Identifier
Mp00137:
Dyck paths
—to symmetric ASM⟶
Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0017;cc-rep-1
[1,0]=>[[1]]=>[1]=>[1]
[1,0,1,0]=>[[1,0],[0,1]]=>[1,2]=>[1,2]
[1,1,0,0]=>[[0,1],[1,0]]=>[2,1]=>[2,1]
[1,0,1,0,1,0]=>[[1,0,0],[0,1,0],[0,0,1]]=>[1,2,3]=>[1,2,3]
[1,0,1,1,0,0]=>[[1,0,0],[0,0,1],[0,1,0]]=>[1,3,2]=>[1,3,2]
[1,1,0,0,1,0]=>[[0,1,0],[1,0,0],[0,0,1]]=>[2,1,3]=>[2,1,3]
[1,1,0,1,0,0]=>[[0,1,0],[1,-1,1],[0,1,0]]=>[1,3,2]=>[1,3,2]
[1,1,1,0,0,0]=>[[0,0,1],[0,1,0],[1,0,0]]=>[3,2,1]=>[2,3,1]
[1,0,1,0,1,0,1,0]=>[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]=>[1,2,3,4]=>[1,2,3,4]
[1,0,1,0,1,1,0,0]=>[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]=>[1,2,4,3]=>[1,2,4,3]
[1,0,1,1,0,0,1,0]=>[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]=>[1,3,2,4]=>[1,3,2,4]
[1,0,1,1,0,1,0,0]=>[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]=>[1,2,4,3]=>[1,2,4,3]
[1,0,1,1,1,0,0,0]=>[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]=>[1,4,3,2]=>[1,3,4,2]
[1,1,0,0,1,0,1,0]=>[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]=>[2,1,3,4]=>[2,1,3,4]
[1,1,0,0,1,1,0,0]=>[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]=>[2,1,4,3]=>[2,1,4,3]
[1,1,0,1,0,0,1,0]=>[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]=>[1,3,2,4]=>[1,3,2,4]
[1,1,0,1,0,1,0,0]=>[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]=>[1,2,4,3]=>[1,2,4,3]
[1,1,0,1,1,0,0,0]=>[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]=>[1,4,3,2]=>[1,3,4,2]
[1,1,1,0,0,0,1,0]=>[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]=>[3,2,1,4]=>[2,3,1,4]
[1,1,1,0,0,1,0,0]=>[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]=>[2,1,4,3]=>[2,1,4,3]
[1,1,1,0,1,0,0,0]=>[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]=>[1,4,3,2]=>[1,3,4,2]
[1,1,1,1,0,0,0,0]=>[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]=>[4,3,2,1]=>[2,3,4,1]
[1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]=>[1,2,3,4,5]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,0,1,0,1,1,0,0,1,0]=>[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[1,2,4,5,3]
[1,0,1,1,0,0,1,0,1,0]=>[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,0,1,1,0,0,1,1,0,0]=>[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,0,1,1,0,1,0,0,1,0]=>[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,0,1,1,0,1,0,1,0,0]=>[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[1,2,4,5,3]
[1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[1,4,3,2,5]=>[1,3,4,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[1,2,4,5,3]
[1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[1,3,4,5,2]
[1,1,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]=>[2,1,3,4,5]=>[2,1,3,4,5]
[1,1,0,0,1,0,1,1,0,0]=>[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,1,0,0,1,1,0,0,1,0]=>[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,1,0,0,1,1,0,1,0,0]=>[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[2,1,5,4,3]=>[2,1,4,5,3]
[1,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,1,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,1,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[1,2,4,5,3]
[1,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[1,4,3,2,5]=>[1,3,4,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[1,2,4,5,3]
[1,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[1,3,4,5,2]
[1,1,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]=>[3,2,1,4,5]=>[2,3,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]=>[3,2,1,5,4]=>[2,3,1,5,4]
[1,1,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[2,1,4,3,5]=>[2,1,4,3,5]
[1,1,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]=>[2,1,3,5,4]=>[2,1,3,5,4]
[1,1,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[2,1,5,4,3]=>[2,1,4,5,3]
[1,1,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[1,4,3,2,5]=>[1,3,4,2,5]
[1,1,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,1,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[1,2,4,5,3]
[1,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[1,3,4,5,2]
[1,1,1,1,0,0,0,0,1,0]=>[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]=>[4,3,2,1,5]=>[2,3,4,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]=>[3,2,1,5,4]=>[2,3,1,5,4]
[1,1,1,1,0,0,1,0,0,0]=>[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]=>[2,1,5,4,3]=>[2,1,4,5,3]
[1,1,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[1,3,4,5,2]
[1,1,1,1,1,0,0,0,0,0]=>[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]=>[5,4,3,2,1]=>[2,3,4,5,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0]]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,0,0,-1,1,0],[0,0,0,1,0,0]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,0,1],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,0,1],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[1,0,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[1,0,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[1,0,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,4,3,6,8,7]=>[1,2,4,5,3,6,8,7]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7,8]=>[1,3,4,5,6,2,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,-1,1],[0,1,-1,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[2,1,7,6,5,4,3,8]=>[2,1,4,5,6,7,3,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,7,6,5,4,8]=>[1,2,3,5,6,7,4,8]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7,8]=>[1,3,4,5,2,6,7,8]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,4,3,6,8,7]=>[1,2,4,5,3,6,8,7]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,1,-1,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,0,1],[0,1,0,0,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,1,0,0,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,0,1],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,5,4,3,8,7,6]=>[2,1,4,5,3,7,8,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,0,1,0,0],[1,0,-1,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,0,0,1,0],[1,0,-1,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,4,3,6,8,7]=>[1,2,4,5,3,6,8,7]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,-1,0,1],[0,0,1,0,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,0,1],[0,1,-1,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,-1,0,1],[0,0,1,0,-1,0,1,0],[0,1,0,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,-1,0,1],[1,-1,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,0,1],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,-1,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,-1,1,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,-1,1,0],[1,0,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,0,1,0],[0,1,0,-1,0,1,-1,1],[1,0,-1,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,-1,0,1],[0,1,0,0,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,-1,1,0],[1,-1,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,-1,0,1],[1,-1,1,0,-1,0,1,0],[0,1,0,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,1,-1,1,-1,0,1,0],[1,-1,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,-1,1],[1,-1,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,-1,1,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,7,6,5,4,8]=>[2,3,1,5,6,7,4,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,6,5,4,8,7]=>[2,3,1,5,6,4,8,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[2,1,7,6,5,4,3,8]=>[2,1,4,5,6,7,3,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,5,4,3,8,7,6]=>[2,1,4,5,3,7,8,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,-1,1],[1,0,-1,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[1,0,0,0,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,1,0,0,0,-1,1,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,2,9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,9,8,7,6,5,4,3,2,10]=>[1,3,4,5,6,7,8,9,2,10]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,8,7,6,5,4,3,9]=>[2,1,4,5,6,7,8,3,9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,2,9]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,4]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[1,2,10,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,10,3]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,2,3,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,4]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0,0,0],[0,1,0,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[1,3,2,10,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,10,4]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[1,2,3,10,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,10,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,-1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,8,7,9]=>[2,3,4,5,6,1,8,7,9]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,2,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,1,9,8]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,5]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[2,1,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,2,9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,10,5]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0]]=>[8,7,6,5,4,3,2,1,10,9]=>[2,3,4,5,6,7,8,1,10,9]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,-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,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,4]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-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]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-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,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-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,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,0,1],[0,0,1,-1,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,5]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,0,0,0,0,0,1],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,0,-1,0,1],[0,0,0,1,0,-1,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,5,4,9,8,7,6]=>[1,2,3,5,4,7,8,9,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,0,1],[0,0,1,-1,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,0,0,0,1,0],[0,1,-1,0,0,0,1,0,0],[1,-1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,-1,1],[0,0,1,0,0,0,-1,1,0],[0,1,0,0,0,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,5,4,3,2,9,8,7,6]=>[1,3,4,5,2,7,8,9,6]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,0,0,0,0,1],[0,1,-1,0,0,0,0,1,0],[1,-1,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,0,1],[1,-1,1,-1,1,-1,0,1,0],[0,1,-1,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,2,3,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,4]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,-1,0,1],[0,1,-1,0,1,-1,0,1,0],[1,-1,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,0,0,1,0],[0,0,1,-1,0,0,1,0,0],[0,1,-1,0,0,1,0,0,0],[1,-1,0,0,1,0,0,-1,1],[0,0,0,1,0,0,-1,1,0],[0,0,1,0,0,-1,1,0,0],[0,1,0,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,4,3,2,9,8,7,6,5]=>[1,3,4,2,6,7,8,9,5]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,0,0,0,1],[0,0,1,-1,0,0,0,1,0],[0,1,-1,0,0,0,1,0,0],[1,-1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,-1,0,1],[0,1,-1,1,0,-1,0,1,0],[1,-1,1,0,-1,0,1,0,0],[0,1,0,-1,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,4]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,-1,0,1],[0,0,1,-1,1,-1,0,1,0],[0,1,-1,1,-1,0,1,0,0],[1,-1,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,-1,1],[0,1,-1,0,1,0,-1,1,0],[1,-1,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,4]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,0,1],[0,0,0,1,-1,0,0,1,0],[0,0,1,-1,0,0,1,0,0],[0,1,-1,0,0,1,0,0,0],[1,-1,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,-1,1],[0,1,0,-1,1,0,-1,1,0],[1,0,-1,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[2,1,4,3,9,8,7,6,5]=>[2,1,4,3,6,7,8,9,5]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,1,9,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[1,0,0,0,0,0,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[6,5,4,3,2,1,9,8,7]=>[2,3,4,5,6,1,8,9,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,-1,1],[0,1,0,0,0,0,-1,1,0],[1,0,0,0,0,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[5,4,3,2,1,9,8,7,6]=>[2,3,4,5,1,7,8,9,6]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,-1,1],[0,0,1,0,0,0,-1,1,0],[0,1,0,0,0,-1,1,0,0],[1,0,0,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[4,3,2,1,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,5]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,1,0,0,-1,1,0],[0,0,1,0,0,-1,1,0,0],[0,1,0,0,-1,1,0,0,0],[1,0,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[3,2,1,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,4]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[2,1,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,3]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0]]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1],[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,-1,1],[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]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,0,1,-1,1],[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]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,-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,-1,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,-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,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[1,-1,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[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]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,8,7,6,5,4,3,9]=>[2,1,4,5,6,7,8,3,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[3,2,1,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[4,3,2,1,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[5,4,3,2,1,9,8,7,6]=>[2,3,4,5,1,7,8,9,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[6,5,4,3,2,1,9,8,7]=>[2,3,4,5,6,1,8,9,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[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]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[3,2,1,10,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,10,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[4,3,2,1,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[5,4,3,2,1,10,9,8,7,6]=>[2,3,4,5,1,7,8,9,10,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[6,5,4,3,2,1,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[7,6,5,4,3,2,1,10,9,8]=>[2,3,4,5,6,7,1,9,10,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0]]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,1,-1,0,1],[0,1,-1,1,-1,1,-1,0,1,0],[0,0,1,-1,1,-1,0,1,0,0],[0,0,0,1,-1,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,10,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[1,-1,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,0,1],[0,0,0,1,-1,1,-1,0,1,0],[0,0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,7,8,9,10,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,-1,0,1,0],[0,0,0,0,1,-1,0,1,0,0],[0,0,0,1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0,0,0,0],[0,1,-1,0,1,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0,0,0],[0,1,0,-1,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,3]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,0,1,0,0,0],[0,0,0,1,-1,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,0,1],[0,0,0,1,-1,1,-1,0,1,0],[0,0,1,-1,1,-1,0,1,0,0],[0,1,-1,1,-1,0,1,0,0,0],[1,-1,1,-1,0,1,0,0,0,0],[0,1,-1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[1,2,10,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,10,3]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,-1,1,0,0,0],[0,0,0,1,0,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0]]=>[2,1,11,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,11,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-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]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[8,7,6,5,4,3,2,1,10,9]=>[2,3,4,5,6,7,8,1,10,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,0,0,1,0]]=>[9,8,7,6,5,4,3,2,1,11,10]=>[2,3,4,5,6,7,8,9,1,11,10]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,-1,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,7,6,8,9]=>[2,3,4,5,1,7,6,8,9]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7,8,9]=>[2,3,4,1,6,5,7,8,9]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7,8,9]=>[2,3,1,5,4,6,7,8,9]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,0,0,1],[0,0,0,0,1,-1,0,0,1,0],[0,0,0,1,-1,0,0,1,0,0],[0,0,1,-1,0,0,1,0,0,0],[0,1,-1,0,0,1,0,0,0,0],[1,-1,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,0,0,0,1],[0,0,0,1,-1,0,0,0,1,0],[0,0,1,-1,0,0,0,1,0,0],[0,1,-1,0,0,0,1,0,0,0],[1,-1,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,0,0,0,0,1],[0,0,1,-1,0,0,0,0,1,0],[0,1,-1,0,0,0,0,1,0,0],[1,-1,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,0,0,0,0,0,1],[0,1,-1,0,0,0,0,0,1,0],[1,-1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,-1,0,0,0,0,0,0,1],[1,-1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[1,3,2,5,6,7,8,9,4]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,4,3,2,9,8,7,6,5]=>[1,3,4,2,6,7,8,9,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,5,4,3,2,9,8,7,6]=>[1,3,4,5,2,7,8,9,6]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,7,8,9,10,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,-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,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,8,9,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-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]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,6,5,9,8,7]=>[1,2,3,4,6,5,8,9,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,5,4,9,8,7,6]=>[1,2,3,5,4,7,8,9,6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,0,0,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[1,-1,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,0,0,0,1,0,0],[1,-1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[1,3,4,5,6,7,2,9,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,-1,1],[1,0,0,0,0,0,0,-1,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[7,6,5,4,3,2,1,10,9,8]=>[2,3,4,5,6,7,1,9,10,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,-1,1],[0,1,0,0,0,0,0,-1,1,0],[1,0,0,0,0,0,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[6,5,4,3,2,1,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,-1,1],[0,0,1,0,0,0,0,-1,1,0],[0,1,0,0,0,0,-1,1,0,0],[1,0,0,0,0,-1,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[5,4,3,2,1,10,9,8,7,6]=>[2,3,4,5,1,7,8,9,10,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,-1,1],[0,0,0,1,0,0,0,-1,1,0],[0,0,1,0,0,0,-1,1,0,0],[0,1,0,0,0,-1,1,0,0,0],[1,0,0,0,-1,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[4,3,2,1,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,5]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1,0,0],[0,0,1,0,0,-1,1,0,0,0],[0,1,0,0,-1,1,0,0,0,0],[1,0,0,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[3,2,1,10,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,10,4]
Map
to symmetric ASM
Description
The diagonally symmetric alternating sign matrix corresponding to a Dyck path.
Map
to left key permutation
Description
Return the permutation of the left key of an alternating sign matrix.
This was originally defined by Lascoux and then further studied by Aval [1].
This was originally defined by Lascoux and then further studied by Aval [1].
Map
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
- $des$ is the number of descents, St000021The number of descents of a permutation.,
- $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
- $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
- $Ebot$ is the sum of the excedance bottoms,
- $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
- $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
- $Res$ is the sum of the (right) embracing numbers,
- $Ine$ is the sum of the side numbers.
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