Identifier
Mp00137:
Dyck paths
—to symmetric ASM⟶
Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ 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]=>[3,1,2]
[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]=>[3,1,2]
[1,1,1,0,0,0]=>[[0,0,1],[0,1,0],[1,0,0]]=>[3,2,1]=>[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]=>[4,1,2,3]
[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]=>[3,1,2,4]
[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]=>[4,1,2,3]
[1,0,1,1,1,0,0,0]=>[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]=>[1,4,3,2]=>[4,3,1,2]
[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]=>[4,2,1,3]
[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]=>[3,1,2,4]
[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]=>[4,1,2,3]
[1,1,0,1,1,0,0,0]=>[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]=>[1,4,3,2]=>[4,3,1,2]
[1,1,1,0,0,0,1,0]=>[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]=>[3,2,1,4]=>[3,2,1,4]
[1,1,1,0,0,1,0,0]=>[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]=>[2,1,4,3]=>[4,2,1,3]
[1,1,1,0,1,0,0,0]=>[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]=>[1,4,3,2]=>[4,3,1,2]
[1,1,1,1,0,0,0,0]=>[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]=>[4,3,2,1]=>[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]=>[5,1,2,3,4]
[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]=>[4,1,2,3,5]
[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]=>[5,1,2,3,4]
[1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[5,4,1,2,3]
[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]=>[3,1,2,4,5]
[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]=>[5,3,1,2,4]
[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]=>[4,1,2,3,5]
[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]=>[5,1,2,3,4]
[1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[5,4,1,2,3]
[1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[1,4,3,2,5]=>[4,3,1,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[5,3,1,2,4]
[1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[5,4,1,2,3]
[1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[5,4,3,1,2]
[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]=>[5,2,1,3,4]
[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]=>[4,2,1,3,5]
[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]=>[5,2,1,3,4]
[1,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[2,1,5,4,3]=>[5,4,2,1,3]
[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]=>[3,1,2,4,5]
[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]=>[5,3,1,2,4]
[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]=>[4,1,2,3,5]
[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]=>[5,1,2,3,4]
[1,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[5,4,1,2,3]
[1,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[1,4,3,2,5]=>[4,3,1,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[5,3,1,2,4]
[1,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[5,4,1,2,3]
[1,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[5,4,3,1,2]
[1,1,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]=>[3,2,1,4,5]=>[3,2,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]=>[3,2,1,5,4]=>[5,3,2,1,4]
[1,1,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]=>[2,1,4,3,5]=>[4,2,1,3,5]
[1,1,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]=>[2,1,3,5,4]=>[5,2,1,3,4]
[1,1,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]=>[2,1,5,4,3]=>[5,4,2,1,3]
[1,1,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]=>[1,4,3,2,5]=>[4,3,1,2,5]
[1,1,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]=>[1,3,2,5,4]=>[5,3,1,2,4]
[1,1,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]=>[1,2,5,4,3]=>[5,4,1,2,3]
[1,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[5,4,3,1,2]
[1,1,1,1,0,0,0,0,1,0]=>[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]=>[4,3,2,1,5]=>[4,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]=>[3,2,1,5,4]=>[5,3,2,1,4]
[1,1,1,1,0,0,1,0,0,0]=>[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]=>[2,1,5,4,3]=>[5,4,2,1,3]
[1,1,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]=>[1,5,4,3,2]=>[5,4,3,1,2]
[1,1,1,1,1,0,0,0,0,0]=>[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]=>[5,4,3,2,1]=>[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]=>[6,1,2,3,4,5]
[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]=>[5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[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]=>[4,1,2,3,5,6]
[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]=>[6,4,1,2,3,5]
[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]=>[5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[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]=>[3,1,2,4,5,6]
[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]=>[6,3,1,2,4,5]
[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]=>[5,3,1,2,4,6]
[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]=>[6,3,1,2,4,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[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]=>[4,1,2,3,5,6]
[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]=>[6,4,1,2,3,5]
[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]=>[5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]
[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]=>[6,2,1,3,4,5]
[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]=>[5,2,1,3,4,6]
[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]=>[6,2,1,3,4,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]
[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]=>[4,2,1,3,5,6]
[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]=>[6,4,2,1,3,5]
[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]=>[5,2,1,3,4,6]
[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]=>[6,2,1,3,4,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]
[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]=>[3,1,2,4,5,6]
[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]=>[6,3,1,2,4,5]
[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]=>[5,3,1,2,4,6]
[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]=>[6,3,1,2,4,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[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]=>[4,1,2,3,5,6]
[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]=>[6,4,1,2,3,5]
[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]=>[5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,0,0,-1,1,0],[0,0,0,1,0,0]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]]=>[6,5,4,3,2,1]=>[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]=>[7,1,2,3,4,5,6]
[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]=>[6,1,2,3,4,5,7]
[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]=>[7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[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]=>[5,1,2,3,4,6,7]
[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]=>[7,5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5,7]
[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]=>[7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[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]=>[4,1,2,3,5,6,7]
[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]=>[7,4,1,2,3,5,6]
[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]=>[6,4,1,2,3,5,7]
[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]=>[7,4,1,2,3,5,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[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]=>[5,1,2,3,4,6,7]
[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]=>[7,5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5,7]
[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]=>[7,1,2,3,4,5,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[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]=>[3,1,2,4,5,6,7]
[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]=>[7,3,1,2,4,5,6]
[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]=>[6,3,1,2,4,5,7]
[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]=>[7,3,1,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[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]=>[5,3,1,2,4,6,7]
[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]=>[7,5,3,1,2,4,6]
[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]=>[6,3,1,2,4,5,7]
[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]=>[7,3,1,2,4,5,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[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]=>[4,1,2,3,5,6,7]
[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]=>[7,4,1,2,3,5,6]
[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]=>[6,4,1,2,3,5,7]
[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]=>[7,4,1,2,3,5,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[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]=>[5,1,2,3,4,6,7]
[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]=>[7,5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5,7]
[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]=>[7,1,2,3,4,5,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]
[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]=>[7,2,1,3,4,5,6]
[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]=>[6,2,1,3,4,5,7]
[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]=>[7,2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[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]=>[5,2,1,3,4,6,7]
[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]=>[7,5,2,1,3,4,6]
[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]=>[6,2,1,3,4,5,7]
[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]=>[7,2,1,3,4,5,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[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]=>[4,2,1,3,5,6,7]
[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]=>[7,4,2,1,3,5,6]
[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]=>[6,4,2,1,3,5,7]
[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]=>[7,4,2,1,3,5,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[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]=>[5,2,1,3,4,6,7]
[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]=>[7,5,2,1,3,4,6]
[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]=>[6,2,1,3,4,5,7]
[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]=>[7,2,1,3,4,5,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]
[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]=>[3,1,2,4,5,6,7]
[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]=>[7,3,1,2,4,5,6]
[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]=>[6,3,1,2,4,5,7]
[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]=>[7,3,1,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[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]=>[5,3,1,2,4,6,7]
[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]=>[7,5,3,1,2,4,6]
[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]=>[6,3,1,2,4,5,7]
[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]=>[7,3,1,2,4,5,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[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]=>[4,1,2,3,5,6,7]
[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]=>[7,4,1,2,3,5,6]
[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]=>[6,4,1,2,3,5,7]
[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]=>[7,4,1,2,3,5,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[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]=>[5,1,2,3,4,6,7]
[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]=>[7,5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5,7]
[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]=>[7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0],[1,-1,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7]=>[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],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[1,-1,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,1,0],[1,-1,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0],[0,1,-1,0,0,0,1],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7]=>[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],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,1,0,0],[1,0,-1,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,1,0],[1,0,-1,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,-1,0,0,1],[1,0,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,-1,0,1],[0,1,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,0,1],[1,-1,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,1,-1,0,1,-1,1],[1,-1,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[1,-1,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7]=>[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],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,1,0],[1,0,0,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,-1,0,1],[1,0,0,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,1,0,-1,1,-1,1],[1,0,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,1,0,-1,0,1,0],[1,0,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,-1,1],[0,1,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,-1,1],[1,-1,1,0,-1,1,0],[0,1,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,1,-1,1,-1,1,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7]=>[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],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,-1,1],[0,0,0,0,0,1,0]]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,-1,1],[1,0,0,0,-1,1,0],[0,0,0,0,1,0,0]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,1,0,0,-1,1,0],[1,0,0,-1,1,0,0],[0,0,0,1,0,0,0]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,1,0,-1,1,0,0],[1,0,-1,1,0,0,0],[0,0,1,0,0,0,0]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0]]=>[7,6,5,4,3,2,1]=>[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]=>[8,1,2,3,4,5,6,7]
[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]=>[8,1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[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]=>[6,1,2,3,4,5,7,8]
[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]=>[8,6,1,2,3,4,5,7]
[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]=>[7,1,2,3,4,5,6,8]
[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]=>[8,1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[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]=>[8,5,1,2,3,4,6,7]
[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]=>[8,1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[8,5,1,2,3,4,6,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]
[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]=>[8,4,1,2,3,5,6,7]
[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]=>[8,4,1,2,3,5,6,7]
[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]=>[8,1,2,3,4,5,6,7]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[8,4,1,2,3,5,6,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[8,5,1,2,3,4,6,7]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,4,3,6,8,7]=>[8,5,4,1,2,3,6,7]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[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]=>[8,3,1,2,4,5,6,7]
[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]=>[8,3,1,2,4,5,6,7]
[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]=>[8,4,1,2,3,5,6,7]
[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]=>[8,4,1,2,3,5,6,7]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]
[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]=>[8,1,2,3,4,5,6,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[8,3,1,2,4,5,6,7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,5,4,3,8,7,6]=>[8,7,5,4,1,2,3,6]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,7,6,8]=>[7,4,1,2,3,5,6,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[8,4,1,2,3,5,6,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[6,5,1,2,3,4,7,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,4,3,2,5,6,8,7]=>[8,4,3,1,2,5,6,7]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,3,2,4,5,8,7,6]=>[8,7,3,1,2,4,5,6]
[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],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,6,5,4,3,8,7]=>[8,6,5,4,1,2,3,7]
[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],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,4,3,5,8,7,6]=>[8,7,4,1,2,3,5,6]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,6,5,4,3,2,7,8]=>[6,5,4,3,1,2,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,4,3,2,5,8,7,6]=>[8,7,4,3,1,2,5,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,-1,1],[0,1,-1,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]
[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]=>[8,2,1,3,4,5,6,7]
[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]=>[7,2,1,3,4,5,6,8]
[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]=>[8,2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[8,7,2,1,3,4,5,6]
[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]=>[6,2,1,3,4,5,7,8]
[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]=>[8,2,1,3,4,5,6,7]
[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]=>[8,2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[8,7,2,1,3,4,5,6]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]
[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]=>[8,2,1,3,4,5,6,7]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7,8]=>[5,4,2,1,3,6,7,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,4,3,5,6,8,7]=>[8,4,2,1,3,5,6,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[8,7,2,1,3,4,5,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[2,1,7,6,5,4,3,8]=>[7,6,5,4,2,1,3,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,4,2,1,3]
[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]=>[3,1,2,4,5,6,7,8]
[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]=>[8,3,1,2,4,5,6,7]
[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]=>[8,3,1,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]
[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]=>[4,1,2,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,4,3,5,8,7,6]=>[8,7,4,1,2,3,5,6]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]
[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]=>[5,1,2,3,4,6,7,8]
[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]=>[8,5,1,2,3,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,5,4,8,7,6]=>[8,7,5,1,2,3,4,6]
[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]=>[6,1,2,3,4,5,7,8]
[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]=>[8,6,1,2,3,4,5,7]
[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]=>[7,1,2,3,4,5,6,8]
[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]=>[8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[6,5,1,2,3,4,7,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,8,7]=>[8,5,1,2,3,4,6,7]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[8,4,1,2,3,5,6,7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[6,5,1,2,3,4,7,8]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,6,5,4,3,7,8]=>[6,5,4,1,2,3,7,8]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[8,3,1,2,4,5,6,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[8,4,1,2,3,5,6,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[6,5,1,2,3,4,7,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[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],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,5,4,3,2,6,8,7]=>[8,5,4,3,1,2,6,7]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,5,4,3,2,8,7,6]=>[8,7,5,4,3,1,2,6]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7,8]=>[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],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,4,5,6,8,7]=>[8,3,2,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,4,5,6,8,7]=>[8,3,2,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[3,2,1,4,5,8,7,6]=>[8,7,3,2,1,4,5,6]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[3,2,1,4,5,8,7,6]=>[8,7,3,2,1,4,5,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[3,2,1,8,7,6,5,4]=>[8,7,6,5,3,2,1,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,4,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,4,3,8,7,6,5]=>[8,7,6,4,2,1,3,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,5,4,6,7,8]=>[5,2,1,3,4,6,7,8]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,4,6,5,7,8]=>[6,2,1,3,4,5,7,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,7,6,8]=>[7,2,1,3,4,5,6,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,8,7]=>[8,2,1,3,4,5,6,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,4,3,5,6,8,7]=>[8,4,2,1,3,5,6,7]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[8,7,2,1,3,4,5,6]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,-1,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,3,2,4,5,7,6,8]=>[7,3,1,2,4,5,6,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,8,7]=>[8,3,1,2,4,5,6,7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,4,3,6,8,7]=>[8,5,4,1,2,3,6,7]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,4,3,6,5,7,8]=>[6,4,1,2,3,5,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,6,5,8,7]=>[8,6,4,1,2,3,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,4,3,5,7,6,8]=>[7,4,1,2,3,5,6,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,8,7]=>[8,4,1,2,3,5,6,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,6,5,4,7,8]=>[6,5,1,2,3,4,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,-1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,5,4,8,7,6]=>[8,7,5,1,2,3,4,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,8,7]=>[8,6,1,2,3,4,5,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,2,6,5,4,3,8,7]=>[8,6,5,4,1,2,3,7]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,1,-1,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,4,3,2,5,8,7,6]=>[8,7,4,3,1,2,5,6]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,0,1],[0,1,0,0,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,1,0,0,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[1,5,4,3,2,8,7,6]=>[8,7,5,4,3,1,2,6]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0],[0,1,-1,0,0,0,0,1],[1,-1,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7,8]=>[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],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[4,3,2,1,5,6,8,7]=>[8,4,3,2,1,5,6,7]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[4,3,2,1,5,8,7,6]=>[8,7,4,3,2,1,5,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[4,3,2,1,8,7,6,5]=>[8,7,6,4,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7,8]=>[5,3,2,1,4,6,7,8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,-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]]=>[3,2,1,4,6,5,7,8]=>[6,3,2,1,4,5,7,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,7,6,8]=>[7,3,2,1,4,5,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,4,5,6,8,7]=>[8,3,2,1,4,5,6,7]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[2,1,5,4,3,6,7,8]=>[5,4,2,1,3,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,5,4,3,8,7,6]=>[8,7,5,4,2,1,3,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,3,4,6,5,8,7]=>[8,6,2,1,3,4,5,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,8,7,6]=>[8,7,2,1,3,4,5,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,0,1,0,0],[1,0,-1,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,0,0,1,0],[1,0,-1,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[1,5,4,3,2,8,7,6]=>[8,7,5,4,3,1,2,6]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,4,3,2,5,6,8,7]=>[8,4,3,1,2,5,6,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,5,4,3,6,8,7]=>[8,5,4,1,2,3,6,7]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,-1,0,1],[0,0,1,0,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,0,1],[0,1,-1,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,-1,0,1],[0,0,1,0,-1,0,1,0],[0,1,0,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,-1,0,1],[1,-1,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0],[0,0,1,-1,0,0,0,1],[0,1,-1,0,0,0,1,0],[1,-1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7,8]=>[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],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[5,4,3,2,1,6,8,7]=>[8,5,4,3,2,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0]]=>[5,4,3,2,1,8,7,6]=>[8,7,5,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7,8]=>[6,4,3,2,1,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,7,6,8]=>[7,4,3,2,1,5,6,8]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,-1,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]]=>[4,3,2,1,5,8,7,6]=>[8,7,4,3,2,1,5,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,6,5,4,7,8]=>[6,5,3,2,1,4,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,-1,1,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,3,5,4,8,7,6]=>[8,7,5,2,1,3,4,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,-1,1,0],[1,0,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,-1,0,1,0],[0,1,0,-1,0,1,-1,1],[1,0,-1,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,-1,0,1],[0,1,0,0,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,-1,1,0],[1,-1,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,-1,0,1],[1,-1,1,0,-1,0,1,0],[0,1,0,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,2,6,5,4,3,8,7]=>[8,6,5,4,1,2,3,7]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,0,1],[0,1,-1,1,-1,0,1,0],[1,-1,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,-1,1],[1,-1,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[1,3,2,8,7,6,5,4]=>[8,7,6,5,3,1,2,4]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,1,-1,0,0,1,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7,8]=>[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],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]=>[6,5,4,3,2,1,8,7]=>[8,6,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,7,6,8]=>[7,5,4,3,2,1,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]=>[5,4,3,2,1,6,8,7]=>[8,5,4,3,2,1,6,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,-1,1,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]]=>[4,3,2,1,7,6,5,8]=>[7,6,4,3,2,1,5,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[3,2,1,7,6,5,4,8]=>[7,6,5,3,2,1,4,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[3,2,1,6,5,4,8,7]=>[8,6,5,3,2,1,4,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[2,1,7,6,5,4,3,8]=>[7,6,5,4,2,1,3,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[2,1,5,4,3,8,7,6]=>[8,7,5,4,2,1,3,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,-1,1],[1,0,-1,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[2,1,4,3,8,7,6,5]=>[8,7,6,4,2,1,3,5]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[1,6,5,4,3,2,8,7]=>[8,6,5,4,3,1,2,7]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]]=>[7,6,5,4,3,2,1,8]=>[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],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,1,0]]=>[6,5,4,3,2,1,8,7]=>[8,6,5,4,3,2,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,-1,1],[1,0,0,0,0,-1,1,0],[0,0,0,0,0,1,0,0]]=>[5,4,3,2,1,8,7,6]=>[8,7,5,4,3,2,1,6]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,1,0,0,0,-1,1,0],[1,0,0,0,-1,1,0,0],[0,0,0,0,1,0,0,0]]=>[4,3,2,1,8,7,6,5]=>[8,7,6,4,3,2,1,5]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,1,0,0,-1,1,0],[0,1,0,0,-1,1,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,0,0,0,0]]=>[3,2,1,8,7,6,5,4]=>[8,7,6,5,3,2,1,4]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,-1,1],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0]]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,4,2,1,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]]=>[8,7,6,5,4,3,2,1]=>[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[8,7,6,5,4,3,2,1,9]=>[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],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]=>[9,8,7,6,5,4,3,2,1,10]=>[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],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]=>[10,9,8,7,6,5,4,3,2,1,11]=>[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],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,9,8,7,6,5,4,3,2,10]=>[9,8,7,6,5,4,3,1,2,10]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,8,7,6,5,4,3,9]=>[8,7,6,5,4,2,1,3,9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[9,8,7,6,5,3,1,2,4]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[1,2,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,1,2,3]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,3,1,2]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,6,5,1,2,3,4]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[1,2,3,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,1,2,3,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,-1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,8,7,9]=>[8,6,5,4,3,2,1,7,9]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[7,6,5,4,3,2,1,9,8]=>[9,7,6,5,4,3,2,1,8]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[2,1,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,2,1,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[7,6,5,4,3,2,1,8,9]=>[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[9,7,6,5,4,3,1,2,8]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,6,1,2,3,4,5]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0]]=>[8,7,6,5,4,3,2,1,10,9]=>[10,8,7,6,5,4,3,2,1,9]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[2,1,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,2,1,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[8,7,6,5,4,3,2,1,9,10]=>[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]=>[9,1,2,3,4,5,6,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[9,7,1,2,3,4,5,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,7,9,8]=>[9,6,1,2,3,4,5,7,8]
[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],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[9,7,1,2,3,4,5,6,8]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[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],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,7,6,5,9,8]=>[9,7,6,1,2,3,4,5,8]
[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],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[9,3,1,2,4,5,6,7,8]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[9,7,6,5,4,3,1,2,8]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[9,8,7,6,5,3,1,2,4]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,7,9,8]=>[9,2,1,3,4,5,6,7,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[9,3,1,2,4,5,6,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[9,7,1,2,3,4,5,6,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,0,1],[0,0,1,-1,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,0,0,0,0,0,1],[1,-1,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0,0,0],[0,1,-1,1,0,-1,1,0,0],[0,0,1,0,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,4,3,5,6,9,8,7]=>[9,8,4,1,2,3,5,6,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,0,1],[0,0,1,-1,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]
[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],[0,0,1,-1,0,0,0,0,1],[0,1,-1,0,0,0,0,1,0],[1,-1,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,0,1],[1,-1,1,-1,1,-1,0,1,0],[0,1,-1,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,6,5,1,2,3,4]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,-1,0,1],[0,1,-1,0,1,-1,0,1,0],[1,-1,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,0,0,0,1],[0,0,1,-1,0,0,0,1,0],[0,1,-1,0,0,0,1,0,0],[1,-1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,-1,0,1],[0,1,-1,1,0,-1,0,1,0],[1,-1,1,0,-1,0,1,0,0],[0,1,0,-1,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[9,8,7,6,5,3,1,2,4]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,-1,0,1],[0,0,1,-1,1,-1,0,1,0],[0,1,-1,1,-1,0,1,0,0],[1,-1,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[9,7,6,5,4,3,1,2,8]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,-1,1],[0,1,-1,0,1,0,-1,1,0],[1,-1,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[9,8,7,6,5,3,1,2,4]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,-1,0,0,1],[0,0,0,1,-1,0,0,1,0],[0,0,1,-1,0,0,1,0,0],[0,1,-1,0,0,1,0,0,0],[1,-1,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[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],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[9,7,6,5,4,3,1,2,8]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,1,-1,0,1,0],[0,0,0,1,-1,0,1,0,0],[0,0,1,-1,0,1,0,0,0],[0,1,-1,0,1,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[7,6,5,4,3,2,1,9,8]=>[9,7,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[1,0,0,0,0,0,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[6,5,4,3,2,1,9,8,7]=>[9,8,6,5,4,3,2,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,-1,1],[0,1,0,0,0,0,-1,1,0],[1,0,0,0,0,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[5,4,3,2,1,9,8,7,6]=>[9,8,7,5,4,3,2,1,6]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,-1,1],[0,0,1,0,0,0,-1,1,0],[0,1,0,0,0,-1,1,0,0],[1,0,0,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[4,3,2,1,9,8,7,6,5]=>[9,8,7,6,4,3,2,1,5]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,-1,1],[0,0,0,1,0,0,-1,1,0],[0,0,1,0,0,-1,1,0,0],[0,1,0,0,-1,1,0,0,0],[1,0,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[3,2,1,9,8,7,6,5,4]=>[9,8,7,6,5,3,2,1,4]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0]]=>[2,1,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,2,1,3]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0]]=>[9,8,7,6,5,4,3,2,1]=>[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]=>[9,1,2,3,4,5,6,7,8]
[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]=>[9,1,2,3,4,5,6,7,8]
[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]=>[9,1,2,3,4,5,6,7,8]
[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]=>[9,1,2,3,4,5,6,7,8]
[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]=>[9,1,2,3,4,5,6,7,8]
[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]=>[9,1,2,3,4,5,6,7,8]
[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]=>[9,1,2,3,4,5,6,7,8]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[9,7,1,2,3,4,5,6,8]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[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],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,6,5,7,9,8]=>[9,6,1,2,3,4,5,7,8]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[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],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,5,4,6,7,9,8]=>[9,5,1,2,3,4,6,7,8]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[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],[0,0,0,1,0,0,0,0,0],[0,0,1,0,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,4,3,5,6,7,9,8]=>[9,4,1,2,3,5,6,7,8]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,3,2,4,5,6,7,9,8]=>[9,3,1,2,4,5,6,7,8]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[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]=>[10,1,2,3,4,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[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]=>[10,1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[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]=>[11,1,2,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[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]=>[11,1,2,3,4,5,6,7,8,9,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[2,1,3,4,5,6,7,8,10,9]=>[10,2,1,3,4,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[0,1,0,0,0,0,0,0,0,0,0],[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]=>[11,1,2,3,4,5,6,7,8,9,10]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,7,6,9,8]=>[9,7,1,2,3,4,5,6,8]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,1,2,3,4,5,6,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[1,-1,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,5,6,8,7,10,9]=>[10,8,1,2,3,4,5,6,7,9]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[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]=>[9,7,1,2,3,4,5,6,8]
[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]=>[5,1,2,3,4,6,7,8,9]
[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]=>[4,1,2,3,5,6,7,8,9]
[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]=>[9,3,1,2,4,5,6,7,8]
[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]=>[5,3,1,2,4,6,7,8,9]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[9,7,6,5,4,3,1,2,8]
[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]=>[9,2,1,3,4,5,6,7,8]
[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]=>[8,2,1,3,4,5,6,7,9]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,8,7,6,5,4,3,9]=>[8,7,6,5,4,2,1,3,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7,8,9]=>[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],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[3,2,1,9,8,7,6,5,4]=>[9,8,7,6,5,3,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7,8,9]=>[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],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[4,3,2,1,9,8,7,6,5]=>[9,8,7,6,4,3,2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7,8,9]=>[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],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[5,4,3,2,1,9,8,7,6]=>[9,8,7,5,4,3,2,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7,8,9]=>[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],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[6,5,4,3,2,1,9,8,7]=>[9,8,6,5,4,3,2,1,7]
[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]=>[7,1,2,3,4,5,6,8,9,10]
[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]=>[10,2,1,3,4,5,6,7,8,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[3,2,1,4,5,6,7,8,9,10]=>[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],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[3,2,1,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,3,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[4,3,2,1,5,6,7,8,9,10]=>[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],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[4,3,2,1,10,9,8,7,6,5]=>[10,9,8,7,6,4,3,2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,6,7,8,9,10]=>[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],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[5,4,3,2,1,10,9,8,7,6]=>[10,9,8,7,5,4,3,2,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[6,5,4,3,2,1,7,8,9,10]=>[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],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[6,5,4,3,2,1,10,9,8,7]=>[10,9,8,6,5,4,3,2,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[7,6,5,4,3,2,1,8,9,10]=>[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],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[7,6,5,4,3,2,1,10,9,8]=>[10,9,7,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0]]=>[10,9,8,7,6,5,4,3,2,1]=>[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]=>[3,1,2,4,5,6,7,8,9]
[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]=>[4,1,2,3,5,6,7,8,9]
[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]=>[5,1,2,3,4,6,7,8,9]
[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]=>[6,1,2,3,4,5,7,8,9]
[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]=>[7,1,2,3,4,5,6,8,9]
[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]=>[8,1,2,3,4,5,6,7,9]
[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]=>[3,1,2,4,5,6,7,8,9,10]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]
[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]=>[4,1,2,3,5,6,7,8,9,10]
[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]=>[5,1,2,3,4,6,7,8,9,10]
[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]=>[6,1,2,3,4,5,7,8,9,10]
[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]=>[7,1,2,3,4,5,6,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]=>[1,2,3,4,5,6,8,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]
[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]=>[9,1,2,3,4,5,6,7,8,10]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,-1,1,-1,0,1],[0,1,-1,1,-1,1,-1,0,1,0],[0,0,1,-1,1,-1,0,1,0,0],[0,0,0,1,-1,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,6,1,2,3,4,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[1,-1,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,0,1],[0,0,0,1,-1,1,-1,0,1,0],[0,0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,1,2,3,4,5,6]
[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]=>[9,2,1,3,4,5,6,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,-1,0,1,0],[0,0,0,0,1,-1,0,1,0,0],[0,0,0,1,-1,0,1,0,0,0],[0,0,1,-1,0,1,0,0,0,0],[0,1,-1,0,1,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0,0,0],[0,1,0,-1,1,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[2,1,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,2,1,3]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,1,-1,0,1,0],[0,0,0,0,0,1,-1,0,1,0,0],[0,0,0,0,1,-1,0,1,0,0,0],[0,0,0,1,-1,0,1,0,0,0,0],[0,0,1,-1,0,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,0,1],[0,0,0,1,-1,1,-1,0,1,0],[0,0,1,-1,1,-1,0,1,0,0],[0,1,-1,1,-1,0,1,0,0,0],[1,-1,1,-1,0,1,0,0,0,0],[0,1,-1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0]]=>[1,2,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,1,2,3]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,-1,1,0,0,0],[0,0,0,1,0,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0]]=>[2,1,11,10,9,8,7,6,5,4,3]=>[11,10,9,8,7,6,5,4,2,1,3]
[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]=>[10,2,1,3,4,5,6,7,8,9]
[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]=>[9,3,1,2,4,5,6,7,8]
[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]=>[9,3,1,2,4,5,6,7,8]
[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]=>[9,3,1,2,4,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[1,4,3,2,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,0,1,0]]=>[8,7,6,5,4,3,2,1,10,9]=>[10,8,7,6,5,4,3,2,1,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,0,0,1,0]]=>[9,8,7,6,5,4,3,2,1,11,10]=>[11,9,8,7,6,5,4,3,2,1,10]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,-1,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[5,4,3,2,1,7,6,8,9]=>[7,5,4,3,2,1,6,8,9]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[4,3,2,1,6,5,7,8,9]=>[6,4,3,2,1,5,7,8,9]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[3,2,1,5,4,6,7,8,9]=>[5,3,2,1,4,6,7,8,9]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,4,3,5,6,7,8,9]=>[4,2,1,3,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,0,0,1],[0,0,0,0,1,-1,0,0,1,0],[0,0,0,1,-1,0,0,1,0,0],[0,0,1,-1,0,0,1,0,0,0],[0,1,-1,0,0,1,0,0,0,0],[1,-1,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,-1,0,0,0,1],[0,0,0,1,-1,0,0,0,1,0],[0,0,1,-1,0,0,0,1,0,0],[0,1,-1,0,0,0,1,0,0,0],[1,-1,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,0,0,0,0,1],[0,0,1,-1,0,0,0,0,1,0],[0,1,-1,0,0,0,0,1,0,0],[1,-1,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,0,0,0,0,0,1],[0,1,-1,0,0,0,0,0,1,0],[1,-1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0,0],[0,1,-1,0,0,0,0,0,0,1],[1,-1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]
[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],[0,1,-1,1,0,0,0,0,0],[1,-1,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,2,3,4,7,6,5,9,8]=>[9,7,6,1,2,3,4,5,8]
[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],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[2,1,3,4,5,6,9,8,7]=>[9,8,2,1,3,4,5,6,7]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,3,1,2]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0]]=>[1,3,2,9,8,7,6,5,4]=>[9,8,7,6,5,3,1,2,4]
[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]=>[5,1,2,3,4,6,7,8,9]
[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]=>[5,1,2,3,4,6,7,8,9]
[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]=>[8,1,2,3,4,5,6,7,9,10]
[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]=>[9,1,2,3,4,5,6,7,8,10]
[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]=>[9,5,1,2,3,4,6,7,8]
[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],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,1,2,3,4,5,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,-1,1,0,0,0],[0,1,0,-1,1,-1,1,0,0],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,3,2,4,5,6,9,8,7]=>[9,8,3,1,2,4,5,6,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]=>[2,1,3,4,5,6,8,7,9]=>[8,2,1,3,4,5,6,7,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]
[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]=>[9,7,1,2,3,4,5,6,8]
[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]=>[9,2,1,3,4,5,6,7,8]
[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],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[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],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,0,0,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,0,0,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0,0],[1,-1,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[1,-1,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,0,0,0,1,0,0],[1,-1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0]]=>[1,7,6,5,4,3,2,9,8]=>[9,7,6,5,4,3,1,2,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,-1,1],[1,0,0,0,0,0,0,-1,1,0],[0,0,0,0,0,0,0,1,0,0]]=>[7,6,5,4,3,2,1,10,9,8]=>[10,9,7,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,-1,1],[0,1,0,0,0,0,0,-1,1,0],[1,0,0,0,0,0,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]]=>[6,5,4,3,2,1,10,9,8,7]=>[10,9,8,6,5,4,3,2,1,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,-1,1],[0,0,1,0,0,0,0,-1,1,0],[0,1,0,0,0,0,-1,1,0,0],[1,0,0,0,0,-1,1,0,0,0],[0,0,0,0,0,1,0,0,0,0]]=>[5,4,3,2,1,10,9,8,7,6]=>[10,9,8,7,5,4,3,2,1,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,-1,1],[0,0,0,1,0,0,0,-1,1,0],[0,0,1,0,0,0,-1,1,0,0],[0,1,0,0,0,-1,1,0,0,0],[1,0,0,0,-1,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]]=>[4,3,2,1,10,9,8,7,6,5]=>[10,9,8,7,6,4,3,2,1,5]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1,0,0],[0,0,1,0,0,-1,1,0,0,0],[0,1,0,0,-1,1,0,0,0,0],[1,0,0,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[3,2,1,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,3,2,1,4]
Map
to symmetric ASM
Description
The diagonally symmetric alternating sign matrix corresponding to a Dyck path.
Map
to left key permutation
Description
Return the permutation of the left key of an alternating sign matrix.
This was originally defined by Lascoux and then further studied by Aval [1].
This was originally defined by Lascoux and then further studied by Aval [1].
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
searching the database
Sorry, this map was not found in the database.