Identifier
Mp00035:
Dyck paths
—to alternating sign matrix⟶
Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ 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],[1,0,0],[0,1,0]]=>[3,1,2]=>[3,2,1]
[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],[0,1,0,0],[0,0,1,0]]=>[1,4,2,3]=>[1,4,3,2]
[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],[0,1,0,0],[0,0,1,0]]=>[1,4,2,3]=>[1,4,3,2]
[1,1,1,0,0,0,1,0]=>[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]=>[3,1,2,4]=>[3,2,1,4]
[1,1,1,0,0,1,0,0]=>[[0,0,1,0],[1,0,0,0],[0,1,-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],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]=>[1,4,2,3]=>[1,4,3,2]
[1,1,1,1,0,0,0,0]=>[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]=>[4,1,2,3]=>[4,3,2,1]
[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],[0,0,1,0,0],[0,0,0,1,0]]=>[1,2,5,3,4]=>[1,2,5,4,3]
[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],[0,0,1,0,0],[0,0,0,1,0]]=>[1,2,5,3,4]=>[1,2,5,4,3]
[1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]=>[1,4,2,3,5]=>[1,4,3,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-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],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]=>[1,2,5,3,4]=>[1,2,5,4,3]
[1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]=>[1,5,2,3,4]=>[1,5,4,3,2]
[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],[0,0,1,0,0],[0,0,0,1,0]]=>[2,1,5,3,4]=>[2,1,5,4,3]
[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],[0,0,1,0,0],[0,0,0,1,0]]=>[1,2,5,3,4]=>[1,2,5,4,3]
[1,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]=>[1,4,2,3,5]=>[1,4,3,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-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],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]=>[1,2,5,3,4]=>[1,2,5,4,3]
[1,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]=>[1,5,2,3,4]=>[1,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]=>[3,1,2,4,5]=>[3,2,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]=>[3,1,2,5,4]=>[3,2,1,5,4]
[1,1,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0],[1,0,0,0,0],[0,1,-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],[1,0,0,0,0],[0,1,-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],[1,0,0,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]=>[2,1,5,3,4]=>[2,1,5,4,3]
[1,1,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]=>[1,4,2,3,5]=>[1,4,3,2,5]
[1,1,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,-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],[1,0,-1,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]=>[1,2,5,3,4]=>[1,2,5,4,3]
[1,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0],[1,0,-1,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]=>[1,5,2,3,4]=>[1,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0]=>[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]=>[4,1,2,3,5]=>[4,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]=>[3,1,2,5,4]=>[3,2,1,5,4]
[1,1,1,1,0,0,1,0,0,0]=>[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]=>[2,1,5,3,4]=>[2,1,5,4,3]
[1,1,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0],[1,0,0,-1,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]=>[1,5,2,3,4]=>[1,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0]=>[[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]=>[5,1,2,3,4]=>[5,4,3,2,1]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]
[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],[0,0,1,0,0,0],[0,0,0,1,-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],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]
[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],[0,0,1,0,0,0],[0,0,0,1,-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],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-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],[0,1,0,0,0,0],[0,0,1,-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],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-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],[0,1,0,-1,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[2,1,5,3,4,6]=>[2,1,5,4,3,6]
[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],[0,0,1,0,0,0],[0,0,0,1,-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],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,6,3,4,5]=>[2,1,6,5,4,3]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[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],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]
[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],[0,0,1,0,0,0],[0,0,0,1,-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],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[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],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-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],[0,1,0,0,0,0],[0,0,1,-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],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-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],[0,1,0,-1,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[3,1,2,4,6,5]=>[3,2,1,4,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[3,1,2,5,4,6]=>[3,2,1,5,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[3,1,2,4,6,5]=>[3,2,1,4,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[3,1,2,6,4,5]=>[3,2,1,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[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],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[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],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[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],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[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],[1,0,0,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[2,1,5,3,4,6]=>[2,1,5,4,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,0,0],[0,0,0,1,-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],[1,0,0,0,0,0],[0,1,-1,0,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,6,3,4,5]=>[2,1,6,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,-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],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[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],[1,0,-1,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-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],[1,0,-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]]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0],[1,0,-1,1,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0],[1,0,-1,0,1,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[4,1,2,3,6,5]=>[4,3,2,1,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[3,1,2,5,4,6]=>[3,2,1,5,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[3,1,2,4,6,5]=>[3,2,1,4,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[3,1,2,6,4,5]=>[3,2,1,6,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[2,1,5,3,4,6]=>[2,1,5,4,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-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],[1,0,0,0,0,0],[0,1,0,-1,1,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,6,3,4,5]=>[2,1,6,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0],[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]]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[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],[0,0,0,0,0,1]]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[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,-1,1],[0,0,0,0,1,0]]=>[4,1,2,3,6,5]=>[4,3,2,1,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[3,1,2,6,4,5]=>[3,2,1,6,5,4]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,-1,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[2,1,6,3,4,5]=>[2,1,6,5,4,3]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0],[1,0,0,0,-1,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,5,6,7]=>[1,4,3,2,5,6,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[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],[0,1,0,0,0,0,0],[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]]=>[1,3,2,5,4,6,7]=>[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],[0,1,0,0,0,0,0],[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]]=>[1,3,2,5,4,7,6]=>[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],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[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],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[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],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,-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]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]
[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],[0,1,0,-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],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,1,0,-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],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,1,0,-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],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[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],[0,1,0,-1,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,1,0,-1,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,1,0,-1,0,1,0],[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]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,1,0,-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],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,2,3,4,6,7]=>[1,5,4,3,2,6,7]
[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],[0,1,0,0,0,0,0],[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]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[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],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,1,0,0,-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]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,1,0,0,-1,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[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]]=>[1,6,2,3,4,5,7]=>[1,6,5,4,3,2,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[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],[0,1,0,0,0,0,0],[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]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,1,0,0,0,-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]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[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]]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,3,4,6,7]=>[2,1,5,4,3,6,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[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],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,3,4,5,7]=>[2,1,6,5,4,3,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[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],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,7,3,4,5,6]=>[2,1,7,6,5,4,3]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,5,6,7]=>[1,4,3,2,5,6,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[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],[0,1,0,0,0,0,0],[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]]=>[1,3,2,5,4,6,7]=>[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],[0,1,0,0,0,0,0],[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]]=>[1,3,2,5,4,7,6]=>[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],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[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],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[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],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,-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]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]
[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],[0,1,0,-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],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,1,0,-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],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[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],[0,1,0,-1,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,1,0,-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],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[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],[0,1,0,-1,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,1,0,-1,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,1,0,-1,0,1,0],[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]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,1,0,-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],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,2,3,4,6,7]=>[1,5,4,3,2,6,7]
[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],[0,1,0,0,0,0,0],[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]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[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],[0,1,0,0,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[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],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[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],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[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],[0,1,0,0,-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]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[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],[0,1,0,0,-1,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[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]]=>[1,6,2,3,4,5,7]=>[1,6,5,4,3,2,7]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[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],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[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],[0,1,0,0,0,0,0],[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]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[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],[0,1,0,0,0,-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]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[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],[0,1,0,0,0,0,0],[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]]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,1,2,4,5,7,6]=>[3,2,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,1,2,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,1,2,4,5,7,6]=>[3,2,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,1,2,5,4,6,7]=>[3,2,1,5,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,1,2,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,1,2,4,5,7,6]=>[3,2,1,4,5,7,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,1,2,6,4,5,7]=>[3,2,1,6,5,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,7,4,5,6]=>[3,2,1,7,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[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]]=>[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],[1,0,0,0,0,0,0],[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]]=>[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],[1,0,0,0,0,0,0],[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]]=>[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],[1,0,0,0,0,0,0],[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]]=>[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],[1,0,0,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[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],[1,0,0,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[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],[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],[0,0,0,0,1,0,0],[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],[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],[0,0,0,0,0,1,0]]=>[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],[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,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[1,0,0,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,3,4,6,7]=>[2,1,5,4,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[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],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-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],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[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]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,3,4,5,7]=>[2,1,6,5,4,3,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,0,1,0],[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]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,0,0,0,0,0],[0,1,-1,0,0,0,1],[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]]=>[2,1,7,3,4,5,6]=>[2,1,7,6,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,5,6,7]=>[1,4,3,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[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,-1,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[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],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[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]]=>[1,3,2,5,4,7,6]=>[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],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[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],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-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],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[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,-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],[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,-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],[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,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[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],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[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,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,-1,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,-1,0,1,0],[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]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,1,0,0,0],[0,1,0,-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],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,2,3,4,6,7]=>[1,5,4,3,2,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[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],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[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,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[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,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[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,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[1,0,-1,0,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[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],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[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,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[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]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,1,0,0],[0,1,0,0,-1,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[1,0,-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],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,6,2,3,4,5,7]=>[1,6,5,4,3,2,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[1,0,-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],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,0,1,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,0,1,0],[0,1,0,0,0,0,0],[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]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-1,0,0,1,0],[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]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[1,0,-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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[4,1,2,3,5,6,7]=>[4,3,2,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[4,1,2,3,5,7,6]=>[4,3,2,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,1]]=>[4,1,2,3,6,5,7]=>[4,3,2,1,6,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,0,1,0]]=>[4,1,2,3,5,7,6]=>[4,3,2,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[4,1,2,3,7,5,6]=>[4,3,2,1,7,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,1,2,5,4,6,7]=>[3,2,1,5,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,1,2,4,6,5,7]=>[3,2,1,4,6,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,0,1,0]]=>[3,1,2,4,5,7,6]=>[3,2,1,4,5,7,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[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,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,1,2,6,4,5,7]=>[3,2,1,6,5,4,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,-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]]=>[3,1,2,7,4,5,6]=>[3,2,1,7,6,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,3,4,6,7]=>[2,1,5,4,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[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],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-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],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-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],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[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],[0,0,0,0,0,0,1]]=>[2,1,6,3,4,5,7]=>[2,1,6,5,4,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[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,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-1,0,1,0],[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]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,-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],[0,0,0,0,0,1,0]]=>[2,1,7,3,4,5,6]=>[2,1,7,6,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,2,3,4,6,7]=>[1,5,4,3,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[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,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[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,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[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,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,-1,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-1,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[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],[1,0,0,-1,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-1,1,0,0],[0,1,0,0,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[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,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[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,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[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]]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-1,1,0,0],[0,1,0,0,-1,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[1,0,0,-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],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,6,2,3,4,5,7]=>[1,6,5,4,3,2,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-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],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-1,0,1,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-1,0,1,0],[0,1,0,0,0,0,0],[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]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-1,0,1,0],[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]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[1,0,0,-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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[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],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[5,1,2,3,4,6,7]=>[5,4,3,2,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[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],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[5,1,2,3,4,7,6]=>[5,4,3,2,1,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[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,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[4,1,2,3,6,5,7]=>[4,3,2,1,6,5,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[0,0,0,0,1,0,0],[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],[0,0,0,0,0,1,0]]=>[4,1,2,3,5,7,6]=>[4,3,2,1,5,7,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[0,0,0,0,1,0,0],[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,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[4,1,2,3,7,5,6]=>[4,3,2,1,7,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[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,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,1,2,6,4,5,7]=>[3,2,1,6,5,4,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[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,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[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,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,7,4,5,6]=>[3,2,1,7,6,5,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[1,0,0,0,0,0,0],[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],[0,0,0,0,0,0,1]]=>[2,1,6,3,4,5,7]=>[2,1,6,5,4,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[1,0,0,0,0,0,0],[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,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[1,0,0,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[1,0,0,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[1,0,0,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[2,1,7,3,4,5,6]=>[2,1,7,6,5,4,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[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],[0,0,0,0,0,0,1]]=>[1,6,2,3,4,5,7]=>[1,6,5,4,3,2,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[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,-1,1],[0,0,0,0,0,1,0]]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[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,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[1,0,0,0,-1,1,0],[0,1,0,0,0,0,0],[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]]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[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]]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[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],[0,0,0,0,0,0,1]]=>[6,1,2,3,4,5,7]=>[6,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[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,-1,1],[0,0,0,0,0,1,0]]=>[5,1,2,3,4,7,6]=>[5,4,3,2,1,7,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[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,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[4,1,2,3,7,5,6]=>[4,3,2,1,7,6,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[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,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[3,1,2,7,4,5,6]=>[3,2,1,7,6,5,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,1,0],[1,0,0,0,0,0,0],[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]]=>[2,1,7,3,4,5,6]=>[2,1,7,6,5,4,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0],[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],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]=>[7,1,2,3,4,5,6]=>[7,6,5,4,3,2,1]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-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],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[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],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,5,4,8,7]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[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],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-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],[0,0,1,0,-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,-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],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,3,4,6,8,7]=>[1,2,5,4,3,6,8,7]
[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],[0,0,1,0,0,-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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,0,1,0,0,0,0,0],[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]]=>[1,2,7,3,4,5,6,8]=>[1,2,7,6,5,4,3,8]
[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],[0,0,1,0,0,0,0,0],[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]]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,7,6,5]
[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],[0,0,1,0,0,0,-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]]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]
[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],[0,0,1,0,0,0,0,0],[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]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,7,6,5]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,2,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[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],[0,1,0,0,0,0,0,0],[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],[0,0,0,0,0,0,1,0]]=>[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]
[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,5,3,4,8,6,7]=>[1,2,5,4,3,8,7,6]
[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-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],[0,1,0,-1,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-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],[0,1,0,-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],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,5,4,7,8]
[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]
[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-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],[0,1,0,-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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,1,0,0,0,0,0,0],[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],[0,0,0,0,0,0,1,0]]=>[1,4,2,3,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,6,3,4,5,8,7]=>[1,2,6,5,4,3,8,7]
[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],[0,1,0,0,-1,1,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,7,6]
[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],[0,1,0,0,-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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,1,0,0,-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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0],[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],[0,0,0,0,0,0,0,1]]=>[1,6,2,3,4,5,7,8]=>[1,6,5,4,3,2,7,8]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,4,2,3,5,8,6,7]=>[1,4,3,2,5,8,7,6]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,7,6,5]
[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],[0,1,0,0,0,-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],[0,0,0,0,0,0,0,1]]=>[1,2,7,3,4,5,6,8]=>[1,2,7,6,5,4,3,8]
[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],[0,1,0,0,0,-1,1,0],[0,0,1,0,0,0,0,0],[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]]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,7,6,5]
[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],[0,1,0,0,0,-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]]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]
[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],[0,1,0,0,0,-1,0,1],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,7,2,3,4,5,6,8]=>[1,7,6,5,4,3,2,8]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,7,6,5]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]
[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],[0,1,0,0,0,0,-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],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,7,6]
[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],[0,0,0,1,0,-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]]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,7,6]
[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],[0,0,0,1,0,0,-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]]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,7,6,5]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,7,6,5]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,5,3,4,6,7,8]=>[2,1,5,4,3,6,7,8]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[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],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,7,6]
[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],[0,0,1,0,0,-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]]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,7,6,5]
[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],[0,0,1,0,0,0,0,0],[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]]=>[2,1,7,3,4,5,6,8]=>[2,1,7,6,5,4,3,8]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,3,4,5,8,7]=>[2,1,6,5,4,3,8,7]
[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],[0,0,1,0,0,0,-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]]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]
[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],[0,0,1,0,0,0,0,0],[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]]=>[2,1,8,3,4,5,6,7]=>[2,1,8,7,6,5,4,3]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,7,6,5]
[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],[0,0,0,1,0,0,-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]]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,7,6,5]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,7,6]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,7,6,5]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,7,6]
[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-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],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,5,4,7,8]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[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],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]
[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],[0,0,0,1,0,-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]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,0,0,1,0,-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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,6,5,4,8]
[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],[0,0,0,1,0,0,-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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[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],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,5,4,7,8]
[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],[0,0,1,0,-1,0,1,0],[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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,6,3,4,5,7,8]=>[1,2,6,5,4,3,7,8]
[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],[0,0,1,0,0,-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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,0,1,0,0,0,0,0],[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]]=>[1,2,7,3,4,5,6,8]=>[1,2,7,6,5,4,3,8]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,2,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[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],[0,1,0,0,0,0,0,0],[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],[0,0,0,0,0,0,1,0]]=>[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]
[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-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],[0,1,0,-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],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,5,4,7,8]
[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]
[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],[0,1,0,-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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[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],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,1,0,-1,0,1,0,0],[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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,5,2,3,4,6,7,8]=>[1,5,4,3,2,6,7,8]
[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],[0,1,0,0,-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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,1,0,0],[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,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,5,2,3,4,6,8,7]=>[1,5,4,3,2,6,8,7]
[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],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,5,2,3,4,8,6,7]=>[1,5,4,3,2,8,7,6]
[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],[0,1,0,0,0,-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]]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,7,2,3,4,5,6,8]=>[1,7,6,5,4,3,2,8]
[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],[0,1,0,0,0,0,0,0],[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,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]
[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],[0,1,0,0,0,0,-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],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0],[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]]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[3,1,2,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[3,1,2,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[3,1,2,4,5,8,6,7]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,1,0,-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]]=>[3,1,2,4,5,8,6,7]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,1,0,-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]]=>[3,1,2,4,8,5,6,7]=>[3,2,1,4,8,7,6,5]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,-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]]=>[3,1,2,4,8,5,6,7]=>[3,2,1,4,8,7,6,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[3,1,2,8,4,5,6,7]=>[3,2,1,8,7,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[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]]=>[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],[1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,7,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[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],[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],[0,0,0,0,1,0,0,0],[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],[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],[0,0,0,0,0,1,0,0],[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],[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],[0,0,0,0,0,0,1,0]]=>[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],[1,0,0,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-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],[1,0,0,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,7,6]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[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]]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,2,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,7,6,5]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-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],[1,0,-1,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-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],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,3,4,6,8,7]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[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,-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],[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,-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],[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,-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],[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,-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],[1,0,-1,1,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,5,4,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,5,4,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,7,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-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],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[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,-1,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[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],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,6,3,4,5,8,7]=>[1,2,6,5,4,3,8,7]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,1,0,0,0],[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]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,1,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,1,0,0,-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],[0,0,0,0,0,0,1,0]]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,0,1,0,0],[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],[0,0,0,0,0,0,1,0]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,-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]]=>[1,4,2,3,5,8,6,7]=>[1,4,3,2,5,8,7,6]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,-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]]=>[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,7,6,5]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,0,1,0,0],[0,1,0,0,0,-1,0,1],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-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],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,5,2,3,4,8,6,7]=>[1,5,4,3,2,8,7,6]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,0,0,1,0],[0,1,0,0,0,0,0,0],[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]]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,0,0,1,0],[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],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[1,0,-1,0,0,0,0,1],[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]]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[4,1,2,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[4,1,2,3,5,6,8,7]=>[4,3,2,1,5,6,8,7]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[4,1,2,3,5,8,6,7]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[4,1,2,3,8,5,6,7]=>[4,3,2,1,8,7,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,1,2,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[3,1,2,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,0,0,1,0]]=>[3,1,2,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,0,0,1,0,0,-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]]=>[3,1,2,4,8,5,6,7]=>[3,2,1,4,8,7,6,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,5,3,4,6,7,8]=>[2,1,5,4,3,6,7,8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-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],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,7,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,-1,0,1,0,0],[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]]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,7,6,5]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,-1,0,0,1,0],[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]]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,5,2,3,4,8,6,7]=>[1,5,4,3,2,8,7,6]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[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,-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]]=>[1,4,2,3,5,6,8,7]=>[1,4,3,2,5,6,8,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[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,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,3,4,6,8,7]=>[1,2,5,4,3,6,8,7]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[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,-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]]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[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,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,5,4,8,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,1,0,0,-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],[0,0,0,0,0,0,1,0]]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-1,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,7,6,5]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-1,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-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],[0,0,0,0,0,0,1,0]]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-1,0,1,0,0],[0,1,0,0,0,-1,0,1],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,2,3,4,5,6,8]=>[1,7,6,5,4,3,2,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-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,-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]]=>[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,7,6,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[1,0,0,-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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[5,1,2,3,4,6,7,8]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,1,0]]=>[5,1,2,3,4,6,8,7]=>[5,4,3,2,1,6,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[5,1,2,3,4,8,6,7]=>[5,4,3,2,1,8,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[4,1,2,3,6,5,7,8]=>[4,3,2,1,6,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[4,1,2,3,5,7,6,8]=>[4,3,2,1,5,7,6,8]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[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,-1,0,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[4,1,2,3,5,8,6,7]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,1,2,6,4,5,7,8]=>[3,2,1,6,5,4,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[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],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,3,4,5,8,7]=>[2,1,6,5,4,3,8,7]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,5,4,8,6,7]=>[2,1,3,5,4,8,7,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,7,6,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,-1,0,1,0],[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]]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[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,-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]]=>[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,7,6,5]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,-1,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,7,6,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,-1,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-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],[0,0,0,0,0,0,1,0]]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,0,1]]=>[1,2,7,3,4,5,6,8]=>[1,2,7,6,5,4,3,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0,0],[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,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,6,3,4,5,8,7]=>[1,2,6,5,4,3,8,7]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[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]]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,-1,1,0,0],[0,1,0,0,0,-1,0,1],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,-1,0,1,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,2,3,4,5,6,8]=>[1,7,6,5,4,3,2,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,-1,0,1,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,-1,0,1,0],[0,1,0,0,0,0,0,0],[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]]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[1,0,0,0,-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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0],[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],[0,0,0,0,0,0,0,1]]=>[6,1,2,3,4,5,7,8]=>[6,5,4,3,2,1,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,1,0,0],[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]]=>[6,1,2,3,4,5,8,7]=>[6,5,4,3,2,1,8,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[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,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[5,1,2,3,4,7,6,8]=>[5,4,3,2,1,7,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[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,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[5,1,2,3,4,6,8,7]=>[5,4,3,2,1,6,8,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[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,-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]]=>[4,1,2,3,7,5,6,8]=>[4,3,2,1,7,6,5,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[3,1,2,7,4,5,6,8]=>[3,2,1,7,6,5,4,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[3,1,2,6,4,5,8,7]=>[3,2,1,6,5,4,8,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[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],[0,0,0,0,0,0,0,1]]=>[2,1,7,3,4,5,6,8]=>[2,1,7,6,5,4,3,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[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,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,3,4,5,8,7]=>[2,1,6,5,4,3,8,7]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,-1,1,0],[0,0,1,0,0,0,0,0],[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]]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,7,6,5]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,-1,1,0],[0,0,1,0,0,0,-1,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,2,3,4,5,6,8]=>[1,7,6,5,4,3,2,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[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,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,2,3,4,5,8,7]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[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],[0,0,0,0,0,0,1,0]]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[1,0,0,0,0,-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],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,1,0],[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]]=>[7,1,2,3,4,5,6,8]=>[7,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,1,0],[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,-1,1],[0,0,0,0,0,0,1,0]]=>[6,1,2,3,4,5,8,7]=>[6,5,4,3,2,1,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,0,1,0],[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,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[5,1,2,3,4,8,6,7]=>[5,4,3,2,1,8,7,6]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[4,1,2,3,8,5,6,7]=>[4,3,2,1,8,7,6,5]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[3,1,2,8,4,5,6,7]=>[3,2,1,8,7,6,5,4]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[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],[0,0,0,0,0,0,1,0]]=>[2,1,8,3,4,5,6,7]=>[2,1,8,7,6,5,4,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[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],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1],[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]]=>[8,1,2,3,4,5,6,7]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,0,1,0],[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],[0,0,0,0,0,0,0,0,1]]=>[8,1,2,3,4,5,6,7,9]=>[8,7,6,5,4,3,2,1,9]
[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],[0,1,0,0,0,0,0,0,0],[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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[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],[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]]=>[9,1,2,3,4,5,6,7,8,10]=>[9,8,7,6,5,4,3,2,1,10]
[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],[1,0,0,0,0,0,-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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,2,3,4,5,6,7,9]=>[1,8,7,6,5,4,3,2,9]
[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],[0,1,0,0,0,0,0,-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],[0,0,0,0,0,0,0,1,0]]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0,0,0],[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]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[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]]=>[10,1,2,3,4,5,6,7,8,9,11]=>[10,9,8,7,6,5,4,3,2,1,11]
[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],[1,0,0,0,0,0,0,-1,1,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[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]]=>[1,9,2,3,4,5,6,7,8,10]=>[1,9,8,7,6,5,4,3,2,10]
[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],[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,-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],[0,0,0,0,0,0,0,0,1]]=>[2,1,8,3,4,5,6,7,9]=>[2,1,8,7,6,5,4,3,9]
[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],[1,0,0,0,0,-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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,2,3,4,5,6,7,9]=>[1,8,7,6,5,4,3,2,9]
[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],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,-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]]=>[1,3,2,9,4,5,6,7,8]=>[1,3,2,9,8,7,6,5,4]
[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],[0,1,0,0,0,0,-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],[0,0,0,0,0,0,0,1,0]]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0,-1,1],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[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]]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,9,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0,0,0,0],[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]]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]
[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],[0,1,0,0,0,0,-1,1,0],[0,0,1,0,0,0,0,-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]]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,8,7,6,5,4]
[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],[0,1,0,0,0,0,0,-1,1,0],[0,0,1,0,0,0,0,0,-1,1],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[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]]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,9,8,7,6,5,4]
[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],[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,-1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[6,1,2,3,4,5,8,7,9]=>[6,5,4,3,2,1,8,7,9]
[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],[0,1,0,0,0,0,0,0,0],[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]]=>[1,8,2,3,4,5,6,7,9]=>[1,8,7,6,5,4,3,2,9]
[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],[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]]=>[7,1,2,3,4,5,6,9,8]=>[7,6,5,4,3,2,1,9,8]
[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],[0,1,0,0,0,-1,1,0,0],[0,0,1,0,0,0,-1,1,0],[0,0,0,1,0,0,0,-1,1],[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]]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]
[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],[0,0,1,0,0,0,0,0,0],[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]]=>[2,1,9,3,4,5,6,7,8]=>[2,1,9,8,7,6,5,4,3]
[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],[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],[0,0,0,0,0,0,0,0,1]]=>[7,1,2,3,4,5,6,8,9]=>[7,6,5,4,3,2,1,8,9]
[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],[0,1,0,0,0,0,0,0,0],[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]]=>[1,8,2,3,4,5,6,7,9]=>[1,8,7,6,5,4,3,2,9]
[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],[1,0,0,0,0,-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],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6,9,8]=>[1,7,6,5,4,3,2,9,8]
[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],[0,1,0,0,0,0,-1,1,0,0],[0,0,1,0,0,0,0,-1,1,0],[0,0,0,1,0,0,0,0,-1,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,9,8,7,6,5]
[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],[0,0,1,0,0,0,0,0,0],[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]]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,8,7,6,5,4,3]
[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],[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],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0]]=>[8,1,2,3,4,5,6,7,10,9]=>[8,7,6,5,4,3,2,1,10,9]
[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],[0,0,1,0,0,0,0,0,0,0],[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]]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,10,9,8,7,6,5,4,3]
[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],[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],[0,0,0,0,0,0,0,0,0,1]]=>[8,1,2,3,4,5,6,7,9,10]=>[8,7,6,5,4,3,2,1,9,10]
[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,-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],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[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,-1,0,1,0,0],[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],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,7,9,8]=>[1,2,3,4,6,5,7,9,8]
[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],[0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[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],[0,0,0,0,1,0,-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]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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],[0,0,0,0,1,0,-1,0,1],[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]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[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,-1,0,0,1,0],[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,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,7,5,6,9,8]=>[1,2,3,4,7,6,5,9,8]
[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],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[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],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[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],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[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],[0,1,0,0,0,0,0,0,0],[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],[0,0,0,0,0,0,0,1,0]]=>[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],[0,1,0,-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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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],[0,1,0,0,-1,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[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],[0,1,0,0,0,0,0,0,0],[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,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6,9,8]=>[1,7,6,5,4,3,2,9,8]
[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],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,-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]]=>[1,3,2,9,4,5,6,7,8]=>[1,3,2,9,8,7,6,5,4]
[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],[0,1,0,0,0,0,0,-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],[0,0,0,0,0,0,0,1,0]]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,8,7,6,5,4,3]
[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],[0,1,0,0,0,0,0,0,0],[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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[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],[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],[0,0,0,0,0,0,0,1,0]]=>[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],[1,0,-1,1,0,0,0,0,0],[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],[0,0,0,0,0,0,0,1,0]]=>[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],[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,-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],[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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],[1,0,-1,0,1,0,0,0,0],[0,1,0,0,-1,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,0,1],[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]]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]
[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],[1,0,-1,0,0,0,0,0,1],[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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,1,0,-1,0,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,9,6,7,8]=>[2,1,3,4,5,9,8,7,6]
[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],[1,0,0,-1,1,0,0,0,0],[0,1,0,0,-1,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[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],[1,0,0,-1,1,0,0,0,0],[0,1,0,0,-1,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,0,1],[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]]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,8,7,6,5]
[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],[1,0,0,-1,0,0,0,0,1],[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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,1,0,0,-1,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,9,6,7,8]=>[2,1,3,4,5,9,8,7,6]
[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],[1,0,0,0,-1,1,0,0,0],[0,1,0,0,0,-1,1,0,0],[0,0,1,0,0,0,-1,0,1],[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]]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,8,7,6,5,4]
[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],[1,0,0,0,-1,0,1,0,0],[0,1,0,0,0,0,-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],[0,0,0,0,0,0,0,1,0]]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,8,7,6,5,4,3]
[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],[1,0,0,0,-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,-1,1],[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]]=>[1,4,2,3,9,5,6,7,8]=>[1,4,3,2,9,8,7,6,5]
[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],[1,0,0,0,-1,0,0,0,1],[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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,-1,1,0,0],[0,0,1,0,0,0,-1,1,0],[0,0,0,1,0,0,0,-1,1],[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]]=>[2,1,3,4,9,5,6,7,8]=>[2,1,3,4,9,8,7,6,5]
[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],[1,0,0,0,0,-1,1,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,-1,0,1],[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]]=>[1,3,2,9,4,5,6,7,8]=>[1,3,2,9,8,7,6,5,4]
[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],[1,0,0,0,0,-1,1,0,0],[0,1,0,0,0,0,-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],[0,0,0,0,0,0,0,1,0]]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,8,7,6,5,4,3]
[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],[1,0,0,0,0,-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],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6,9,8]=>[1,7,6,5,4,3,2,9,8]
[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],[1,0,0,0,0,-1,0,1,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,-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]]=>[1,3,2,9,4,5,6,7,8]=>[1,3,2,9,8,7,6,5,4]
[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],[1,0,0,0,0,-1,0,0,1],[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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[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],[1,0,0,0,0,0,-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],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6,9,8]=>[1,7,6,5,4,3,2,9,8]
[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],[1,0,0,0,0,0,-1,1,0],[0,1,0,0,0,0,0,-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],[0,0,0,0,0,0,0,1,0]]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,8,7,6,5,4,3]
[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],[1,0,0,0,0,0,-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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[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],[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,-1,1],[0,0,0,0,0,0,0,1,0]]=>[7,1,2,3,4,5,6,9,8]=>[7,6,5,4,3,2,1,9,8]
[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],[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,-1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[6,1,2,3,4,5,9,7,8]=>[6,5,4,3,2,1,9,8,7]
[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],[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,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[5,1,2,3,4,9,6,7,8]=>[5,4,3,2,1,9,8,7,6]
[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],[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,-1,1],[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]]=>[4,1,2,3,9,5,6,7,8]=>[4,3,2,1,9,8,7,6,5]
[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],[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,-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]]=>[3,1,2,9,4,5,6,7,8]=>[3,2,1,9,8,7,6,5,4]
[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],[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,1,0,0,0,0,0,0],[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]]=>[2,1,9,3,4,5,6,7,8]=>[2,1,9,8,7,6,5,4,3]
[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],[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],[0,0,0,0,1,0,0,0,0],[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]]=>[1,9,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]
[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],[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]]=>[9,1,2,3,4,5,6,7,8]=>[9,8,7,6,5,4,3,2,1]
[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,-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]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[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],[0,0,0,0,0,0,1,0,0],[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],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,7,9,8]=>[1,2,3,4,6,5,7,9,8]
[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]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[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],[0,0,0,0,1,-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]]=>[1,2,3,5,4,6,7,9,8]=>[1,2,3,5,4,6,7,9,8]
[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]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[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],[0,0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,7,9,8]=>[1,2,4,3,5,6,7,9,8]
[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],[0,1,0,0,0,0,0,0,0],[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],[0,0,0,0,0,0,0,1,0]]=>[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],[1,0,0,0,0,0,0,0,0,0],[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]]=>[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],[0,1,0,-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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,-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],[0,1,0,-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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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],[0,1,0,0,-1,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,8,7,6]
[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],[0,1,0,-1,1,0,0,0,0,0],[0,0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,-1,1,0,0,0],[0,0,0,0,1,0,-1,1,0,0],[0,0,0,0,0,1,0,-1,1,0],[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]]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,9,8]
[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],[1,0,-1,1,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0,0],[0,0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,-1,1,0,0,0],[0,0,0,0,1,0,-1,1,0,0],[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,-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],[0,1,0,0,-1,1,0,0,0,0],[0,0,1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[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],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[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]]=>[1,4,2,3,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]
[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],[0,1,0,0,0,0,0,0,0],[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]]=>[1,7,2,3,4,5,6,9,8]=>[1,7,6,5,4,3,2,9,8]
[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],[0,0,1,0,0,0,0,0,0],[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]]=>[2,1,8,3,4,5,6,7,9]=>[2,1,8,7,6,5,4,3,9]
[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],[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],[0,0,0,0,1,0,0,0,0],[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]]=>[3,1,2,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]
[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],[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],[0,0,0,1,0,0,0,0,0],[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]]=>[3,1,2,9,4,5,6,7,8]=>[3,2,1,9,8,7,6,5,4]
[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],[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],[0,0,0,0,0,1,0,0,0],[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]]=>[4,1,2,3,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]
[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],[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],[0,0,0,0,0,0,0,0,1],[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]]=>[4,1,2,3,9,5,6,7,8]=>[4,3,2,1,9,8,7,6,5]
[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],[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[5,1,2,3,4,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]
[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],[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],[0,0,0,0,0,0,0,0,1],[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]]=>[5,1,2,3,4,9,6,7,8]=>[5,4,3,2,1,9,8,7,6]
[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],[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],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[6,1,2,3,4,5,7,8,9]=>[6,5,4,3,2,1,7,8,9]
[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],[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],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[6,1,2,3,4,5,9,7,8]=>[6,5,4,3,2,1,9,8,7]
[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],[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],[0,0,0,0,1,0,0,0,0,0],[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]]=>[3,1,2,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]
[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],[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[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]]=>[3,1,2,10,4,5,6,7,8,9]=>[3,2,1,10,9,8,7,6,5,4]
[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],[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],[0,0,0,0,0,1,0,0,0,0],[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]]=>[4,1,2,3,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]
[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],[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],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[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]]=>[4,1,2,3,10,5,6,7,8,9]=>[4,3,2,1,10,9,8,7,6,5]
[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],[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],[0,0,0,0,0,0,1,0,0,0],[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]]=>[5,1,2,3,4,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]
[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],[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],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[5,1,2,3,4,10,6,7,8,9]=>[5,4,3,2,1,10,9,8,7,6]
[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],[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],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[6,1,2,3,4,5,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]
[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],[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],[0,0,0,0,0,0,0,0,0,1],[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]]=>[6,1,2,3,4,5,10,7,8,9]=>[6,5,4,3,2,1,10,9,8,7]
[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],[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],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[7,1,2,3,4,5,6,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]
[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],[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],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[7,1,2,3,4,5,6,10,8,9]=>[7,6,5,4,3,2,1,10,9,8]
[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],[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]]=>[10,1,2,3,4,5,6,7,8,9]=>[10,9,8,7,6,5,4,3,2,1]
[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],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[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]]=>[1,4,2,3,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]
[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]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[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,-1,0,1,0],[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]]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,8,7,6,9]
[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],[1,0,0,0,-1,1,0,0,0,0],[0,1,0,0,0,-1,1,0,0,0],[0,0,1,0,0,0,-1,1,0,0],[0,0,0,1,0,0,0,-1,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,9,8,7,6,5]
[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],[1,0,0,-1,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0,0,0],[0,0,1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,-1,0,1],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,9,8,7,6]
[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],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,9,8]
[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],[1,0,0,0,0,0,0,-1,0,1],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[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]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,-1,1],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[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]]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,10,9,8,7,6,5,4,3]
[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],[1,0,0,0,0,0,0,0,-1,0,1],[0,1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[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]]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]
[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],[1,0,0,0,0,0,-1,1,0,0],[0,1,0,0,0,0,0,-1,0,1],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[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]]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,9,8,7,6,5,4,3]
[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],[1,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,-1,1],[0,0,1,0,0,0,0,0,0,0,0],[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]]=>[2,1,11,3,4,5,6,7,8,9,10]=>[2,1,11,10,9,8,7,6,5,4,3]
[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]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,8,7,6,9]
[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],[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],[0,0,0,0,1,0,0,0,0],[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]]=>[1,4,2,3,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]
[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],[0,1,0,0,0,0,0,0,0,0],[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]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[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,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[8,1,2,3,4,5,6,7,10,9]=>[8,7,6,5,4,3,2,1,10,9]
[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],[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,-1,1],[0,0,0,0,0,0,0,0,0,1,0]]=>[9,1,2,3,4,5,6,7,8,11,10]=>[9,8,7,6,5,4,3,2,1,11,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,-1,1,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[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,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,8,2,3,4,5,6,7,10,9]=>[1,8,7,6,5,4,3,2,10,9]
[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],[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,-1,1,0,0],[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]]=>[5,1,2,3,4,7,6,8,9]=>[5,4,3,2,1,7,6,8,9]
[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],[1,0,0,0,0,0,0,0,0],[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]]=>[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],[1,0,0,0,0,0,0,0,-1,1],[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]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[1,0,0,0,0,0,-1,0,0,1],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[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]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[1,0,0,0,0,-1,0,0,0,1],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[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]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[1,0,0,0,-1,0,0,0,0,1],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[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]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[1,0,0,-1,0,0,0,0,0,1],[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],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[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],[1,0,-1,0,0,0,0,0,0,1],[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],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[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],[0,0,0,0,1,0,0,0,0],[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]]=>[1,2,3,4,7,5,6,9,8]=>[1,2,3,4,7,6,5,9,8]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0,0],[0,0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,9,7,8]=>[2,1,3,4,5,6,9,8,7]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,8,7,6,9]
[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],[0,1,0,-1,1,0,0,0,0,0],[0,0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,-1,1,0,0,0],[0,0,0,0,1,0,-1,1,0,0],[0,0,0,0,0,1,0,-1,1,0],[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]]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,9,8]
[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],[1,0,0,0,0,0,0,0,0,-1,1],[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]]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]
[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],[0,0,0,1,0,0,0,0,0],[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]]=>[1,3,2,9,4,5,6,7,8]=>[1,3,2,9,8,7,6,5,4]
[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],[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],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,4,2,3,9,5,6,7,8]=>[1,4,3,2,9,8,7,6,5]
[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]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-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],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,7,9,8]=>[1,2,3,5,4,6,7,9,8]
[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],[0,1,0,0,0,-1,1,0,0,0],[0,0,1,0,0,0,-1,1,0,0],[0,0,0,1,0,0,0,-1,1,0],[0,0,0,0,1,0,0,0,-1,1],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,9,8,7,6]
[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],[0,1,0,0,0,0,0,0,0],[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,9,7,8]=>[1,3,2,4,5,6,9,8,7]
[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],[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],[0,0,0,0,0,0,1,0,0],[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]
[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[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],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[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],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[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],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[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],[0,0,0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,1,0,0,-1,1,0,0],[0,0,0,1,0,0,-1,1,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,9,6,7,8]=>[2,1,3,4,5,9,8,7,6]
[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],[0,0,1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[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],[0,1,0,0,-1,1,0,0,0,0],[0,0,1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[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],[1,0,0,-1,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0,0,0],[0,0,1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,9,8,7]
[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],[1,0,-1,0,0,0,1,0,0],[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],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,2,3,4,5,6,9,8]=>[1,7,6,5,4,3,2,9,8]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[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],[0,0,0,0,0,0,0,1,0]]=>[4,1,2,3,5,9,6,7,8]=>[4,3,2,1,5,9,8,7,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[[0,0,0,0,0,1,0,0,0],[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],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[6,1,2,3,4,5,7,9,8]=>[6,5,4,3,2,1,7,9,8]
[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],[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,-1,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[7,1,2,3,4,5,6,10,8,9]=>[7,6,5,4,3,2,1,10,9,8]
[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],[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,-1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[6,1,2,3,4,5,10,7,8,9]=>[6,5,4,3,2,1,10,9,8,7]
[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],[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,-1,1],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]]=>[5,1,2,3,4,10,6,7,8,9]=>[5,4,3,2,1,10,9,8,7,6]
[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],[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,-1,1],[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]]=>[4,1,2,3,10,5,6,7,8,9]=>[4,3,2,1,10,9,8,7,6,5]
[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],[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,-1,1],[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]]=>[3,1,2,10,4,5,6,7,8,9]=>[3,2,1,10,9,8,7,6,5,4]
Map
to alternating sign matrix
Description
Return the Dyck path as an alternating sign matrix.
This is an inclusion map from Dyck words of length $2n$ to certain
$n \times n$ alternating sign matrices.
This is an inclusion map from Dyck words of length $2n$ to certain
$n \times n$ alternating sign matrices.
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
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
searching the database
Sorry, this map was not found in the database.