Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[1]=>[1]=>[1]
[1,0,1,0]=>[1,0,1,0]=>[2,1]=>[2,1]=>[2,1]
[1,1,0,0]=>[1,1,0,0]=>[1,2]=>[1,2]=>[1,2]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[2,3,1]=>[3,2,1]=>[2,3,1]
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]
[1,1,0,0,1,0]=>[1,1,0,0,1,0]=>[1,3,2]=>[1,3,2]=>[1,3,2]
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[4,2,3,1]=>[2,3,4,1]
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[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]=>[2,3,1,4]
[1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[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]=>[1,3,4,2]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[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]=>[1,3,2,4]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[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]=>[1,2,4,3]
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]
[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[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]=>[1,2,3,4]
[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]=>[2,3,4,5,1]
[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]=>[2,3,4,1,5]
[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]=>[2,3,1,5,4]
[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]=>[2,3,4,1,5]
[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]=>[2,3,1,4,5]
[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]=>[2,1,4,5,3]
[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]=>[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]=>[2,3,1,5,4]
[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]=>[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]=>[2,3,1,4,5]
[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]=>[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]=>[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]=>[2,3,1,4,5]
[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]=>[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]=>[1,3,4,5,2]
[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]=>[1,3,4,2,5]
[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]=>[1,3,2,5,4]
[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]=>[1,3,4,2,5]
[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]=>[1,3,2,4,5]
[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]=>[2,1,4,5,3]
[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]=>[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]=>[1,3,2,5,4]
[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]=>[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]=>[1,3,2,4,5]
[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]=>[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]=>[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]=>[1,3,2,4,5]
[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]=>[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]=>[1,2,4,5,3]
[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]=>[1,2,4,3,5]
[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]=>[1,3,2,5,4]
[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]=>[1,2,4,3,5]
[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]=>[1,3,2,4,5]
[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]=>[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]=>[1,2,4,3,5]
[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]=>[1,3,2,4,5]
[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]=>[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]=>[1,2,3,5,4]
[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]=>[1,2,4,3,5]
[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]=>[1,3,2,4,5]
[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]=>[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]=>[1,2,3,4,5]
[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]=>[2,3,4,5,6,1]
[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]=>[2,3,4,5,1,6]
[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]=>[2,3,4,1,6,5]
[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]=>[2,3,4,5,1,6]
[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]=>[2,3,4,1,5,6]
[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]=>[2,3,1,5,6,4]
[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]=>[2,3,1,5,4,6]
[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]=>[2,3,4,1,6,5]
[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]=>[2,3,1,5,4,6]
[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]=>[2,3,4,1,5,6]
[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]=>[2,3,1,4,6,5]
[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]=>[2,3,1,5,4,6]
[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]=>[2,3,4,1,5,6]
[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]=>[2,3,1,4,5,6]
[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]=>[2,1,4,5,6,3]
[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]=>[2,1,4,5,3,6]
[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]=>[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]=>[2,1,4,5,3,6]
[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]=>[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]=>[2,3,1,5,6,4]
[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]=>[2,3,1,5,4,6]
[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]=>[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]=>[2,3,1,5,4,6]
[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]=>[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]=>[2,3,1,4,6,5]
[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]=>[2,3,1,5,4,6]
[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]=>[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]=>[2,3,1,4,5,6]
[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]=>[2,1,3,5,6,4]
[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]=>[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]=>[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]=>[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]=>[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]=>[2,3,1,4,6,5]
[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]=>[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]=>[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]=>[2,3,1,4,5,6]
[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]=>[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]=>[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]=>[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]=>[2,3,1,4,5,6]
[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]=>[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]=>[1,3,4,5,6,2]
[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]=>[1,3,4,5,2,6]
[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]=>[1,3,4,2,6,5]
[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]=>[1,3,4,5,2,6]
[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]=>[1,3,4,2,5,6]
[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]=>[1,3,2,5,6,4]
[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]=>[1,3,2,5,4,6]
[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]=>[1,3,4,2,6,5]
[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]=>[1,3,2,5,4,6]
[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]=>[1,3,4,2,5,6]
[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]=>[1,3,2,4,6,5]
[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]=>[1,3,2,5,4,6]
[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]=>[1,3,4,2,5,6]
[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]=>[1,3,2,4,5,6]
[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]=>[2,1,4,5,6,3]
[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]=>[2,1,4,5,3,6]
[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]=>[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]=>[2,1,4,5,3,6]
[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]=>[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]=>[1,3,2,5,6,4]
[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]=>[1,3,2,5,4,6]
[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]=>[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]=>[1,3,2,5,4,6]
[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]=>[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]=>[1,3,2,4,6,5]
[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]=>[1,3,2,5,4,6]
[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]=>[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]=>[1,3,2,4,5,6]
[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]=>[2,1,3,5,6,4]
[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]=>[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]=>[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]=>[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]=>[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]=>[1,3,2,4,6,5]
[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]=>[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]=>[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]=>[1,3,2,4,5,6]
[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]=>[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]=>[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]=>[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]=>[1,3,2,4,5,6]
[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]=>[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]=>[1,2,4,5,6,3]
[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]=>[1,2,4,5,3,6]
[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]=>[1,2,4,3,6,5]
[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]=>[1,2,4,5,3,6]
[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,5,6,4]
[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]=>[1,3,2,5,4,6]
[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]=>[1,2,4,3,6,5]
[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]=>[1,3,2,5,4,6]
[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,6,5]
[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]=>[1,3,2,5,4,6]
[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,5,6]
[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]=>[2,1,3,5,6,4]
[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]=>[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]=>[1,2,4,3,6,5]
[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]=>[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,6,5]
[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]=>[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,5,6]
[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]=>[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]=>[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,5,6]
[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]=>[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]=>[1,2,3,5,6,4]
[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]=>[1,2,3,5,4,6]
[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]=>[1,2,4,3,6,5]
[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]=>[1,2,3,5,4,6]
[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,6,5]
[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]=>[1,2,3,5,4,6]
[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,5,6]
[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]=>[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]=>[1,2,3,5,4,6]
[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,5,6]
[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]=>[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]=>[1,2,3,4,6,5]
[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]=>[1,2,3,5,4,6]
[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]=>[1,2,4,3,5,6]
[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]=>[1,3,2,4,5,6]
[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]=>[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]=>[1,2,3,4,5,6]
[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]=>[2,3,4,5,6,7,1]
[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]=>[2,3,4,5,6,1,7]
[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]=>[2,3,4,5,1,7,6]
[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]=>[2,3,4,5,6,1,7]
[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]=>[2,3,4,5,1,6,7]
[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]=>[2,3,4,1,6,7,5]
[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]=>[2,3,4,1,6,5,7]
[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]=>[2,3,4,5,1,7,6]
[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]=>[2,3,4,1,6,5,7]
[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]=>[2,3,4,5,1,6,7]
[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]=>[2,3,4,1,5,7,6]
[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]=>[2,3,4,1,6,5,7]
[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]=>[2,3,4,5,1,6,7]
[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]=>[2,3,4,1,5,6,7]
[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]=>[2,3,1,5,6,7,4]
[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]=>[2,3,1,5,6,4,7]
[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]=>[2,3,1,5,4,7,6]
[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]=>[2,3,1,5,6,4,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[2,3,4,1,6,7,5]
[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]=>[2,3,4,1,6,5,7]
[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]=>[2,3,1,5,4,7,6]
[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]=>[2,3,4,1,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[2,3,4,1,5,7,6]
[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]=>[2,3,4,1,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[2,3,4,1,5,6,7]
[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]=>[2,3,1,4,6,7,5]
[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,7,6]
[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[2,3,4,1,5,7,6]
[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[2,3,4,1,5,6,7]
[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]=>[2,3,1,4,5,7,6]
[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[2,3,4,1,5,6,7]
[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]=>[2,3,1,4,5,6,7]
[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]=>[2,1,4,5,6,7,3]
[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]=>[2,1,4,5,6,3,7]
[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]=>[2,1,4,5,3,7,6]
[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]=>[2,1,4,5,6,3,7]
[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]=>[2,1,4,5,3,6,7]
[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]=>[2,1,4,3,6,7,5]
[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]=>[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]=>[2,1,4,5,3,7,6]
[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]=>[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]=>[2,1,4,5,3,6,7]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,7]
[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]=>[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]=>[2,3,1,5,6,7,4]
[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]=>[2,3,1,5,6,4,7]
[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]=>[2,3,1,5,4,7,6]
[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]=>[2,3,1,5,6,4,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[2,1,4,3,6,7,5]
[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]=>[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]=>[2,3,1,5,4,7,6]
[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]=>[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]=>[2,3,1,5,4,6,7]
[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]=>[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]=>[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]=>[2,3,1,5,4,6,7]
[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]=>[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]=>[2,3,1,4,6,7,5]
[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,7,6]
[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[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]=>[2,3,1,4,5,7,6]
[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]=>[2,3,1,4,6,5,7]
[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]=>[2,3,1,5,4,6,7]
[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]=>[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]=>[2,3,1,4,5,6,7]
[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]=>[2,1,3,5,6,7,4]
[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]=>[2,1,3,5,6,4,7]
[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]=>[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]=>[2,1,3,5,6,4,7]
[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]=>[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]=>[2,1,4,3,6,7,5]
[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,3,1,4,6,7,5]
[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]=>[2,3,1,4,6,5,7]
[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]=>[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]=>[2,3,1,4,6,5,7]
[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]=>[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]=>[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]=>[2,3,1,4,6,5,7]
[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]=>[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]=>[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]=>[2,3,1,4,5,7,6]
[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]=>[2,3,1,4,6,5,7]
[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]=>[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]=>[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]=>[2,3,1,4,5,6,7]
[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]=>[2,1,3,4,6,7,5]
[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,3,1,4,5,7,6]
[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]=>[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]=>[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]=>[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]=>[2,3,1,4,5,6,7]
[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]=>[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]=>[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]=>[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]=>[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]=>[2,3,1,4,5,6,7]
[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]=>[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]=>[1,3,4,5,6,7,2]
[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]=>[1,3,4,5,6,2,7]
[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]=>[1,3,4,5,2,7,6]
[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]=>[1,3,4,5,6,2,7]
[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]=>[1,3,4,5,2,6,7]
[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]=>[1,3,4,2,6,7,5]
[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]=>[1,3,4,2,6,5,7]
[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]=>[1,3,4,5,2,7,6]
[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]=>[1,3,4,2,6,5,7]
[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]=>[1,3,4,5,2,6,7]
[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]=>[1,3,4,2,5,7,6]
[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]=>[1,3,4,2,6,5,7]
[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]=>[1,3,4,5,2,6,7]
[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]=>[1,3,4,2,5,6,7]
[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]=>[1,3,2,5,6,7,4]
[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]=>[1,3,2,5,6,4,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,5,6,4,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,6,7,5]
[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]=>[1,3,4,2,6,5,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,3,4,2,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,7,6]
[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]=>[1,3,4,2,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,6,7]
[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]=>[1,3,2,4,6,7,5]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,6,7]
[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]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,3,4,2,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[2,1,4,5,6,7,3]
[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]=>[2,1,4,5,6,3,7]
[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]=>[2,1,4,5,3,7,6]
[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]=>[2,1,4,5,6,3,7]
[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]=>[2,1,4,5,3,6,7]
[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]=>[2,1,4,3,6,7,5]
[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]=>[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]=>[2,1,4,5,3,7,6]
[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]=>[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]=>[2,1,4,5,3,6,7]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,7]
[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]=>[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]=>[1,3,2,5,6,7,4]
[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]=>[1,3,2,5,6,4,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,5,6,4,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[2,1,4,3,6,7,5]
[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]=>[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]=>[1,3,2,5,4,7,6]
[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]=>[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]=>[1,3,2,5,4,6,7]
[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]=>[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]=>[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]=>[1,3,2,5,4,6,7]
[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]=>[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]=>[1,3,2,4,6,7,5]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[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]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[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]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,5,6,7,4]
[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]=>[2,1,3,5,6,4,7]
[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]=>[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]=>[2,1,3,5,6,4,7]
[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]=>[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]=>[2,1,4,3,6,7,5]
[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,3,2,4,6,7,5]
[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[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]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[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]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,4,6,7,5]
[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,3,2,4,5,7,6]
[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]=>[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]=>[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]=>[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[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]=>[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]=>[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[1,2,4,5,6,7,3]
[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]=>[1,2,4,5,6,3,7]
[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]=>[1,2,4,5,3,7,6]
[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]=>[1,2,4,5,6,3,7]
[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]=>[1,2,4,5,3,6,7]
[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]=>[1,2,4,3,6,7,5]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,2,4,5,3,7,6]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,2,4,5,3,6,7]
[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]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,2,4,5,3,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,5,6,7,4]
[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]=>[1,3,2,5,6,4,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,5,6,4,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,6,7,5]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,3,2,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,5,6,7,4]
[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]=>[2,1,3,5,6,4,7]
[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]=>[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]=>[2,1,3,5,6,4,7]
[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]=>[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]=>[1,2,4,3,6,7,5]
[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]=>[1,2,4,3,6,5,7]
[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]=>[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]=>[1,2,4,3,6,5,7]
[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]=>[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]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]
[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]=>[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]
[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[1,2,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,4,6,7,5]
[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]=>[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]=>[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]=>[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]=>[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]=>[1,2,4,3,5,7,6]
[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]=>[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]=>[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,7,6]
[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]=>[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]=>[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[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]=>[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[1,2,3,5,6,7,4]
[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]=>[1,2,3,5,6,4,7]
[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]=>[1,2,3,5,4,7,6]
[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]=>[1,2,3,5,6,4,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,6,7,5]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,2,3,5,4,7,6]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,7,6]
[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]=>[1,2,4,3,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,6,7,5]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,2,3,5,4,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,7,6]
[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]=>[1,3,2,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[2,1,3,4,6,7,5]
[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]=>[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]=>[1,2,3,5,4,7,6]
[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]=>[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,7,6]
[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]=>[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,7,6]
[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]=>[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[1,2,3,4,6,7,5]
[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]=>[1,2,3,4,6,5,7]
[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]=>[1,2,3,5,4,7,6]
[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]=>[1,2,3,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,7,6]
[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]=>[1,2,3,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,7,6]
[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]=>[1,2,3,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[1,2,3,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[1,2,3,4,5,7,6]
[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]=>[1,2,3,4,6,5,7]
[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]=>[1,2,3,5,4,6,7]
[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]=>[1,2,4,3,5,6,7]
[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]=>[1,3,2,4,5,6,7]
[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]=>[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]=>[1,2,3,4,5,6,7]
[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]=>[2,3,4,5,6,7,8,1]
[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]=>[2,3,4,5,6,7,1,8]
[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]=>[2,3,4,5,6,1,8,7]
[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]=>[2,3,4,5,6,7,1,8]
[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]=>[2,3,4,5,6,1,7,8]
[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]=>[2,3,4,5,1,7,8,6]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]
[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]=>[2,3,4,5,6,1,7,8]
[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]=>[2,3,4,5,1,6,8,7]
[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]=>[2,3,4,5,6,1,7,8]
[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]=>[2,3,4,5,1,6,7,8]
[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]=>[2,3,4,1,6,7,8,5]
[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]=>[2,3,4,1,6,7,5,8]
[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]=>[2,3,4,1,6,5,8,7]
[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]=>[2,3,4,1,6,7,5,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,4,5,1,7,8,6]
[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]=>[2,3,4,1,6,5,8,7]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,4,5,1,6,8,7]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,4,5,1,6,7,8]
[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]=>[2,3,4,1,5,7,8,6]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,8,7]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,4,5,1,6,8,7]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,4,5,1,6,7,8]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,4,5,1,6,7,8]
[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]=>[2,3,4,1,5,6,7,8]
[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]=>[2,3,1,5,6,7,8,4]
[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]=>[2,3,1,5,6,7,4,8]
[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]=>[2,3,1,5,6,4,8,7]
[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]=>[2,3,1,5,6,7,4,8]
[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]=>[2,3,1,5,6,4,7,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,6,4,8,7]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,6,4,7,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,6,4,7,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,6,7,8,5]
[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]=>[2,3,4,1,6,7,5,8]
[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]=>[2,3,4,1,6,5,8,7]
[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]=>[2,3,4,1,6,7,5,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,4,1,6,5,8,7]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,7,8,6]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,8,7]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,6,5,7,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,6,7,8]
[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]=>[2,3,1,4,6,7,8,5]
[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]=>[2,3,1,4,6,7,5,8]
[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]=>[2,3,1,4,6,7,5,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,7,8,6]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,6,7,8]
[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]=>[2,3,1,4,5,7,8,6]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,6,7,8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,3,4,1,5,6,7,8]
[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]=>[2,3,1,4,5,6,7,8]
[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]=>[2,1,4,5,6,7,8,3]
[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]=>[2,1,4,5,6,3,8,7]
[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]=>[2,1,4,5,3,7,8,6]
[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]=>[2,1,4,5,6,3,8,7]
[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]=>[2,1,4,5,3,6,8,7]
[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]=>[2,1,4,5,3,6,7,8]
[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]=>[2,1,4,3,6,7,8,5]
[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]=>[2,1,4,3,6,5,8,7]
[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]=>[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]=>[2,1,4,5,3,7,8,6]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,8,7]
[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]=>[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]=>[2,1,4,5,3,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,8,7]
[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]=>[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]=>[2,1,4,5,3,6,7,8]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,7,8]
[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]=>[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]=>[2,3,1,5,6,7,8,4]
[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]=>[2,3,1,5,6,7,4,8]
[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]=>[2,3,1,5,6,4,8,7]
[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]=>[2,3,1,5,6,7,4,8]
[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]=>[2,3,1,5,6,4,7,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,6,4,8,7]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,6,4,7,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,6,4,7,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,1,4,3,6,7,8,5]
[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]=>[2,1,4,3,6,5,8,7]
[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]=>[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]=>[2,3,1,5,4,7,6,8]
[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]=>[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]=>[2,3,1,5,4,7,6,8]
[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]=>[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]=>[2,3,1,5,4,7,6,8]
[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]=>[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,3,1,5,4,6,7,8]
[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]=>[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]=>[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]=>[2,3,1,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,6,7,8,5]
[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]=>[2,3,1,4,6,7,5,8]
[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]=>[2,3,1,4,6,7,5,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,4,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[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]=>[2,3,1,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,7,8,6]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,3,1,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,6,7,8]
[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]=>[2,1,3,5,6,7,8,4]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]
[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]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,6,7,8,5]
[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]=>[2,1,4,3,6,5,8,7]
[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]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,6,7,8,5]
[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]=>[2,3,1,4,6,7,5,8]
[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]=>[2,3,1,4,6,7,5,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,7,8,6]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,6,7,8]
[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]=>[2,1,3,4,6,7,8,5]
[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,7,8,6]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[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]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,6,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,6,7,8]
[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]=>[2,1,3,4,5,6,8,7]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,3,1,4,5,6,7,8]
[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]=>[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]=>[1,3,4,5,6,7,8,2]
[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]=>[1,3,4,5,6,7,2,8]
[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]=>[1,3,4,5,6,7,2,8]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[1,3,4,5,6,2,7,8]
[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]=>[1,3,4,5,2,7,8,6]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[1,3,4,5,6,2,7,8]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[1,3,4,5,6,2,7,8]
[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]=>[1,3,4,5,2,6,7,8]
[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]=>[1,3,4,2,6,7,8,5]
[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]=>[1,3,4,2,6,7,5,8]
[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]=>[1,3,4,2,6,7,5,8]
[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]=>[1,3,4,5,2,7,8,6]
[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]=>[1,3,4,5,2,6,7,8]
[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]=>[1,3,4,2,5,7,8,6]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,4,5,2,6,7,8]
[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]=>[1,3,4,2,5,6,8,7]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,4,5,2,6,7,8]
[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]=>[1,3,4,2,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,6,7,8,5]
[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]=>[1,3,4,2,6,7,5,8]
[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]=>[1,3,4,2,6,7,5,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,7,8,6]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,6,8,7]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,6,7,8]
[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]=>[1,3,2,4,6,7,8,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,7,8,6]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,6,8,7]
[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]=>[1,3,4,2,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,6,7,8]
[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,6,7,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,3,4,2,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,4,5,6,7,8,3]
[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]=>[2,1,4,5,6,3,8,7]
[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]=>[2,1,4,5,3,7,8,6]
[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]=>[2,1,4,5,6,3,8,7]
[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]=>[2,1,4,5,3,6,8,7]
[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]=>[2,1,4,5,3,6,7,8]
[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]=>[2,1,4,3,6,7,8,5]
[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]=>[2,1,4,3,6,5,8,7]
[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]=>[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]=>[2,1,4,5,3,7,8,6]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,8,7]
[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]=>[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]=>[2,1,4,5,3,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,8,7]
[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]=>[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]=>[2,1,4,5,3,6,7,8]
[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]=>[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]=>[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]=>[2,1,4,5,3,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[2,1,4,3,6,7,8,5]
[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]=>[2,1,4,3,6,5,8,7]
[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]=>[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[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]=>[1,3,2,5,4,7,6,8]
[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]=>[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]=>[1,3,2,5,4,7,6,8]
[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]=>[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]=>[1,3,2,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[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]=>[1,3,2,5,4,6,7,8]
[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]=>[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]=>[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]=>[1,3,2,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,6,7,8,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,5,6,7,8,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]
[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]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,6,7,8,5]
[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]=>[2,1,4,3,6,5,8,7]
[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]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,1,4,3,6,5,7,8]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,6,7,8,5]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[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]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[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]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,4,6,7,8,5]
[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,8,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[2,1,3,5,4,6,8,7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,8,7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[2,1,4,3,5,6,7,8]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,4,5,6,8,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[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]=>[1,3,2,4,5,6,7,8]
[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]=>[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]=>[1,2,4,5,6,7,8,3]
[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]=>[1,2,4,5,6,3,7,8]
[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]=>[1,2,4,5,3,7,8,6]
[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]=>[1,2,4,5,6,3,7,8]
[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]=>[1,2,4,5,3,6,8,7]
[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]=>[1,2,4,5,6,3,7,8]
[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]=>[1,2,4,5,3,6,7,8]
[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]=>[1,2,4,3,6,7,8,5]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,4,5,3,7,8,6]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,4,5,3,6,8,7]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,4,5,3,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,4,5,3,6,8,7]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,4,5,3,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,4,5,3,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,5,6,4,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,6,7,8,5]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,6,7,8,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,7,8,6]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,3,2,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,5,6,7,8,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]
[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]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,6,7,8,5]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[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]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,6,7,8,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,4,6,7,8,5]
[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[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]=>[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]=>[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]=>[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[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]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,4,5,6,8,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[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]=>[1,2,3,5,6,7,8,4]
[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]=>[1,2,3,5,6,7,4,8]
[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]=>[1,2,3,5,6,4,8,7]
[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]=>[1,2,3,5,6,7,4,8]
[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]=>[1,2,3,5,6,4,7,8]
[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]=>[1,2,3,5,4,7,8,6]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,3,5,6,4,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,3,5,6,4,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,3,5,6,4,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,6,7,8,5]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,3,5,4,7,8,6]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,4,3,6,5,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,8,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,4,3,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,6,7,8,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,7,8,6]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,3,2,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,4,6,7,8,5]
[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]=>[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]=>[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]=>[1,2,3,5,4,7,8,6]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[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]=>[1,2,3,5,4,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,4,5,6,8,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[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]=>[1,2,3,4,6,7,8,5]
[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]=>[1,2,3,4,6,7,5,8]
[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]=>[1,2,3,4,6,5,8,7]
[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]=>[1,2,3,4,6,7,5,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,7,8,6]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,3,4,6,5,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,2,3,5,4,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,7,8,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,7,8,6]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,3,2,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[2,1,3,4,5,6,8,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[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]=>[1,2,3,4,5,7,8,6]
[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]=>[1,2,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,8,7]
[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]=>[1,2,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,8,7]
[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]=>[1,2,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,8,7]
[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]=>[1,2,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[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]=>[1,2,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[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]=>[1,2,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[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]=>[1,2,3,4,5,6,8,7]
[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]=>[1,2,3,4,5,7,6,8]
[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]=>[1,2,3,4,6,5,7,8]
[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]=>[1,2,3,5,4,6,7,8]
[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]=>[1,2,4,3,5,6,7,8]
[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]=>[1,3,2,4,5,6,7,8]
[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]=>[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]=>[1,2,3,4,5,6,7,8]
[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]=>[1,2,3,4,5,6,7,9,8]
[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]=>[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]=>[1,2,3,4,5,6,7,8,10,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[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]=>[2,3,1,4,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[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]=>[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]=>[2,3,1,4,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[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]=>[2,3,1,4,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[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]=>[2,3,1,4,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[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]=>[2,3,1,4,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[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]=>[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[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]=>[1,2,3,4,5,6,8,9,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[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]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[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]=>[2,3,4,1,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9,10]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,8,9,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
[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]=>[2,3,1,5,4,6,7,8,9]
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[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]=>[2,3,4,1,5,6,7,8,9]
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[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]=>[2,3,1,4,5,6,7,8,9,10]
[]=>[]=>[]=>[]=>[]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[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]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[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]=>[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[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]=>[1,3,2,4,5,6,7,8,9]
[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]=>[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]=>[1,2,3,4,5,6,7,8,9]
[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]=>[2,3,4,5,6,7,8,9,1]
[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]=>[2,3,4,5,6,7,8,1,9]
[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]=>[2,3,4,5,6,7,8,1,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[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]=>[2,3,4,5,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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]=>[2,3,4,5,6,7,8,9,1,10]
[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]=>[2,3,4,5,6,7,1,8,9]
[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]=>[2,3,4,5,6,7,8,9,1,10]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[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]=>[2,3,4,5,6,7,8,9,10,11,1]
[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]=>[2,3,4,5,6,7,1,8,9]
[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]=>[2,3,4,5,6,1,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[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]=>[2,3,4,5,1,6,7,8,9]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[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]=>[2,3,4,5,1,6,7,8,9]
[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]=>[2,3,4,1,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
[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]=>[2,3,4,5,6,7,1,9,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[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]=>[2,3,1,5,4,6,7,8,9]
[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]=>[2,1,4,5,6,7,8,9,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[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]=>[1,3,4,5,6,7,8,9,2]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,8,9,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[1,2,4,5,6,7,8,9,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[1,2,3,5,6,7,8,9,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[1,2,3,4,6,7,8,9,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[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]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,9,10,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,10,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[1,2,3,4,6,7,8,9,10,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[1,2,3,4,5,7,8,9,10,6]
[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[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]=>[1,2,3,4,5,6,7,8,9,10]
[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]=>[2,1,4,5,6,7,8,9,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,9,10,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[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]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[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]=>[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]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]
[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]=>[1,2,3,4,5,6,7,9,8,10]
[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[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]=>[1,2,3,5,4,6,7,8,9,10]
[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[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]=>[1,2,3,4,5,6,7,8,9,10,11]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[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]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,3,4,1,5,6,7,8,9]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[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]=>[2,3,4,5,1,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]
[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]=>[2,3,4,5,6,7,1,8,9]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[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]=>[2,3,4,5,6,7,1,9,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,8,9,7]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,2,3,4,5,6,7,8,10,11,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,8,9,7]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,8,9,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[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]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[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]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,9,10,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[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]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[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]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,1,4,3,5,6,7,8,9]
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[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]=>[2,3,1,5,4,6,7,8,9]
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
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