Identifier
Mp00137:
Dyck paths
—to symmetric ASM⟶
Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
=>
Cc0005;cc-rep-0Cc0017;cc-rep-1
[1,0]=>[[1]]=>[1]=>
[1,0,1,0]=>[[1,0],[0,1]]=>[1,2]=>0
[1,1,0,0]=>[[0,1],[1,0]]=>[2,1]=>1
[1,0,1,0,1,0]=>[[1,0,0],[0,1,0],[0,0,1]]=>[1,2,3]=>00
[1,0,1,1,0,0]=>[[1,0,0],[0,0,1],[0,1,0]]=>[1,3,2]=>01
[1,1,0,0,1,0]=>[[0,1,0],[1,0,0],[0,0,1]]=>[2,1,3]=>10
[1,1,0,1,0,0]=>[[0,1,0],[1,-1,1],[0,1,0]]=>[1,3,2]=>01
[1,1,1,0,0,0]=>[[0,0,1],[0,1,0],[1,0,0]]=>[3,2,1]=>11
[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]=>000
[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]=>001
[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]=>010
[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]=>001
[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]=>011
[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]=>100
[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]=>101
[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]=>010
[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]=>001
[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]=>011
[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]=>110
[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]=>101
[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]=>011
[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]=>111
[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]=>0000
[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]=>0001
[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]=>0010
[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]=>0001
[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]=>0011
[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]=>0100
[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]=>0101
[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]=>0010
[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]=>0001
[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]=>0011
[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]=>0110
[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]=>0101
[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]=>0011
[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]=>0111
[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]=>1000
[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]=>1001
[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]=>1010
[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]=>1001
[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]=>1011
[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]=>0100
[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]=>0101
[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]=>0010
[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]=>0001
[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]=>0011
[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]=>0110
[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]=>0101
[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]=>0011
[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]=>0111
[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]=>1100
[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]=>1101
[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]=>1010
[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]=>1001
[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]=>1011
[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]=>0110
[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]=>0101
[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]=>0011
[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]=>0111
[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]=>1110
[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]=>1101
[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]=>1011
[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]=>0111
[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]=>1111
[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]=>00000
[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]=>00001
[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]=>00010
[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]=>00001
[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]=>00011
[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]=>00100
[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]=>00101
[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]=>00010
[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]=>00001
[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]=>00011
[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]=>00110
[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]=>00101
[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]=>00011
[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]=>00111
[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]=>01000
[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]=>01001
[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]=>01010
[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]=>01001
[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]=>01011
[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]=>00100
[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]=>00101
[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]=>00010
[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]=>00001
[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]=>00011
[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]=>00110
[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]=>00101
[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]=>00011
[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]=>00111
[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]=>01100
[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]=>01101
[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]=>01010
[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]=>01001
[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]=>01011
[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]=>00110
[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]=>00101
[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]=>00011
[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]=>00111
[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]=>01110
[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]=>01101
[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]=>01011
[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]=>00111
[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]=>01111
[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]=>10000
[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]=>10001
[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]=>10010
[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]=>10001
[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]=>10011
[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]=>10100
[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]=>10101
[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]=>10010
[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]=>10001
[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]=>10011
[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]=>10110
[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]=>10101
[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]=>10011
[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]=>10111
[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]=>01000
[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]=>01001
[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]=>01010
[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]=>01001
[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]=>01011
[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]=>00100
[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]=>00101
[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]=>00010
[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]=>00001
[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]=>00011
[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]=>00110
[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]=>00101
[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]=>00011
[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]=>00111
[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]=>01100
[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]=>01101
[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]=>01010
[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]=>01001
[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]=>01011
[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]=>00110
[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]=>00101
[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]=>00011
[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]=>00111
[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]=>01110
[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]=>01101
[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]=>01011
[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]=>00111
[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]=>01111
[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]=>11000
[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]=>11001
[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]=>11010
[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]=>11001
[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]=>11011
[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]=>10100
[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]=>10101
[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]=>10010
[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]=>10001
[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]=>10011
[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]=>10110
[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]=>10101
[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]=>10011
[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]=>10111
[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]=>01100
[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]=>01101
[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]=>01010
[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]=>01001
[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]=>01011
[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]=>00110
[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]=>00101
[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]=>00011
[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]=>00111
[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]=>01110
[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]=>01101
[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]=>01011
[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]=>00111
[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]=>01111
[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]=>11100
[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]=>11101
[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]=>11010
[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]=>11001
[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]=>11011
[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]=>10110
[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]=>10101
[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]=>10011
[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]=>10111
[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]=>01110
[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]=>01101
[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]=>01011
[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]=>00111
[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]=>01111
[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]=>11110
[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]=>11101
[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]=>11011
[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]=>10111
[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]=>01111
[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]=>11111
[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]=>000000
[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]=>000001
[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]=>000010
[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]=>000001
[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]=>000011
[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]=>000100
[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]=>000101
[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]=>000010
[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]=>000001
[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]=>000011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001000
[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]=>001001
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000100
[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]=>000101
[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]=>000010
[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]=>000001
[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]=>000011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001100
[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]=>001101
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>010000
[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]=>010001
[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]=>010010
[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]=>010001
[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]=>010011
[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]=>010100
[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]=>010101
[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]=>010010
[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]=>010001
[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]=>010011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001000
[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]=>001001
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000100
[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]=>000101
[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]=>000010
[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]=>000001
[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]=>000011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001100
[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]=>001101
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011000
[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]=>011001
[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]=>011010
[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]=>011001
[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]=>011011
[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]=>010100
[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]=>010101
[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]=>010010
[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]=>010001
[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]=>010011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001100
[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]=>001101
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011100
[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]=>011101
[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]=>011010
[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]=>011001
[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]=>011011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011110
[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]=>011101
[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]=>011011
[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]=>010111
[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]=>001111
[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]=>011111
[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]=>100000
[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]=>100001
[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]=>100010
[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]=>100001
[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]=>100011
[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]=>100100
[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]=>100101
[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]=>100010
[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]=>100001
[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]=>100011
[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]=>100110
[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]=>100101
[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]=>100011
[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]=>100111
[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]=>101000
[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]=>101001
[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]=>101010
[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]=>101001
[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]=>101011
[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]=>100100
[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]=>100101
[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]=>100010
[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]=>100001
[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]=>100011
[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]=>100110
[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]=>100101
[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]=>100111
[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]=>101100
[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]=>101101
[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]=>101010
[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]=>101001
[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]=>101011
[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]=>100110
[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]=>100101
[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]=>100011
[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]=>100111
[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]=>101110
[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]=>101101
[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]=>101011
[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]=>100111
[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]=>101111
[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]=>010000
[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]=>010001
[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]=>010010
[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]=>010001
[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]=>010011
[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]=>010100
[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]=>010101
[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]=>010010
[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]=>010001
[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]=>010011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001000
[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]=>001001
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000100
[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]=>000101
[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]=>000010
[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]=>000001
[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]=>000011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001100
[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]=>001101
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011000
[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]=>011001
[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]=>011010
[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]=>011001
[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]=>011011
[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]=>010100
[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]=>010101
[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]=>010010
[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]=>010001
[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]=>010011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001100
[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]=>001101
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011100
[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]=>011101
[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]=>011010
[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]=>011001
[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]=>011011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011110
[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]=>011101
[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]=>011011
[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]=>010111
[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]=>001111
[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]=>011111
[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]=>110000
[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]=>110001
[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]=>110010
[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]=>110001
[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]=>110011
[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]=>110100
[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]=>110101
[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]=>110010
[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]=>110001
[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]=>110011
[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]=>110110
[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]=>110101
[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]=>110011
[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]=>110111
[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]=>101000
[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]=>101001
[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]=>101010
[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]=>101001
[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]=>101011
[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]=>100100
[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]=>100101
[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]=>100010
[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]=>100001
[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]=>100011
[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]=>100110
[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]=>100101
[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]=>100011
[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]=>100111
[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]=>101100
[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]=>101101
[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]=>101010
[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]=>101001
[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]=>101011
[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]=>100110
[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]=>100101
[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]=>100011
[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]=>100111
[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]=>101110
[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]=>101101
[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]=>101011
[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]=>100111
[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]=>101111
[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]=>011000
[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]=>011001
[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]=>011010
[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]=>011001
[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]=>011011
[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]=>010100
[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]=>010101
[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]=>010010
[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]=>010001
[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]=>010011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001100
[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]=>001101
[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]=>001010
[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]=>001001
[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]=>001011
[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]=>000110
[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]=>000101
[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]=>000011
[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]=>000111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011100
[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]=>011101
[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]=>011010
[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]=>011001
[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]=>011011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011110
[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]=>011101
[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]=>011011
[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]=>010111
[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]=>001111
[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]=>011111
[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]=>111000
[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]=>111001
[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]=>111010
[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]=>111001
[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]=>111011
[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]=>110100
[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]=>110101
[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]=>110010
[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]=>110001
[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]=>110011
[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]=>110110
[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]=>110101
[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]=>110011
[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]=>110111
[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]=>101100
[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]=>101101
[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]=>101010
[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]=>101001
[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]=>101011
[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]=>100110
[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]=>100101
[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]=>100011
[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]=>100111
[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]=>101110
[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]=>101101
[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]=>101011
[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]=>100111
[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]=>101111
[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]=>011100
[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]=>011101
[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]=>011010
[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]=>011001
[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]=>011011
[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]=>010110
[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]=>010101
[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]=>010011
[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]=>010111
[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]=>001110
[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]=>001101
[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]=>001011
[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]=>000111
[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]=>001111
[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]=>011110
[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]=>011101
[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]=>011011
[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]=>010111
[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]=>001111
[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]=>011111
[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]=>111100
[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]=>111101
[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]=>111010
[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]=>111001
[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]=>111011
[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]=>110110
[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]=>110101
[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]=>110011
[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]=>110111
[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]=>101110
[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]=>101101
[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]=>101011
[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]=>100111
[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]=>101111
[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]=>011110
[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]=>011101
[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]=>011011
[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]=>010111
[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]=>001111
[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]=>011111
[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]=>111110
[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]=>111101
[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]=>111011
[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]=>110111
[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]=>101111
[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]=>011111
[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]=>111111
[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]=>0000000
[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]=>0000001
[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]=>0000001
[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]=>0000011
[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]=>0000100
[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]=>0000101
[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]=>0000010
[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]=>0000001
[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]=>0000011
[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]=>0000110
[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]=>0000101
[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]=>0000011
[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]=>0000111
[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]=>0001001
[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]=>0000001
[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]=>0001001
[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]=>0000101
[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]=>0001101
[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]=>0001111
[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]=>0010001
[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]=>0010001
[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]=>0000001
[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]=>0000011
[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]=>0011000
[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]=>0010001
[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]=>0001001
[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]=>0000101
[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]=>0011001
[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]=>0000111
[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]=>0011110
[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]=>0010111
[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]=>0001111
[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]=>0011111
[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]=>0100001
[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]=>0100001
[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]=>0010001
[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]=>0010001
[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]=>0010111
[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]=>0000001
[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]=>0000011
[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]=>0110000
[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]=>0100001
[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]=>0011000
[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]=>0011011
[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]=>0010010
[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]=>0010001
[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]=>0001100
[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]=>0000110
[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]=>0000101
[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]=>0000011
[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]=>0110001
[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]=>0100011
[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]=>0010011
[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]=>0000111
[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]=>0011111
[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]=>0111100
[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]=>0111101
[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]=>0110011
[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]=>0100111
[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]=>0011110
[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]=>0010111
[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]=>0001111
[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]=>0011111
[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]=>0111110
[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]=>0110111
[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]=>0101111
[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]=>0011111
[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]=>0111111
[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]=>1000000
[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]=>1000001
[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]=>1000010
[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]=>1000001
[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]=>1000011
[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]=>1000100
[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]=>1000001
[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]=>1000001
[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]=>1000011
[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]=>1000111
[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]=>1001111
[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]=>1000001
[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]=>1000111
[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]=>1001111
[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]=>1011000
[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]=>1010001
[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]=>1000011
[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]=>1000111
[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]=>1011110
[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]=>1011101
[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]=>1001111
[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]=>1011111
[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]=>0100000
[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]=>0100001
[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]=>0100001
[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]=>0100111
[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]=>0100111
[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]=>0101111
[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]=>0010000
[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]=>0010011
[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]=>0010111
[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]=>0001000
[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]=>0001001
[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]=>0001011
[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]=>0000100
[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]=>0000101
[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]=>0000010
[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]=>0000001
[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]=>0000011
[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]=>0000110
[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]=>0000101
[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]=>0000011
[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]=>0000111
[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]=>0001100
[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]=>0001001
[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]=>0000110
[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]=>0000011
[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]=>0000111
[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]=>0001110
[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]=>0000111
[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]=>0011000
[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]=>0010001
[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]=>0001100
[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]=>0000111
[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]=>0011100
[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]=>0000111
[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]=>0011110
[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]=>0110000
[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]=>0100001
[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]=>0011000
[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]=>0010001
[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]=>0001100
[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]=>0000110
[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]=>0000011
[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]=>0000111
[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]=>0000111
[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]=>0111000
[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]=>0000111
[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]=>0111101
[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]=>0111011
[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]=>0001111
[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]=>0111110
[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]=>0111101
[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]=>0101111
[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]=>0011111
[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]=>0111111
[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]=>1100000
[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]=>1100001
[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]=>1100001
[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]=>1100011
[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]=>1100011
[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]=>1100111
[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]=>1100111
[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]=>1101111
[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]=>1010000
[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]=>1010111
[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]=>1001000
[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]=>1000100
[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]=>1000010
[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]=>1000001
[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]=>1010001
[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]=>1000011
[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]=>1001111
[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]=>0110000
[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]=>0110111
[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]=>0100010
[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]=>0100001
[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]=>0011000
[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]=>0011001
[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]=>0010100
[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]=>0010101
[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]=>0010010
[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]=>0010001
[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]=>0001100
[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]=>0001101
[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]=>0001011
[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]=>0000110
[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]=>0000101
[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]=>0000011
[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]=>0000111
[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]=>0000111
[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]=>0001111
[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]=>0111101
[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]=>0110011
[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]=>0110111
[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]=>0011111
[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]=>0111011
[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]=>0101111
[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]=>0011111
[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]=>0111111
[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]=>1110000
[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]=>1110001
[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]=>1110011
[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]=>1110111
[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]=>1101000
[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]=>1100010
[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]=>1100001
[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]=>1100111
[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]=>1011000
[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]=>1011011
[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]=>1000101
[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]=>1000011
[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]=>1000111
[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]=>1001111
[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]=>0111011
[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]=>0110001
[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]=>0011001
[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]=>0010111
[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]=>0001101
[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]=>0000111
[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]=>0001111
[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]=>0100111
[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]=>0101111
[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]=>0011111
[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]=>0111110
[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]=>0111101
[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]=>0110111
[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]=>0111111
[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]=>1111000
[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]=>1111001
[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]=>1111011
[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]=>1110100
[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]=>1110010
[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]=>1110011
[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]=>1101100
[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]=>1011101
[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]=>1001011
[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]=>1000111
[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]=>1001111
[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]=>0111101
[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]=>0110111
[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]=>0100111
[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]=>0101111
[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]=>0011110
[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]=>0001111
[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]=>0011111
[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]=>0111110
[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]=>0111101
[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]=>0101111
[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]=>0111111
[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]=>1111100
[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]=>1111101
[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]=>1111010
[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]=>1111001
[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]=>1110110
[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]=>1101110
[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]=>1101101
[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]=>1011110
[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]=>1011101
[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]=>1011011
[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]=>1010111
[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]=>1001111
[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]=>0111110
[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]=>0111101
[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]=>0011111
[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]=>0111111
[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]=>1111110
[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]=>1111101
[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]=>1111011
[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]=>1110111
[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]=>1101111
[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]=>1011111
[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]=>0111111
[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]=>1111111
[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]=>11111110
[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]=>01111111
[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]=>111111110
[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]=>01111110
[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]=>00111111
[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]=>011111111
[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]=>1111111110
[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]=>011111110
[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]=>10111110
[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]=>01111110
[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]=>01011111
[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]=>00111111
[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]=>001111111
[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]=>0111111111
[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]=>00011111
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0,0,0],[0,1,0,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]]=>[1,3,2,10,9,8,7,6,5,4]=>010111111
[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]=>000111111
[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]=>11111010
[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]=>01111110
[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]=>11111101
[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]=>00001111
[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]=>10111111
[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]=>11111100
[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]=>01111110
[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]=>01111101
[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]=>000011111
[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]=>00111111
[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]=>111111101
[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]=>101111111
[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]=>111111100
[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]=>00000001
[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]=>00000011
[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]=>00000101
[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]=>00000011
[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]=>00000111
[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]=>00000101
[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]=>00000011
[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]=>00000111
[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]=>00000111
[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]=>00000111
[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]=>00000111
[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]=>01000001
[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]=>00000011
[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]=>00000111
[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]=>01111101
[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]=>01011111
[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]=>00111111
[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]=>01111111
[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]=>10000001
[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]=>01000001
[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]=>00000101
[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]=>00000011
[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]=>00001111
[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]=>01111111
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0,0,0],[0,0,1,-1,1,0,-1,0,1],[0,0,0,1,0,-1,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,5,4,9,8,7,6]=>00010111
[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]=>00000111
[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]=>00001111
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,0,0,0,1,0],[0,1,-1,0,0,0,1,0,0],[1,-1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,-1,1],[0,0,1,0,0,0,-1,1,0],[0,1,0,0,0,-1,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,5,4,3,2,9,8,7,6]=>01110111
[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]=>01111111
[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]=>00011111
[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]=>00111111
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,0,0,1,0],[0,0,1,-1,0,0,1,0,0],[0,1,-1,0,0,1,0,0,0],[1,-1,0,0,1,0,0,-1,1],[0,0,0,1,0,0,-1,1,0],[0,0,1,0,0,-1,1,0,0],[0,1,0,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,4,3,2,9,8,7,6,5]=>01101111
[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]=>01111111
[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]=>01011111
[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]=>00111111
[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]=>01111101
[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]=>01011111
[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]=>01111111
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,-1,1],[0,1,0,-1,1,0,-1,1,0],[1,0,-1,1,0,-1,1,0,0],[0,0,1,0,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[2,1,4,3,9,8,7,6,5]=>10101111
[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]=>01111101
[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]=>00111111
[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]=>01111111
[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]=>11111101
[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]=>11111011
[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]=>11110111
[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]=>11101111
[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]=>11011111
[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]=>10111111
[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]=>01111111
[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]=>11111111
[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]=>00000000
[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]=>00000001
[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]=>00000001
[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]=>00000001
[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]=>00000001
[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]=>00000001
[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]=>00000001
[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]=>00000001
[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]=>000000000
[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]=>000000001
[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]=>00000011
[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]=>000000001
[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]=>00000101
[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]=>000000001
[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]=>000000001
[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]=>000000001
[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]=>000000001
[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]=>01000001
[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]=>000000001
[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]=>000000001
[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]=>000000001
[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]=>0000000001
[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]=>0000000001
[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]=>100000001
[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]=>0000000001
[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]=>00000101
[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]=>00000011
[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]=>00000111
[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]=>000000011
[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]=>000000101
[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]=>000000111
[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]=>00000101
[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]=>00010000
[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]=>00100000
[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]=>01000001
[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]=>01010000
[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]=>01100000
[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]=>01111101
[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]=>10000000
[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]=>10000001
[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]=>10000010
[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]=>10111110
[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]=>11000000
[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]=>11011111
[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]=>11100000
[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]=>11101111
[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]=>11110000
[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]=>11110111
[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]=>11111000
[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]=>11111011
[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]=>000001000
[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]=>100000000
[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]=>100000001
[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]=>110000000
[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]=>110111111
[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]=>111000000
[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]=>111011111
[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]=>111100000
[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]=>111101111
[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]=>111110000
[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]=>111110111
[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]=>111111000
[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]=>111111011
[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]=>111111111
[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]=>01000000
[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]=>00100000
[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]=>00010000
[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]=>00001000
[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]=>00000100
[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]=>00000010
[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]=>010000000
[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]=>01100000
[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]=>001000000
[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]=>000100000
[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]=>000010000
[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]=>000001000
[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]=>000000100
[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]=>000000010
[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]=>000011111
[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]=>000001111
[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]=>1000000000
[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]=>10000001
[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]=>000000011
[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]=>011111111
[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]=>101111111
[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]=>0111111111
[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]=>001111111
[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]=>1011111111
[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]=>100000001
[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]=>01000001
[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]=>01000001
[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]=>01000001
[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]=>01100000
[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]=>011111111
[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]=>111111101
[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]=>1111111101
[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]=>11110100
[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]=>11101000
[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]=>11010000
[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]=>10100000
[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]=>011111111
[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]=>011111111
[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]=>011111111
[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]=>011111111
[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]=>011111111
[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]=>011111111
[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]=>000000011
[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]=>0111111111
[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]=>01011111
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0]]=>[1,4,3,2,9,8,7,6,5]=>01101111
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,5,4,3,2,9,8,7,6]=>01110111
[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]=>00010000
[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]=>00010000
[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]=>000000100
[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]=>000000010
[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]=>000001111
[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]=>01000011
[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]=>10000010
[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]=>00000011
[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]=>00000101
[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]=>10000001
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0]]=>[1,2,3,4,6,5,9,8,7]=>00001011
[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]=>000000111
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0]]=>[1,2,3,5,4,9,8,7,6]=>00010111
[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]=>000000111
[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]=>000000111
[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]=>000000111
[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]=>000000111
[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]=>000000111
[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]=>000000111
[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]=>01111101
[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]=>111111011
[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]=>111110111
[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]=>111101111
[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]=>111011111
[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]=>110111111
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
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
searching the database
Sorry, this map was not found in the database.