Identifier
Mp00137:
Dyck paths
—to symmetric ASM⟶
Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
[1,0] => [[1]] => [1] => [1] =>
[1,0,1,0] => [[1,0],[0,1]] => [1,2] => [1,2] => 0
[1,1,0,0] => [[0,1],[1,0]] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [[1,0,0],[0,1,0],[0,0,1]] => [1,2,3] => [1,2,3] => 00
[1,0,1,1,0,0] => [[1,0,0],[0,0,1],[0,1,0]] => [1,3,2] => [3,1,2] => 01
[1,1,0,0,1,0] => [[0,1,0],[1,0,0],[0,0,1]] => [2,1,3] => [2,1,3] => 10
[1,1,0,1,0,0] => [[0,1,0],[1,-1,1],[0,1,0]] => [1,3,2] => [3,1,2] => 01
[1,1,1,0,0,0] => [[0,0,1],[0,1,0],[1,0,0]] => [3,2,1] => [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] => [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] => [4,1,2,3] => 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] => [3,1,2,4] => 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] => [4,1,2,3] => 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] => [4,3,1,2] => 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] => [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] => [4,2,1,3] => 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] => [3,1,2,4] => 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] => [4,1,2,3] => 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] => [4,3,1,2] => 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] => [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] => [4,2,1,3] => 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] => [4,3,1,2] => 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] => [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] => [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] => [5,1,2,3,4] => 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] => [4,1,2,3,5] => 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] => [5,1,2,3,4] => 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] => [5,4,1,2,3] => 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] => [3,1,2,4,5] => 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] => [5,3,1,2,4] => 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] => [4,1,2,3,5] => 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] => [5,1,2,3,4] => 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] => [5,4,1,2,3] => 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] => [4,3,1,2,5] => 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] => [5,3,1,2,4] => 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] => [5,4,1,2,3] => 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] => [5,4,3,1,2] => 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] => [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] => [5,2,1,3,4] => 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] => [4,2,1,3,5] => 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] => [5,2,1,3,4] => 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] => [5,4,2,1,3] => 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] => [3,1,2,4,5] => 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] => [5,3,1,2,4] => 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] => [4,1,2,3,5] => 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] => [5,1,2,3,4] => 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] => [5,4,1,2,3] => 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] => [4,3,1,2,5] => 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] => [5,3,1,2,4] => 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] => [5,4,1,2,3] => 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] => [5,4,3,1,2] => 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] => [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] => [5,3,2,1,4] => 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] => [4,2,1,3,5] => 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] => [5,2,1,3,4] => 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] => [5,4,2,1,3] => 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] => [4,3,1,2,5] => 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] => [5,3,1,2,4] => 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] => [5,4,1,2,3] => 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] => [5,4,3,1,2] => 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] => [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] => [5,3,2,1,4] => 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] => [5,4,2,1,3] => 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] => [5,4,3,1,2] => 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] => [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] => [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] => [6,1,2,3,4,5] => 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] => [5,1,2,3,4,6] => 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] => [6,1,2,3,4,5] => 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] => [6,5,1,2,3,4] => 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] => [4,1,2,3,5,6] => 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] => [6,4,1,2,3,5] => 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] => [5,1,2,3,4,6] => 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] => [6,1,2,3,4,5] => 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] => [6,5,1,2,3,4] => 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] => [5,4,1,2,3,6] => 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] => [6,4,1,2,3,5] => 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] => [6,5,1,2,3,4] => 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] => [6,5,4,1,2,3] => 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] => [3,1,2,4,5,6] => 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] => [6,3,1,2,4,5] => 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] => [5,3,1,2,4,6] => 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] => [6,3,1,2,4,5] => 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] => [6,5,3,1,2,4] => 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] => [4,1,2,3,5,6] => 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] => [6,4,1,2,3,5] => 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] => [5,1,2,3,4,6] => 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] => [6,1,2,3,4,5] => 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] => [6,5,1,2,3,4] => 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] => [5,4,1,2,3,6] => 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] => [6,4,1,2,3,5] => 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] => [6,5,1,2,3,4] => 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] => [6,5,4,1,2,3] => 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] => [4,3,1,2,5,6] => 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] => [6,4,3,1,2,5] => 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] => [5,3,1,2,4,6] => 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] => [6,3,1,2,4,5] => 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] => [6,5,3,1,2,4] => 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] => [5,4,1,2,3,6] => 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] => [6,4,1,2,3,5] => 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] => [6,5,1,2,3,4] => 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] => [6,5,4,1,2,3] => 00111
>>> Load all 1080 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => 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] => [6,4,3,1,2,5] => 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] => [6,5,3,1,2,4] => 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] => [6,5,4,1,2,3] => 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] => [6,5,4,3,1,2] => 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] => [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] => [6,2,1,3,4,5] => 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] => [5,2,1,3,4,6] => 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] => [6,2,1,3,4,5] => 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] => [6,5,2,1,3,4] => 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] => [4,2,1,3,5,6] => 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] => [6,4,2,1,3,5] => 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] => [5,2,1,3,4,6] => 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] => [6,2,1,3,4,5] => 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] => [6,5,2,1,3,4] => 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] => [5,4,2,1,3,6] => 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] => [6,4,2,1,3,5] => 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] => [6,5,2,1,3,4] => 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] => [6,5,4,2,1,3] => 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] => [3,1,2,4,5,6] => 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] => [6,3,1,2,4,5] => 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] => [5,3,1,2,4,6] => 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] => [6,3,1,2,4,5] => 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] => [6,5,3,1,2,4] => 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] => [4,1,2,3,5,6] => 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] => [6,4,1,2,3,5] => 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] => [5,1,2,3,4,6] => 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] => [6,1,2,3,4,5] => 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] => [6,5,1,2,3,4] => 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] => [5,4,1,2,3,6] => 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] => [6,4,1,2,3,5] => 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] => [6,5,1,2,3,4] => 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] => [6,5,4,1,2,3] => 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] => [4,3,1,2,5,6] => 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] => [6,4,3,1,2,5] => 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] => [5,3,1,2,4,6] => 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] => [6,3,1,2,4,5] => 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] => [6,5,3,1,2,4] => 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] => [5,4,1,2,3,6] => 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] => [6,4,1,2,3,5] => 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] => [6,5,1,2,3,4] => 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] => [6,5,4,1,2,3] => 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] => [5,4,3,1,2,6] => 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] => [6,4,3,1,2,5] => 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] => [6,5,3,1,2,4] => 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] => [6,5,4,1,2,3] => 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] => [6,5,4,3,1,2] => 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] => [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] => [6,3,2,1,4,5] => 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] => [5,3,2,1,4,6] => 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] => [6,3,2,1,4,5] => 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] => [6,5,3,2,1,4] => 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] => [4,2,1,3,5,6] => 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] => [6,4,2,1,3,5] => 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] => [5,2,1,3,4,6] => 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] => [6,2,1,3,4,5] => 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] => [6,5,2,1,3,4] => 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] => [5,4,2,1,3,6] => 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] => [6,4,2,1,3,5] => 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] => [6,5,2,1,3,4] => 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] => [6,5,4,2,1,3] => 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] => [4,3,1,2,5,6] => 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] => [6,4,3,1,2,5] => 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] => [5,3,1,2,4,6] => 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] => [6,3,1,2,4,5] => 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] => [6,5,3,1,2,4] => 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] => [5,4,1,2,3,6] => 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] => [6,4,1,2,3,5] => 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] => [6,5,1,2,3,4] => 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] => [6,5,4,1,2,3] => 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] => [5,4,3,1,2,6] => 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] => [6,4,3,1,2,5] => 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] => [6,5,3,1,2,4] => 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] => [6,5,4,1,2,3] => 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] => [6,5,4,3,1,2] => 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] => [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] => [6,4,3,2,1,5] => 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] => [5,3,2,1,4,6] => 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] => [6,3,2,1,4,5] => 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] => [6,5,3,2,1,4] => 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] => [5,4,2,1,3,6] => 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] => [6,4,2,1,3,5] => 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] => [6,5,2,1,3,4] => 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] => [6,5,4,2,1,3] => 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] => [5,4,3,1,2,6] => 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] => [6,4,3,1,2,5] => 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] => [6,5,3,1,2,4] => 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] => [6,5,4,1,2,3] => 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] => [6,5,4,3,1,2] => 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] => [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] => [6,4,3,2,1,5] => 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] => [6,5,3,2,1,4] => 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] => [6,5,4,2,1,3] => 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] => [6,5,4,3,1,2] => 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] => [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] => [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] => [7,1,2,3,4,5,6] => 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] => [6,1,2,3,4,5,7] => 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] => [7,1,2,3,4,5,6] => 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] => [7,6,1,2,3,4,5] => 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] => [5,1,2,3,4,6,7] => 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] => [7,5,1,2,3,4,6] => 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] => [6,1,2,3,4,5,7] => 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] => [7,1,2,3,4,5,6] => 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] => [7,6,1,2,3,4,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [4,1,2,3,5,6,7] => 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] => [7,4,1,2,3,5,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [5,1,2,3,4,6,7] => 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] => [7,5,1,2,3,4,6] => 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] => [6,1,2,3,4,5,7] => 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] => [7,1,2,3,4,5,6] => 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] => [7,6,1,2,3,4,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [5,4,1,2,3,6,7] => 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] => [7,5,4,1,2,3,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [3,1,2,4,5,6,7] => 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] => [7,3,1,2,4,5,6] => 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] => [6,3,1,2,4,5,7] => 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] => [7,3,1,2,4,5,6] => 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] => [7,6,3,1,2,4,5] => 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] => [5,3,1,2,4,6,7] => 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] => [7,5,3,1,2,4,6] => 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] => [6,3,1,2,4,5,7] => 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] => [7,3,1,2,4,5,6] => 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] => [7,6,3,1,2,4,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [4,1,2,3,5,6,7] => 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] => [7,4,1,2,3,5,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [5,1,2,3,4,6,7] => 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] => [7,5,1,2,3,4,6] => 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] => [6,1,2,3,4,5,7] => 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] => [7,1,2,3,4,5,6] => 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] => [7,6,1,2,3,4,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [5,4,1,2,3,6,7] => 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] => [7,5,4,1,2,3,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [4,3,1,2,5,6,7] => 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] => [7,4,3,1,2,5,6] => 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] => [6,4,3,1,2,5,7] => 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] => [7,4,3,1,2,5,6] => 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] => [7,6,4,3,1,2,5] => 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] => [5,3,1,2,4,6,7] => 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] => [7,5,3,1,2,4,6] => 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] => [6,3,1,2,4,5,7] => 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] => [7,3,1,2,4,5,6] => 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] => [7,6,3,1,2,4,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [5,4,1,2,3,6,7] => 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] => [7,5,4,1,2,3,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [5,4,3,1,2,6,7] => 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] => [7,5,4,3,1,2,6] => 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] => [6,4,3,1,2,5,7] => 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] => [7,4,3,1,2,5,6] => 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] => [7,6,4,3,1,2,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [6,5,4,3,1,2,7] => 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] => [7,5,4,3,1,2,6] => 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] => [7,6,4,3,1,2,5] => 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] => [7,6,5,3,1,2,4] => 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] => [7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2] => 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] => [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] => [7,2,1,3,4,5,6] => 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] => [6,2,1,3,4,5,7] => 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] => [7,2,1,3,4,5,6] => 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] => [7,6,2,1,3,4,5] => 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] => [5,2,1,3,4,6,7] => 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] => [7,5,2,1,3,4,6] => 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] => [6,2,1,3,4,5,7] => 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] => [7,2,1,3,4,5,6] => 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] => [7,6,2,1,3,4,5] => 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] => [6,5,2,1,3,4,7] => 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] => [7,5,2,1,3,4,6] => 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] => [7,6,2,1,3,4,5] => 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] => [7,6,5,2,1,3,4] => 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] => [4,2,1,3,5,6,7] => 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] => [7,4,2,1,3,5,6] => 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] => [6,4,2,1,3,5,7] => 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] => [7,4,2,1,3,5,6] => 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] => [7,6,4,2,1,3,5] => 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] => [5,2,1,3,4,6,7] => 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] => [7,5,2,1,3,4,6] => 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] => [6,2,1,3,4,5,7] => 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] => [7,2,1,3,4,5,6] => 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] => [7,6,2,1,3,4,5] => 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] => [6,5,2,1,3,4,7] => 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] => [7,5,2,1,3,4,6] => 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] => [7,6,5,2,1,3,4] => 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] => [5,4,2,1,3,6,7] => 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] => [7,5,4,2,1,3,6] => 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] => [6,4,2,1,3,5,7] => 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] => [7,4,2,1,3,5,6] => 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] => [7,6,4,2,1,3,5] => 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] => [6,5,2,1,3,4,7] => 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] => [7,5,2,1,3,4,6] => 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] => [7,6,2,1,3,4,5] => 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] => [7,6,5,2,1,3,4] => 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] => [6,5,4,2,1,3,7] => 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] => [7,5,4,2,1,3,6] => 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] => [7,6,4,2,1,3,5] => 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] => [7,6,5,2,1,3,4] => 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] => [7,6,5,4,2,1,3] => 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] => [3,1,2,4,5,6,7] => 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] => [7,3,1,2,4,5,6] => 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] => [6,3,1,2,4,5,7] => 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] => [7,3,1,2,4,5,6] => 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] => [7,6,3,1,2,4,5] => 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] => [5,3,1,2,4,6,7] => 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] => [7,5,3,1,2,4,6] => 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] => [6,3,1,2,4,5,7] => 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] => [7,3,1,2,4,5,6] => 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] => [7,6,3,1,2,4,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [4,1,2,3,5,6,7] => 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] => [7,4,1,2,3,5,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [5,1,2,3,4,6,7] => 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] => [7,5,1,2,3,4,6] => 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] => [6,1,2,3,4,5,7] => 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] => [7,1,2,3,4,5,6] => 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] => [7,6,1,2,3,4,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [5,4,1,2,3,6,7] => 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] => [7,5,4,1,2,3,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [4,3,1,2,5,6,7] => 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] => [7,4,3,1,2,5,6] => 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] => [6,4,3,1,2,5,7] => 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] => [7,4,3,1,2,5,6] => 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] => [7,6,4,3,1,2,5] => 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] => [5,3,1,2,4,6,7] => 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] => [7,5,3,1,2,4,6] => 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] => [6,3,1,2,4,5,7] => 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] => [7,3,1,2,4,5,6] => 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] => [7,6,3,1,2,4,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [5,4,1,2,3,6,7] => 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] => [7,5,4,1,2,3,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [5,4,3,1,2,6,7] => 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] => [7,5,4,3,1,2,6] => 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] => [6,4,3,1,2,5,7] => 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] => [7,4,3,1,2,5,6] => 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] => [7,6,4,3,1,2,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [6,5,4,3,1,2,7] => 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] => [7,5,4,3,1,2,6] => 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] => [7,6,4,3,1,2,5] => 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] => [7,6,5,3,1,2,4] => 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] => [7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2] => 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] => [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] => [7,3,2,1,4,5,6] => 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] => [6,3,2,1,4,5,7] => 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] => [7,3,2,1,4,5,6] => 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] => [7,6,3,2,1,4,5] => 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] => [5,3,2,1,4,6,7] => 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] => [7,5,3,2,1,4,6] => 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] => [6,3,2,1,4,5,7] => 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] => [7,3,2,1,4,5,6] => 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] => [7,6,3,2,1,4,5] => 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] => [6,5,3,2,1,4,7] => 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] => [7,5,3,2,1,4,6] => 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] => [7,6,3,2,1,4,5] => 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] => [7,6,5,3,2,1,4] => 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] => [4,2,1,3,5,6,7] => 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] => [7,4,2,1,3,5,6] => 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] => [6,4,2,1,3,5,7] => 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] => [7,4,2,1,3,5,6] => 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] => [7,6,4,2,1,3,5] => 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] => [5,2,1,3,4,6,7] => 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] => [7,5,2,1,3,4,6] => 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] => [6,2,1,3,4,5,7] => 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] => [7,2,1,3,4,5,6] => 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] => [7,6,2,1,3,4,5] => 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] => [6,5,2,1,3,4,7] => 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] => [7,5,2,1,3,4,6] => 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] => [7,6,2,1,3,4,5] => 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] => [7,6,5,2,1,3,4] => 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] => [5,4,2,1,3,6,7] => 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] => [7,5,4,2,1,3,6] => 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] => [6,4,2,1,3,5,7] => 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] => [7,4,2,1,3,5,6] => 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] => [7,6,4,2,1,3,5] => 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] => [6,5,2,1,3,4,7] => 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] => [7,5,2,1,3,4,6] => 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] => [7,6,2,1,3,4,5] => 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] => [7,6,5,2,1,3,4] => 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] => [6,5,4,2,1,3,7] => 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] => [7,5,4,2,1,3,6] => 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] => [7,6,4,2,1,3,5] => 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] => [7,6,5,2,1,3,4] => 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] => [7,6,5,4,2,1,3] => 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] => [4,3,1,2,5,6,7] => 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] => [7,4,3,1,2,5,6] => 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] => [6,4,3,1,2,5,7] => 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] => [7,4,3,1,2,5,6] => 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] => [7,6,4,3,1,2,5] => 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] => [5,3,1,2,4,6,7] => 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] => [7,5,3,1,2,4,6] => 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] => [6,3,1,2,4,5,7] => 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] => [7,3,1,2,4,5,6] => 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] => [7,6,3,1,2,4,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [5,4,1,2,3,6,7] => 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] => [7,5,4,1,2,3,6] => 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] => [6,4,1,2,3,5,7] => 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] => [7,4,1,2,3,5,6] => 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] => [7,6,4,1,2,3,5] => 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] => [6,5,1,2,3,4,7] => 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] => [7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [5,4,3,1,2,6,7] => 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] => [7,5,4,3,1,2,6] => 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] => [6,4,3,1,2,5,7] => 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] => [7,4,3,1,2,5,6] => 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] => [7,6,4,3,1,2,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [6,5,4,3,1,2,7] => 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] => [7,5,4,3,1,2,6] => 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] => [7,6,4,3,1,2,5] => 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] => [7,6,5,3,1,2,4] => 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] => [7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2] => 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] => [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] => [7,4,3,2,1,5,6] => 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] => [6,4,3,2,1,5,7] => 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] => [7,4,3,2,1,5,6] => 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] => [7,6,4,3,2,1,5] => 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] => [5,3,2,1,4,6,7] => 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] => [7,5,3,2,1,4,6] => 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] => [6,3,2,1,4,5,7] => 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] => [7,3,2,1,4,5,6] => 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] => [7,6,3,2,1,4,5] => 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] => [6,5,3,2,1,4,7] => 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] => [7,5,3,2,1,4,6] => 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] => [7,6,3,2,1,4,5] => 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] => [7,6,5,3,2,1,4] => 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] => [5,4,2,1,3,6,7] => 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] => [7,5,4,2,1,3,6] => 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] => [6,4,2,1,3,5,7] => 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] => [7,4,2,1,3,5,6] => 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] => [7,6,4,2,1,3,5] => 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] => [6,5,2,1,3,4,7] => 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] => [7,5,2,1,3,4,6] => 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] => [7,6,2,1,3,4,5] => 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] => [7,6,5,2,1,3,4] => 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] => [6,5,4,2,1,3,7] => 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] => [7,5,4,2,1,3,6] => 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] => [7,6,4,2,1,3,5] => 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] => [7,6,5,2,1,3,4] => 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] => [7,6,5,4,2,1,3] => 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] => [5,4,3,1,2,6,7] => 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] => [7,5,4,3,1,2,6] => 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] => [6,4,3,1,2,5,7] => 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] => [7,4,3,1,2,5,6] => 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] => [7,6,4,3,1,2,5] => 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] => [6,5,3,1,2,4,7] => 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] => [7,5,3,1,2,4,6] => 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] => [7,6,3,1,2,4,5] => 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] => [7,6,5,3,1,2,4] => 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] => [6,5,4,1,2,3,7] => 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] => [7,5,4,1,2,3,6] => 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] => [7,6,4,1,2,3,5] => 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] => [7,6,5,1,2,3,4] => 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] => [7,6,5,4,1,2,3] => 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] => [6,5,4,3,1,2,7] => 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] => [7,5,4,3,1,2,6] => 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] => [7,6,4,3,1,2,5] => 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] => [7,6,5,3,1,2,4] => 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] => [7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2] => 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] => [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] => [7,5,4,3,2,1,6] => 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] => [6,4,3,2,1,5,7] => 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] => [7,4,3,2,1,5,6] => 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] => [7,6,4,3,2,1,5] => 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] => [6,5,3,2,1,4,7] => 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] => [7,5,3,2,1,4,6] => 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] => [7,6,3,2,1,4,5] => 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] => [7,6,5,3,2,1,4] => 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] => [6,5,4,2,1,3,7] => 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] => [7,5,4,2,1,3,6] => 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] => [7,6,4,2,1,3,5] => 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] => [7,6,5,2,1,3,4] => 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] => [7,6,5,4,2,1,3] => 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] => [6,5,4,3,1,2,7] => 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] => [7,5,4,3,1,2,6] => 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] => [7,6,4,3,1,2,5] => 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] => [7,6,5,3,1,2,4] => 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] => [7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2] => 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] => [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] => [7,5,4,3,2,1,6] => 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] => [7,6,4,3,2,1,5] => 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] => [7,6,5,3,2,1,4] => 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] => [7,6,5,4,2,1,3] => 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] => [7,6,5,4,3,1,2] => 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] => [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] => [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] => [8,1,2,3,4,5,6,7] => 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] => [8,1,2,3,4,5,6,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [6,1,2,3,4,5,7,8] => 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] => [8,6,1,2,3,4,5,7] => 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] => [7,1,2,3,4,5,6,8] => 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] => [8,1,2,3,4,5,6,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [7,6,1,2,3,4,5,8] => 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] => [8,6,1,2,3,4,5,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [8,7,6,1,2,3,4,5] => 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] => [8,5,1,2,3,4,6,7] => 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] => [8,1,2,3,4,5,6,7] => 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] => [8,5,1,2,3,4,6,7] => 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] => [8,6,1,2,3,4,5,7] => 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] => [8,6,5,1,2,3,4,7] => 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] => [8,7,6,5,1,2,3,4] => 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] => [8,4,1,2,3,5,6,7] => 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] => [8,4,1,2,3,5,6,7] => 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] => [8,1,2,3,4,5,6,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [5,4,1,2,3,6,7,8] => 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] => [8,4,1,2,3,5,6,7] => 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] => [8,5,1,2,3,4,6,7] => 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] => [8,6,1,2,3,4,5,7] => 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] => [8,5,4,1,2,3,6,7] => 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] => [8,7,6,1,2,3,4,5] => 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] => [7,6,5,4,1,2,3,8] => 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] => [8,7,6,4,1,2,3,5] => 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] => [8,7,6,5,1,2,3,4] => 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] => [8,7,6,5,4,1,2,3] => 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] => [8,3,1,2,4,5,6,7] => 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] => [8,3,1,2,4,5,6,7] => 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] => [8,4,1,2,3,5,6,7] => 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] => [8,4,1,2,3,5,6,7] => 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] => [8,7,6,4,1,2,3,5] => 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] => [8,1,2,3,4,5,6,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [4,3,1,2,5,6,7,8] => 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] => [8,3,1,2,4,5,6,7] => 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] => [5,4,1,2,3,6,7,8] => 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] => [8,7,5,4,1,2,3,6] => 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] => [7,4,1,2,3,5,6,8] => 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] => [8,4,1,2,3,5,6,7] => 0010001
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => 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] => [8,6,1,2,3,4,5,7] => 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] => [8,7,1,2,3,4,5,6] => 0000011
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => [1,2,6,5,4,3,8,7] => [8,6,5,4,1,2,3,7] => 0011101
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]] => [1,2,4,3,5,8,7,6] => [8,7,4,1,2,3,5,6] => 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] => [8,7,6,1,2,3,4,5] => 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] => [8,7,6,5,4,1,2,3] => 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] => [6,5,4,3,1,2,7,8] => 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] => [8,6,5,4,3,1,2,7] => 0111101
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,-1,1],[0,1,0,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]] => [1,3,2,4,8,7,6,5] => [8,7,6,3,1,2,4,5] => 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] => [7,6,5,4,1,2,3,8] => 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] => [8,7,6,4,1,2,3,5] => 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] => [8,7,6,5,1,2,3,4] => 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] => [8,7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2,8] => 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] => [8,7,6,4,3,1,2,5] => 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] => [8,7,6,5,3,1,2,4] => 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] => [8,7,6,5,4,1,2,3] => 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] => [8,7,6,5,4,3,1,2] => 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] => [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] => [8,2,1,3,4,5,6,7] => 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] => [7,2,1,3,4,5,6,8] => 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] => [8,2,1,3,4,5,6,7] => 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] => [8,7,2,1,3,4,5,6] => 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] => [6,2,1,3,4,5,7,8] => 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] => [8,2,1,3,4,5,6,7] => 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] => [8,2,1,3,4,5,6,7] => 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] => [8,7,2,1,3,4,5,6] => 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] => [8,7,6,2,1,3,4,5] => 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] => [8,7,6,5,2,1,3,4] => 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] => [8,2,1,3,4,5,6,7] => 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] => [8,7,6,2,1,3,4,5] => 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] => [8,7,6,5,2,1,3,4] => 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] => [5,4,2,1,3,6,7,8] => 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] => [8,4,2,1,3,5,6,7] => 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] => [8,7,2,1,3,4,5,6] => 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] => [8,7,6,2,1,3,4,5] => 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] => [7,6,5,4,2,1,3,8] => 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] => [8,6,5,4,2,1,3,7] => 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] => [8,7,6,5,2,1,3,4] => 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] => [8,7,6,5,4,2,1,3] => 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] => [3,1,2,4,5,6,7,8] => 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] => [8,3,1,2,4,5,6,7] => 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] => [8,3,1,2,4,5,6,7] => 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] => [8,7,6,3,1,2,4,5] => 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] => [8,7,6,3,1,2,4,5] => 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] => [8,7,6,5,3,1,2,4] => 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] => [4,1,2,3,5,6,7,8] => 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] => [8,7,4,1,2,3,5,6] => 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] => [8,7,6,4,1,2,3,5] => 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] => [5,1,2,3,4,6,7,8] => 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] => [8,5,1,2,3,4,6,7] => 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] => [8,7,5,1,2,3,4,6] => 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] => [6,1,2,3,4,5,7,8] => 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] => [8,6,1,2,3,4,5,7] => 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] => [7,1,2,3,4,5,6,8] => 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] => [8,1,2,3,4,5,6,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [7,6,1,2,3,4,5,8] => 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] => [8,6,1,2,3,4,5,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [8,7,6,1,2,3,4,5] => 0000111
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]] => [1,2,3,5,4,6,8,7] => [8,5,1,2,3,4,6,7] => 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] => [7,6,1,2,3,4,5,8] => 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] => [8,7,1,2,3,4,5,6] => 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] => [8,7,6,1,2,3,4,5] => 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] => [7,6,5,1,2,3,4,8] => 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] => [8,7,6,1,2,3,4,5] => 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] => [5,4,1,2,3,6,7,8] => 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] => [8,4,1,2,3,5,6,7] => 0010001
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,1,-1,0,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => 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] => [6,5,4,1,2,3,7,8] => 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] => [8,7,6,1,2,3,4,5] => 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] => [7,6,5,4,1,2,3,8] => 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] => [4,3,1,2,5,6,7,8] => 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] => [8,3,1,2,4,5,6,7] => 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] => [5,4,1,2,3,6,7,8] => 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] => [8,4,1,2,3,5,6,7] => 0010001
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[0,1,0,0,0,0,0,0],[1,-1,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1]] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => 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] => [8,7,1,2,3,4,5,6] => 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] => [8,7,6,1,2,3,4,5] => 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] => [8,7,6,1,2,3,4,5] => 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] => [5,4,3,1,2,6,7,8] => 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] => [8,7,6,1,2,3,4,5] => 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] => [8,6,5,4,3,1,2,7] => 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] => [8,7,5,4,3,1,2,6] => 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] => [8,7,6,5,1,2,3,4] => 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] => [7,6,5,4,3,1,2,8] => 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] => [8,6,5,4,3,1,2,7] => 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] => [8,7,6,5,3,1,2,4] => 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] => [8,7,6,5,4,1,2,3] => 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] => [8,7,6,5,4,3,1,2] => 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] => [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] => [8,3,2,1,4,5,6,7] => 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] => [8,3,2,1,4,5,6,7] => 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] => [8,7,3,2,1,4,5,6] => 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] => [8,7,3,2,1,4,5,6] => 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] => [8,7,6,3,2,1,4,5] => 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] => [8,7,6,3,2,1,4,5] => 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] => [8,7,6,5,3,2,1,4] => 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] => [4,2,1,3,5,6,7,8] => 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] => [8,7,6,4,2,1,3,5] => 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] => [5,2,1,3,4,6,7,8] => 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] => [6,2,1,3,4,5,7,8] => 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] => [7,2,1,3,4,5,6,8] => 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] => [8,2,1,3,4,5,6,7] => 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] => [8,4,2,1,3,5,6,7] => 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] => [8,7,2,1,3,4,5,6] => 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] => [8,7,6,5,2,1,3,4] => 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] => [4,3,1,2,5,6,7,8] => 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] => [8,7,6,4,3,1,2,5] => 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] => [7,3,1,2,4,5,6,8] => 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] => [8,3,1,2,4,5,6,7] => 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] => [5,4,1,2,3,6,7,8] => 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] => [8,5,4,1,2,3,6,7] => 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] => [6,4,1,2,3,5,7,8] => 0010100
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]] => [1,2,4,3,5,7,6,8] => [7,4,1,2,3,5,6,8] => 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] => [8,4,1,2,3,5,6,7] => 0010001
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => [1,2,3,6,5,4,8,7] => [8,6,5,1,2,3,4,7] => 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] => [8,7,5,1,2,3,4,6] => 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] => [7,6,1,2,3,4,5,8] => 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] => [8,6,1,2,3,4,5,7] => 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] => [8,7,1,2,3,4,5,6] => 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] => [8,7,6,1,2,3,4,5] => 0000111
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[1,-1,1,-1,0,1,0,0],[0,1,-1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => [1,2,6,5,4,3,8,7] => [8,6,5,4,1,2,3,7] => 0011101
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[0,0,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[1,-1,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0]] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => 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] => [8,7,6,5,1,2,3,4] => 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] => [8,6,5,4,3,1,2,7] => 0111101
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [[0,0,1,0,0,0,0,0],[0,1,-1,0,0,1,0,0],[1,-1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,-1,0,1],[0,1,0,0,-1,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]] => [1,4,3,2,8,7,6,5] => [8,7,6,4,3,1,2,5] => 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] => [8,7,6,5,4,1,2,3] => 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] => [8,7,5,4,3,1,2,6] => 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] => [8,7,6,5,3,1,2,4] => 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] => [8,7,6,5,4,1,2,3] => 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] => [8,7,6,5,4,3,1,2] => 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] => [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] => [8,4,3,2,1,5,6,7] => 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] => [8,7,4,3,2,1,5,6] => 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] => [8,7,6,4,3,2,1,5] => 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] => [5,3,2,1,4,6,7,8] => 1101000
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]] => [3,2,1,4,6,5,7,8] => [6,3,2,1,4,5,7,8] => 1100100
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]] => [3,2,1,4,5,7,6,8] => [7,3,2,1,4,5,6,8] => 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] => [8,3,2,1,4,5,6,7] => 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] => [8,7,6,3,2,1,4,5] => 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] => [5,4,2,1,3,6,7,8] => 1011000
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,-1,1,0,0,0],[1,0,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0]] => [2,1,3,4,5,8,7,6] => [8,7,2,1,3,4,5,6] => 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] => [8,7,6,2,1,3,4,5] => 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] => [8,7,6,5,2,1,3,4] => 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] => [8,7,5,4,3,1,2,6] => 0111011
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]] => [1,2,5,4,3,6,8,7] => [8,5,4,1,2,3,6,7] => 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] => [8,7,6,4,1,2,3,5] => 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] => [8,6,5,1,2,3,4,7] => 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] => [8,7,6,1,2,3,4,5] => 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] => [8,7,6,5,1,2,3,4] => 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] => [8,7,6,3,1,2,4,5] => 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] => [8,7,6,5,3,1,2,4] => 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] => [8,7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2,8] => 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] => [8,6,5,4,3,1,2,7] => 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] => [8,7,6,4,3,1,2,5] => 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] => [8,7,6,5,4,3,1,2] => 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] => [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] => [8,5,4,3,2,1,6,7] => 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] => [8,7,5,4,3,2,1,6] => 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] => [6,4,3,2,1,5,7,8] => 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] => [7,4,3,2,1,5,6,8] => 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] => [8,7,4,3,2,1,5,6] => 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] => [6,5,3,2,1,4,7,8] => 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] => [8,6,5,4,2,1,3,7] => 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] => [8,7,5,2,1,3,4,6] => 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] => [8,7,6,2,1,3,4,5] => 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] => [8,7,6,5,2,1,3,4] => 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] => [8,6,5,4,3,1,2,7] => 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] => [8,7,6,4,3,1,2,5] => 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] => [8,7,6,3,1,2,4,5] => 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] => [8,7,6,5,3,1,2,4] => 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] => [7,6,5,4,1,2,3,8] => 0011110
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[1,-1,1,-1,1,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,0,0,0,1,0]] => [1,2,6,5,4,3,8,7] => [8,6,5,4,1,2,3,7] => 0011101
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,-1,1],[1,-1,1,-1,1,-1,1,0],[0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0]] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => 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] => [8,7,6,5,4,1,2,3] => 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] => [7,6,5,4,3,1,2,8] => 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] => [8,6,5,4,3,1,2,7] => 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] => [8,7,6,5,3,1,2,4] => 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] => [8,7,6,5,4,3,1,2] => 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] => [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] => [8,6,5,4,3,2,1,7] => 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] => [7,5,4,3,2,1,6,8] => 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] => [8,5,4,3,2,1,6,7] => 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] => [7,6,4,3,2,1,5,8] => 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] => [7,6,5,3,2,1,4,8] => 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] => [8,6,5,3,2,1,4,7] => 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] => [7,6,5,4,2,1,3,8] => 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] => [8,6,5,4,2,1,3,7] => 1011101
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,1,0,-1,1,0,-1,1],[1,0,-1,1,0,-1,1,0],[0,0,1,0,-1,1,0,0],[0,0,0,0,1,0,0,0]] => [2,1,4,3,8,7,6,5] => [8,7,6,4,2,1,3,5] => 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] => [8,7,6,5,2,1,3,4] => 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] => [7,6,5,4,3,1,2,8] => 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] => [8,6,5,4,3,1,2,7] => 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] => [8,7,6,5,4,1,2,3] => 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] => [8,7,6,5,4,3,1,2] => 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] => [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] => [8,6,5,4,3,2,1,7] => 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] => [8,7,5,4,3,2,1,6] => 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] => [8,7,6,4,3,2,1,5] => 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] => [8,7,6,5,3,2,1,4] => 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] => [8,7,6,5,4,2,1,3] => 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] => [8,7,6,5,4,3,1,2] => 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] => [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] => [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] => [9,8,7,6,5,4,3,1,2] => 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] => [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] => [8,7,6,5,4,3,1,2,9] => 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] => [9,8,7,6,5,4,1,2,3] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [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] => [9,8,7,6,5,4,3,1,2,10] => 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] => [8,7,6,5,4,2,1,3,9] => 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] => [8,7,6,5,4,3,1,2,9] => 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] => [9,8,7,6,5,3,1,2,4] => 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] => [9,8,7,6,5,4,1,2,3] => 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] => [10,9,8,7,6,5,4,1,2,3] => 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] => [11,10,9,8,7,6,5,4,3,1,2] => 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] => [9,8,7,6,5,1,2,3,4] => 00011111
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0]] => [1,2,3,10,9,8,7,6,5,4] => [10,9,8,7,6,5,1,2,3,4] => 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] => [8,6,5,4,3,2,1,7,9] => 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] => [8,7,6,5,4,3,1,2,9] => 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] => [9,7,6,5,4,3,2,1,8] => 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] => [9,8,7,6,1,2,3,4,5] => 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] => [9,8,7,6,5,4,2,1,3] => 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] => [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] => [8,7,6,5,4,3,1,2,9] => 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] => [9,7,6,5,4,3,1,2,8] => 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] => [10,9,8,7,6,1,2,3,4,5] => 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] => [9,8,7,6,5,4,1,2,3] => 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] => [10,8,7,6,5,4,3,2,1,9] => 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] => [10,9,8,7,6,5,4,2,1,3] => 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] => [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] => [9,1,2,3,4,5,6,7,8] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [9,7,1,2,3,4,5,6,8] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [9,8,7,1,2,3,4,5,6] => 00000111
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]] => [1,2,3,4,6,5,7,9,8] => [9,6,1,2,3,4,5,7,8] => 00001001
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[0,1,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,-1,1],[0,0,0,0,0,0,0,1,0]] => [1,2,3,4,5,7,6,9,8] => [9,7,1,2,3,4,5,6,8] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [9,8,7,1,2,3,4,5,6] => 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] => [9,8,7,1,2,3,4,5,6] => 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] => [9,8,7,1,2,3,4,5,6] => 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] => [9,8,7,1,2,3,4,5,6] => 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] => [9,3,1,2,4,5,6,7,8] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [9,8,7,1,2,3,4,5,6] => 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] => [9,7,6,5,4,3,1,2,8] => 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] => [9,8,7,6,5,3,1,2,4] => 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] => [9,8,7,6,5,4,1,2,3] => 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] => [9,8,7,6,5,4,3,1,2] => 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] => [9,2,1,3,4,5,6,7,8] => 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] => [9,3,1,2,4,5,6,7,8] => 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] => [9,7,1,2,3,4,5,6,8] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [9,8,7,6,1,2,3,4,5] => 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] => [9,8,7,6,5,4,3,1,2] => 01111111
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0,0,0],[0,1,-1,1,0,-1,1,0,0],[0,0,1,0,-1,1,-1,1,0],[0,0,0,0,1,-1,1,-1,1],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0]] => [1,2,4,3,5,6,9,8,7] => [9,8,4,1,2,3,5,6,7] => 00100011
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[0,0,0,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,-1,1,0,0,0],[1,-1,1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1,-1,1],[0,0,0,1,-1,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,0,0,0]] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => 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] => [9,8,7,6,1,2,3,4,5] => 00001111
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[0,0,0,1,0,0,0,0,0],[0,0,1,-1,0,0,0,0,1],[0,1,-1,0,0,0,0,1,0],[1,-1,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => 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] => [9,8,7,6,5,1,2,3,4] => 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] => [9,8,7,6,5,4,1,2,3] => 00111111
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [[0,0,0,0,1,0,0,0,0],[0,0,0,1,-1,0,0,0,1],[0,0,1,-1,0,0,0,1,0],[0,1,-1,0,0,0,1,0,0],[1,-1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => 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] => [9,8,7,6,5,3,1,2,4] => 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] => [9,8,7,6,5,4,1,2,3] => 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] => [9,7,6,5,4,3,1,2,8] => 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] => [9,8,7,6,5,3,1,2,4] => 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] => [9,8,7,6,5,4,3,1,2] => 01111111
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,-1,1],[0,0,0,0,0,0,0,1,0]] => [1,7,6,5,4,3,2,9,8] => [9,7,6,5,4,3,1,2,8] => 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] => [9,8,7,6,5,4,1,2,3] => 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] => [9,8,7,6,5,4,3,1,2] => 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] => [9,7,6,5,4,3,2,1,8] => 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] => [9,8,6,5,4,3,2,1,7] => 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] => [9,8,7,5,4,3,2,1,6] => 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] => [9,8,7,6,4,3,2,1,5] => 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] => [9,8,7,6,5,3,2,1,4] => 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] => [9,8,7,6,5,4,2,1,3] => 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] => [9,8,7,6,5,4,3,1,2] => 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] => [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] => [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] => [9,1,2,3,4,5,6,7,8] => 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] => [9,1,2,3,4,5,6,7,8] => 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] => [9,1,2,3,4,5,6,7,8] => 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] => [9,1,2,3,4,5,6,7,8] => 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] => [9,1,2,3,4,5,6,7,8] => 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] => [9,1,2,3,4,5,6,7,8] => 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] => [9,1,2,3,4,5,6,7,8] => 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] => [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] => [10,1,2,3,4,5,6,7,8,9] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [10,1,2,3,4,5,6,7,8,9] => 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] => [9,7,1,2,3,4,5,6,8] => 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] => [10,1,2,3,4,5,6,7,8,9] => 000000001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]] => [1,2,3,4,6,5,7,9,8] => [9,6,1,2,3,4,5,7,8] => 00001001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 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] => [10,1,2,3,4,5,6,7,8,9] => 000000001
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,1,0]] => [1,2,4,3,5,6,7,9,8] => [9,4,1,2,3,5,6,7,8] => 00100001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 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] => [9,3,1,2,4,5,6,7,8] => 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] => [10,1,2,3,4,5,6,7,8,9] => 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] => [10,1,2,3,4,5,6,7,8,9] => 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] => [10,1,2,3,4,5,6,7,8,9] => 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] => [11,1,2,3,4,5,6,7,8,9,10] => 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] => [11,1,2,3,4,5,6,7,8,9,10] => 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] => [10,2,1,3,4,5,6,7,8,9] => 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] => [11,1,2,3,4,5,6,7,8,9,10] => 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] => [9,7,1,2,3,4,5,6,8] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [9,8,7,1,2,3,4,5,6] => 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] => [10,9,1,2,3,4,5,6,7,8] => 000000011
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,-1,1,0,0,0],[0,1,-1,1,-1,1,-1,1,0,0],[0,0,1,-1,1,-1,1,-1,1,0],[0,0,0,1,-1,1,-1,1,-1,1],[0,0,0,0,1,-1,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => 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] => [9,7,1,2,3,4,5,6,8] => 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] => [5,1,2,3,4,6,7,8,9] => 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] => [4,1,2,3,5,6,7,8,9] => 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] => [9,3,1,2,4,5,6,7,8] => 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] => [5,3,1,2,4,6,7,8,9] => 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] => [4,3,1,2,5,6,7,8,9] => 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] => [9,7,6,5,4,3,1,2,8] => 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] => [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] => [9,2,1,3,4,5,6,7,8] => 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] => [8,2,1,3,4,5,6,7,9] => 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] => [8,7,6,5,4,2,1,3,9] => 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] => [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] => [9,8,7,6,5,3,2,1,4] => 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] => [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] => [9,8,7,6,4,3,2,1,5] => 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] => [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] => [9,8,7,5,4,3,2,1,6] => 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] => [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] => [9,8,6,5,4,3,2,1,7] => 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] => [7,1,2,3,4,5,6,8,9,10] => 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] => [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] => [10,2,1,3,4,5,6,7,8,9] => 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] => [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] => [10,9,8,7,6,5,3,2,1,4] => 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] => [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] => [10,9,8,7,6,4,3,2,1,5] => 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] => [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] => [10,9,8,7,5,4,3,2,1,6] => 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] => [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] => [10,9,8,6,5,4,3,2,1,7] => 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] => [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] => [10,9,7,6,5,4,3,2,1,8] => 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] => [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] => [3,1,2,4,5,6,7,8,9] => 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] => [4,1,2,3,5,6,7,8,9] => 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] => [5,1,2,3,4,6,7,8,9] => 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] => [6,1,2,3,4,5,7,8,9] => 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] => [7,1,2,3,4,5,6,8,9] => 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] => [8,1,2,3,4,5,6,7,9] => 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] => [3,1,2,4,5,6,7,8,9,10] => 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] => [4,3,1,2,5,6,7,8,9] => 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] => [4,1,2,3,5,6,7,8,9,10] => 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] => [5,1,2,3,4,6,7,8,9,10] => 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] => [6,1,2,3,4,5,7,8,9,10] => 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] => [7,1,2,3,4,5,6,8,9,10] => 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] => [8,1,2,3,4,5,6,7,9,10] => 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] => [9,1,2,3,4,5,6,7,8,10] => 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] => [10,9,8,7,6,1,2,3,4,5] => 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] => [10,9,8,7,1,2,3,4,5,6] => 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] => [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] => [9,2,1,3,4,5,6,7,8] => 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] => [10,9,1,2,3,4,5,6,7,8] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,8,7,6,5,4,2,1,3] => 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] => [11,10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,8,7,6,5,4,1,2,3] => 001111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,0,0,1,0]] => [2,1,3,4,5,6,7,8,10,9] => [10,2,1,3,4,5,6,7,8,9] => 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] => [9,3,1,2,4,5,6,7,8] => 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] => [9,3,1,2,4,5,6,7,8] => 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] => [9,3,1,2,4,5,6,7,8] => 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] => [4,3,1,2,5,6,7,8,9] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,8,7,6,5,4,3,2,1,9] => 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] => [11,9,8,7,6,5,4,3,2,1,10] => 1111111101
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,8,7,6,5,4,3,1,2] => 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] => [10,9,1,2,3,4,5,6,7,8] => 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] => [11,10,9,8,7,6,5,4,3,1,2] => 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] => [9,8,7,6,5,3,1,2,4] => 01011111
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => 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] => [5,1,2,3,4,6,7,8,9] => 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] => [8,1,2,3,4,5,6,7,9,10] => 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] => [9,1,2,3,4,5,6,7,8,10] => 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] => [10,9,8,7,1,2,3,4,5,6] => 000001111
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,-1,1,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0],[0,0,0,1,-1,1,0,0,0],[0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]] => [2,1,3,4,5,6,8,7,9] => [8,2,1,3,4,5,6,7,9] => 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] => [9,8,1,2,3,4,5,6,7] => 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] => [9,7,1,2,3,4,5,6,8] => 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] => [9,2,1,3,4,5,6,7,8] => 10000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,1,0,0,0],[0,0,0,0,0,1,-1,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0]] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => 000000111
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[0,1,0,0,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0,0,0],[0,1,-1,1,0,0,0,0,0,0],[0,0,1,-1,1,0,0,0,0,0],[0,0,0,1,-1,1,0,0,0,0],[0,0,0,0,1,-1,0,0,1,0],[0,0,0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1,0,0],[0,0,0,0,0,0,1,0,0,0]] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => 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] => [10,9,8,1,2,3,4,5,6,7] => 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] => [10,9,8,1,2,3,4,5,6,7] => 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] => [10,9,8,1,2,3,4,5,6,7] => 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] => [10,9,8,1,2,3,4,5,6,7] => 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] => [10,9,8,1,2,3,4,5,6,7] => 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] => [9,7,6,5,4,3,1,2,8] => 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] => [10,9,7,6,5,4,3,2,1,8] => 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] => [10,9,8,6,5,4,3,2,1,7] => 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] => [10,9,8,7,5,4,3,2,1,6] => 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] => [10,9,8,7,6,4,3,2,1,5] => 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] => [10,9,8,7,6,5,3,2,1,4] => 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
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection ϕ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word w1w2...wn, compute the image inductively by starting with ϕ(w1)=w1.
At the i-th step, if ϕ(w1w2...wi)=v1v2...vi, define ϕ(w1w2...wiwi+1) by placing wi+1 on the end of the word v1v2...vi and breaking the word up into blocks as follows.
To compute ϕ([1,4,2,5,3]), the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection ϕ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word w1w2...wn, compute the image inductively by starting with ϕ(w1)=w1.
At the i-th step, if ϕ(w1w2...wi)=v1v2...vi, define ϕ(w1w2...wiwi+1) by placing wi+1 on the end of the word v1v2...vi and breaking the word up into blocks as follows.
- If wi+1≥vi, place a vertical line to the right of each vk for which wi+1≥vk.
- If wi+1<vi, place a vertical line to the right of each vk for which wi+1<vk.
To compute ϕ([1,4,2,5,3]), the sequence of words is
- 1
- |1|4→14
- |14|2→412
- |4|1|2|5→4125
- |4|125|3→45123.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
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