Identifier
-
Mp00068:
Permutations
—Simion-Schmidt map⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤ
Values
[1,2] => [1,2] => [1,2] => [1,0,1,0] => 1
[1,2,3] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0] => 1
[1,3,2] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0] => 1
[2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 1
[1,2,3,4] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[1,2,4,3] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[1,3,2,4] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[1,3,4,2] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[1,4,2,3] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[2,1,3,4] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 1
[2,3,1,4] => [2,4,1,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[2,4,1,3] => [2,4,1,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[1,2,3,4,5] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,5,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,4,3,5] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,4,5,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,5,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,4,5] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,5,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,4,2,5] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,4,5,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,5,2,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,5,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,2,3,5] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,2,5,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,3,2,5] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,3,5,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,5,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,2,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,3,2,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,4,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,4,5] => [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,3,5,4] => [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,4,3,5] => [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,3,1,4,5] => [2,5,1,4,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,3,1,5,4] => [2,5,1,4,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,3,4,1,5] => [2,5,4,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,3,5,1,4] => [2,5,4,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,4,1,3,5] => [2,5,1,4,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,4,1,5,3] => [2,5,1,4,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,4,3,1,5] => [2,5,4,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,4,5,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,5,1,3,4] => [2,5,1,4,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,5,1,4,3] => [2,5,1,4,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,5,3,1,4] => [2,5,4,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,5,4,1,3] => [2,5,4,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,2,1,4,5] => [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,4,1,5] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[3,2,5,1,4] => [3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 1
[3,4,2,1,5] => [3,5,2,1,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,5,2,1,4] => [3,5,2,1,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,3,4,5,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,4,6,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,5,4,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,5,6,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,6,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,6,5,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,3,5,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,3,6,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,5,3,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,5,6,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,3,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,3,4,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,3,6,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,4,3,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,4,6,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,6,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,6,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,3,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,3,5,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,4,3,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,4,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,5,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,5,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,4,5,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,4,6,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,5,4,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,5,6,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,6,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,6,5,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,2,5,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,2,6,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,5,2,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,5,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,6,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,6,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,5,2,4,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
>>> Load all 1956 entries. <<<[1,3,5,2,6,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,5,4,2,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,5,4,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,5,6,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,2,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,2,5,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,4,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,5,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,3,5,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,3,6,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,5,3,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,5,6,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,6,3,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,6,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,3,2,5,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,3,2,6,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,3,5,2,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,3,5,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,3,6,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,3,6,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,5,2,3,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,5,2,6,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,5,3,2,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,5,3,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,6,2,3,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,6,3,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,6,5,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,2,3,4,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,2,3,6,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,2,4,3,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,2,4,6,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,2,6,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,2,6,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,3,2,4,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,3,2,6,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,3,4,2,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,3,4,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,4,2,3,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,4,2,6,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,4,3,2,6] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,4,3,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,6,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,2,3,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,2,3,5,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,2,4,3,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,2,4,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,2,5,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,2,5,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,3,2,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,3,2,5,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,4,2,3,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,5,2,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,5,3,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,5,3,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,5,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,5,6] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,4,6,5] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,5,4,6] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,5,6,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,6,4,5] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,6,5,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,4,3,5,6] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,4,3,6,5] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,4,5,3,6] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,4,5,6,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,4,6,3,5] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,5,3,4,6] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,5,3,6,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,5,4,3,6] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,5,4,6,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,6,3,4,5] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,6,3,5,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,3,1,4,5,6] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,4,6,5] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,5,4,6] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,5,6,4] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,6,4,5] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,6,5,4] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,4,1,5,6] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,3,4,1,6,5] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,3,4,5,1,6] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,3,4,6,1,5] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,3,5,1,4,6] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,3,5,1,6,4] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,3,5,4,1,6] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,3,5,6,1,4] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,3,6,1,4,5] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,3,6,1,5,4] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,3,6,4,1,5] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,3,6,5,1,4] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,4,1,3,5,6] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,4,1,3,6,5] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,4,1,5,3,6] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,4,1,5,6,3] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,4,1,6,3,5] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,4,1,6,5,3] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,4,3,1,5,6] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,4,3,1,6,5] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,4,3,5,1,6] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,4,3,6,1,5] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,4,5,1,3,6] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,4,5,1,6,3] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,4,5,3,1,6] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,4,5,6,1,3] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,4,6,1,3,5] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,4,6,1,5,3] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,4,6,3,1,5] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,4,6,5,1,3] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,5,1,3,4,6] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,5,1,3,6,4] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,5,1,4,3,6] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,5,1,4,6,3] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,5,1,6,3,4] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,5,1,6,4,3] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,5,3,1,4,6] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,5,3,1,6,4] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,5,3,4,1,6] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,5,3,6,1,4] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,5,4,1,3,6] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,5,4,1,6,3] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,5,4,3,1,6] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,5,4,6,1,3] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,5,6,1,3,4] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,5,6,1,4,3] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,5,6,3,1,4] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,5,6,4,1,3] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,6,1,3,4,5] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,6,1,3,5,4] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,6,1,4,3,5] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,6,1,4,5,3] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,6,1,5,3,4] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,6,1,5,4,3] => [2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,6,3,1,4,5] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,6,3,1,5,4] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,6,3,4,1,5] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,6,3,5,1,4] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,6,4,1,3,5] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,6,4,1,5,3] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,6,4,3,1,5] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,6,4,5,1,3] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,6,5,1,3,4] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,6,5,1,4,3] => [2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,6,5,3,1,4] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,6,5,4,1,3] => [2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,2,1,4,5,6] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,1,4,6,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,1,5,4,6] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,1,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,4,1,5,6] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[3,2,4,1,6,5] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[3,2,4,5,1,6] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[3,2,4,6,1,5] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[3,2,5,1,4,6] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[3,2,5,1,6,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[3,2,5,4,1,6] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[3,2,5,6,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[3,2,6,1,4,5] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[3,2,6,1,5,4] => [3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[3,2,6,4,1,5] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[3,2,6,5,1,4] => [3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[3,4,2,1,5,6] => [3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,4,2,1,6,5] => [3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,4,2,5,1,6] => [3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,4,2,6,1,5] => [3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,4,5,2,1,6] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,4,6,2,1,5] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,5,2,1,4,6] => [3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,5,2,1,6,4] => [3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,5,2,4,1,6] => [3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,5,2,6,1,4] => [3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,5,4,2,1,6] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,5,6,2,1,4] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,6,2,1,4,5] => [3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,6,2,4,1,5] => [3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,6,4,2,1,5] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,3,2,1,5,6] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,2,5,1,6] => [4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[4,3,5,2,1,6] => [4,3,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[4,3,6,2,1,5] => [4,3,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[4,5,3,2,1,6] => [4,6,3,2,1,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,6,3,2,1,5] => [4,6,3,2,1,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,4,5,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,4,5,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,4,6,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,4,6,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,4,7,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,4,7,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,5,4,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,5,4,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,5,6,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,5,6,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,5,7,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,5,7,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,6,4,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,6,4,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,6,5,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,6,5,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,6,7,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,6,7,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,7,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,7,4,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,7,5,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,7,5,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,7,6,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,7,6,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,3,5,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,3,5,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,3,6,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,3,6,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,3,7,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,3,7,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,5,3,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,5,3,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,5,6,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,5,6,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,5,7,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,5,7,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,6,3,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,6,3,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,6,5,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,6,5,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,6,7,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,6,7,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,7,3,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,7,3,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,7,5,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,7,5,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,7,6,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,7,6,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,3,4,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,3,4,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,3,6,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,3,6,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,3,7,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,3,7,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,4,3,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,4,3,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,4,6,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,4,6,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,4,7,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,4,7,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,6,3,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,6,3,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,6,4,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,6,4,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,6,7,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,6,7,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,7,3,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,7,3,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,7,4,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,7,4,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,7,6,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,7,6,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,3,4,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,3,4,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,3,5,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,3,5,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,3,7,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,3,7,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,4,3,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,4,3,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,4,5,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,4,5,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,4,7,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,4,7,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,5,3,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,5,3,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,5,4,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,5,4,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,5,7,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,5,7,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,7,3,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,7,3,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,7,4,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,7,4,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,7,5,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,6,7,5,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,3,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,3,4,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,3,5,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,3,5,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,3,6,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,3,6,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,4,3,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,4,3,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,4,5,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,4,5,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,4,6,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,4,6,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,5,3,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,5,3,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,5,4,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,5,4,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,5,6,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,5,6,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,6,3,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,6,3,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,6,4,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,6,4,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,6,5,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,7,6,5,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,4,5,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,4,5,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,4,6,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,4,6,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,4,7,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,4,7,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,5,4,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,5,4,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,5,6,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,5,6,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,5,7,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,5,7,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,6,4,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,6,4,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,6,5,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,6,5,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,6,7,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,6,7,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,7,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,7,4,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,7,5,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,7,5,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,7,6,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,7,6,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,2,5,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,2,5,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,2,6,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,2,6,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,2,7,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,2,7,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,2,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,2,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,6,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,6,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,7,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,7,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,2,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,2,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,5,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,5,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,7,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,7,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,2,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,2,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,5,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,5,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,6,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,6,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,2,4,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,2,4,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,2,6,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,2,6,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,2,7,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,2,7,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,2,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,2,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,6,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,6,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,7,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,7,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,6,2,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,6,2,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,6,4,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,6,4,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,6,7,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,6,7,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,7,2,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,7,2,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,7,4,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,7,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,7,6,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,7,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,4,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,4,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,5,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,5,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,7,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,7,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,4,2,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,4,2,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,4,5,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,4,5,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,4,7,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,4,7,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,5,2,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,5,2,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,5,4,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,5,4,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,5,7,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,5,7,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,7,2,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,7,2,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,7,4,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,7,4,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,7,5,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,7,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,4,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,5,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,5,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,6,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,6,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,4,2,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,4,2,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,4,5,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,4,5,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,4,6,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,4,6,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,5,2,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,5,2,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,5,4,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,5,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,5,6,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,5,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,6,2,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,6,2,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,6,4,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,6,4,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,6,5,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,6,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,3,5,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,3,5,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,3,6,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,3,6,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,3,7,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,3,7,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,3,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,3,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,6,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,6,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,7,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,7,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,3,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,3,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,5,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,5,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,7,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,7,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,3,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,3,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,5,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,5,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,6,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,6,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,2,5,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,2,5,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,2,6,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,2,6,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,2,7,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,2,7,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,2,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,2,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,6,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,6,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,7,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,7,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,2,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,2,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,5,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,5,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,7,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,7,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,2,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,2,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,5,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,5,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,6,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,6,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,3,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,3,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,6,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,6,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,7,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,7,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,2,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,2,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,6,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,6,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,7,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,7,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,6,2,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,6,2,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,6,3,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,6,3,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,6,7,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,6,7,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,7,2,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,7,2,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,7,3,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,7,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,7,6,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,7,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,2,3,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,2,3,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,2,5,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,2,5,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,2,7,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,2,7,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,3,2,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,3,2,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,3,5,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,3,5,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,3,7,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,3,7,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,5,2,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,5,2,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,5,3,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,5,3,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,5,7,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,5,7,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,7,2,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,7,2,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,7,3,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,7,3,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,7,5,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,6,7,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,2,3,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,2,3,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,2,5,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,2,5,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,2,6,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,2,6,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,3,2,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,3,2,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,3,5,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,3,5,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,3,6,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,3,6,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,5,2,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,5,2,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,5,3,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,5,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,5,6,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,5,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,6,2,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,6,2,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,6,3,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,6,3,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,6,5,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,7,6,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,4,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,4,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,6,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,6,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,7,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,7,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,3,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,3,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,6,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,6,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,7,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,7,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,6,3,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,6,3,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,6,4,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,6,4,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,6,7,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,6,7,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,7,3,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,7,3,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,7,4,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,7,4,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,7,6,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,7,6,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,4,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,4,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,6,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,6,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,7,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,7,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,2,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,2,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,6,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,6,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,7,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,7,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,6,2,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,6,2,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,6,4,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,6,4,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,6,7,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,6,7,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,7,2,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,7,2,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,7,4,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,7,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,7,6,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,7,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,3,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,3,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,6,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,6,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,7,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,7,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,2,6,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,2,7,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,6,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,6,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,7,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,7,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,6,2,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,6,2,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,6,3,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,6,7,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,6,7,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,7,2,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,7,2,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,7,3,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,7,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,7,6,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,7,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,2,3,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,2,3,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,2,4,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,2,4,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,2,7,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,2,7,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,3,2,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,3,2,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,3,4,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,3,4,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,3,7,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,3,7,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,4,2,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,4,2,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,4,3,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,4,3,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,4,7,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,4,7,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,7,2,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,7,2,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,7,3,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,7,3,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,7,4,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,6,7,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,2,3,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,2,3,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,2,4,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,2,4,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,2,6,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,2,6,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,3,2,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,3,2,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,3,4,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,3,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,3,6,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,3,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,4,2,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,4,2,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,4,3,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,4,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,4,6,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,4,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,6,2,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,6,2,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,6,3,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,6,3,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,6,4,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,7,6,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,4,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,4,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,5,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,5,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,7,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,7,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,4,3,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,4,3,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,4,5,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,4,5,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,4,7,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,4,7,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,5,3,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,5,3,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,5,4,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,5,4,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,5,7,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,5,7,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,7,3,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,7,3,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,7,4,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,7,4,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,7,5,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,7,5,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,4,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,4,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,5,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,5,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,7,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,7,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,4,2,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,4,2,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,4,5,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,4,5,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,4,7,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,4,7,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,5,2,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,5,2,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,5,4,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,5,4,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,5,7,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,5,7,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,7,2,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,7,2,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,7,4,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,7,4,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,7,5,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,7,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,2,3,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,2,3,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,2,5,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,2,5,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,2,7,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,2,7,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,3,2,5,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,3,2,7,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,3,5,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,3,5,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,3,7,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,3,7,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,5,2,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,5,2,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,5,3,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,5,3,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,5,7,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,5,7,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,7,2,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,7,2,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,7,3,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,7,3,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,7,5,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,4,7,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,2,3,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,2,3,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,2,4,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,2,4,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,2,7,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,2,7,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,3,2,4,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,3,2,7,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,3,4,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,3,4,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,3,7,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,3,7,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,4,2,3,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,4,2,7,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,4,3,2,7] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,4,3,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,4,7,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,4,7,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,7,2,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,7,2,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,7,3,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,7,3,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,7,4,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,5,7,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,2,3,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,2,3,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,2,4,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,2,4,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,2,5,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,2,5,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,3,2,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,3,2,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,3,4,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,3,4,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,3,5,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,3,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,4,2,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,4,2,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,4,3,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,4,3,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,4,5,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,4,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,5,2,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,5,2,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,5,3,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,5,3,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,5,4,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,7,5,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,4,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,5,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,5,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,6,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,6,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,4,3,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,4,3,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,4,5,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,4,5,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,4,6,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,4,6,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,5,3,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,5,3,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,5,4,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,5,4,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,5,6,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,5,6,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,6,3,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,6,3,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,6,4,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,6,4,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,6,5,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,6,5,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,4,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,5,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,5,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,6,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,6,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,4,2,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,4,2,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,4,5,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,4,5,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,4,6,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,4,6,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,5,2,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,5,2,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,5,4,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,5,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,5,6,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,5,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,6,2,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,6,2,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,6,4,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,6,4,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,6,5,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,6,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,2,3,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,2,3,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,2,5,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,2,5,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,2,6,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,2,6,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,3,2,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,3,2,6,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,3,5,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,3,5,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,3,6,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,3,6,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,5,2,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,5,2,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,5,3,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,5,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,5,6,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,5,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,6,2,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,6,2,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,6,3,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,6,3,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,6,5,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,4,6,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,2,3,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,2,3,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,2,4,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,2,4,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,2,6,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,2,6,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,3,2,4,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,3,2,6,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,3,4,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,3,4,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,3,6,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,3,6,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,4,2,3,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,4,2,6,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,4,3,2,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,4,6,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,4,6,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,6,2,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,6,2,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,6,3,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,6,3,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,6,4,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,5,6,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,2,3,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,2,3,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,2,4,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,2,4,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,2,5,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,2,5,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,3,2,4,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,3,2,5,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,3,4,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,3,4,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,3,5,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,3,5,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,4,2,3,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,4,2,5,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,4,3,2,5] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,4,3,5,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,4,5,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,5,2,3,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,5,2,4,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,5,3,2,4] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,5,3,4,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,5,4,2,3] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,3,4,5,6,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,5,7,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,6,5,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,6,7,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,7,5,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,7,6,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,5,4,6,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,5,4,7,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,5,6,4,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,5,6,7,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,5,7,4,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,5,7,6,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,6,4,5,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,6,4,7,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,6,5,4,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,6,5,7,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,6,7,4,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,6,7,5,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,7,4,5,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,7,4,6,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,7,5,4,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,7,5,6,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,7,6,4,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,7,6,5,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,3,5,6,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,3,5,7,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,3,6,5,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,3,6,7,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,3,7,5,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,3,7,6,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,5,3,6,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,5,3,7,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,5,6,3,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,5,6,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,5,7,3,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,5,7,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,6,3,5,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,6,3,7,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,6,5,3,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,6,5,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,6,7,3,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,6,7,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,7,3,5,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,7,3,6,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,7,5,3,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,7,5,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,7,6,3,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,7,6,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,3,4,6,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,3,4,7,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,3,6,4,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,3,6,7,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,3,7,4,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,3,7,6,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,4,3,6,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,4,3,7,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,4,6,3,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,4,6,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,4,7,3,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,4,7,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,6,3,4,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,6,3,7,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,6,4,3,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,6,7,3,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,6,7,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,7,3,4,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,7,3,6,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,7,4,3,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,7,4,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,7,6,3,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,7,6,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,3,4,5,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,3,4,7,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,3,5,4,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,3,5,7,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,3,7,4,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,3,7,5,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,3,5,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,3,7,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,5,3,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,5,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,7,3,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,7,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,5,3,4,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,5,3,7,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,5,4,3,7] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,5,4,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,5,7,3,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,5,7,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,7,3,4,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,7,3,5,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,7,4,3,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,7,4,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,7,5,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,3,4,5,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,3,4,6,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,3,5,4,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,3,5,6,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,3,6,4,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,3,6,5,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,4,3,5,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,4,3,6,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,4,5,3,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,4,6,3,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,5,3,4,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,5,3,6,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,5,4,3,6] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,5,6,3,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,5,6,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,6,3,4,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,6,3,5,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,6,4,3,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,6,4,5,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,6,5,3,4] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,4,5,6,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,4,5,7,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,4,6,5,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,4,6,7,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,4,7,5,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,4,7,6,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,5,4,6,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,5,4,7,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,5,6,4,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,5,6,7,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,5,7,4,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,5,7,6,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,6,4,5,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,6,4,7,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,6,5,4,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,6,5,7,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,6,7,4,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,6,7,5,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,7,4,5,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,7,4,6,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,7,5,4,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,7,5,6,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,7,6,4,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,7,6,5,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,4,1,5,6,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,4,1,5,7,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,4,1,6,5,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,4,1,6,7,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,4,1,7,5,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,4,1,7,6,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,4,5,1,6,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,4,5,1,7,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,4,5,6,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,4,5,7,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,4,6,1,5,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,4,6,1,7,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,4,6,5,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,4,6,7,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,4,7,1,5,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,4,7,1,6,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,4,7,5,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,4,7,6,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,5,1,4,6,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,5,1,4,7,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,5,1,6,4,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,5,1,6,7,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,5,1,7,4,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,5,1,7,6,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,5,4,1,6,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,5,4,1,7,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,5,4,6,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,5,4,7,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,5,6,1,4,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,5,6,1,7,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,5,6,4,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,5,6,7,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,5,7,1,4,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,5,7,1,6,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,5,7,4,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,5,7,6,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,6,1,4,5,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,6,1,4,7,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,6,1,5,4,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,6,1,5,7,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,6,1,7,4,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,6,1,7,5,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,6,4,1,5,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,6,4,1,7,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,6,4,5,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,6,4,7,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,6,5,1,4,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,6,5,1,7,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,6,5,4,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,6,5,7,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,6,7,1,4,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,6,7,1,5,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,6,7,4,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,6,7,5,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,7,1,4,5,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,7,1,4,6,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,7,1,5,4,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,7,1,5,6,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,7,1,6,4,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,7,1,6,5,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,3,7,4,1,5,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,7,4,1,6,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,7,4,5,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,7,4,6,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,7,5,1,4,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,7,5,1,6,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,7,5,4,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,7,5,6,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,7,6,1,4,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,7,6,1,5,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,3,7,6,4,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,7,6,5,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,1,3,5,6,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,3,5,7,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,3,6,5,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,3,6,7,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,3,7,5,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,3,7,6,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,5,3,6,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,5,3,7,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,5,6,3,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,5,6,7,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,5,7,3,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,5,7,6,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,6,3,5,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,6,3,7,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,6,5,3,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,6,5,7,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,6,7,3,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,6,7,5,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,7,3,5,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,7,3,6,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,7,5,3,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,7,5,6,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,7,6,3,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,7,6,5,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,3,1,5,6,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,3,1,5,7,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,3,1,6,5,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,3,1,6,7,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,3,1,7,5,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,3,1,7,6,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,3,5,1,6,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,3,5,1,7,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,3,5,6,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,3,5,7,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,3,6,1,5,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,3,6,1,7,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,3,6,5,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,3,6,7,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,3,7,1,5,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,3,7,1,6,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,3,7,5,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,3,7,6,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,5,1,3,6,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,5,1,3,7,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,5,1,6,3,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,5,1,6,7,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,5,1,7,3,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,5,1,7,6,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,5,3,1,6,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,5,3,1,7,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,5,3,6,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,5,3,7,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,5,6,1,3,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,5,6,1,7,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,5,6,3,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,5,6,7,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,5,7,1,3,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,5,7,1,6,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,5,7,3,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,5,7,6,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,6,1,3,5,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,6,1,3,7,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,6,1,5,3,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,6,1,5,7,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,6,1,7,3,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,6,1,7,5,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,6,3,1,5,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,6,3,1,7,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,6,3,5,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,6,3,7,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,6,5,1,3,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,6,5,1,7,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,6,5,3,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,6,5,7,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,6,7,1,3,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,6,7,1,5,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,6,7,3,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,6,7,5,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,7,1,3,5,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,7,1,3,6,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,7,1,5,3,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,7,1,5,6,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,7,1,6,3,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,7,1,6,5,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,4,7,3,1,5,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,7,3,1,6,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,7,3,5,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,7,3,6,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,7,5,1,3,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,7,5,1,6,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,7,5,3,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,7,5,6,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,7,6,1,3,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,7,6,1,5,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,4,7,6,3,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,4,7,6,5,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,1,3,4,6,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,3,4,7,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,3,6,4,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,3,6,7,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,3,7,4,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,3,7,6,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,4,3,6,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,4,3,7,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,4,6,3,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,4,6,7,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,4,7,3,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,4,7,6,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,6,3,4,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,6,3,7,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,6,4,3,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,6,4,7,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,6,7,3,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,6,7,4,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,7,3,4,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,7,3,6,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,7,4,3,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,7,4,6,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,7,6,3,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,7,6,4,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,3,1,4,6,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,3,1,4,7,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,3,1,6,4,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,3,1,6,7,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,3,1,7,4,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,3,1,7,6,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,3,4,1,6,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,3,4,1,7,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,3,4,6,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,3,4,7,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,3,6,1,4,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,3,6,1,7,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,3,6,4,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,3,6,7,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,3,7,1,4,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,3,7,1,6,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,3,7,4,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,3,7,6,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,4,1,3,6,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,4,1,3,7,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,4,1,6,3,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,4,1,6,7,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,4,1,7,3,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,4,1,7,6,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,4,3,1,6,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,4,3,1,7,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,4,3,6,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,4,3,7,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,4,6,1,3,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,4,6,1,7,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,4,6,3,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,4,6,7,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,4,7,1,3,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,4,7,1,6,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,4,7,3,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,4,7,6,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,6,1,3,4,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,6,1,3,7,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,6,1,4,3,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,6,1,4,7,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,6,1,7,3,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,6,1,7,4,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,6,3,1,4,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,6,3,1,7,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,6,3,4,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,6,3,7,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,6,4,1,3,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,6,4,1,7,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,6,4,3,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,6,4,7,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,6,7,1,3,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,6,7,1,4,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,6,7,3,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,6,7,4,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,7,1,3,4,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,7,1,3,6,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,7,1,4,3,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,7,1,4,6,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,7,1,6,3,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,7,1,6,4,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,5,7,3,1,4,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,7,3,1,6,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,7,3,4,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,7,3,6,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,7,4,1,3,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,7,4,1,6,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,7,4,3,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,7,4,6,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,7,6,1,3,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,7,6,1,4,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,5,7,6,3,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,5,7,6,4,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,1,3,4,5,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,3,4,7,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,3,5,4,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,3,5,7,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,3,7,4,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,3,7,5,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,4,3,5,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,4,3,7,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,4,5,3,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,4,5,7,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,4,7,3,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,4,7,5,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,5,3,4,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,5,3,7,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,5,4,3,7] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,5,4,7,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,5,7,3,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,5,7,4,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,7,3,4,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,7,3,5,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,7,4,3,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,7,4,5,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,7,5,3,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1,7,5,4,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,3,1,4,5,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,3,1,4,7,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,3,1,5,4,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,3,1,5,7,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,3,1,7,4,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,3,1,7,5,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,3,4,1,5,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,3,4,1,7,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,3,4,5,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,3,4,7,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,3,5,1,4,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,3,5,1,7,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,3,5,4,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,3,5,7,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,3,7,1,4,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,3,7,1,5,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,3,7,4,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,3,7,5,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,4,1,3,5,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,4,1,3,7,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,4,1,5,3,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,4,1,5,7,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,4,1,7,3,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,4,1,7,5,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,4,3,1,5,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,4,3,1,7,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,4,3,5,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,4,3,7,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,4,5,1,3,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,4,5,1,7,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,4,5,3,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,4,5,7,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,4,7,1,3,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,4,7,1,5,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,4,7,3,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,4,7,5,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,5,1,3,4,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,5,1,3,7,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,5,1,4,3,7] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,5,1,4,7,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,5,1,7,3,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,5,1,7,4,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,5,3,1,4,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,5,3,1,7,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,5,3,4,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,5,3,7,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,5,4,1,3,7] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,5,4,1,7,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,5,4,3,1,7] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,5,4,7,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,5,7,1,3,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,5,7,1,4,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,5,7,3,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,5,7,4,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,7,1,3,4,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,7,1,3,5,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,7,1,4,3,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,7,1,4,5,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,7,1,5,3,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,7,1,5,4,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,6,7,3,1,4,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,7,3,1,5,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,7,3,4,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,7,3,5,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,7,4,1,3,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,7,4,1,5,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,7,4,3,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,7,4,5,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,7,5,1,3,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,7,5,1,4,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,6,7,5,3,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,6,7,5,4,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,1,3,4,5,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,3,4,6,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,3,5,4,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,3,5,6,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,3,6,4,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,3,6,5,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,4,3,5,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,4,3,6,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,4,5,3,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,4,5,6,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,4,6,3,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,4,6,5,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,5,3,4,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,5,3,6,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,5,4,3,6] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,5,4,6,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,5,6,3,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,5,6,4,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,6,3,4,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,6,3,5,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,6,4,3,5] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,6,4,5,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,6,5,3,4] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,1,6,5,4,3] => [2,7,1,6,5,4,3] => [3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,7,3,1,4,5,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,3,1,4,6,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,3,1,5,4,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,3,1,5,6,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,3,1,6,4,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,3,1,6,5,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,3,4,1,5,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,3,4,1,6,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,3,4,5,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,3,4,6,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,3,5,1,4,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,3,5,1,6,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,3,5,4,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,3,5,6,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,3,6,1,4,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,3,6,1,5,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,3,6,4,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,3,6,5,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,4,1,3,5,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,4,1,3,6,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,4,1,5,3,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,4,1,5,6,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,4,1,6,3,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,4,1,6,5,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,4,3,1,5,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,4,3,1,6,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,4,3,5,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,4,3,6,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,4,5,1,3,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,4,5,1,6,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,4,5,3,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,4,5,6,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,4,6,1,3,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,4,6,1,5,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,4,6,3,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,4,6,5,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,5,1,3,4,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,5,1,3,6,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,5,1,4,3,6] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,5,1,4,6,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,5,1,6,3,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,5,1,6,4,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,5,3,1,4,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,5,3,1,6,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,5,3,4,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,5,3,6,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,5,4,1,3,6] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,5,4,1,6,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,5,4,3,1,6] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,5,4,6,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,5,6,1,3,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,5,6,1,4,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,5,6,3,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,5,6,4,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,6,1,3,4,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,6,1,3,5,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,6,1,4,3,5] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,6,1,4,5,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,6,1,5,3,4] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,6,1,5,4,3] => [2,7,6,1,5,4,3] => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[2,7,6,3,1,4,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,6,3,1,5,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,6,3,4,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,6,3,5,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,6,4,1,3,5] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,6,4,1,5,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,6,4,3,1,5] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,6,4,5,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,6,5,1,3,4] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,6,5,1,4,3] => [2,7,6,5,1,4,3] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,7,6,5,3,1,4] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,7,6,5,4,1,3] => [2,7,6,5,4,1,3] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,2,1,4,5,6,7] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,4,5,7,6] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,4,6,5,7] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,4,6,7,5] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,4,7,5,6] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,4,7,6,5] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,5,4,6,7] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,5,4,7,6] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,5,6,4,7] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,5,6,7,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,5,7,4,6] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,5,7,6,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,6,4,5,7] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,6,4,7,5] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,6,5,4,7] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,6,5,7,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,6,7,4,5] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,6,7,5,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,7,4,5,6] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,7,4,6,5] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,7,5,4,6] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,7,6,4,5] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,4,1,5,6,7] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,4,1,5,7,6] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,4,1,6,5,7] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,4,1,6,7,5] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,4,1,7,5,6] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,4,1,7,6,5] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,4,5,1,6,7] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,4,5,1,7,6] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,4,5,6,1,7] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,4,5,7,1,6] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,4,6,1,5,7] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,4,6,1,7,5] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,4,6,5,1,7] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,4,6,7,1,5] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,4,7,1,5,6] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,4,7,1,6,5] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,4,7,5,1,6] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,4,7,6,1,5] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,5,1,4,6,7] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,5,1,4,7,6] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,5,1,6,4,7] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,5,1,6,7,4] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,5,1,7,4,6] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,5,1,7,6,4] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,5,4,1,6,7] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,5,4,1,7,6] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,5,4,6,1,7] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,5,4,7,1,6] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,5,6,1,4,7] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,5,6,1,7,4] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,5,6,4,1,7] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,5,6,7,1,4] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,5,7,1,4,6] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,5,7,1,6,4] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,5,7,4,1,6] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,5,7,6,1,4] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,6,1,4,5,7] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,6,1,4,7,5] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,6,1,5,4,7] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,6,1,5,7,4] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,6,1,7,4,5] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,6,1,7,5,4] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,6,4,1,5,7] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,6,4,1,7,5] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,6,4,5,1,7] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,6,4,7,1,5] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,6,5,1,4,7] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,6,5,1,7,4] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,6,5,4,1,7] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,6,5,7,1,4] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,6,7,1,4,5] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,6,7,1,5,4] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,6,7,4,1,5] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,6,7,5,1,4] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,7,1,4,5,6] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,7,1,4,6,5] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,7,1,5,4,6] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,7,1,5,6,4] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,7,1,6,4,5] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,7,1,6,5,4] => [3,2,7,1,6,5,4] => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[3,2,7,4,1,5,6] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,7,4,1,6,5] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,7,4,5,1,6] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,7,4,6,1,5] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,7,5,1,4,6] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,7,5,1,6,4] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,7,5,4,1,6] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,7,5,6,1,4] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,7,6,1,4,5] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,7,6,1,5,4] => [3,2,7,6,1,5,4] => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[3,2,7,6,4,1,5] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,2,7,6,5,1,4] => [3,2,7,6,5,1,4] => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[3,4,2,1,5,6,7] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,4,2,1,5,7,6] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,4,2,1,6,5,7] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,4,2,1,6,7,5] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,4,2,1,7,5,6] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,4,2,1,7,6,5] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,4,2,5,1,6,7] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,2,5,1,7,6] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,2,5,6,1,7] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,2,5,7,1,6] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,2,6,1,5,7] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,2,6,1,7,5] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,2,6,5,1,7] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,2,6,7,1,5] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,2,7,1,5,6] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,2,7,1,6,5] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,2,7,5,1,6] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,2,7,6,1,5] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,5,2,1,6,7] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,5,2,1,7,6] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,5,2,6,1,7] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,5,2,7,1,6] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,5,6,2,1,7] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,5,7,2,1,6] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,6,2,1,5,7] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,6,2,1,7,5] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,6,2,5,1,7] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,6,2,7,1,5] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,6,5,2,1,7] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,6,7,2,1,5] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,7,2,1,5,6] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,7,2,1,6,5] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,4,7,2,5,1,6] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,7,2,6,1,5] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,7,5,2,1,6] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,4,7,6,2,1,5] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,2,1,4,6,7] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,5,2,1,4,7,6] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,5,2,1,6,4,7] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,5,2,1,6,7,4] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,5,2,1,7,4,6] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,5,2,1,7,6,4] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,5,2,4,1,6,7] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,2,4,1,7,6] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,2,4,6,1,7] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,2,4,7,1,6] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,2,6,1,4,7] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,2,6,1,7,4] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,2,6,4,1,7] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,2,6,7,1,4] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,2,7,1,4,6] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,2,7,1,6,4] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,2,7,4,1,6] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,2,7,6,1,4] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,4,2,1,6,7] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,4,2,1,7,6] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,4,2,6,1,7] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,4,2,7,1,6] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,4,6,2,1,7] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,4,7,2,1,6] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,6,2,1,4,7] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,6,2,1,7,4] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,6,2,4,1,7] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,6,2,7,1,4] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,6,4,2,1,7] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,6,7,2,1,4] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,7,2,1,4,6] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,7,2,1,6,4] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,5,7,2,4,1,6] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,7,2,6,1,4] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,7,4,2,1,6] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,5,7,6,2,1,4] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,2,1,4,5,7] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,6,2,1,4,7,5] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,6,2,1,5,4,7] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,6,2,1,5,7,4] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,6,2,1,7,4,5] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,6,2,1,7,5,4] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,6,2,4,1,5,7] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,2,4,1,7,5] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,2,4,5,1,7] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,2,4,7,1,5] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,2,5,1,4,7] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,2,5,1,7,4] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,2,5,4,1,7] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,2,5,7,1,4] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,2,7,1,4,5] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,2,7,1,5,4] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,2,7,4,1,5] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,2,7,5,1,4] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,4,2,1,5,7] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,4,2,1,7,5] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,4,2,5,1,7] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,4,2,7,1,5] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,4,5,2,1,7] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,4,7,2,1,5] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,5,2,1,4,7] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,5,2,1,7,4] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,5,2,4,1,7] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,5,2,7,1,4] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,5,4,2,1,7] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,5,7,2,1,4] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,7,2,1,4,5] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,7,2,1,5,4] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,6,7,2,4,1,5] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,7,2,5,1,4] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,7,4,2,1,5] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,6,7,5,2,1,4] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,2,1,4,5,6] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,7,2,1,4,6,5] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,7,2,1,5,4,6] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,7,2,1,5,6,4] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,7,2,1,6,4,5] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,7,2,1,6,5,4] => [3,7,2,1,6,5,4] => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,7,2,4,1,5,6] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,2,4,1,6,5] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,2,4,5,1,6] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,2,4,6,1,5] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,2,5,1,4,6] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,2,5,1,6,4] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,2,5,4,1,6] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,2,5,6,1,4] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,2,6,1,4,5] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,2,6,1,5,4] => [3,7,2,6,1,5,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,2,6,4,1,5] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,2,6,5,1,4] => [3,7,2,6,5,1,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,4,2,1,5,6] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,4,2,1,6,5] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,4,2,5,1,6] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,4,2,6,1,5] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,4,5,2,1,6] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,4,6,2,1,5] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,5,2,1,4,6] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,5,2,1,6,4] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,5,2,4,1,6] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,5,2,6,1,4] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,5,4,2,1,6] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,5,6,2,1,4] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,6,2,1,4,5] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,6,2,1,5,4] => [3,7,6,2,1,5,4] => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,7,6,2,4,1,5] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,6,2,5,1,4] => [3,7,6,2,5,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,6,4,2,1,5] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[3,7,6,5,2,1,4] => [3,7,6,5,2,1,4] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,3,2,1,5,6,7] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,3,2,1,5,7,6] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,3,2,1,6,5,7] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,3,2,1,6,7,5] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,3,2,1,7,5,6] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,3,2,5,1,6,7] => [4,3,2,7,1,6,5] => [5,3,2,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[4,3,2,5,1,7,6] => [4,3,2,7,1,6,5] => [5,3,2,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[4,3,2,5,6,1,7] => [4,3,2,7,6,1,5] => [6,3,2,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[4,3,2,5,7,1,6] => [4,3,2,7,6,1,5] => [6,3,2,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[4,3,2,6,1,5,7] => [4,3,2,7,1,6,5] => [5,3,2,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[4,3,2,6,1,7,5] => [4,3,2,7,1,6,5] => [5,3,2,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[4,3,2,6,5,1,7] => [4,3,2,7,6,1,5] => [6,3,2,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[4,3,2,6,7,1,5] => [4,3,2,7,6,1,5] => [6,3,2,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[4,3,2,7,1,5,6] => [4,3,2,7,1,6,5] => [5,3,2,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[4,3,2,7,1,6,5] => [4,3,2,7,1,6,5] => [5,3,2,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[4,3,2,7,5,1,6] => [4,3,2,7,6,1,5] => [6,3,2,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[4,3,2,7,6,1,5] => [4,3,2,7,6,1,5] => [6,3,2,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[4,3,5,2,1,6,7] => [4,3,7,2,1,6,5] => [5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[4,3,5,2,1,7,6] => [4,3,7,2,1,6,5] => [5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[4,3,5,2,6,1,7] => [4,3,7,2,6,1,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,5,2,7,1,6] => [4,3,7,2,6,1,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,5,6,2,1,7] => [4,3,7,6,2,1,5] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,5,7,2,1,6] => [4,3,7,6,2,1,5] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,6,2,1,5,7] => [4,3,7,2,1,6,5] => [5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[4,3,6,2,1,7,5] => [4,3,7,2,1,6,5] => [5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[4,3,6,2,5,1,7] => [4,3,7,2,6,1,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,6,2,7,1,5] => [4,3,7,2,6,1,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,6,5,2,1,7] => [4,3,7,6,2,1,5] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,6,7,2,1,5] => [4,3,7,6,2,1,5] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,7,2,1,5,6] => [4,3,7,2,1,6,5] => [5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[4,3,7,2,1,6,5] => [4,3,7,2,1,6,5] => [5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[4,3,7,2,5,1,6] => [4,3,7,2,6,1,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,7,2,6,1,5] => [4,3,7,2,6,1,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,7,5,2,1,6] => [4,3,7,6,2,1,5] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,3,7,6,2,1,5] => [4,3,7,6,2,1,5] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[4,5,3,2,1,6,7] => [4,7,3,2,1,6,5] => [5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[4,5,3,2,1,7,6] => [4,7,3,2,1,6,5] => [5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[4,5,3,2,6,1,7] => [4,7,3,2,6,1,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,5,3,2,7,1,6] => [4,7,3,2,6,1,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,5,3,6,2,1,7] => [4,7,3,6,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,5,3,7,2,1,6] => [4,7,3,6,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,5,6,3,2,1,7] => [4,7,6,3,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,5,7,3,2,1,6] => [4,7,6,3,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,6,3,2,1,5,7] => [4,7,3,2,1,6,5] => [5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[4,6,3,2,1,7,5] => [4,7,3,2,1,6,5] => [5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[4,6,3,2,5,1,7] => [4,7,3,2,6,1,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,6,3,2,7,1,5] => [4,7,3,2,6,1,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,6,3,5,2,1,7] => [4,7,3,6,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,6,3,7,2,1,5] => [4,7,3,6,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,6,5,3,2,1,7] => [4,7,6,3,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,6,7,3,2,1,5] => [4,7,6,3,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,7,3,2,1,5,6] => [4,7,3,2,1,6,5] => [5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[4,7,3,2,1,6,5] => [4,7,3,2,1,6,5] => [5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[4,7,3,2,5,1,6] => [4,7,3,2,6,1,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,7,3,2,6,1,5] => [4,7,3,2,6,1,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,7,3,5,2,1,6] => [4,7,3,6,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,7,3,6,2,1,5] => [4,7,3,6,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,7,5,3,2,1,6] => [4,7,6,3,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[4,7,6,3,2,1,5] => [4,7,6,3,2,1,5] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[5,4,3,2,1,6,7] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[5,4,3,2,6,1,7] => [5,4,3,2,7,1,6] => [6,4,3,2,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[5,4,3,2,7,1,6] => [5,4,3,2,7,1,6] => [6,4,3,2,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[5,4,3,6,2,1,7] => [5,4,3,7,2,1,6] => [6,5,3,7,2,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[5,4,3,7,2,1,6] => [5,4,3,7,2,1,6] => [6,5,3,7,2,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[5,4,6,3,2,1,7] => [5,4,7,3,2,1,6] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[5,4,7,3,2,1,6] => [5,4,7,3,2,1,6] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[5,6,4,3,2,1,7] => [5,7,4,3,2,1,6] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[5,7,4,3,2,1,6] => [5,7,4,3,2,1,6] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
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Description
The dominant dimension of eAe for the corresponding Nakayama algebra A with minimal faithful projective-injective module eA.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a 123-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between 132-avoiding permutations and 123-avoiding permutations, see [1, Proposition 19].
Details can be found in [1].
In particular, this is a bijection between 132-avoiding permutations and 123-avoiding permutations, see [1, Proposition 19].
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
Demazure product with inverse
Description
This map sends a permutation π to π−1⋆π where ⋆ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
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