Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001493: Dyck paths ⟶ ℤ
Values
[1] => [1] => [1,0] => [1,0] => 1
[1,2] => [1,2] => [1,0,1,0] => [1,1,0,0] => 1
[2,1] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[1,2,3] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
[1,3,2] => [1,3,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,1,3] => [2,1,3] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[2,3,1] => [3,2,1] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
[3,1,2] => [3,2,1] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
[3,2,1] => [3,2,1] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 1
[1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[2,3,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[2,4,1,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 1
[2,4,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,1,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,2,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[3,4,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[3,4,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,1,2,3] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,1,3,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,2,1,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,2,3,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,3,1,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,4,5,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,2,5,3,4] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,3,4,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,3,4,5,2] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,3,5,2,4] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,3,5,4,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,4,2,3,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,4,2,5,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,4,3,5,2] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,4,5,2,3] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,4,5,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,5,2,3,4] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,5,2,4,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,5,3,2,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,5,3,4,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,5,4,2,3] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[2,1,4,5,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[2,1,5,3,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[2,3,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,3,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[2,3,4,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,3,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,3,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[2,3,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,4,1,3,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,4,1,5,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[2,4,3,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,4,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,4,5,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[2,4,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,5,1,3,4] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[2,5,1,4,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[2,5,3,1,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[2,5,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,5,4,1,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[2,5,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,1,2,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[3,1,4,2,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,1,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,1,5,2,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[3,1,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[3,2,4,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,2,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,2,5,1,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[3,2,5,4,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,4,1,2,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,4,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,4,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,4,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,4,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,4,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,5,1,2,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[3,5,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
>>> Load all 873 entries. <<<[3,5,2,1,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[3,5,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,5,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,5,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,1,2,3,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,1,2,5,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,1,3,2,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,1,3,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,1,5,2,3] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,1,5,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,2,1,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,2,1,5,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,2,3,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,2,3,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,2,5,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,2,5,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,3,1,2,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,3,1,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,3,2,5,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,3,5,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,3,5,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,5,1,2,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,5,1,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,5,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,5,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,5,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,1,2,3,4] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,1,2,4,3] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,1,3,2,4] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,1,3,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,1,4,2,3] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,1,4,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,2,1,3,4] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,2,1,4,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,2,3,1,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,2,3,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,2,4,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,2,4,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,3,1,2,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,3,1,4,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,3,2,1,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,3,2,4,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,3,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,3,4,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,4,1,2,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,4,1,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,4,2,1,3] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,4,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,4,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,3,5,2,6,4] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,3,6,2,4,5] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,3,6,2,5,4] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,4,3,6,5,2] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,4,5,2,6,3] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,6,5,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,2,6,3,4] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,2,6,4,3] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,6,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,2,4,3,5] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,2,4,5,3] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,2,5,3,4] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,2,5,4,3] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,3,2,4,5] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,3,2,5,4] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,4,2,3,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,5,2,4,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,5,3,2,4] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,5,3,4,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,5,4,2,3] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[2,1,4,5,3,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,6,3,4,5] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,3,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,3,4,6,5,1] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,3,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,3,5,4,6,1] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[2,3,5,6,4,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,3,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[2,3,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[2,3,6,4,5,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[2,3,6,5,4,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[2,4,1,5,6,3] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[2,4,1,6,5,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,4,3,5,6,1] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,4,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,4,3,6,5,1] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,4,5,3,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,4,5,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,4,5,6,3,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,4,6,1,3,5] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[2,4,6,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,4,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,4,6,5,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[2,5,1,3,6,4] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[2,5,1,4,6,3] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,5,1,6,3,4] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,5,1,6,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,5,3,4,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,5,3,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,5,3,6,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[2,5,4,1,6,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,5,4,3,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,5,4,6,1,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,5,4,6,3,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,5,6,1,3,4] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,5,6,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,5,6,3,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,5,6,3,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,5,6,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,5,6,4,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,6,1,3,4,5] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,6,1,3,5,4] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,6,1,4,3,5] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,6,1,4,5,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,6,1,5,3,4] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,6,3,1,4,5] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,6,3,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,6,3,4,1,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,6,3,4,5,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,6,3,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,6,3,5,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,6,4,1,3,5] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,6,4,1,5,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,6,4,3,1,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,6,4,3,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,6,4,5,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,6,4,5,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,6,5,1,3,4] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,6,5,3,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,6,5,3,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,6,5,4,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[3,1,2,5,6,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[3,1,2,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[3,1,4,2,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,1,4,2,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,1,4,5,6,2] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,1,4,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,1,4,6,5,2] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,1,5,4,6,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,1,5,6,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,1,5,6,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,1,6,2,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,1,6,4,5,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,1,6,5,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,1,6,5,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[3,2,1,5,6,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[3,2,1,6,4,5] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[3,2,4,1,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,2,4,1,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,2,4,5,6,1] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,2,4,6,5,1] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,2,5,4,6,1] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,2,5,6,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,2,5,6,4,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,2,6,4,5,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,2,6,5,4,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,4,1,5,6,2] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,1,6,2,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,4,1,6,5,2] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,4,2,5,6,1] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,4,2,6,5,1] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,4,5,1,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,4,5,2,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,5,6,1,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,5,6,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,6,1,2,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,6,5,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,4,6,5,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[3,5,1,2,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,5,1,4,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,1,6,2,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,5,1,6,4,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[3,5,2,1,6,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,5,2,4,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,2,6,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,5,2,6,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,5,4,1,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,5,4,2,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,4,6,1,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,4,6,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,5,6,1,4,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,5,6,2,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,6,4,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,5,6,4,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,1,2,4,5] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[3,6,1,2,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[3,6,1,4,2,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,1,4,5,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,1,5,2,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,1,5,4,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,2,1,4,5] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[3,6,2,4,1,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,2,4,5,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,2,5,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,4,1,2,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,4,1,5,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,4,2,1,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,4,2,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,4,5,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,4,5,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,5,1,2,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,5,1,4,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,6,5,2,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,5,4,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,6,5,4,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,2,3,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[4,1,2,3,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,1,2,5,6,3] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,2,6,3,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[4,1,2,6,5,3] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,3,2,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[4,1,3,2,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,1,3,5,6,2] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[4,1,3,6,5,2] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,1,5,2,6,3] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,1,5,3,6,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,5,6,2,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,5,6,3,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,6,2,3,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[4,1,6,2,5,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,6,3,2,5] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[4,1,6,3,5,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,6,5,2,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,1,6,5,3,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,2,1,5,6,3] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[4,2,1,6,5,3] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,2,3,5,6,1] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[4,2,3,6,5,1] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,2,5,1,6,3] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,2,5,3,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,5,6,1,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,5,6,3,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,6,1,3,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[4,2,6,1,5,3] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[4,2,6,3,5,1] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,6,5,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,6,5,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,3,1,5,6,2] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,1,6,2,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[4,3,1,6,5,2] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,3,2,5,6,1] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[4,3,2,6,5,1] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,3,5,1,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,3,5,2,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,5,6,1,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,5,6,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,6,1,2,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[4,3,6,1,5,2] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,6,2,1,5] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[4,3,6,2,5,1] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,6,5,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,3,6,5,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,5,1,2,6,3] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,5,1,3,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,1,6,2,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,1,6,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,5,2,1,6,3] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,5,2,3,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,2,6,1,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,2,6,3,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,5,3,1,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,5,3,2,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,3,6,1,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,3,6,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,1,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,2,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,1,2,3,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,6,1,2,5,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,1,3,2,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,6,1,3,5,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,1,5,2,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,1,5,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,2,1,3,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,6,2,1,5,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,2,3,1,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,6,2,3,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,2,5,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,2,5,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,3,1,2,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,6,3,1,5,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,3,2,1,5] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,6,3,2,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,3,5,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,3,5,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,5,1,2,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,5,1,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,5,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,5,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,5,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,2,3,4,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,1,2,3,6,4] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,2,4,3,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,1,2,4,6,3] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,2,6,3,4] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,2,6,4,3] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,3,2,4,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,1,3,2,6,4] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,3,4,2,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,1,3,4,6,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,3,6,2,4] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,3,6,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,4,2,3,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,1,4,2,6,3] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,4,3,2,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,1,4,3,6,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,4,6,2,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,4,6,3,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,6,2,3,4] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,6,2,4,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,6,3,2,4] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,6,3,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,6,4,2,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,1,6,4,3,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,1,3,4,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,2,1,3,6,4] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,1,4,3,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,2,1,4,6,3] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,1,6,3,4] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,1,6,4,3] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,2,3,1,6,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,2,3,4,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,3,6,1,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,3,6,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,2,4,1,6,3] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,2,4,3,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,4,6,1,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,4,6,3,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,6,1,3,4] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,6,1,4,3] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,6,3,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,6,3,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,6,4,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,2,6,4,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,3,1,2,6,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,3,1,4,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,1,6,2,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,1,6,4,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,3,2,1,6,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,3,2,4,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,2,6,1,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,2,6,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,3,4,1,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,3,4,2,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,4,6,1,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,4,6,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,6,1,2,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,6,1,4,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,6,2,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,6,2,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,6,4,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,6,4,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,4,1,2,6,3] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,4,1,3,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,1,6,2,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,1,6,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,4,2,1,6,3] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,4,2,3,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,2,6,1,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,2,6,3,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,4,3,1,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,4,3,2,6,1] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,3,6,1,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,3,6,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,6,1,2,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,6,2,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,6,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,6,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,4,6,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,1,2,3,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,1,2,4,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,1,3,2,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,1,3,4,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,1,4,2,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,1,4,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,2,1,3,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,2,1,4,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,2,3,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,2,3,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,2,4,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,2,4,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,3,1,2,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,3,1,4,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,3,2,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,3,2,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,3,4,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,4,1,2,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,4,1,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,4,2,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,6,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,2,3,4,5] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,2,3,5,4] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,2,4,3,5] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,2,4,5,3] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,2,5,3,4] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,2,5,4,3] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,3,2,4,5] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,3,2,5,4] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,3,4,2,5] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,3,4,5,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,3,5,2,4] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,3,5,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,4,2,3,5] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,4,2,5,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,4,3,2,5] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,4,3,5,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,4,5,2,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,4,5,3,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,5,2,3,4] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,5,2,4,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,5,3,2,4] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,5,3,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,5,4,2,3] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,1,5,4,3,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,1,3,4,5] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,1,3,5,4] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,1,4,3,5] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,1,4,5,3] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,1,5,3,4] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,1,5,4,3] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,3,1,4,5] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,3,1,5,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,3,4,1,5] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,3,4,5,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,3,5,1,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,3,5,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,4,1,3,5] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,4,1,5,3] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,4,3,1,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,4,3,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,4,5,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,4,5,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,5,1,3,4] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,5,1,4,3] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,5,3,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,5,3,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,5,4,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,2,5,4,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,1,2,4,5] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,1,2,5,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,1,4,2,5] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,1,4,5,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,1,5,2,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,1,5,4,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,2,1,4,5] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,2,1,5,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,2,4,1,5] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,2,4,5,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,2,5,1,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,2,5,4,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,4,1,2,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,4,1,5,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,4,2,1,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,4,2,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,4,5,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,4,5,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,5,1,2,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,5,1,4,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,5,2,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,5,2,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,5,4,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,3,5,4,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,1,2,3,5] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,1,2,5,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,1,3,2,5] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,1,3,5,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,1,5,2,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,1,5,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,2,1,3,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,2,1,5,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,2,3,1,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,2,3,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,2,5,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,2,5,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,1,2,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,1,5,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,2,1,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,2,5,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,5,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,5,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,5,1,2,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,5,1,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,5,2,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,5,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,1,2,3,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,1,2,4,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,1,3,2,4] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,1,3,4,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,1,4,2,3] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,1,4,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,2,1,3,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,2,1,4,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,2,3,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,2,3,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,2,4,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,2,4,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,3,1,2,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,3,1,4,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,3,2,1,4] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,3,2,4,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,3,4,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,1,2,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,1,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,2,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
23,1 111,9 660,59,1
F1=q
F2=2 q
F3=6 q
F4=23 q+q2
F5=111 q+9 q2
F6=660 q+59 q2+q3
Description
The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra.
Map
Demazure product with inverse
Description
This map sends a permutation π to π−1⋆π where ⋆ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
Map
Delest-Viennot-inverse
Description
Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
Let D be a Dyck path of semilength n. The parallelogram polyomino γ(D) is defined as follows: let ˜D=d0d1…d2n+1 be the Dyck path obtained by prepending an up step and appending a down step to D. Then, the upper path of γ(D) corresponds to the sequence of steps of ˜D with even indices, and the lower path of γ(D) corresponds to the sequence of steps of ˜D with odd indices.
The Delest-Viennot bijection β returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path (β(−1)∘γ)(D).
Let D be a Dyck path of semilength n. The parallelogram polyomino γ(D) is defined as follows: let ˜D=d0d1…d2n+1 be the Dyck path obtained by prepending an up step and appending a down step to D. Then, the upper path of γ(D) corresponds to the sequence of steps of ˜D with even indices, and the lower path of γ(D) corresponds to the sequence of steps of ˜D with odd indices.
The Delest-Viennot bijection β returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path (β(−1)∘γ)(D).
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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