Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]=>[1]
[1,0,1,0]=>[2,1]=>[2,1]=>[2,1]=>[2,1]
[1,1,0,0]=>[1,2]=>[1,2]=>[1,2]=>[1,2]
[1,0,1,0,1,0]=>[3,2,1]=>[3,2,1]=>[2,3,1]=>[3,2,1]
[1,0,1,1,0,0]=>[2,3,1]=>[3,2,1]=>[2,3,1]=>[3,2,1]
[1,1,0,0,1,0]=>[3,1,2]=>[3,2,1]=>[2,3,1]=>[3,2,1]
[1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>[2,1,3]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>[1,2,3]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]=>[2,3,4,1]=>[4,3,2,1]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[4,3,2,1]=>[2,3,4,1]=>[4,3,2,1]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[4,3,2,1]=>[2,3,4,1]=>[4,3,2,1]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[4,2,3,1]=>[3,4,2,1]=>[4,2,3,1]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[3,4,2,1]=>[4,2,3,1]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[4,3,2,1]=>[2,3,4,1]=>[4,3,2,1]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[4,3,2,1]=>[2,3,4,1]=>[4,3,2,1]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[4,3,2,1]=>[2,3,4,1]=>[4,3,2,1]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,1,4]=>[3,2,1,4]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]=>[3,2,1,4]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[4,2,3,1]=>[3,4,2,1]=>[4,2,3,1]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[3,2,1,4]=>[2,3,1,4]=>[3,2,1,4]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5,3,2,4,1]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5,3,2,4,1]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5,3,2,4,1]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5,2,3,4,1]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5,2,3,4,1]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,3,2,1,5]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,3,2,1,5]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,3,2,1,5]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[4,2,3,1,5]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[4,2,3,1,5]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,3,2,1,5]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,3,2,1,5]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5,3,2,4,1]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,3,2,1,5]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5,2,3,4,1]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[4,2,3,1,5]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6,3,2,4,5,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6,3,2,4,5,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6,3,2,4,5,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6,2,3,4,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6,2,3,4,5,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,3,2,4,1,6]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,3,2,4,1,6]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,3,2,4,1,6]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,2,3,4,1,6]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,2,3,4,1,6]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,2,3,1,5,6]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,2,3,1,5,6]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,5,3,4,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,4,3,2,5,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,4,3,2,1,6]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6,3,2,4,5,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,3,2,4,1,6]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6,2,3,4,5,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,2,3,4,1,6]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,2,3,1,5,6]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7,3,2,4,5,6,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7,3,2,4,5,6,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7,3,2,4,5,6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7,2,3,4,5,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7,2,3,4,5,6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,3,2,4,5,1,7]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,3,2,4,5,1,7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,3,2,4,5,1,7]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,2,3,4,5,1,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,2,3,4,5,1,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,3,2,4,1,6,7]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,3,2,4,1,6,7]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,3,2,4,1,6,7]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,2,3,4,1,6,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,2,3,4,1,6,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,6,4,3,5,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,5,4,3,2,6,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,2,3,1,5,6,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,2,3,1,5,6,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,6,3,4,5,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,5,3,4,2,6,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,5,3,4,2,1,7]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,4,3,2,5,6,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,4,3,2,5,1,7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7,3,2,4,5,6,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,3,2,4,5,1,7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,3,2,4,1,6,7]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7,2,3,4,5,6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,2,3,4,5,1,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,2,3,4,1,6,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,2,3,1,5,6,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[8,5,3,4,2,6,7,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[8,5,3,4,2,6,7,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,6,4,3,5,2,1,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,3,2,4,1,6,7,8]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,3,2,4,1,6,7,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[8,5,3,4,2,6,7,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,3,2,4,1,6,7,8]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,7,6,4,5,3,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,7,4,3,5,6,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8,5,4,3,2,6,7,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,3,2,4,1,6,7,8]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
This is the inverse of the map $\Phi$ in [1, sec.3].
searching the database
Sorry, this map was not found in the database.