Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001498: Dyck paths ⟶ ℤ
Values
[1,2] => [1,2] => [1,2] => [1,0,1,0] => 1
[1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 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] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 1
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 1
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 2
[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] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 2
[2,3,1,4] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 3
[3,1,2,4] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 3
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 3
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,3,4,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,5,2,4] => [1,4,5,2,3] => [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] => [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,4,2,5,3] => [1,5,3,4,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,4,3,5,2] => [1,5,3,4,2] => [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] => [1,5,3,4,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,2,4,3] => [1,5,3,4,2] => [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] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 2
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 2
[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] => 2
[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] => 2
[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] => 2
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[2,3,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,4,1,3,5] => [3,4,1,2,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,4,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[3,1,4,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[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] => 3
[3,2,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[3,4,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[4,1,2,3,5] => [4,2,3,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[4,1,3,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[4,2,1,3,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[4,3,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 4
[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] => 4
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [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] => [1,5,3,6,2,4] => [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] => [1,6,3,5,4,2] => [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] => [1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
>>> Load all 1936 entries. <<<[1,3,5,2,6,4] => [1,4,6,2,5,3] => [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] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [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] => [1,5,6,4,2,3] => [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] => [1,4,6,2,5,3] => [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] => [1,4,6,2,5,3] => [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] => [1,5,6,4,2,3] => [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] => [1,5,6,4,2,3] => [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] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [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] => [1,5,3,6,2,4] => [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] => [1,6,3,5,4,2] => [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] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [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] => [1,5,3,6,2,4] => [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] => [1,6,3,5,4,2] => [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] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,4,5,2,6,3] => [1,6,4,3,5,2] => [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] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [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] => [1,5,6,4,2,3] => [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] => [1,5,6,4,2,3] => [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] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [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] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [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] => [1,6,3,5,4,2] => [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] => [1,6,3,5,4,2] => [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] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [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] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [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] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [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] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [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] => [1,6,3,4,5,2] => [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] => [1,6,3,4,5,2] => [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] => [1,6,3,5,4,2] => [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] => [1,6,3,5,4,2] => [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] => [1,6,3,5,4,2] => [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] => [1,6,3,5,4,2] => [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] => [1,6,4,3,5,2] => [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] => [1,6,4,3,5,2] => [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] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 2
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 2
[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] => 2
[2,1,6,3,4,5] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[3,1,2,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[3,1,2,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[3,1,4,2,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[3,1,4,2,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[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] => 3
[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] => 3
[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] => 3
[3,2,4,1,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[3,2,4,1,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,1,2,3,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[4,1,2,3,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,1,3,2,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[4,1,3,2,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[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] => 4
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,1,2,3,4,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,1,2,4,3,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,1,3,2,4,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,1,3,4,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,1,4,2,3,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,1,4,3,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,2,1,3,4,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,2,1,4,3,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[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] => 5
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,4,7,5,6] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,5,7,4,6] => [1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,5,7,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,6,4,5,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,3,6,4,7,5] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,2,3,6,5,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,6,7,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,7,4,5,6] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,7,4,6,5] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,7,5,4,6] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,7,6,4,5] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,2,4,3,7,5,6] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,5,7,3,6] => [1,2,6,4,7,3,5] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,5,7,6,3] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,4,6,3,7,5] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,4,6,5,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,7,3,5] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,7,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,7,3,5,6] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,7,3,6,5] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,7,5,3,6] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,7,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,7,6,3,5] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,7,6,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,2,5,3,4,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,2,5,3,6,4,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,5,3,6,7,4] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,3,7,4,6] => [1,2,6,4,7,3,5] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,3,7,6,4] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,2,5,4,6,3,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,5,4,6,7,3] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,4,7,3,6] => [1,2,6,4,7,3,5] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,4,7,6,3] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,5,6,3,7,4] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,6,4,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,5,6,4,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,6,7,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,6,7,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,7,3,4,6] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,7,4,3,6] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,7,4,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,7,6,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,7,6,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,3,4,5,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,6,3,4,7,5] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,3,5,4,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,6,3,5,7,4] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,3,7,4,5] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,3,7,5,4] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,4,3,5,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,6,4,3,7,5] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,6,4,5,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,4,7,3,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,4,7,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,5,3,4,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,6,5,3,7,4] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,2,6,5,4,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,5,7,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,5,7,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,7,3,4,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,7,3,5,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,7,4,3,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,7,4,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,6,7,5,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,3,4,5,6] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,3,4,6,5] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,3,5,4,6] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,3,5,6,4] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,3,6,4,5] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,3,6,5,4] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,4,3,5,6] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,4,3,6,5] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,4,5,3,6] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,4,6,3,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,5,3,4,6] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,5,3,6,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,5,4,3,6] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,5,6,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,5,6,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,6,3,4,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,6,3,5,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,6,4,3,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,6,4,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,6,5,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,3,2,4,7,5,6] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,5,7,4,6] => [1,3,2,6,7,4,5] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,5,7,6,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,6,4,5,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,3,2,6,4,7,5] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,3,2,6,5,7,4] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,6,7,4,5] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,6,7,5,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,7,4,5,6] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,7,4,6,5] => [1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,7,5,4,6] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,7,5,6,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,7,6,4,5] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,3,4,2,7,5,6] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,3,4,2,7,6,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,7,2,6] => [1,6,3,4,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,5,7,6,2] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,2,5,7] => [1,5,3,6,2,4,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,4,6,2,7,5] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,6,5,2,7] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,4,6,5,7,2] => [1,7,3,5,4,6,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,2,6,5] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,4,7,5,2,6] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,4,5,2,3,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,3,5,2,4,7,6] => [1,4,5,2,3,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,3,5,2,6,4,7] => [1,4,6,2,5,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,5,2,6,7,4] => [1,4,7,2,5,6,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,2,7,4,6] => [1,4,6,2,7,3,5] => [1,6,7,4,5,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,3,5,2,7,6,4] => [1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,3,5,4,2,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,3,5,4,6,2,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,5,4,6,7,2] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,7,2,6] => [1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,4,7,6,2] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,5,6,2,4,7] => [1,5,6,4,2,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,5,6,2,7,4] => [1,5,7,4,2,6,3] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,5,6,4,7,2] => [1,7,5,4,3,6,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,5,6,7,2,3,4] => [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] => [1,5,7,6,2,4,3] => [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] => [1,6,5,7,3,2,4] => [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] => [1,7,5,6,3,4,2] => [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] => [1,6,7,5,4,2,3] => [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] => [1,4,6,2,5,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,6,2,4,7,5] => [1,4,7,2,5,6,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,5,4,7] => [1,4,6,2,5,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,6,2,5,7,4] => [1,4,7,2,5,6,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,7,4,5] => [1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,2,7,5,4] => [1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,6,4,2,5,7] => [1,5,6,4,2,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,6,4,2,7,5] => [1,5,7,4,2,6,3] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,6,4,5,7,2] => [1,7,5,4,3,6,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,5,6,4,2,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,6,5,2,7,4] => [1,5,7,4,2,6,3] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,3,6,5,4,7,2] => [1,7,5,4,3,6,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,5,7,6,2,4,3] => [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] => [1,5,7,6,2,4,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,4,7,2,5,6,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,4,6,5] => [1,4,7,2,5,6,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,5,4,6] => [1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,5,6,4] => [1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,6,4,5] => [1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,2,6,5,4] => [1,4,7,2,6,5,3] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,7,4,2,5,6] => [1,5,7,4,2,6,3] => [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] => [1,5,7,4,2,6,3] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,5,7,6,2,4,3] => [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] => [1,5,7,6,2,4,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,5,7,6,2,4,3] => [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] => [1,5,7,6,2,4,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,4,2,3,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,4,2,3,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,4,2,3,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,4,2,3,7,5,6] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,4,2,3,7,6,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,4,2,5,3,6,7] => [1,5,3,4,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,4,2,5,3,7,6] => [1,5,3,4,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,4,2,5,6,3,7] => [1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,2,5,6,7,3] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,7,3,6] => [1,6,3,4,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,5,7,6,3] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,3,5,7] => [1,5,3,6,2,4,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,2,6,3,7,5] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,6,5,3,7] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,2,6,5,7,3] => [1,7,3,5,4,6,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,3,6,5] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,7,5,3,6] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,4,3,2,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,4,3,2,7,5,6] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,4,3,5,2,6,7] => [1,5,3,4,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,4,3,5,2,7,6] => [1,5,3,4,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,4,3,5,6,2,7] => [1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,3,5,6,7,2] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,7,2,6] => [1,6,3,4,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,5,7,6,2] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,2,5,7] => [1,5,3,6,2,4,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,3,6,2,7,5] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,6,5,2,7] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,3,6,5,7,2] => [1,7,3,5,4,6,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,2,6,5] => [1,5,3,7,2,6,4] => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,7,5,2,6] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,4,5,2,3,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,4,5,2,6,3,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,5,2,6,7,3] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,7,3,6] => [1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,2,7,6,3] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,4,5,3,2,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,4,5,3,6,2,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,5,3,6,7,2] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,7,2,6] => [1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,3,7,6,2] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,5,6,2,3,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,5,6,2,7,3] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,5,6,3,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,7,3,2,4] => [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] => [1,7,5,6,3,4,2] => [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] => [1,6,5,7,3,2,4] => [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] => [1,7,5,6,3,4,2] => [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] => [1,5,6,4,2,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,6,2,3,7,5] => [1,5,7,4,2,6,3] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,6,2,5,7,3] => [1,7,5,4,3,6,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,5,6,4,2,3,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,6,3,2,7,5] => [1,5,7,4,2,6,3] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,6,3,5,7,2] => [1,7,5,4,3,6,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,6,5,2,7,3] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,4,6,5,3,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,5,7,4,2,6,3] => [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] => [1,5,7,4,2,6,3] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,5,7,4,2,6,3] => [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] => [1,5,7,4,2,6,3] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,5,3,4,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,5,2,3,4,7,6] => [1,5,3,4,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,5,2,3,6,4,7] => [1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,2,3,6,7,4] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,7,4,6] => [1,6,3,4,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,3,7,6,4] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,3,6,7] => [1,5,3,4,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,5,2,4,3,7,6] => [1,5,3,4,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,5,2,4,6,3,7] => [1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,2,4,6,7,3] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,7,3,6] => [1,6,3,4,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,4,7,6,3] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,2,6,3,4,7] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,2,6,3,7,4] => [1,7,3,5,4,6,2] => [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] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,2,6,4,7,3] => [1,7,3,5,4,6,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,6,3,7,5,2,4] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,5,3,2,4,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,5,3,2,6,4,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,3,2,6,7,4] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,7,4,6] => [1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,2,7,6,4] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,5,3,4,2,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,5,3,4,6,2,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,3,4,6,7,2] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,7,2,6] => [1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,4,7,6,2] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,3,6,2,4,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,3,6,2,7,4] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,3,6,4,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,7,3,2,4] => [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] => [1,7,5,6,3,4,2] => [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] => [1,6,5,7,3,2,4] => [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] => [1,7,5,6,3,4,2] => [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] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,5,4,2,3,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,5,4,2,6,3,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,4,2,6,7,3] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,7,3,6] => [1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,2,7,6,3] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,5,4,3,6,2,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,4,3,6,7,2] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,7,2,6] => [1,6,4,3,7,2,5] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,3,7,6,2] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,4,6,2,3,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,4,6,2,7,3] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,4,6,3,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,7,3,2,4] => [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] => [1,7,5,6,3,4,2] => [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] => [1,6,5,7,3,2,4] => [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] => [1,7,5,6,3,4,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,6,2,3,7,4] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,6,2,4,7,3] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,6,3,2,7,4] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,6,3,4,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,6,4,2,7,3] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,5,6,4,3,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,4,5,2,3] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,7,5,4,2,3] => [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] => [1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,2,3,4,7,5] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,5,4,7] => [1,6,3,4,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,2,3,5,7,4] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,7,4,5] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,3,7,5,4] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,2,4,3,5,7] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,2,4,3,7,5] => [1,7,3,5,4,6,2] => [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] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,2,4,5,7,3] => [1,7,3,5,4,6,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,2,5,3,7,4] => [1,7,3,5,4,6,2] => [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] => [1,6,3,5,4,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,2,5,4,7,3] => [1,7,3,5,4,6,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,3,2,4,7,5] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,5,4,7] => [1,6,4,3,5,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,3,2,5,7,4] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,7,4,5] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,2,7,5,4] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,6,3,4,2,5,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,3,4,2,7,5] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,3,4,5,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,3,5,2,7,4] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,3,5,4,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,5,6,3,4,2] => [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] => [1,7,5,6,3,4,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,4,2,3,7,5] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,4,2,5,7,3] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,4,3,2,7,5] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,4,3,5,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,4,5,2,7,3] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,4,5,3,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,5,2,3,7,4] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,5,2,4,7,3] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,5,3,2,7,4] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,5,3,4,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,5,4,2,7,3] => [1,7,5,4,3,6,2] => [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] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,6,5,4,3,7,2] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,4,6,5] => [1,7,3,4,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,5,4,6] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,5,6,4] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,6,4,5] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,3,6,5,4] => [1,7,3,4,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,2,4,3,5,6] => [1,7,3,5,4,6,2] => [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] => [1,7,3,5,4,6,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,3,6,5,4,2] => [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] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,4,6,5] => [1,7,4,3,5,6,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,5,4,6] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,5,6,4] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,6,4,5] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,2,6,5,4] => [1,7,4,3,6,5,2] => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,7,3,4,2,5,6] => [1,7,5,4,3,6,2] => [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] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,5,6,3,4,2] => [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] => [1,7,5,6,3,4,2] => [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] => [1,7,5,6,3,4,2] => [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] => [1,7,5,6,3,4,2] => [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] => [1,7,5,4,3,6,2] => [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] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,5,4,3,6,2] => [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] => [1,7,5,4,3,6,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [1,7,6,4,5,3,2] => [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] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[2,1,3,4,7,5,6] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,5,7,4,6] => [2,1,3,6,7,4,5] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,5,7,6,4] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,6,4,5,7] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[2,1,3,6,4,7,5] => [2,1,3,7,5,6,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[2,1,3,6,5,7,4] => [2,1,3,7,5,6,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,6,7,4,5] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,6,7,5,4] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,7,4,5,6] => [2,1,3,7,5,6,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,7,4,6,5] => [2,1,3,7,5,6,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,7,5,4,6] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,7,5,6,4] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,7,6,4,5] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[2,1,4,3,7,5,6] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,4,5,7,3,6] => [2,1,6,4,7,3,5] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,4,5,7,6,3] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,4,6,3,5,7] => [2,1,5,6,3,4,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,4,6,3,7,5] => [2,1,5,7,3,6,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,4,6,5,3,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,4,6,5,7,3] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,4,6,7,3,5] => [2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[2,1,4,7,3,5,6] => [2,1,5,7,3,6,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,4,7,3,6,5] => [2,1,5,7,3,6,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,4,7,5,3,6] => [2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[2,1,4,7,6,3,5] => [2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[2,1,5,3,4,6,7] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[2,1,5,3,4,7,6] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[2,1,5,3,6,4,7] => [2,1,6,4,5,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,5,3,6,7,4] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,3,7,4,6] => [2,1,6,4,7,3,5] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,3,7,6,4] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[2,1,5,4,6,3,7] => [2,1,6,4,5,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,5,4,6,7,3] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,4,7,3,6] => [2,1,6,4,7,3,5] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,4,7,6,3] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,6,3,4,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,5,6,3,7,4] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,6,4,3,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,5,6,4,7,3] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[2,1,5,7,3,4,6] => [2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[2,1,5,7,4,3,6] => [2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[2,1,6,3,4,5,7] => [2,1,6,4,5,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,6,3,4,7,5] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,6,3,5,4,7] => [2,1,6,4,5,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,6,3,5,7,4] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,6,3,7,4,5] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,6,3,7,5,4] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,6,4,3,5,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,6,4,3,7,5] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,6,4,5,3,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,6,4,5,7,3] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[2,1,6,5,3,4,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,6,5,3,7,4] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[2,1,6,5,4,7,3] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[2,1,7,3,4,5,6] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,7,3,4,6,5] => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,7,3,5,4,6] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,7,3,5,6,4] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,7,3,6,4,5] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,7,3,6,5,4] => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,7,4,3,5,6] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,7,4,3,6,5] => [2,1,7,5,4,6,3] => [2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[2,3,1,4,7,5,6] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[2,3,1,4,7,6,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[2,3,1,5,7,4,6] => [3,2,1,6,7,4,5] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[2,3,1,5,7,6,4] => [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] => 3
[2,3,1,6,4,5,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[2,3,1,6,4,7,5] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[2,3,1,6,5,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[2,3,1,6,5,7,4] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[2,3,1,6,7,4,5] => [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] => 3
[2,3,1,6,7,5,4] => [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] => 3
[2,3,1,7,4,5,6] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[2,3,1,7,4,6,5] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[2,3,1,7,5,4,6] => [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] => 3
[2,3,1,7,5,6,4] => [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] => 3
[2,3,1,7,6,4,5] => [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] => 3
[2,3,1,7,6,5,4] => [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] => 3
[2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[2,3,4,1,7,5,6] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[2,3,4,1,7,6,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,4,6,1,5,7] => [5,2,3,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,4,6,5,1,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,5,1,4,6,7] => [4,2,5,1,3,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,3,5,1,4,7,6] => [4,2,5,1,3,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,3,5,1,6,4,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,5,1,7,4,6] => [4,2,6,1,7,3,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[2,3,5,4,1,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,3,5,4,1,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,3,5,4,6,1,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,5,6,1,4,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,5,6,4,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,6,1,4,5,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,6,1,5,4,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,6,4,1,5,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,6,4,5,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,6,5,1,4,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,3,6,5,4,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,1,3,5,6,7] => [3,4,1,2,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[2,4,1,3,5,7,6] => [3,4,1,2,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[2,4,1,3,6,5,7] => [3,4,1,2,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[2,4,1,3,6,7,5] => [3,4,1,2,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[2,4,1,3,7,5,6] => [3,4,1,2,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[2,4,1,3,7,6,5] => [3,4,1,2,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[2,4,1,5,3,6,7] => [3,5,1,4,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,4,1,5,3,7,6] => [3,5,1,4,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,4,1,5,6,3,7] => [3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,1,5,7,3,6] => [3,6,1,4,7,2,5] => [6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,4,1,6,3,5,7] => [3,5,1,6,2,4,7] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[2,4,1,6,3,7,5] => [3,5,1,7,2,6,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[2,4,1,6,5,3,7] => [3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,1,6,7,3,5] => [3,6,1,7,5,2,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,4,1,7,3,5,6] => [3,5,1,7,2,6,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[2,4,1,7,3,6,5] => [3,5,1,7,2,6,4] => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[2,4,1,7,5,3,6] => [3,6,1,7,5,2,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,4,1,7,6,3,5] => [3,6,1,7,5,2,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,4,3,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[2,4,3,1,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[2,4,3,1,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[2,4,3,1,6,7,5] => [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] => 4
[2,4,3,1,7,5,6] => [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] => 4
[2,4,3,1,7,6,5] => [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] => 4
[2,4,3,5,1,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,4,3,5,1,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,4,3,5,6,1,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,3,6,1,5,7] => [5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,3,6,5,1,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,5,1,3,6,7] => [4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,4,5,1,3,7,6] => [4,5,3,1,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,4,5,1,6,3,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,5,1,7,3,6] => [4,6,3,1,7,2,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,4,5,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,4,5,3,1,7,6] => [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] => 5
[2,4,5,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,5,6,1,3,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,5,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,6,1,3,5,7] => [4,5,6,1,2,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,6,1,5,3,7] => [4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,6,3,1,5,7] => [5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,6,3,5,1,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,6,5,1,3,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,4,6,5,3,1,7] => [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] => 6
[2,5,1,3,4,6,7] => [3,5,1,4,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,5,1,3,4,7,6] => [3,5,1,4,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,5,1,3,6,4,7] => [3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,1,3,7,4,6] => [3,6,1,4,7,2,5] => [6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,5,1,4,3,6,7] => [3,5,1,4,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,5,1,4,3,7,6] => [3,5,1,4,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,5,1,4,6,3,7] => [3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,1,4,7,3,6] => [3,6,1,4,7,2,5] => [6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,5,1,6,3,4,7] => [3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,1,6,4,3,7] => [3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,1,7,3,4,6] => [3,6,1,7,5,2,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,5,1,7,4,3,6] => [3,6,1,7,5,2,4] => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,5,3,1,4,6,7] => [4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,5,3,1,4,7,6] => [4,5,3,1,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,5,3,1,6,4,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,3,1,7,4,6] => [4,6,3,1,7,2,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,5,3,4,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,5,3,4,1,7,6] => [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] => 5
[2,5,3,4,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,3,6,1,4,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,3,6,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,4,1,3,6,7] => [4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,5,4,1,3,7,6] => [4,5,3,1,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[2,5,4,1,6,3,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,4,1,7,3,6] => [4,6,3,1,7,2,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[2,5,4,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[2,5,4,3,1,7,6] => [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] => 5
[2,5,4,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,4,6,1,3,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,4,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,6,1,3,4,7] => [4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,6,1,4,3,7] => [4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,6,3,1,4,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,6,3,4,1,7] => [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] => 6
[2,5,6,4,1,3,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,5,6,4,3,1,7] => [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] => 6
[2,6,1,3,4,5,7] => [3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,1,3,5,4,7] => [3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,1,4,3,5,7] => [3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,1,4,5,3,7] => [3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,1,5,3,4,7] => [3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,1,5,4,3,7] => [3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,3,1,4,5,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,3,1,5,4,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,3,4,1,5,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,3,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,3,5,1,4,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,3,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,4,1,3,5,7] => [4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,4,1,5,3,7] => [4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,4,3,1,5,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,4,3,5,1,7] => [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] => 6
[2,6,4,5,1,3,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,4,5,3,1,7] => [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] => 6
[2,6,5,1,3,4,7] => [4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,5,1,4,3,7] => [4,6,5,1,3,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,5,3,1,4,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,5,3,4,1,7] => [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] => 6
[2,6,5,4,1,3,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,6,5,4,3,1,7] => [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] => 6
[3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[3,1,2,4,5,7,6] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[3,1,2,4,6,5,7] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[3,1,2,4,6,7,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,1,2,4,7,5,6] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,1,2,4,7,6,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,1,2,5,4,6,7] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[3,1,2,5,4,7,6] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[3,1,2,5,6,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[3,1,2,5,6,7,4] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,1,2,5,7,4,6] => [3,2,1,6,7,4,5] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,1,2,5,7,6,4] => [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] => 3
[3,1,2,6,4,5,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[3,1,2,6,4,7,5] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,1,2,6,5,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[3,1,2,6,5,7,4] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,1,2,6,7,4,5] => [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] => 3
[3,1,2,6,7,5,4] => [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] => 3
[3,1,2,7,4,5,6] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,1,2,7,4,6,5] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,1,2,7,5,4,6] => [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] => 3
[3,1,2,7,5,6,4] => [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] => 3
[3,1,2,7,6,4,5] => [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] => 3
[3,1,2,7,6,5,4] => [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] => 3
[3,1,4,2,5,6,7] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[3,1,4,2,5,7,6] => [4,2,3,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[3,1,4,2,6,5,7] => [4,2,3,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[3,1,4,2,6,7,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[3,1,4,2,7,5,6] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[3,1,4,2,7,6,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[3,1,4,5,2,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,1,4,5,2,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,1,4,5,6,2,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,4,6,2,5,7] => [5,2,3,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,4,6,5,2,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,5,2,4,6,7] => [4,2,5,1,3,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,1,5,2,4,7,6] => [4,2,5,1,3,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,1,5,2,6,4,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,5,2,7,4,6] => [4,2,6,1,7,3,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[3,1,5,4,2,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,1,5,4,2,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,1,5,4,6,2,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,5,6,2,4,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,5,6,4,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,6,2,4,5,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,6,2,5,4,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,6,4,2,5,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,6,4,5,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,6,5,2,4,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,1,6,5,4,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[3,2,1,4,6,7,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,2,1,4,7,5,6] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[3,2,1,5,6,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[3,2,1,5,6,7,4] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,2,1,5,7,4,6] => [3,2,1,6,7,4,5] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[3,2,1,6,4,5,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[3,2,1,6,4,7,5] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[3,2,1,6,5,7,4] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[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] => 3
[3,2,1,7,4,5,6] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,2,1,7,4,6,5] => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[3,2,4,1,5,6,7] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[3,2,4,1,5,7,6] => [4,2,3,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[3,2,4,1,6,5,7] => [4,2,3,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[3,2,4,1,6,7,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[3,2,4,1,7,5,6] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[3,2,4,1,7,6,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[3,2,4,5,1,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,2,4,5,1,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,2,4,5,6,1,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,4,6,1,5,7] => [5,2,3,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,4,6,5,1,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,5,1,4,6,7] => [4,2,5,1,3,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,2,5,1,4,7,6] => [4,2,5,1,3,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,2,5,1,6,4,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,5,1,7,4,6] => [4,2,6,1,7,3,5] => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[3,2,5,4,1,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,2,5,4,1,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,2,5,4,6,1,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,5,6,1,4,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,5,6,4,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,6,1,4,5,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,6,1,5,4,7] => [4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,6,4,1,5,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,6,4,5,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,6,5,1,4,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,2,6,5,4,1,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,1,2,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[3,4,1,2,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[3,4,1,2,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[3,4,1,2,6,7,5] => [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] => 4
[3,4,1,2,7,5,6] => [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] => 4
[3,4,1,2,7,6,5] => [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] => 4
[3,4,1,5,2,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,4,1,5,2,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,4,1,5,6,2,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,1,6,2,5,7] => [5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,1,6,5,2,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[3,4,2,1,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[3,4,2,1,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[3,4,2,1,6,7,5] => [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] => 4
[3,4,2,1,7,5,6] => [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] => 4
[3,4,2,1,7,6,5] => [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] => 4
[3,4,2,5,1,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,4,2,5,1,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,4,2,5,6,1,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,2,6,1,5,7] => [5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,2,6,5,1,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,5,1,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,4,5,1,2,7,6] => [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] => 5
[3,4,5,1,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,5,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,4,5,2,1,7,6] => [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] => 5
[3,4,5,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,5,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,5,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,6,1,2,5,7] => [5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,6,1,5,2,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,6,2,1,5,7] => [5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,6,2,5,1,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,4,6,5,1,2,7] => [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] => 6
[3,4,6,5,2,1,7] => [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] => 6
[3,5,1,2,4,6,7] => [4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,5,1,2,4,7,6] => [4,5,3,1,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,5,1,2,6,4,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,1,2,7,4,6] => [4,6,3,1,7,2,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[3,5,1,4,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,5,1,4,2,7,6] => [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] => 5
[3,5,1,4,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,1,6,2,4,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,1,6,4,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,2,1,4,6,7] => [4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,5,2,1,4,7,6] => [4,5,3,1,2,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[3,5,2,1,6,4,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,2,1,7,4,6] => [4,6,3,1,7,2,5] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[3,5,2,4,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,5,2,4,1,7,6] => [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] => 5
[3,5,2,4,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,2,6,1,4,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,2,6,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,4,1,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,5,4,1,2,7,6] => [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] => 5
[3,5,4,1,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,4,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[3,5,4,2,1,7,6] => [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] => 5
[3,5,4,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,4,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,4,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,6,1,2,4,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,6,1,4,2,7] => [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] => 6
[3,5,6,2,1,4,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,5,6,2,4,1,7] => [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] => 6
[3,5,6,4,1,2,7] => [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] => 6
[3,5,6,4,2,1,7] => [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] => 6
[3,6,1,2,4,5,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,1,2,5,4,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,1,4,2,5,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,1,5,2,4,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,2,1,4,5,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,2,1,5,4,7] => [4,6,3,1,5,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,2,4,1,5,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,2,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,2,5,1,4,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,2,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,4,1,2,5,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,4,1,5,2,7] => [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] => 6
[3,6,4,2,1,5,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,4,2,5,1,7] => [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] => 6
[3,6,4,5,1,2,7] => [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] => 6
[3,6,4,5,2,1,7] => [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] => 6
[3,6,5,1,2,4,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,5,1,4,2,7] => [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] => 6
[3,6,5,2,1,4,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[3,6,5,2,4,1,7] => [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] => 6
[3,6,5,4,1,2,7] => [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] => 6
[3,6,5,4,2,1,7] => [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] => 6
[4,1,2,3,5,6,7] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[4,1,2,3,5,7,6] => [4,2,3,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[4,1,2,3,6,5,7] => [4,2,3,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[4,1,2,3,6,7,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[4,1,2,3,7,5,6] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[4,1,2,3,7,6,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[4,1,2,5,3,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,1,2,5,3,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,1,2,5,6,3,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,2,6,3,5,7] => [5,2,3,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,2,6,5,3,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,3,2,5,6,7] => [4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[4,1,3,2,5,7,6] => [4,2,3,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[4,1,3,2,6,5,7] => [4,2,3,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[4,1,3,2,6,7,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[4,1,3,2,7,5,6] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[4,1,3,2,7,6,5] => [4,2,3,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[4,1,3,5,2,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,1,3,5,2,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,1,3,5,6,2,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,3,6,2,5,7] => [5,2,3,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,3,6,5,2,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,5,2,3,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,1,5,2,3,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,1,5,2,6,3,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,5,3,2,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,1,5,3,2,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,1,5,3,6,2,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,5,6,2,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,5,6,3,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,6,2,3,5,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,6,2,5,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,6,3,2,5,7] => [5,2,6,4,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,6,3,5,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,6,5,2,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,1,6,5,3,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,1,3,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[4,2,1,3,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[4,2,1,3,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[4,2,1,3,6,7,5] => [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] => 4
[4,2,1,3,7,5,6] => [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] => 4
[4,2,1,3,7,6,5] => [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] => 4
[4,2,1,5,3,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,2,1,5,3,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,2,1,5,6,3,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,1,6,3,5,7] => [5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,1,6,5,3,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,3,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[4,2,3,1,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[4,2,3,1,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[4,2,3,1,6,7,5] => [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] => 4
[4,2,3,1,7,5,6] => [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] => 4
[4,2,3,1,7,6,5] => [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] => 4
[4,2,3,5,1,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,2,3,5,1,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,2,3,5,6,1,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,3,6,1,5,7] => [5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,3,6,5,1,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,5,1,3,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,2,5,1,3,7,6] => [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] => 5
[4,2,5,1,6,3,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,5,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,2,5,3,1,7,6] => [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] => 5
[4,2,5,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,5,6,1,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,5,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,6,1,3,5,7] => [5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,6,3,1,5,7] => [5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,6,3,5,1,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,2,6,5,1,3,7] => [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] => 6
[4,2,6,5,3,1,7] => [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] => 6
[4,3,1,2,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[4,3,1,2,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[4,3,1,2,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[4,3,1,2,6,7,5] => [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] => 4
[4,3,1,2,7,5,6] => [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] => 4
[4,3,1,2,7,6,5] => [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] => 4
[4,3,1,5,2,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,3,1,5,2,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,3,1,5,6,2,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,1,6,2,5,7] => [5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,1,6,5,2,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[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] => 4
[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] => 4
[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] => 4
[4,3,2,5,1,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,3,2,5,1,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[4,3,2,5,6,1,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,2,6,1,5,7] => [5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,2,6,5,1,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,5,1,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,3,5,1,2,7,6] => [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] => 5
[4,3,5,1,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,5,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,3,5,2,1,7,6] => [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] => 5
[4,3,5,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,5,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,5,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,6,1,2,5,7] => [5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,6,1,5,2,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,6,2,1,5,7] => [5,4,6,2,1,3,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,6,2,5,1,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,3,6,5,1,2,7] => [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] => 6
[4,3,6,5,2,1,7] => [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] => 6
[4,5,1,2,3,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,5,1,2,3,7,6] => [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] => 5
[4,5,1,2,6,3,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,1,3,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,5,1,3,2,7,6] => [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] => 5
[4,5,1,3,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,1,6,2,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,1,6,3,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,2,1,3,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,5,2,1,3,7,6] => [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] => 5
[4,5,2,1,6,3,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,2,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,5,2,3,1,7,6] => [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] => 5
[4,5,2,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,2,6,1,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,2,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,5,3,1,2,7,6] => [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] => 5
[4,5,3,1,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[4,5,3,2,1,7,6] => [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] => 5
[4,5,3,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,3,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,3,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,5,6,1,2,3,7] => [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] => 6
[4,5,6,1,3,2,7] => [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] => 6
[4,5,6,2,1,3,7] => [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] => 6
[4,5,6,2,3,1,7] => [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] => 6
[4,5,6,3,1,2,7] => [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] => 6
[4,5,6,3,2,1,7] => [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] => 6
[4,6,1,2,3,5,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,1,2,5,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,1,3,2,5,7] => [5,6,3,4,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,1,3,5,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,1,5,2,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,1,5,3,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,2,1,3,5,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,2,1,5,3,7] => [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] => 6
[4,6,2,3,1,5,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,2,3,5,1,7] => [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] => 6
[4,6,2,5,1,3,7] => [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] => 6
[4,6,2,5,3,1,7] => [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] => 6
[4,6,3,1,2,5,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,3,1,5,2,7] => [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] => 6
[4,6,3,2,1,5,7] => [5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[4,6,3,2,5,1,7] => [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] => 6
[4,6,3,5,1,2,7] => [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] => 6
[4,6,3,5,2,1,7] => [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] => 6
[4,6,5,1,2,3,7] => [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] => 6
[4,6,5,1,3,2,7] => [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] => 6
[4,6,5,2,1,3,7] => [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] => 6
[4,6,5,2,3,1,7] => [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] => 6
[4,6,5,3,1,2,7] => [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] => 6
[4,6,5,3,2,1,7] => [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] => 6
[5,1,2,3,4,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,1,2,3,4,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,1,2,3,6,4,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,2,4,3,6,7] => [5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,1,2,4,3,7,6] => [5,2,3,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,1,2,4,6,3,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,2,6,3,4,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,2,6,4,3,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,3,2,4,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,1,3,2,4,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,1,3,2,6,4,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,3,4,2,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,1,3,4,2,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,1,3,4,6,2,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,3,6,2,4,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,3,6,4,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,4,2,3,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,1,4,2,3,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,1,4,2,6,3,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,4,3,2,6,7] => [5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,1,4,3,2,7,6] => [5,2,4,3,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,1,4,3,6,2,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,4,6,2,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,4,6,3,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,6,2,3,4,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,6,2,4,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,6,3,2,4,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,6,3,4,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,6,4,2,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1,6,4,3,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,1,3,4,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,2,1,3,4,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,2,1,3,6,4,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,1,4,3,6,7] => [5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,2,1,4,3,7,6] => [5,3,2,4,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,2,1,4,6,3,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,1,6,3,4,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,1,6,4,3,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,3,1,4,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,2,3,1,4,7,6] => [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] => 5
[5,2,3,1,6,4,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,3,4,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,2,3,4,1,7,6] => [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] => 5
[5,2,3,4,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,3,6,1,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,3,6,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,4,1,3,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,2,4,1,3,7,6] => [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] => 5
[5,2,4,1,6,3,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,4,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,2,4,3,1,7,6] => [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] => 5
[5,2,4,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,4,6,1,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,4,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,6,1,3,4,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,6,1,4,3,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,2,6,3,1,4,7] => [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] => 6
[5,2,6,3,4,1,7] => [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] => 6
[5,2,6,4,1,3,7] => [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] => 6
[5,2,6,4,3,1,7] => [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] => 6
[5,3,1,2,4,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,3,1,2,4,7,6] => [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] => 5
[5,3,1,2,6,4,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,1,4,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,3,1,4,2,7,6] => [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] => 5
[5,3,1,4,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,1,6,2,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,1,6,4,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,2,1,4,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,3,2,1,4,7,6] => [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] => 5
[5,3,2,1,6,4,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,2,4,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,3,2,4,1,7,6] => [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] => 5
[5,3,2,4,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,2,6,1,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,2,6,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,4,1,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,3,4,1,2,7,6] => [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] => 5
[5,3,4,1,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,4,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,3,4,2,1,7,6] => [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] => 5
[5,3,4,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,4,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,4,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,3,6,1,2,4,7] => [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] => 6
[5,3,6,1,4,2,7] => [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] => 6
[5,3,6,2,1,4,7] => [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] => 6
[5,3,6,2,4,1,7] => [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] => 6
[5,3,6,4,1,2,7] => [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] => 6
[5,3,6,4,2,1,7] => [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] => 6
[5,4,1,2,3,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,4,1,2,3,7,6] => [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] => 5
[5,4,1,2,6,3,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,1,3,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,4,1,3,2,7,6] => [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] => 5
[5,4,1,3,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,1,6,2,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,1,6,3,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,2,1,3,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,4,2,1,3,7,6] => [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] => 5
[5,4,2,1,6,3,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,2,3,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,4,2,3,1,7,6] => [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] => 5
[5,4,2,3,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,2,6,1,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,2,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,3,1,2,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[5,4,3,1,2,7,6] => [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] => 5
[5,4,3,1,6,2,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[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] => 5
[5,4,3,2,6,1,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,3,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,3,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,4,6,1,2,3,7] => [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] => 6
[5,4,6,1,3,2,7] => [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] => 6
[5,4,6,2,1,3,7] => [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] => 6
[5,4,6,2,3,1,7] => [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] => 6
[5,4,6,3,1,2,7] => [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] => 6
[5,4,6,3,2,1,7] => [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] => 6
[5,6,1,2,3,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,6,1,2,4,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,6,1,3,2,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,6,1,3,4,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,6,1,4,2,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,6,1,4,3,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,6,2,1,3,4,7] => [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] => 6
[5,6,2,1,4,3,7] => [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] => 6
[5,6,2,3,1,4,7] => [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] => 6
[5,6,2,3,4,1,7] => [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] => 6
[5,6,2,4,1,3,7] => [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] => 6
[5,6,2,4,3,1,7] => [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] => 6
[5,6,3,1,2,4,7] => [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] => 6
[5,6,3,1,4,2,7] => [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] => 6
[5,6,3,2,1,4,7] => [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] => 6
[5,6,3,2,4,1,7] => [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] => 6
[5,6,3,4,1,2,7] => [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] => 6
[5,6,3,4,2,1,7] => [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] => 6
[5,6,4,1,2,3,7] => [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] => 6
[5,6,4,1,3,2,7] => [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] => 6
[5,6,4,2,1,3,7] => [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] => 6
[5,6,4,2,3,1,7] => [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] => 6
[5,6,4,3,1,2,7] => [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] => 6
[5,6,4,3,2,1,7] => [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] => 6
[6,1,2,3,4,5,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,2,3,5,4,7] => [6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,2,4,3,5,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,2,4,5,3,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,2,5,3,4,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,2,5,4,3,7] => [6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,3,2,4,5,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,3,2,5,4,7] => [6,2,4,3,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,3,4,2,5,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,3,4,5,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,3,5,2,4,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,3,5,4,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,4,2,3,5,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,4,2,5,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,4,3,2,5,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,4,3,5,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,4,5,2,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,4,5,3,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,5,2,3,4,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,5,2,4,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,5,3,2,4,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,5,3,4,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,5,4,2,3,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,1,5,4,3,2,7] => [6,2,5,4,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,1,3,4,5,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,1,3,5,4,7] => [6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,1,4,3,5,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,1,4,5,3,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,1,5,3,4,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,1,5,4,3,7] => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,3,1,4,5,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,3,1,5,4,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,3,4,1,5,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,3,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,3,5,1,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,3,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,4,1,3,5,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,4,1,5,3,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,4,3,1,5,7] => [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] => 6
[6,2,4,3,5,1,7] => [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] => 6
[6,2,4,5,1,3,7] => [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] => 6
[6,2,4,5,3,1,7] => [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] => 6
[6,2,5,1,3,4,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,5,1,4,3,7] => [6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,2,5,3,1,4,7] => [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] => 6
[6,2,5,3,4,1,7] => [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] => 6
[6,2,5,4,1,3,7] => [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] => 6
[6,2,5,4,3,1,7] => [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] => 6
[6,3,1,2,4,5,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,1,2,5,4,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,1,4,2,5,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,1,4,5,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,1,5,2,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,1,5,4,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,2,1,4,5,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,2,1,5,4,7] => [6,4,3,2,5,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,2,4,1,5,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,2,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,2,5,1,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,3,4,1,2,5,7] => [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] => 6
[6,3,4,1,5,2,7] => [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] => 6
[6,3,4,2,1,5,7] => [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] => 6
[6,3,4,2,5,1,7] => [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] => 6
[6,3,4,5,1,2,7] => [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] => 6
[6,3,4,5,2,1,7] => [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] => 6
[6,3,5,1,2,4,7] => [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] => 6
[6,3,5,1,4,2,7] => [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] => 6
[6,3,5,2,1,4,7] => [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] => 6
[6,3,5,2,4,1,7] => [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] => 6
[6,3,5,4,1,2,7] => [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] => 6
[6,3,5,4,2,1,7] => [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] => 6
[6,4,1,2,3,5,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,4,1,2,5,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,4,1,3,2,5,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,4,1,3,5,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,4,1,5,2,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,4,1,5,3,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,4,2,1,3,5,7] => [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] => 6
[6,4,2,1,5,3,7] => [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] => 6
[6,4,2,3,1,5,7] => [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] => 6
[6,4,2,3,5,1,7] => [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] => 6
[6,4,2,5,1,3,7] => [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] => 6
[6,4,2,5,3,1,7] => [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] => 6
[6,4,3,1,2,5,7] => [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] => 6
[6,4,3,1,5,2,7] => [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] => 6
[6,4,3,2,1,5,7] => [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] => 6
[6,4,3,2,5,1,7] => [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] => 6
[6,4,3,5,1,2,7] => [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] => 6
[6,4,3,5,2,1,7] => [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] => 6
[6,4,5,1,2,3,7] => [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] => 6
[6,4,5,1,3,2,7] => [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] => 6
[6,4,5,2,1,3,7] => [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] => 6
[6,4,5,2,3,1,7] => [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] => 6
[6,4,5,3,1,2,7] => [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] => 6
[6,4,5,3,2,1,7] => [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] => 6
[6,5,1,2,3,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,5,1,2,4,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,5,1,3,2,4,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,5,1,3,4,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,5,1,4,2,3,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,5,1,4,3,2,7] => [6,5,3,4,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[6,5,2,1,3,4,7] => [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] => 6
[6,5,2,1,4,3,7] => [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] => 6
[6,5,2,3,1,4,7] => [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] => 6
[6,5,2,3,4,1,7] => [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] => 6
[6,5,2,4,1,3,7] => [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] => 6
[6,5,2,4,3,1,7] => [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] => 6
[6,5,3,1,2,4,7] => [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] => 6
[6,5,3,1,4,2,7] => [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] => 6
[6,5,3,2,1,4,7] => [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] => 6
[6,5,3,2,4,1,7] => [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] => 6
[6,5,3,4,1,2,7] => [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] => 6
[6,5,3,4,2,1,7] => [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] => 6
[6,5,4,1,2,3,7] => [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] => 6
[6,5,4,1,3,2,7] => [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] => 6
[6,5,4,2,1,3,7] => [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] => 6
[6,5,4,2,3,1,7] => [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] => 6
[6,5,4,3,1,2,7] => [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] => 6
[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] => 6
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Description
The normalised height of a Nakayama algebra with magnitude 1.
We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.
We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
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 $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
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.
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