Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[2,1]=>[2,1]=>[2,1]
[1,0,1,0]=>[1,0,1,0]=>[3,1,2]=>[3,1,2]=>[3,1,2]
[1,1,0,0]=>[1,1,0,0]=>[2,3,1]=>[3,2,1]=>[2,3,1]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[3,1,4,2]=>[4,3,1,2]=>[3,1,4,2]
[1,1,0,0,1,0]=>[1,1,0,0,1,0]=>[2,4,1,3]=>[4,2,1,3]=>[2,4,1,3]
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[3,1,4,2]=>[4,3,1,2]=>[3,1,4,2]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[2,3,4,1]=>[4,3,2,1]=>[2,3,4,1]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[5,4,1,2,3]=>[4,1,2,5,3]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[5,3,1,2,4]=>[3,1,5,2,4]
[1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[5,4,1,2,3]=>[4,1,2,5,3]
[1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[5,4,3,1,2]=>[3,1,4,5,2]
[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[2,5,1,3,4]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[5,4,2,1,3]=>[2,4,1,5,3]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[5,3,1,2,4]=>[3,1,5,2,4]
[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[5,4,2,1,3]=>[2,4,1,5,3]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[5,4,3,1,2]=>[3,1,4,5,2]
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[5,3,2,1,4]=>[2,3,5,1,4]
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[5,4,2,1,3]=>[2,4,1,5,3]
[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[5,4,3,1,2]=>[3,1,4,5,2]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
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].
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 $\chi(\pi)$.
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