Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[1]=>[1]
[1,0,1,0]=>[1,0,1,0]=>[2,1]=>[2,1]
[1,1,0,0]=>[1,1,0,0]=>[1,2]=>[1,2]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[2,3,1]=>[3,2,1]
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[2,1,3]=>[2,1,3]
[1,1,0,0,1,0]=>[1,1,0,0,1,0]=>[1,3,2]=>[1,3,2]
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[2,1,3]=>[2,1,3]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[4,2,3,1]
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[3,2,1,4]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[2,1,4,3]
[1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[3,2,1,4]
[1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]
[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[1,4,3,2]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[1,3,2,4]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[2,1,4,3]
[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[1,3,2,4]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[1,2,4,3]
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[1,3,2,4]
[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[5,2,3,4,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[3,2,1,5,4]
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[3,2,1,5,4]
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[1,5,3,4,2]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>[1,2,5,4,3]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]
[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]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]
[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]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]
[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]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]
[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]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]
[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]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]
[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]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]
[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]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]
[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]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]
[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]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]
[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]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]
[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]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[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]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]
[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]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]
[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]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[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]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]
[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]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]
[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]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]
[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]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[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]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]
[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]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[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]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]
[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]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]
[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]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[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]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[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]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]
[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]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]
[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]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]
[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]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]
[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]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]
[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]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]
[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]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]
[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]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]
[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]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]
[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]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[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]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]
[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]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]
[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]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]
[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]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[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]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[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]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]
[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]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]
[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]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]
[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]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]
[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]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[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]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[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]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]
[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]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]
[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]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[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]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[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]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[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]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[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]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[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]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[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]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]=>[2,1,6,4,5,3,7,8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]=>[2,1,6,4,5,3,7,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]=>[2,1,6,4,5,3,7,8]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,2,8,7]=>[1,6,3,4,5,2,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,2,8,7]=>[1,6,3,4,5,2,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,5,2,6,8,7]=>[1,5,3,4,2,6,8,7]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,5,2,6,8,7]=>[1,5,3,4,2,6,8,7]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,5,2,6,8,7]=>[1,5,3,4,2,6,8,7]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,5,6,7,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]=>[2,1,6,4,5,3,7,8]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]=>[2,1,6,4,5,3,7,8]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]=>[2,1,6,4,5,3,7,8]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,5,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>[2,1,4,3,7,6,5,8]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,7,3,8]=>[1,2,7,4,5,6,3,8]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,6,3,8,7]=>[1,2,6,4,5,3,8,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,7,3,8]=>[1,2,7,4,5,6,3,8]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,6,3,8,7]=>[1,2,6,4,5,3,8,7]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,5,6,7,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]=>[2,1,3,6,5,4,7,8]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]=>[6,2,3,4,5,1,8,7,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]=>[6,2,3,4,5,1,8,7,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]=>[6,2,3,4,5,1,8,7,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[8,2,3,4,5,6,7,1,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[8,2,3,4,5,6,7,1,9,10]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,7,6,8,9]=>[5,2,3,4,1,7,6,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[7,2,3,4,5,6,1,8,9,10]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[6,2,3,4,5,1,7,8,9,10]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[5,2,3,4,1,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]=>[6,2,3,4,5,1,8,7,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,7,6,8,9]=>[5,2,3,4,1,7,6,8,9]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,6,5,7,8,9]=>[4,2,3,1,6,5,7,8,9]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,9,4]=>[1,3,2,9,5,6,7,8,4]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[4,2,3,1,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,9,4]=>[1,3,2,9,5,6,7,8,4]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10,11]=>[1,3,2,4,5,6,7,8,9,10,11]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,9,4]=>[1,3,2,9,5,6,7,8,4]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10,11]=>[1,3,2,4,5,6,7,8,9,10,11]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10,11]=>[1,3,2,4,5,6,7,8,9,10,11]
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
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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 $\chi(\pi)$.
searching the database
Sorry, this map was not found in the database.