,1,3,4,6]=>[5,7,1,3,2,4,6]=>[7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[2,6,1,5,3,4,7]=>[6,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,1,3,7,4]=>[7,2,1,6,5,3,4]=>[2,7,5,3,6,1,4]=>[7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[7,2,6,1,5,3,4]=>[6,7,5,3,1,2,4]=>[7]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[2,7,1,6,3,5,4]=>[7]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]=>[7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,7,5]=>[7,2,1,3,6,4,5]=>[2,7,1,6,4,3,5]=>[7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,7,4,5]=>[7,2,1,6,3,4,5]=>[2,7,6,3,4,1,5]=>[7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,1,7,3,4,5]=>[7,2,6,1,3,4,5]=>[6,7,1,3,4,2,5]=>[7]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]=>[7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]=>[3,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[3,3,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]=>[3,3,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[3,1,2,6,7,5,4]=>[4,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]=>[4,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,6,4,7,5]=>[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]=>[4,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[3,1,2,7,6,4,5]=>[4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,5,7,6]=>[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>[4,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,7]=>[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>[4,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,7,5]=>[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>[4,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,7,5,6]=>[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]=>[4,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2,6,7]=>[5,3,1,4,2,6,7]=>[3,5,4,2,1,6,7]=>[5,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6]=>[5,3,1,4,2,7,6]=>[3,5,4,2,1,7,6]=>[5,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,2,7]=>[6,3,1,4,5,2,7]=>[3,6,5,2,4,1,7]=>[6,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,2]=>[7,3,1,4,5,6,2]=>[3,7,6,2,4,5,1]=>[7]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6]=>[7,3,1,4,5,2,6]=>[3,7,5,2,4,1,6]=>[7]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,7]=>[6,3,1,4,2,5,7]=>[3,6,4,2,1,5,7]=>[6,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,7,5]=>[7,3,1,4,6,2,5]=>[3,7,6,2,1,4,5]=>[7]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,7,2,5]=>[7,3,1,4,2,6,5]=>[3,7,4,2,6,1,5]=>[7]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,4,7,2,5,6]=>[7,3,1,4,2,5,6]=>[3,7,4,2,1,5,6]=>[7]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6]=>[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]=>[5,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4,7]=>[6,3,1,5,2,4,7]=>[3,6,5,1,2,4,7]=>[6,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,6,7,4]=>[7,3,1,5,2,6,4]=>[3,7,5,6,2,1,4]=>[7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6]=>[7,3,1,5,2,4,6]=>[3,7,5,1,2,4,6]=>[7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,2,4,7]=>[6,3,1,2,5,4,7]=>[3,1,6,5,2,4,7]=>[6,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,6,2,7,4]=>[7,3,1,6,5,2,4]=>[3,7,5,1,6,2,4]=>[7]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,2,4]=>[7,3,1,2,5,6,4]=>[3,1,7,6,2,5,4]=>[7]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6]=>[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]=>[7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,7]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,7,5]=>[7,3,1,2,6,4,5]=>[3,1,7,6,4,2,5]=>[7]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,7,4,5]=>[7,3,1,6,2,4,5]=>[3,7,6,1,4,2,5]=>[7]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,6,7,2,4,5]=>[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]=>[7]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[4,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[4,3,1,2,5,7,6]=>[4,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[4,3,1,2,6,5,7]=>[4,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[4,3,1,2,6,7,5]=>[4,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[4,3,1,2,7,5,6]=>[4,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,5,2,6,7]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6]=>[5,4,3,1,2,7,6]=>[3,1,4,5,2,7,6]=>[5,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,2,7]=>[6,4,3,1,5,2,7]=>[3,4,6,5,1,2,7]=>[6,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,2]=>[7,4,3,1,5,6,2]=>[3,4,7,6,1,5,2]=>[7]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6]=>[7,4,3,1,5,2,6]=>[3,4,7,5,1,2,6]=>[7]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,7]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,7,5]=>[7,4,3,1,6,2,5]=>[3,4,7,6,2,1,5]=>[7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,7,2,5]=>[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]=>[7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,7,2,5,6]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[5,4,1,3,2,6,7]=>[5,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[5,4,1,3,2,7,6]=>[5,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,1,6,2,7]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,1,6,7,2]=>[7,5,3,4,1,6,2]=>[4,6,5,3,7,1,2]=>[7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[6,5,1,3,4,2,7]=>[6,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,1,7,2]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[7,6,1,3,4,5,2]=>[7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[7,5,1,3,4,2,6]=>[7]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[6,4,1,3,2,5,7]=>[6,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,7,5]=>[7,1,3,4,6,2,5]=>[7,6,1,3,2,4,5]=>[7]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[7,4,1,3,6,2,5]=>[7]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[7,4,1,3,2,5,6]=>[7]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[5,3,1,2,4,6,7]=>[5,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[5,3,1,2,4,7,6]=>[5,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,6,4,7]=>[6,1,3,5,2,4,7]=>[6,5,1,2,3,4,7]=>[6,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,6,7,4]=>[7,1,3,5,2,6,4]=>[7,5,1,6,3,2,4]=>[7]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6]=>[7,1,3,5,2,4,6]=>[7,5,1,2,3,4,6]=>[7]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,6,2,4,7]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,2,7,4]=>[7,6,3,5,1,2,4]=>[5,1,6,2,3,7,4]=>[7]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,6,7,2,4]=>[7,5,3,1,2,6,4]=>[3,1,5,7,6,4,2]=>[7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[6,3,1,5,2,4,7]=>[6,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,1,2,7,4]=>[7,1,3,6,5,2,4]=>[7,5,1,2,6,3,4]=>[7]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[7,6,3,1,5,2,4]=>[3,6,5,1,2,7,4]=>[7]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[7,3,1,6,2,5,4]=>[7]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[7,3,1,5,2,4,6]=>[7]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[6,3,1,2,4,5,7]=>[6,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,7,5]=>[7,1,3,2,6,4,5]=>[7,3,1,6,4,2,5]=>[7]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,7,4,5]=>[7,1,3,6,2,4,5]=>[7,6,1,2,4,3,5]=>[7]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,1,7,2,4,5]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]=>[7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]=>[7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]=>[4,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[4,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,5,3,6,7]=>[5,1,4,2,3,6,7]=>[5,4,2,1,3,6,7]=>[5,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6]=>[5,1,4,2,3,7,6]=>[5,4,2,1,3,7,6]=>[5,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,3,7]=>[6,1,4,2,5,3,7]=>[6,4,5,1,2,3,7]=>[6,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,3]=>[7,1,4,2,5,6,3]=>[7,4,6,1,2,5,3]=>[7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6]=>[7,1,4,2,5,3,6]=>[7,4,5,1,2,3,6]=>[7]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,7]=>[6,1,4,2,3,5,7]=>[6,4,2,1,3,5,7]=>[6,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,7,5]=>[7,1,4,2,6,3,5]=>[7,4,6,1,3,2,5]=>[7]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,7,3,5]=>[7,1,4,2,3,6,5]=>[7,4,2,1,6,3,5]=>[7]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,7,3,5,6]=>[7,1,4,2,3,5,6]=>[7,4,2,1,3,5,6]=>[7]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6]=>[5,4,1,2,3,7,6]=>[4,1,2,5,3,7,6]=>[5,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3,7]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,5,2,6,7,3]=>[7,5,4,1,2,6,3]=>[4,1,5,7,6,2,3]=>[7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,2,3,7]=>[6,4,1,2,5,3,7]=>[4,1,6,5,3,2,7]=>[6,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,2,7,3]=>[7,6,4,1,5,2,3]=>[4,6,1,5,2,7,3]=>[7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,2,3]=>[7,4,1,2,5,6,3]=>[4,1,7,6,3,5,2]=>[7]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6]=>[7,4,1,2,5,3,6]=>[4,1,7,5,3,2,6]=>[7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,7]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,7,5]=>[7,4,1,2,6,3,5]=>[4,1,7,6,2,3,5]=>[7]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,7,3,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,7,2,3,5]=>[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]=>[7]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[5,1,4,2,3,6,7]=>[5,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[5,1,4,2,3,7,6]=>[5,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,6,3,7]=>[6,1,5,4,2,3,7]=>[6,4,2,5,1,3,7]=>[6,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,6,7,3]=>[7,1,5,4,2,6,3]=>[7,4,5,6,1,3,2]=>[7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6]=>[7,1,5,4,2,3,6]=>[7,4,2,5,1,3,6]=>[7]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,1,6,2,3,7]=>[6,5,1,4,2,3,7]=>[5,4,2,1,6,3,7]=>[6,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,1,6,2,7,3]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,1,6,7,2,3]=>[7,5,1,4,2,6,3]=>[5,4,7,3,6,2,1]=>[7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6]=>[7,5,1,4,2,3,6]=>[5,4,2,1,7,3,6]=>[7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[6,1,5,2,4,3,7]=>[6,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,1,2,7,3]=>[7,1,6,4,5,2,3]=>[7,5,2,6,4,1,3]=>[7]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[7,6,1,4,5,2,3]=>[6,5,2,1,4,7,3]=>[7]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[7,1,6,2,4,5,3]=>[7]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[7,1,5,2,4,3,6]=>[7]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[6,1,4,2,3,5,7]=>[6,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,7,5]=>[7,1,2,4,6,3,5]=>[7,1,6,2,3,4,5]=>[7]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,7,3,5]=>[7,1,6,4,2,3,5]=>[7,4,2,6,3,1,5]=>[7]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,7,2,3,5]=>[7,6,1,4,2,3,5]=>[6,4,2,1,3,7,5]=>[7]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[7,1,4,2,6,3,5]=>[7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]=>[7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,6,4,7]=>[6,1,2,5,3,4,7]=>[6,1,5,3,2,4,7]=>[6,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,6,7,4]=>[7,1,2,5,3,6,4]=>[7,1,5,6,2,3,4]=>[7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6]=>[7,1,2,5,3,4,6]=>[7,1,5,3,2,4,6]=>[7]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,6,3,4,7]=>[6,1,5,2,3,4,7]=>[6,5,2,3,1,4,7]=>[6,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,6,3,7,4]=>[7,1,6,5,2,3,4]=>[7,5,2,3,6,1,4]=>[7]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,6,7,3,4]=>[7,1,5,2,3,6,4]=>[7,5,2,6,1,3,4]=>[7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6]=>[7,1,5,2,3,4,6]=>[7,5,2,3,1,4,6]=>[7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,7]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,6,2,3,7,4]=>[7,6,1,5,2,3,4]=>[6,5,2,3,1,7,4]=>[7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,6,2,7,3,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,6,7,2,3,4]=>[7,5,1,2,3,6,4]=>[5,1,2,7,6,4,3]=>[7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[6,1,2,5,3,4,7]=>[6,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,7,4]=>[7,1,2,6,5,3,4]=>[7,1,5,3,6,2,4]=>[7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,1,2,7,3,4]=>[7,1,6,2,5,3,4]=>[7,6,5,3,2,1,4]=>[7]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,1,7,2,3,4]=>[7,6,1,2,5,3,4]=>[6,1,5,3,2,7,4]=>[7]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[7,1,2,6,3,5,4]=>[7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]=>[7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,7,5]=>[7,1,2,3,6,4,5]=>[7,1,2,6,4,3,5]=>[7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,7,4,5]=>[7,1,2,6,3,4,5]=>[7,1,6,3,4,2,5]=>[7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,7,3,4,5]=>[7,1,6,2,3,4,5]=>[7,6,2,3,4,1,5]=>[7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1,7,2,3,4,5]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]=>[7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[1,2,3,4,7,8,6,5]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,5,7]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,8,7,5,6]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[1,2,3,6,7,5,4,8]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,2,3,7,8,5,6,4]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,4,7]=>[1,2,3,8,5,6,4,7]=>[1,2,3,6,8,5,4,7]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]=>[1,2,3,5,7,4,6,8]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,4,8,6]=>[1,2,3,8,5,7,4,6]=>[1,2,3,7,8,4,5,6]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>[1,2,3,5,8,7,4,6]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,4,6,7]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5,8]=>[1,2,3,7,6,4,5,8]=>[1,2,3,6,4,7,5,8]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,4,7,8,5]=>[1,2,3,8,6,4,7,5]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,4,8,5,7]=>[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,7,6,4,5,8]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,4,8,5]=>[1,2,3,8,7,6,4,5]=>[1,2,3,6,4,7,8,5]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,6,7,5]=>[1,2,3,8,7,4,6,5]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,4,5,8,6]=>[1,2,3,8,4,7,5,6]=>[1,2,3,8,7,5,4,6]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,4,8,5,6]=>[1,2,3,8,7,4,5,6]=>[1,2,3,7,4,5,8,6]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]=>[1,2,3,8,4,7,5,6]=>[5,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[5,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,6,7,5,8]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[1,2,4,3,7,8,6,5]=>[4,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,8,6,5,7]=>[1,2,4,3,6,8,5,7]=>[4,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,6,7]=>[3,3,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,4,5,7,3,8,6]=>[1,2,8,4,5,7,3,6]=>[1,2,7,8,4,3,5,6]=>[6,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,3,8,5,7]=>[1,2,8,4,6,3,5,7]=>[1,2,6,8,3,4,5,7]=>[6,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,3,8,5,6]=>[1,2,8,4,7,3,5,6]=>[1,2,7,8,3,5,4,6]=>[6,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>[1,2,4,8,3,5,6,7]=>[6,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]=>[1,2,5,3,4,7,8,6]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,8,6]=>[1,2,8,5,3,7,4,6]=>[1,2,5,8,7,3,4,6]=>[6,1,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,8,4,6,7]=>[1,2,8,5,3,4,6,7]=>[1,2,5,3,8,4,6,7]=>[6,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,3,7,8,4]=>[1,2,8,6,5,3,7,4]=>[1,2,5,6,8,7,3,4]=>[6,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,3,4,8,6]=>[1,2,8,3,5,7,4,6]=>[1,2,8,7,3,4,5,6]=>[6,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>[1,2,8,3,5,4,7,6]=>[1,2,8,5,3,7,4,6]=>[6,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]=>[1,2,8,5,3,4,6,7]=>[6,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>[4,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]=>[4,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,6,3,4,7,5,8]=>[1,2,7,3,6,4,5,8]=>[1,2,7,6,4,3,5,8]=>[5,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>[1,2,8,3,6,4,5,7]=>[1,2,8,6,4,3,5,7]=>[6,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,8,5]=>[1,2,8,7,6,3,4,5]=>[1,2,6,3,4,7,8,5]=>[6,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[1,2,8,6,3,4,7,5]=>[1,2,6,3,8,7,5,4]=>[6,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,6,7,3,4,8,5]=>[1,2,8,3,7,6,4,5]=>[1,2,8,6,4,7,3,5]=>[6,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[1,2,8,3,7,4,5,6]=>[1,2,8,7,4,5,3,6]=>[6,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>[6,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[3,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>[1,3,2,4,6,8,5,7]=>[4,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[4,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>[1,3,2,5,8,7,4,6]=>[5,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,4,6,7]=>[1,3,2,8,5,4,6,7]=>[1,3,2,5,8,4,6,7]=>[5,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[3,2,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5,8]=>[1,3,2,7,6,4,5,8]=>[1,3,2,6,4,7,5,8]=>[4,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[4,2,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[3,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>[3,3,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>[1,3,4,2,5,8,6,7]=>[3,3,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[3,3,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,3,4,2,7,8,6,5]=>[4,3,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>[4,3,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,2,8,5]=>[1,8,3,4,7,6,2,5]=>[1,6,7,2,3,8,4,5]=>[7,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,8,2,5,7]=>[1,8,3,4,2,6,5,7]=>[1,4,8,3,6,2,5,7]=>[7,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,2,5,8,6]=>[1,8,3,4,2,7,5,6]=>[1,4,8,3,7,5,2,6]=>[7,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[1,8,3,4,2,5,6,7]=>[1,4,8,3,2,5,6,7]=>[7,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]=>[1,3,5,2,4,6,8,7]=>[4,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>[1,5,3,2,4,8,6,7]=>[1,3,5,2,4,8,6,7]=>[4,3,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,2,6,7,4,8]=>[1,7,3,5,2,6,4,8]=>[1,5,7,6,3,2,4,8]=>[6,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>[1,3,6,5,2,4,7,8]=>[5,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,2,4]=>[1,8,3,2,5,6,7,4]=>[1,3,8,7,2,5,6,4]=>[7,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]=>[1,3,7,5,2,4,6,8]=>[6,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,2,4,8,6]=>[1,8,3,2,5,7,4,6]=>[1,3,8,7,2,4,5,6]=>[7,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,2,8,4,6]=>[1,8,3,7,5,2,4,6]=>[1,5,7,3,8,4,2,6]=>[7,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]=>[1,3,8,5,2,7,4,6]=>[7,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,6,2,4,5,7,8]=>[1,6,3,2,4,5,7,8]=>[1,3,6,2,4,5,7,8]=>[5,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,6,2,4,7,8,5]=>[1,8,3,2,6,4,7,5]=>[1,3,8,6,7,2,4,5]=>[7,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[1,8,3,2,6,4,5,7]=>[1,3,8,6,4,2,5,7]=>[7,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,7,2,8,4,5,6]=>[1,8,3,7,2,4,5,6]=>[1,7,8,2,4,5,3,6]=>[7,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>[1,3,8,2,4,5,6,7]=>[7,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[3,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[3,2,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[3,2,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>[3,3,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,3,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>[3,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[3,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>[1,4,2,3,8,6,7,5]=>[1,4,2,3,7,8,6,5]=>[4,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,5,7,6]=>[1,4,2,3,8,7,5,6]=>[4,3,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,3,6,7,8]=>[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[4,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,3,6,8,7]=>[1,5,4,2,3,6,8,7]=>[1,4,2,5,3,6,8,7]=>[4,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,8]=>[1,5,4,2,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>[4,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,8,6,7]=>[1,5,4,2,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[4,3,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,2,5,8,3,6,7]=>[1,8,4,2,5,3,6,7]=>[1,4,8,5,3,2,6,7]=>[7,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,6,3,5,7,8]=>[1,6,4,2,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>[5,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,6,3,5,8,7]=>[1,6,4,2,3,5,8,7]=>[1,4,2,6,3,5,8,7]=>[5,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5,8]=>[1,7,4,2,6,3,5,8]=>[1,4,7,6,2,3,5,8]=>[6,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,8,5,7]=>[1,8,4,2,6,3,5,7]=>[1,4,8,6,2,3,5,7]=>[7,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,2,6,7,8,3,5]=>[1,8,4,2,3,6,7,5]=>[1,4,2,8,7,3,6,5]=>[7,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,2,6,8,3,5,7]=>[1,8,4,2,3,6,5,7]=>[1,4,2,8,6,3,5,7]=>[7,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>[1,8,4,2,3,7,5,6]=>[1,4,2,8,7,5,3,6]=>[7,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[1,8,4,2,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>[7,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[1,5,4,2,3,6,7,8]=>[4,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,2,3,7,8,6]=>[1,5,2,4,3,8,7,6]=>[1,5,4,2,3,7,8,6]=>[4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>[1,5,4,2,3,8,6,7]=>[4,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,2,6,7,8,3]=>[1,8,5,4,2,6,7,3]=>[1,4,5,8,7,2,6,3]=>[7,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,2,8,3,7]=>[1,8,6,4,5,2,3,7]=>[1,5,2,6,4,8,3,7]=>[7,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,2,7,3,5,8]=>[1,7,6,4,2,3,5,8]=>[1,4,2,6,3,7,5,8]=>[6,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,8,5]=>[1,8,7,4,6,2,3,5]=>[1,6,2,7,3,4,8,5]=>[7,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[1,8,6,4,2,3,7,5]=>[1,4,2,6,8,7,5,3]=>[7,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,2,8,3,5,7]=>[1,8,6,4,2,3,5,7]=>[1,4,2,6,3,8,5,7]=>[7,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]=>[1,8,4,2,6,3,5,7]=>[7,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,7,2,3,5,8,6]=>[1,8,2,4,3,7,5,6]=>[1,8,4,2,7,5,3,6]=>[7,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,4,7,2,8,3,5,6]=>[1,8,7,4,2,3,5,6]=>[1,4,2,7,3,5,8,6]=>[7,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,8,4,2,3,5,6,7]=>[7,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[4,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>[1,5,2,3,4,8,7,6]=>[1,5,2,3,4,7,8,6]=>[4,3,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>[4,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,2,3,6,8,4,7]=>[1,8,2,5,3,6,4,7]=>[1,8,5,6,2,3,4,7]=>[7,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,2,3,7,8,4,6]=>[1,8,2,5,3,4,7,6]=>[1,8,5,3,2,7,4,6]=>[7,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,2,3,8,4,6,7]=>[1,8,2,5,3,4,6,7]=>[1,8,5,3,2,4,6,7]=>[7,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,6,3,4,8,7]=>[1,6,5,2,3,4,8,7]=>[1,5,2,3,6,4,8,7]=>[5,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,8,4,7]=>[1,8,6,5,2,3,4,7]=>[1,5,2,3,6,8,4,7]=>[7,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[1,8,5,2,3,7,4,6]=>[1,5,2,8,7,3,4,6]=>[7,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,8,4,6]=>[1,8,7,5,2,3,4,6]=>[1,5,2,3,7,4,8,6]=>[7,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[1,8,5,2,3,4,6,7]=>[1,5,2,3,8,4,6,7]=>[7,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,2,3,8,4]=>[1,8,2,7,5,6,3,4]=>[1,8,6,3,7,5,2,4]=>[7,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[1,8,2,3,5,6,4,7]=>[1,8,2,6,3,5,4,7]=>[7,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,7,2,3,4,8,6]=>[1,8,2,3,5,7,4,6]=>[1,8,2,7,3,4,5,6]=>[7,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>[1,8,2,3,5,4,7,6]=>[1,8,2,5,3,7,4,6]=>[7,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[5,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>[5,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[1,8,2,7,6,3,4,5]=>[1,8,6,3,4,7,2,5]=>[7,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,2,3,8,4,5,7]=>[1,8,2,6,3,4,5,7]=>[1,8,6,3,4,2,5,7]=>[7,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,7,3,4,5,8]=>[1,7,6,2,3,4,5,8]=>[1,6,2,3,4,7,5,8]=>[6,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>[1,8,7,2,6,3,4,5]=>[1,7,6,3,4,2,8,5]=>[7,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,8,4,5]=>[1,8,7,6,2,3,4,5]=>[1,6,2,3,4,7,8,5]=>[7,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[1,8,6,2,3,4,5,7]=>[1,6,2,3,4,8,5,7]=>[7,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,2,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,5,7,6]=>[2,1,3,4,8,7,5,6]=>[4,2,1,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[4,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,2,2,1,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[5,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,7,8,6,5]=>[4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]=>[4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>[4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]=>[4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[4,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[3,2,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>[4,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[2,1,7,8,4,5,6,3]=>[6,2]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,3,7]=>[2,1,8,4,5,6,3,7]=>[2,1,6,8,4,5,3,7]=>[6,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,3,8,6]=>[2,1,8,4,5,7,3,6]=>[2,1,7,8,4,3,5,6]=>[6,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,3,6,7]=>[2,1,8,4,5,3,6,7]=>[2,1,5,8,4,3,6,7]=>[6,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]=>[4,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,3,7,8,5]=>[2,1,8,4,6,3,7,5]=>[2,1,6,8,7,4,3,5]=>[6,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[2,1,8,4,3,5,6,7]=>[2,1,4,8,3,5,6,7]=>[6,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]=>[3,2,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>[4,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,3,6,7,8,4]=>[2,1,8,5,3,6,7,4]=>[2,1,5,8,7,4,6,3]=>[6,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,8,6]=>[2,1,8,5,3,7,4,6]=>[2,1,5,8,7,3,4,6]=>[6,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,8,4,6,7]=>[2,1,8,5,3,4,6,7]=>[2,1,5,3,8,4,6,7]=>[6,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,6,5,3,4,8,7]=>[4,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]=>[2,1,7,6,5,3,4,8]=>[2,1,5,3,6,7,4,8]=>[5,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,3,8,4]=>[2,1,8,7,5,6,3,4]=>[2,1,6,3,7,5,8,4]=>[6,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,3,4,8,6]=>[2,1,8,3,5,7,4,6]=>[2,1,8,7,3,4,5,6]=>[6,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,3,8,4,6]=>[2,1,8,7,5,3,4,6]=>[2,1,5,3,7,4,8,6]=>[6,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[2,1,8,5,3,7,4,6]=>[6,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[4,2,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,3,4,7,8,5]=>[2,1,8,3,6,4,7,5]=>[2,1,8,6,7,3,4,5]=>[6,2]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,3,4,8,5,7]=>[2,1,8,3,6,4,5,7]=>[2,1,8,6,4,3,5,7]=>[6,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,8,5]=>[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]=>[6,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[2,1,8,3,7,4,6,5]=>[6,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[3,3,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[3,3,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[2,3,1,4,7,8,6,5]=>[4,3,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]=>[4,3,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[2,3,1,6,7,5,4,8]=>[4,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[2,3,1,7,8,5,6,4]=>[5,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5,8]=>[3,2,1,7,6,4,5,8]=>[2,3,1,6,4,7,5,8]=>[4,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,8,5,7]=>[3,2,1,8,6,4,5,7]=>[2,3,1,6,4,8,5,7]=>[5,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>[2,3,1,8,6,4,5,7]=>[5,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[3,2,1,8,4,7,5,6]=>[2,3,1,8,7,5,4,6]=>[5,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,4,5,6]=>[3,2,1,8,4,5,7,6]=>[2,3,1,8,4,7,5,6]=>[5,3]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>[2,3,1,8,4,5,6,7]=>[5,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[4,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5]=>[4,4]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[3,4,2,1,8,7,5,6]=>[4,4]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>[3,4,2,1,8,5,6,7]=>[4,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,1,5]=>[8,2,3,4,1,6,7,5]=>[4,8,2,3,7,1,6,5]=>[8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,1,5,8,6]=>[8,2,3,4,1,7,5,6]=>[4,8,2,3,7,5,1,6]=>[8]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>[8]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>[3,6,2,5,1,4,8,7]=>[6,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,1,8,4]=>[8,2,3,7,5,6,1,4]=>[6,8,2,1,7,5,3,4]=>[8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>[3,6,2,1,4,5,8,7]=>[6,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,1,4,7,8,5]=>[8,2,3,1,6,4,7,5]=>[3,8,2,6,7,1,4,5]=>[8]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[8,2,3,6,1,4,7,5]=>[6,8,2,1,7,3,4,5]=>[8]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>[8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[4,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>[4,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]=>[4,4]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,3,7,5,8,6]=>[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>[4,4]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]=>[4,4]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,8]=>[5,2,4,1,3,7,6,8]=>[4,5,1,2,3,7,6,8]=>[5,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,8,6,7]=>[5,2,4,1,3,8,6,7]=>[4,5,1,2,3,8,6,7]=>[5,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3,7,8]=>[6,2,4,1,5,3,7,8]=>[4,6,5,2,1,3,7,8]=>[6,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,2,4,1,5,7,3,6]=>[4,8,7,2,1,3,5,6]=>[8]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[8,2,4,1,6,3,7,5]=>[4,8,6,2,7,1,3,5]=>[8]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7]=>[8,2,4,1,6,3,5,7]=>[4,8,6,2,3,1,5,7]=>[8]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,1,6,7,8,3,5]=>[8,2,4,1,3,6,7,5]=>[4,8,1,2,7,3,6,5]=>[8]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[8,2,4,1,3,7,5,6]=>[4,8,1,2,7,5,3,6]=>[8]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[8,2,4,1,3,5,6,7]=>[4,8,1,2,3,5,6,7]=>[8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,1,3,7,8,6]=>[5,2,1,4,3,8,7,6]=>[2,5,4,1,3,7,8,6]=>[5,3]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[8,2,5,4,1,6,3,7]=>[4,5,8,6,3,2,1,7]=>[8]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,1,7,8,3]=>[8,2,6,4,5,1,7,3]=>[5,8,7,6,4,2,1,3]=>[8]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,1,3,7,8,5]=>[8,2,1,4,6,3,7,5]=>[2,8,6,1,7,4,3,5]=>[8]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,1,8,3,5,7]=>[8,2,6,4,1,3,5,7]=>[4,6,2,8,3,1,5,7]=>[8]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[5,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,2,1,5,3,7,4,6]=>[2,8,5,7,1,4,3,6]=>[8]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[8,2,7,5,1,6,3,4]=>[5,7,8,1,6,2,3,4]=>[8]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[8,2,1,3,5,6,7,4]=>[2,8,1,7,3,5,6,4]=>[8]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,5,7,1,3,4,8,6]=>[8,2,1,3,5,7,4,6]=>[2,8,1,7,3,4,5,6]=>[8]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,6,1,3,7,4,8,5]=>[8,2,1,7,6,3,4,5]=>[2,8,6,3,4,7,1,5]=>[8]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,8,4,5]=>[8,2,7,6,1,3,4,5]=>[6,7,2,3,4,8,1,5]=>[8]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,1,3,8,4,5,6]=>[8,2,1,7,3,4,5,6]=>[2,8,7,3,4,5,1,6]=>[8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[3,3,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>[3,1,2,4,6,8,5,7]=>[4,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]=>[3,3,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,2,4,7,5,8,6]=>[3,1,2,4,8,7,5,6]=>[3,1,2,4,7,5,8,6]=>[4,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>[3,1,2,4,8,7,5,6]=>[4,3,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[4,3,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,2,5,6,8,4,7]=>[3,1,2,8,5,6,4,7]=>[3,1,2,6,8,5,4,7]=>[5,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,5,7,4,8,6]=>[3,1,2,8,5,7,4,6]=>[3,1,2,7,8,4,5,6]=>[5,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,2,5,8,4,6,7]=>[3,1,2,8,5,4,6,7]=>[3,1,2,5,8,4,6,7]=>[5,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]=>[3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]=>[3,1,2,7,6,4,5,8]=>[3,1,2,6,4,7,5,8]=>[4,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,2,6,4,7,8,5]=>[3,1,2,8,6,4,7,5]=>[3,1,2,6,8,7,5,4]=>[5,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,2,6,7,4,8,5]=>[3,1,2,8,7,6,4,5]=>[3,1,2,6,4,7,8,5]=>[5,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,5,7,6]=>[3,1,2,8,4,7,5,6]=>[5,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>[5,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[4,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,2,5,7,8,6]=>[4,3,1,2,5,8,7,6]=>[3,1,4,2,5,7,8,6]=>[4,3,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[4,3,1,2,6,5,7,8]=>[3,1,4,2,6,5,7,8]=>[4,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>[4,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,2,6,8,5,7]=>[4,3,1,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>[4,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,7,5,6,8]=>[4,3,1,2,7,5,6,8]=>[3,1,4,2,7,5,6,8]=>[4,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,8,6]=>[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]=>[4,4]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]=>[4,4]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[5,3,1,4,2,7,6,8]=>[3,5,4,2,1,7,6,8]=>[5,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,5,2,7,8,6]=>[5,3,1,4,2,8,7,6]=>[3,5,4,2,1,7,8,6]=>[5,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,6,2,8,7]=>[6,3,1,4,5,2,8,7]=>[3,6,5,2,4,1,8,7]=>[6,2]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[8,3,1,4,2,5,6,7]=>[3,8,4,2,1,5,6,7]=>[8]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,5,2,4,8,6,7]=>[5,3,1,2,4,8,6,7]=>[3,1,5,2,4,8,6,7]=>[5,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7]=>[6,3,1,5,2,4,8,7]=>[3,6,5,1,2,4,8,7]=>[6,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,2,6,7,8,4]=>[8,3,1,5,2,6,7,4]=>[3,8,5,7,2,1,6,4]=>[8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,3,1,5,2,7,4,6]=>[3,8,5,7,2,4,1,6]=>[8]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,8,4,6,7]=>[8,3,1,5,2,4,6,7]=>[3,8,5,1,2,4,6,7]=>[8]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,8,2,4]=>[8,3,1,2,5,6,7,4]=>[3,1,8,7,2,5,6,4]=>[8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,1,5,7,2,4,8,6]=>[8,3,1,2,5,7,4,6]=>[3,1,8,7,2,4,5,6]=>[8]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,1,5,7,8,2,4,6]=>[8,3,1,2,5,4,7,6]=>[3,1,8,5,2,7,4,6]=>[8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>[6,3,1,2,4,5,7,8]=>[3,1,6,2,4,5,7,8]=>[6,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,6,2,4,5,8,7]=>[6,3,1,2,4,5,8,7]=>[3,1,6,2,4,5,8,7]=>[6,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,6,2,4,7,8,5]=>[8,3,1,2,6,4,7,5]=>[3,1,8,6,7,2,4,5]=>[8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,8,5]=>[8,3,1,7,6,2,4,5]=>[3,8,6,1,4,7,2,5]=>[8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>[7,3,1,2,4,6,5,8]=>[3,1,7,2,6,4,5,8]=>[7,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[4,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,2,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[4,3,1,2,5,7,6,8]=>[4,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[4,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[4,3,1,2,7,8,6,5]=>[4,4]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]=>[4,4]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>[4,4]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6,8]=>[5,4,3,1,2,7,6,8]=>[3,1,4,5,2,7,6,8]=>[5,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2,7,8]=>[6,4,3,1,5,2,7,8]=>[3,4,6,5,1,2,7,8]=>[6,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>[8,4,3,1,5,7,2,6]=>[3,4,8,7,1,2,5,6]=>[8]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,1,6,8,2,5,7]=>[8,4,3,1,2,6,5,7]=>[3,1,4,8,6,2,5,7]=>[8]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[8]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>[5,1,3,4,2,8,6,7]=>[5,4,1,3,2,8,6,7]=>[5,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,8,7]=>[6,5,3,4,1,2,8,7]=>[4,1,5,3,6,2,8,7]=>[6,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,1,6,7,8,2]=>[8,5,3,4,1,6,7,2]=>[4,7,5,3,8,1,6,2]=>[8]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>[8,1,3,4,2,5,6,7]=>[8,4,1,3,2,5,6,7]=>[8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>[5,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>[5,3,1,2,4,6,8,7]=>[5,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,4,7,8,6]=>[5,1,3,2,4,8,7,6]=>[5,3,1,2,4,7,8,6]=>[5,3]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[5,3,1,2,4,8,6,7]=>[5,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,1,2,7,4,6,8]=>[7,1,3,5,2,4,6,8]=>[7,5,1,2,3,4,6,8]=>[7,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,1,6,2,4,8,7]=>[6,5,3,1,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>[6,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4,8]=>[7,6,3,5,1,2,4,8]=>[5,1,6,2,3,7,4,8]=>[7,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[8,6,3,5,1,2,7,4]=>[5,1,6,8,4,7,2,3]=>[8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>[8,5,3,1,2,7,4,6]=>[3,1,5,8,7,2,4,6]=>[8]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,8,4,6]=>[8,7,3,5,1,2,4,6]=>[5,1,7,2,3,4,8,6]=>[8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[6,3,1,5,2,4,8,7]=>[6,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,1,7,2,4,8]=>[7,6,3,1,5,2,4,8]=>[3,6,5,1,2,7,4,8]=>[7,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[8,6,3,1,5,2,7,4]=>[3,6,5,8,4,7,1,2]=>[8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[7,3,1,5,2,4,6,8]=>[7,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,1,2,4,8,6]=>[8,1,3,2,5,7,4,6]=>[8,3,1,7,2,4,5,6]=>[8]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,1,2,4,7,8,5]=>[8,1,3,2,6,4,7,5]=>[8,3,1,6,7,2,4,5]=>[8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,1,2,7,4,8,5]=>[8,1,3,7,6,2,4,5]=>[8,6,1,2,4,7,3,5]=>[8]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,8,4,5]=>[8,7,3,6,1,2,4,5]=>[6,1,7,2,4,3,8,5]=>[8]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,1,7,8,2,4,5]=>[8,6,3,1,2,4,7,5]=>[3,1,6,2,8,7,5,4]=>[8]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,6,7,1,2,4,5,8]=>[7,1,3,2,4,6,5,8]=>[7,3,1,2,6,4,5,8]=>[7,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[8,1,3,7,2,6,4,5]=>[8,7,1,6,4,2,3,5]=>[8]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[8,1,3,2,4,6,5,7]=>[8,3,1,2,6,4,5,7]=>[8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]=>[7,3,1,2,4,5,6,8]=>[7,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,1,2,4,8,5,6]=>[8,1,3,2,7,4,5,6]=>[8,3,1,7,4,5,2,6]=>[8]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,1,2,8,4,5,6]=>[8,1,3,7,2,4,5,6]=>[8,7,1,2,4,5,3,6]=>[8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[4,1,2,3,7,8,6,5]=>[4,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]=>[4,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,3,7,5,8,6]=>[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]=>[4,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>[4,1,2,3,8,7,5,6]=>[4,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,5,3,7,8,6]=>[5,1,4,2,3,8,7,6]=>[5,4,2,1,3,7,8,6]=>[5,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,2,5,6,3,8,7]=>[6,1,4,2,5,3,8,7]=>[6,4,5,1,2,3,8,7]=>[6,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,8,3]=>[8,1,4,2,5,6,7,3]=>[8,4,7,1,2,5,6,3]=>[8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,2,6,3,5,8,7]=>[6,1,4,2,3,5,8,7]=>[6,4,2,1,3,5,8,7]=>[6,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,2,6,3,7,8,5]=>[8,1,4,2,6,3,7,5]=>[8,4,6,1,7,2,3,5]=>[8]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[8,1,4,2,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>[8]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,5,2,3,7,8,6]=>[5,4,1,2,3,8,7,6]=>[4,1,2,5,3,7,8,6]=>[5,3]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,5,2,3,8,6,7]=>[5,4,1,2,3,8,6,7]=>[4,1,2,5,3,8,6,7]=>[5,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7]=>[6,5,4,1,2,3,8,7]=>[4,1,2,5,6,3,8,7]=>[6,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,7,3,6,8]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[7,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,8,6]=>[8,5,4,1,2,7,3,6]=>[4,1,5,8,7,3,2,6]=>[8]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,2,7,8,3,6]=>[8,5,4,1,2,3,7,6]=>[4,1,2,5,8,7,3,6]=>[8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,7,3,5,8]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[7,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,8,5]=>[8,7,4,1,6,2,3,5]=>[4,7,1,6,3,2,8,5]=>[8]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,8,3,5,7]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,7,2,3,5,8,6]=>[8,4,1,2,3,7,5,6]=>[4,1,2,8,7,5,3,6]=>[8]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,8,3,5,6]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[5,1,4,2,3,6,7,8]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,1,2,3,8,6,7]=>[5,1,2,4,3,8,6,7]=>[5,1,4,2,3,8,6,7]=>[5,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>[6,1,5,4,2,3,8,7]=>[6,4,2,5,1,3,8,7]=>[6,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,5,1,6,2,3,7,8]=>[6,5,1,4,2,3,7,8]=>[5,4,2,1,6,3,7,8]=>[6,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,8,3,7]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[8,7,5,4,1,6,2,3]=>[4,5,2,7,6,1,8,3]=>[8]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,1,6,7,8,2,3]=>[8,5,1,4,2,6,7,3]=>[5,4,8,3,7,2,6,1]=>[8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,1,7,2,3,6,8]=>[7,5,1,4,2,3,6,8]=>[5,4,2,1,7,3,6,8]=>[7,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,8,3,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[6,1,5,2,4,3,8,7]=>[6,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,1,2,8,3]=>[8,1,7,4,5,6,2,3]=>[8,6,2,7,4,5,1,3]=>[8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[8,1,7,2,4,5,6,3]=>[8]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[8,1,6,2,4,5,3,7]=>[8]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[8,1,7,4,5,2,3,6]=>[8,5,2,7,4,3,1,6]=>[8]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,1,2,3,8,5,7]=>[8,1,2,4,6,3,5,7]=>[8,1,6,2,3,4,5,7]=>[8]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,1,2,8,3,5,7]=>[8,1,6,4,2,3,5,7]=>[8,4,2,6,3,1,5,7]=>[8]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[8,6,1,4,2,3,5,7]=>[6,4,2,1,3,8,5,7]=>[8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,1,2,3,8,5]=>[8,1,2,4,7,6,3,5]=>[8,1,6,2,3,7,4,5]=>[8]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,1,8,2,3,5]=>[8,7,1,4,2,6,3,5]=>[7,4,6,1,3,2,8,5]=>[8]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[8,1,4,2,6,3,5,7]=>[8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[8,1,4,2,3,5,6,7]=>[8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,2,6,7,3,8,4]=>[8,1,7,5,2,6,3,4]=>[8,5,7,2,6,3,1,4]=>[8]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,2,6,7,8,3,4]=>[8,1,5,2,3,6,7,4]=>[8,5,2,7,1,3,6,4]=>[8]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,1,2,7,3,8,4,6]=>[8,1,7,5,2,3,4,6]=>[8,5,2,3,7,4,1,6]=>[8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,7,3,4,8]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[7,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,8,4]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[8]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,8,3,4,7]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[8]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,6,7,2,8,3,4]=>[8,7,5,1,2,6,3,4]=>[5,1,7,2,6,3,8,4]=>[8]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,8,3,4,6]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[8]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,8,4,7]=>[8,1,2,6,5,3,4,7]=>[8,1,5,3,6,2,4,7]=>[8]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,8,3,4,7]=>[8,1,6,2,5,3,4,7]=>[8,6,5,3,2,1,4,7]=>[8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[7,1,2,6,3,5,4,8]=>[7,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[8,1,7,2,5,6,3,4]=>[8,7,6,3,2,5,1,4]=>[8]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,1,8,2,3,4]=>[8,7,1,2,5,6,3,4]=>[7,1,6,3,2,5,8,4]=>[8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[8,1,2,7,3,5,6,4]=>[8]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,1,2,8,3,4,6]=>[8,1,7,2,5,3,4,6]=>[8,7,5,3,2,4,1,6]=>[8]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>[8,1,2,5,3,4,6,7]=>[8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[6,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,2,7,3,4,8,5]=>[8,1,7,2,6,3,4,5]=>[8,7,6,3,4,2,1,5]=>[8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,7,2,3,4,8,5]=>[8,7,1,2,6,3,4,5]=>[7,1,6,3,4,2,8,5]=>[8]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,7,2,3,8,4,5]=>[8,7,1,6,2,3,4,5]=>[7,6,2,3,4,1,8,5]=>[8]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,8,3,4,5]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[8]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[8,6,1,2,3,4,7,5]=>[6,1,2,3,8,7,5,4]=>[8]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,1,2,3,8,4,5]=>[8,1,2,7,3,6,4,5]=>[8,1,7,6,4,3,2,5]=>[8]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[8,7,1,2,3,6,4,5]=>[7,1,2,6,4,3,8,5]=>[8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,8,4,5,6]=>[8,1,2,7,3,4,5,6]=>[8,1,7,3,4,5,2,6]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Map
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
- $des$ is the number of descents, St000021The number of descents of a permutation.,
- $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
- $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
- $Ebot$ is the sum of the excedance bottoms,
- $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
- $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
- $Res$ is the sum of the (right) embracing numbers,
- $Ine$ is the sum of the side numbers.
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 maxima 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 weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
cycle type
Description
The cycle type of a permutation as a partition.
searching the database
Sorry, this map was not found in the database.