Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00237: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00237: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]
[1,0,1,0]=>[1,2]=>[1,2]=>[1,2]
[1,1,0,0]=>[2,1]=>[2,1]=>[2,1]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[1,3,2]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[3,1,2]
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[2,3,1]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,2,3]=>[1,4,2,3]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,4,3,2]=>[1,3,4,2]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[3,1,2,4]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[4,1,2,3]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,3,1,2]=>[3,1,4,2]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,1,4]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,1,3,2]=>[4,3,1,2]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,2,1,3]=>[2,4,1,3]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[2,3,4,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[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]
[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]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[1,2,5,3,4]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[1,2,4,5,3]
[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]
[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]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[1,4,2,3,5]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[1,5,2,3,4]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,5,4,2,3]=>[1,4,2,5,3]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,2,4,3]=>[1,5,4,2,3]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,5,3,2,4]=>[1,3,5,2,4]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[1,3,4,5,2]
[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]
[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]
[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]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[2,1,5,3,4]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[2,1,4,5,3]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[4,1,2,3,5]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[5,1,2,3,4]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,4,1,2,3]=>[4,1,2,5,3]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,3,1,2,5]=>[3,1,4,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,1,2,4,3]=>[5,1,4,2,3]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,3,1,2,4]=>[3,1,5,2,4]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,3,1,2]=>[3,1,4,5,2]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,1,3,2,5]=>[4,3,1,2,5]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,1,3,2,4]=>[5,3,1,2,4]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,4,1,3,2]=>[4,3,1,5,2]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,2,1,3,5]=>[2,4,1,3,5]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,1,4,2,3]=>[5,4,2,1,3]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,2,1,3,4]=>[2,5,1,3,4]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,1,3]=>[2,4,1,5,3]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,1,4,3,2]=>[5,3,4,1,2]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,2,1,4,3]=>[2,5,4,1,3]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,3,2,1,4]=>[2,3,5,1,4]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[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]
[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]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[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]
[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]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,6,5,3,4]=>[1,2,5,3,6,4]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,6,3,5,4]=>[1,2,6,5,3,4]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,6,4,3,5]=>[1,2,4,6,3,5]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[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]
[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]
[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]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,6,5,2,3,4]=>[1,5,2,3,6,4]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,5,4,2,3,6]=>[1,4,2,5,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,2,3,5,4]=>[1,6,2,5,3,4]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,6,4,2,3,5]=>[1,4,2,6,3,5]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,6,5,4,2,3]=>[1,4,2,5,6,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,5,2,4,3,6]=>[1,5,4,2,3,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,2,4,3,5]=>[1,6,4,2,3,5]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,6,5,2,4,3]=>[1,5,4,2,6,3]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,5,3,2,4,6]=>[1,3,5,2,4,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,6,2,5,3,4]=>[1,6,5,3,2,4]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,6,3,2,4,5]=>[1,3,6,2,4,5]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,6,5,3,2,4]=>[1,3,5,2,6,4]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,2,5,4,3]=>[1,6,4,5,2,3]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,6,3,2,5,4]=>[1,3,6,5,2,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,6,4,3,2,5]=>[1,3,4,6,2,5]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[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]
[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]
[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]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[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]
[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]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,6,5,3,4]=>[2,1,5,3,6,4]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,3,5,4]=>[2,1,6,5,3,4]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,6,4,3,5]=>[2,1,4,6,3,5]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,1,2,6,5,4]=>[3,1,2,5,6,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,1,2,3,5,4]=>[6,1,2,5,3,4]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[4,3,1,2,6,5]=>[3,1,4,2,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,1,2,4,3,6]=>[5,1,4,2,3,6]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,1,2,4,3,5]=>[6,1,4,2,3,5]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,5,1,2,4,3]=>[5,1,4,2,6,3]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,1,2,5,3,4]=>[6,1,5,3,2,4]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,1,2,5,4,3]=>[6,1,4,5,2,3]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,1,2,5,4]=>[3,1,6,5,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,2,1,6,4,5]=>[2,3,1,6,4,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,1,3,2,5,6]=>[4,3,1,2,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,1,3,2,6,5]=>[4,3,1,2,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,1,3,2,4,6]=>[5,3,1,2,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,1,3,2,4,5]=>[6,3,1,2,4,5]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,5,1,3,2,4]=>[5,3,1,2,6,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,4,1,3,2,6]=>[4,3,1,5,2,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,1,3,2,5,4]=>[6,3,1,5,2,4]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,4,1,3,2,5]=>[4,3,1,6,2,5]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,5,4,1,3,2]=>[4,3,1,5,6,2]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[4,2,1,3,6,5]=>[2,4,1,3,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,1,4,2,3,6]=>[5,4,2,1,3,6]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,1,4,2,3,5]=>[6,4,2,1,3,5]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,5,1,4,2,3]=>[5,4,2,1,6,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,1,5,2,3,4]=>[6,5,2,3,1,4]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,1,5,4,2,3]=>[6,4,2,5,1,3]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,2,1,3,5,4]=>[2,6,1,5,3,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,1,4,3,2,6]=>[5,3,4,1,2,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,1,4,3,2,5]=>[6,3,4,1,2,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,5,1,4,3,2]=>[5,3,4,1,6,2]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,2,1,4,3,6]=>[2,5,4,1,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,1,5,2,4,3]=>[6,5,4,2,1,3]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,2,1,4,3,5]=>[2,6,4,1,3,5]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[2,5,4,1,6,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,1,5,3,2,4]=>[6,3,5,2,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,2,1,5,3,4]=>[2,6,5,3,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,1,5,4,3,2]=>[6,3,4,5,1,2]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,2,1,5,4,3]=>[2,6,4,5,1,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,3,2,1,5,4]=>[2,3,6,5,1,4]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[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]
[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]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[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]
[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]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,7,4,6,5]=>[1,2,3,7,6,4,5]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[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]
[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]
[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]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,7,6,3,4,5]=>[1,2,6,3,4,7,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,7,3,4,6,5]=>[1,2,7,3,6,4,5]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,7,6,5,3,4]=>[1,2,5,3,6,7,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,6,3,5,4,7]=>[1,2,6,5,3,4,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,7,3,5,4,6]=>[1,2,7,5,3,4,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,7,6,3,5,4]=>[1,2,6,5,3,7,4]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,7,3,6,4,5]=>[1,2,7,6,4,3,5]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,7,6,4,3,5]=>[1,2,4,6,3,7,5]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,7,3,6,5,4]=>[1,2,7,5,6,3,4]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,7,4,3,6,5]=>[1,2,4,7,6,3,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,7,5,4,3,6]=>[1,2,4,5,7,3,6]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[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]
[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]
[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]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[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]
[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]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,7,4,6,5]=>[1,3,2,7,6,4,5]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,7,6,2,3,4,5]=>[1,6,2,3,4,7,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,6,5,2,3,4,7]=>[1,5,2,3,6,4,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,2,3,4,6,5]=>[1,7,2,3,6,4,5]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,7,5,2,3,4,6]=>[1,5,2,3,7,4,6]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,7,6,5,2,3,4]=>[1,5,2,3,6,7,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,6,2,3,5,4,7]=>[1,6,2,5,3,4,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,2,3,5,4,6]=>[1,7,2,5,3,4,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,7,6,2,3,5,4]=>[1,6,2,5,3,7,4]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,7,2,3,6,4,5]=>[1,7,2,6,4,3,5]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,7,6,4,2,3,5]=>[1,4,2,6,3,7,5]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,6,5,4,2,3,7]=>[1,4,2,5,6,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,2,3,6,5,4]=>[1,7,2,5,6,3,4]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,7,4,2,3,6,5]=>[1,4,2,7,6,3,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,7,5,4,2,3,6]=>[1,4,2,5,7,3,6]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,2,3]=>[1,4,2,5,6,7,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,5,2,4,3,6,7]=>[1,5,4,2,3,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,5,2,4,3,7,6]=>[1,5,4,2,3,7,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,6,2,4,3,5,7]=>[1,6,4,2,3,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,2,4,3,5,6]=>[1,7,4,2,3,5,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,7,6,2,4,3,5]=>[1,6,4,2,3,7,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,6,5,2,4,3,7]=>[1,5,4,2,6,3,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,2,4,3,6,5]=>[1,7,4,2,6,3,5]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,7,5,2,4,3,6]=>[1,5,4,2,7,3,6]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,7,6,5,2,4,3]=>[1,5,4,2,6,7,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,6,2,5,3,4,7]=>[1,6,5,3,2,4,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,7,2,5,3,4,6]=>[1,7,5,3,2,4,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,7,6,2,5,3,4]=>[1,6,5,3,2,7,4]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,7,2,6,3,4,5]=>[1,7,6,3,4,2,5]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,7,6,3,2,4,5]=>[1,3,6,2,4,7,5]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,6,5,3,2,4,7]=>[1,3,5,2,6,4,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,7,2,6,5,3,4]=>[1,7,5,3,6,2,4]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,7,3,2,4,6,5]=>[1,3,7,2,6,4,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,7,5,3,2,4,6]=>[1,3,5,2,7,4,6]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,7,6,5,3,2,4]=>[1,3,5,2,6,7,4]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,6,2,5,4,3,7]=>[1,6,4,5,2,3,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,2,5,4,3,6]=>[1,7,4,5,2,3,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,7,6,2,5,4,3]=>[1,6,4,5,2,7,3]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,6,3,2,5,4,7]=>[1,3,6,5,2,4,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,7,2,6,3,5,4]=>[1,7,6,5,3,2,4]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,7,3,2,5,4,6]=>[1,3,7,5,2,4,6]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,7,6,3,2,5,4]=>[1,3,6,5,2,7,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,6,4,3,2,5,7]=>[1,3,4,6,2,5,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,7,2,6,4,3,5]=>[1,7,4,6,3,2,5]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,7,3,2,6,4,5]=>[1,3,7,6,4,2,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,7,4,3,2,5,6]=>[1,3,4,7,2,5,6]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,7,6,4,3,2,5]=>[1,3,4,6,2,7,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,2,6,5,4,3]=>[1,7,4,5,6,2,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,7,3,2,6,5,4]=>[1,3,7,5,6,2,4]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,7,4,3,2,6,5]=>[1,3,4,7,6,2,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,7,5,4,3,2,6]=>[1,3,4,5,7,2,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[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]
[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]
[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]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[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]
[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]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,7,4,6,5]=>[2,1,3,7,6,4,5]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[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]
[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]
[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]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,7,6,3,4,5]=>[2,1,6,3,4,7,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,3,4,6,5]=>[2,1,7,3,6,4,5]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,7,6,5,3,4]=>[2,1,5,3,6,7,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,6,3,5,4,7]=>[2,1,6,5,3,4,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,3,5,4,6]=>[2,1,7,5,3,4,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,7,6,3,5,4]=>[2,1,6,5,3,7,4]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,7,3,6,4,5]=>[2,1,7,6,4,3,5]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,7,6,4,3,5]=>[2,1,4,6,3,7,5]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,3,6,5,4]=>[2,1,7,5,6,3,4]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,7,4,3,6,5]=>[2,1,4,7,6,3,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,7,5,4,3,6]=>[2,1,4,5,7,3,6]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,1,2,7,4,6,5]=>[3,1,2,7,6,4,5]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,1,2,7,6,5,4]=>[3,1,2,5,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[5,4,1,2,3,7,6]=>[4,1,2,5,3,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,1,2,3,5,4,7]=>[6,1,2,5,3,4,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,6,1,2,3,5,4]=>[6,1,2,5,3,7,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,1,2,3,6,4,5]=>[7,1,2,6,4,3,5]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,1,2,3,6,5,4]=>[7,1,2,5,6,3,4]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,1,2,4,3,6,7]=>[5,1,4,2,3,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[5,1,2,4,3,7,6]=>[5,1,4,2,3,7,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,1,2,4,3,5,7]=>[6,1,4,2,3,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,6,1,2,4,3,5]=>[6,1,4,2,3,7,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,5,1,2,4,3,7]=>[5,1,4,2,6,3,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,1,2,4,3,6,5]=>[7,1,4,2,6,3,5]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,5,1,2,4,3,6]=>[5,1,4,2,7,3,6]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,6,5,1,2,4,3]=>[5,1,4,2,6,7,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,1,2,5,3,4,7]=>[6,1,5,3,2,4,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,1,2,5,3,4,6]=>[7,1,5,3,2,4,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,6,1,2,5,3,4]=>[6,1,5,3,2,7,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,1,2,6,3,4,5]=>[7,1,6,3,4,2,5]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,1,2,6,5,3,4]=>[7,1,5,3,6,2,4]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[5,4,3,1,2,7,6]=>[3,1,4,5,2,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,1,2,5,4,3,7]=>[6,1,4,5,2,3,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,1,2,5,4,3,6]=>[7,1,4,5,2,3,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,6,1,2,5,4,3]=>[6,1,4,5,2,7,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,3,1,2,5,4,7]=>[3,1,6,5,2,4,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,1,2,6,3,5,4]=>[7,1,6,5,3,2,4]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,6,3,1,2,5,4]=>[3,1,6,5,2,7,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,1,2,6,4,3,5]=>[7,1,4,6,3,2,5]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,3,1,2,6,4,5]=>[3,1,7,6,4,2,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,1,2,6,5,4,3]=>[7,1,4,5,6,2,3]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,3,1,2,6,5,4]=>[3,1,7,5,6,2,4]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,2,1,7,4,6,5]=>[2,3,1,7,6,4,5]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,1,3,2,5,6,7]=>[4,3,1,2,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,1,3,2,5,7,6]=>[4,3,1,2,5,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,1,3,2,6,5,7]=>[4,3,1,2,6,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,1,3,2,7,5,6]=>[4,3,1,2,7,5,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,1,3,2,7,6,5]=>[4,3,1,2,6,7,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,1,3,2,4,6,7]=>[5,3,1,2,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[5,1,3,2,4,7,6]=>[5,3,1,2,4,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,1,3,2,4,5,7]=>[6,3,1,2,4,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,6,1,3,2,4,5]=>[6,3,1,2,4,7,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,5,1,3,2,4,7]=>[5,3,1,2,6,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,5,1,3,2,4,6]=>[5,3,1,2,7,4,6]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,6,5,1,3,2,4]=>[5,3,1,2,6,7,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,4,1,3,2,6,7]=>[4,3,1,5,2,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[5,4,1,3,2,7,6]=>[4,3,1,5,2,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,1,3,2,5,4,7]=>[6,3,1,5,2,4,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,1,3,2,5,4,6]=>[7,3,1,5,2,4,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,6,1,3,2,5,4]=>[6,3,1,5,2,7,4]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,4,1,3,2,5,7]=>[4,3,1,6,2,5,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,1,3,2,6,4,5]=>[7,3,1,6,4,2,5]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,4,1,3,2,5,6]=>[4,3,1,7,2,5,6]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,6,4,1,3,2,5]=>[4,3,1,6,2,7,5]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,5,4,1,3,2,7]=>[4,3,1,5,6,2,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,1,3,2,6,5,4]=>[7,3,1,5,6,2,4]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,4,1,3,2,6,5]=>[4,3,1,7,6,2,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,5,4,1,3,2,6]=>[4,3,1,5,7,2,6]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,5,4,1,3,2]=>[4,3,1,5,6,7,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,1,4,2,3,6,7]=>[5,4,2,1,3,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[5,1,4,2,3,7,6]=>[5,4,2,1,3,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,1,4,2,3,5,7]=>[6,4,2,1,3,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,1,4,2,3,5,6]=>[7,4,2,1,3,5,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,6,1,4,2,3,5]=>[6,4,2,1,3,7,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,5,1,4,2,3,7]=>[5,4,2,1,6,3,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,1,4,2,3,6,5]=>[7,4,2,1,6,3,5]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,5,1,4,2,3,6]=>[5,4,2,1,7,3,6]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,6,5,1,4,2,3]=>[5,4,2,1,6,7,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,1,5,2,3,4,7]=>[6,5,2,3,1,4,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,1,5,2,3,4,6]=>[7,5,2,3,1,4,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,6,1,5,2,3,4]=>[6,5,2,3,1,7,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,1,6,2,3,4,5]=>[7,6,2,3,4,1,5]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,1,6,5,2,3,4]=>[7,5,2,3,6,1,4]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[5,4,2,1,3,7,6]=>[2,4,1,5,3,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,1,5,4,2,3,7]=>[6,4,2,5,1,3,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,1,5,4,2,3,6]=>[7,4,2,5,1,3,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,6,1,5,4,2,3]=>[6,4,2,5,1,7,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,2,1,3,5,4,7]=>[2,6,1,5,3,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,1,6,2,3,5,4]=>[7,6,2,5,3,1,4]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,6,2,1,3,5,4]=>[2,6,1,5,3,7,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,1,6,4,2,3,5]=>[7,4,2,6,3,1,5]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,2,1,3,6,4,5]=>[2,7,1,6,4,3,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,1,6,5,4,2,3]=>[7,4,2,5,6,1,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,2,1,3,6,5,4]=>[2,7,1,5,6,3,4]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,4,2,1,3,6,5]=>[2,4,1,7,6,3,5]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,3,2,1,7,5,6]=>[2,3,4,1,7,5,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,1,4,3,2,6,7]=>[5,3,4,1,2,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,1,4,3,2,7,6]=>[5,3,4,1,2,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,1,4,3,2,5,7]=>[6,3,4,1,2,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,1,4,3,2,5,6]=>[7,3,4,1,2,5,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,6,1,4,3,2,5]=>[6,3,4,1,2,7,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,5,1,4,3,2,7]=>[5,3,4,1,6,2,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,1,4,3,2,6,5]=>[7,3,4,1,6,2,5]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,5,1,4,3,2,6]=>[5,3,4,1,7,2,6]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,6,5,1,4,3,2]=>[5,3,4,1,6,7,2]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,2,1,4,3,6,7]=>[2,5,4,1,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[5,2,1,4,3,7,6]=>[2,5,4,1,3,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,1,5,2,4,3,7]=>[6,5,4,2,1,3,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,1,5,2,4,3,6]=>[7,5,4,2,1,3,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,6,1,5,2,4,3]=>[6,5,4,2,1,7,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,2,1,4,3,5,7]=>[2,6,4,1,3,5,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,1,6,2,4,3,5]=>[7,6,4,2,3,1,5]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,6,2,1,4,3,5]=>[2,6,4,1,3,7,5]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,5,2,1,4,3,7]=>[2,5,4,1,6,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,1,6,5,2,4,3]=>[7,5,4,2,6,1,3]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,2,1,4,3,6,5]=>[2,7,4,1,6,3,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,5,2,1,4,3,6]=>[2,5,4,1,7,3,6]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,5,2,1,4,3]=>[2,5,4,1,6,7,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[5,3,2,1,4,7,6]=>[2,3,5,1,4,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,1,5,3,2,4,7]=>[6,3,5,2,1,4,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,1,5,3,2,4,6]=>[7,3,5,2,1,4,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,6,1,5,3,2,4]=>[6,3,5,2,1,7,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,2,1,5,3,4,7]=>[2,6,5,3,1,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,1,6,2,5,3,4]=>[7,6,5,3,2,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,2,1,5,3,4,6]=>[2,7,5,3,1,4,6]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,6,2,1,5,3,4]=>[2,6,5,3,1,7,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,1,6,3,2,4,5]=>[7,3,6,2,4,1,5]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,2,1,6,3,4,5]=>[2,7,6,3,4,1,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,1,6,5,3,2,4]=>[7,3,5,2,6,1,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,2,1,6,5,3,4]=>[2,7,5,3,6,1,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,3,2,1,4,6,5]=>[2,3,7,1,6,4,5]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,1,5,4,3,2,7]=>[6,3,4,5,1,2,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,1,5,4,3,2,6]=>[7,3,4,5,1,2,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,6,1,5,4,3,2]=>[6,3,4,5,1,7,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,2,1,5,4,3,7]=>[2,6,4,5,1,3,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,1,6,2,5,4,3]=>[7,6,4,5,2,1,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,2,1,5,4,3,6]=>[2,7,4,5,1,3,6]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,6,2,1,5,4,3]=>[2,6,4,5,1,7,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,3,2,1,5,4,7]=>[2,3,6,5,1,4,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,1,6,3,2,5,4]=>[7,3,6,5,2,1,4]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,2,1,6,3,5,4]=>[2,7,6,5,3,1,4]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,3,2,1,5,4,6]=>[2,3,7,5,1,4,6]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,6,3,2,1,5,4]=>[2,3,6,5,1,7,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,1,6,4,3,2,5]=>[7,3,4,6,2,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,2,1,6,4,3,5]=>[2,7,4,6,3,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,3,2,1,6,4,5]=>[2,3,7,6,4,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,1,6,5,4,3,2]=>[7,3,4,5,6,1,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,2,1,6,5,4,3]=>[2,7,4,5,6,1,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,3,2,1,6,5,4]=>[2,3,7,5,6,1,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,4,3,2,1,6,5]=>[2,3,4,7,6,1,5]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[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]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,8,7,5,6]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[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]
[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]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,7,4,5,6]=>[1,2,3,7,4,5,8,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,4,5,7,6]=>[1,2,3,8,4,7,5,6]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,7,6,4,5]=>[1,2,3,6,4,7,8,5]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,4,6,5,7]=>[1,2,3,8,6,4,5,7]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,7,4,6,5]=>[1,2,3,7,6,4,8,5]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,4,7,5,6]=>[1,2,3,8,7,5,4,6]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,4,6,7]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,7,5,4,6]=>[1,2,3,5,7,4,8,6]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,4,7,6,5]=>[1,2,3,8,6,7,4,5]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,5,4,7,6]=>[1,2,3,5,8,7,4,6]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,6,5,4,7]=>[1,2,3,5,6,8,4,7]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,8,7,5,6]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[1,2,8,4,3,5,6,7]=>[1,2,4,8,3,5,6,7]
[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]
[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]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,5,7,6]=>[1,3,2,4,8,7,5,6]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[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]
[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]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,4,2,3,8,5,7,6]=>[1,4,2,3,8,7,5,6]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>[1,4,2,3,6,7,8,5]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,8,7,6,5,2,3,4]=>[1,5,2,3,6,7,8,4]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[1,8,4,2,3,5,6,7]=>[1,4,2,8,3,5,6,7]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[1,8,6,4,2,3,5,7]=>[1,4,2,6,3,8,5,7]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[1,8,4,2,3,6,5,7]=>[1,4,2,8,6,3,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,8,7,6,5,2,4,3]=>[1,5,4,2,6,7,8,3]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[1,8,4,3,2,5,6,7]=>[1,3,4,8,2,5,6,7]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[1,8,4,3,2,7,6,5]=>[1,3,4,8,6,7,2,5]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,5,7,6]=>[2,1,3,4,8,7,5,6]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[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]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[2,1,8,7,3,4,6,5]=>[2,1,7,3,6,4,8,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[2,1,8,7,6,5,3,4]=>[2,1,5,3,6,7,8,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[2,1,8,4,3,7,5,6]=>[2,1,4,8,7,5,3,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[2,1,8,5,4,3,6,7]=>[2,1,4,5,8,3,6,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,8,5,7,6]=>[3,1,2,4,8,7,5,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[3,1,2,4,6,7,8,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[3,1,2,8,7,6,5,4]=>[3,1,2,5,6,7,8,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,8,5,7,6]=>[4,1,2,3,8,7,5,6]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[4,1,2,3,6,7,8,5]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[5,1,2,3,4,8,7,6]=>[5,1,2,3,4,7,8,6]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[8,1,2,3,4,7,6,5]=>[8,1,2,3,6,7,4,5]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[5,4,1,2,3,8,7,6]=>[4,1,2,5,3,7,8,6]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[6,5,4,1,2,3,8,7]=>[4,1,2,5,6,3,8,7]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[4,3,1,2,8,5,7,6]=>[3,1,4,2,8,7,5,6]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[3,1,4,2,6,7,8,5]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>[5,1,2,4,3,8,7,6]=>[5,1,4,2,3,7,8,6]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[6,5,1,2,4,3,8,7]=>[5,1,4,2,6,3,8,7]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[8,7,1,2,4,3,6,5]=>[7,1,4,2,6,3,8,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[8,1,2,4,3,7,6,5]=>[8,1,4,2,6,7,3,5]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[8,7,6,5,1,2,4,3]=>[5,1,4,2,6,7,8,3]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[5,3,1,2,4,8,7,6]=>[3,1,5,2,4,7,8,6]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[5,4,3,1,2,8,7,6]=>[3,1,4,5,2,7,8,6]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[8,1,2,5,4,3,6,7]=>[8,1,4,5,2,3,6,7]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[8,7,1,2,5,4,3,6]=>[7,1,4,5,2,3,8,6]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[8,6,1,2,5,4,3,7]=>[6,1,4,5,2,8,3,7]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[8,7,6,1,2,5,4,3]=>[6,1,4,5,2,7,8,3]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[8,3,1,2,7,6,5,4]=>[3,1,8,5,6,7,2,4]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[3,2,1,4,8,5,7,6]=>[2,3,1,4,8,7,5,6]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[3,2,1,4,8,6,5,7]=>[2,3,1,4,6,8,5,7]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[3,2,1,8,4,5,6,7]=>[2,3,1,8,4,5,6,7]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[3,2,1,8,7,4,5,6]=>[2,3,1,7,4,5,8,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[3,2,1,8,4,5,7,6]=>[2,3,1,8,4,7,5,6]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[3,2,1,8,6,4,5,7]=>[2,3,1,6,4,8,5,7]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[3,2,1,8,7,6,4,5]=>[2,3,1,6,4,7,8,5]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[3,2,1,8,4,6,5,7]=>[2,3,1,8,6,4,5,7]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[3,2,1,8,7,4,6,5]=>[2,3,1,7,6,4,8,5]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[3,2,1,8,4,7,5,6]=>[2,3,1,8,7,5,4,6]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>[3,2,1,8,5,4,6,7]=>[2,3,1,5,8,4,6,7]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[3,2,1,8,7,5,4,6]=>[2,3,1,5,7,4,8,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[3,2,1,8,4,7,6,5]=>[2,3,1,8,6,7,4,5]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[3,2,1,8,5,4,7,6]=>[2,3,1,5,8,7,4,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[3,2,1,8,6,5,4,7]=>[2,3,1,5,6,8,4,7]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[4,1,3,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[4,1,3,2,8,6,5,7]=>[4,3,1,2,6,8,5,7]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[4,3,1,2,6,7,8,5]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[5,1,3,2,4,8,7,6]=>[5,3,1,2,4,7,8,6]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[8,1,3,2,4,7,6,5]=>[8,3,1,2,6,7,4,5]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[8,7,6,5,1,3,2,4]=>[5,3,1,2,6,7,8,4]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[5,4,1,3,2,8,7,6]=>[4,3,1,5,2,7,8,6]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[7,5,4,1,3,2,6,8]=>[4,3,1,5,7,2,6,8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[4,2,1,3,8,5,7,6]=>[2,4,1,3,8,7,5,6]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[2,4,1,3,6,7,8,5]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[5,1,4,2,3,8,7,6]=>[5,4,2,1,3,7,8,6]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>[8,1,4,2,3,7,6,5]=>[8,4,2,1,6,7,3,5]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[8,7,6,5,1,4,2,3]=>[5,4,2,1,6,7,8,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[5,2,1,3,4,8,7,6]=>[2,5,1,3,4,7,8,6]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[5,4,2,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[7,1,5,4,2,3,6,8]=>[7,4,2,5,1,3,6,8]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,8,6,7]=>[2,3,4,1,5,8,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,7,5,6,8]=>[2,3,4,1,7,5,6,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,5,6]=>[2,3,4,1,7,5,8,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,5,7,6]=>[2,3,4,1,8,7,5,6]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,6,5,7]=>[2,3,4,1,6,8,5,7]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[5,1,4,3,2,8,7,6]=>[5,3,4,1,2,7,8,6]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[8,1,4,3,2,7,6,5]=>[8,3,4,1,6,7,2,5]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[8,7,6,5,1,4,3,2]=>[5,3,4,1,6,7,8,2]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[5,2,1,4,3,8,7,6]=>[2,5,4,1,3,7,8,6]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[5,3,2,1,4,8,7,6]=>[2,3,5,1,4,7,8,6]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[6,3,2,1,4,5,8,7]=>[2,3,6,1,4,5,8,7]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[8,2,1,7,3,4,5,6]=>[2,8,7,3,4,5,1,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,8,6,7]=>[2,3,4,5,1,8,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[6,1,5,4,3,2,8,7]=>[6,3,4,5,1,2,8,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[8,1,5,4,3,2,6,7]=>[8,3,4,5,1,2,6,7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[8,1,5,4,3,2,7,6]=>[8,3,4,5,1,7,2,6]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[8,6,1,5,4,3,2,7]=>[6,3,4,5,1,8,2,7]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[8,7,6,1,5,4,3,2]=>[6,3,4,5,1,7,8,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[8,1,7,2,6,3,5,4]=>[8,7,6,5,3,2,1,4]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[8,2,1,7,3,5,4,6]=>[2,8,7,5,3,4,1,6]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]
Map
to 312-avoiding permutation
Description
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
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.
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
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
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
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