Identifier
-
Mp00090:
Permutations
—cycle-as-one-line notation⟶
Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001291: Dyck paths ⟶ ℤ
Values
[1] => [1] => [1] => [1,0] => 1
[1,2] => [1,2] => [2,1] => [1,1,0,0] => 1
[2,1] => [1,2] => [2,1] => [1,1,0,0] => 1
[1,2,3] => [1,2,3] => [2,3,1] => [1,1,0,1,0,0] => 2
[1,3,2] => [1,2,3] => [2,3,1] => [1,1,0,1,0,0] => 2
[2,1,3] => [1,2,3] => [2,3,1] => [1,1,0,1,0,0] => 2
[2,3,1] => [1,2,3] => [2,3,1] => [1,1,0,1,0,0] => 2
[3,1,2] => [1,3,2] => [3,2,1] => [1,1,1,0,0,0] => 1
[3,2,1] => [1,3,2] => [3,2,1] => [1,1,1,0,0,0] => 1
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[1,2,4,3] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[1,3,2,4] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[1,3,4,2] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[1,4,2,3] => [1,2,4,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => 2
[1,4,3,2] => [1,2,4,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => 2
[2,1,3,4] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[2,1,4,3] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[2,3,1,4] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[2,4,1,3] => [1,2,4,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => 2
[2,4,3,1] => [1,2,4,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => 2
[3,1,2,4] => [1,3,2,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 3
[3,1,4,2] => [1,3,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => 1
[3,2,1,4] => [1,3,2,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 3
[3,2,4,1] => [1,3,4,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => 1
[3,4,1,2] => [1,3,2,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 3
[3,4,2,1] => [1,3,2,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 3
[4,1,2,3] => [1,4,3,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 1
[4,1,3,2] => [1,4,2,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 2
[4,2,1,3] => [1,4,3,2] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 1
[4,2,3,1] => [1,4,2,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 2
[4,3,1,2] => [1,4,2,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 2
[4,3,2,1] => [1,4,2,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,2,3,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,2,4,3,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,2,4,5,3] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,2,5,3,4] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[1,2,5,4,3] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[1,3,2,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,3,2,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,3,4,2,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,3,4,5,2] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,3,5,2,4] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[1,3,5,4,2] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[1,4,2,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[1,4,2,5,3] => [1,2,4,5,3] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,4,3,2,5] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[1,4,3,5,2] => [1,2,4,5,3] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,4,5,2,3] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[1,4,5,3,2] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[1,5,2,3,4] => [1,2,5,4,3] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,5,2,4,3] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[1,5,3,2,4] => [1,2,5,4,3] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,5,3,4,2] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[1,5,4,2,3] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[1,5,4,3,2] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[2,1,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,1,3,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,1,4,3,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,1,4,5,3] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,1,5,3,4] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[2,1,5,4,3] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[2,3,1,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,3,1,5,4] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,3,4,1,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,3,4,5,1] => [1,2,3,4,5] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[2,3,5,1,4] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 3
[2,4,1,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[2,4,1,5,3] => [1,2,4,5,3] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,4,3,1,5] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[2,4,3,5,1] => [1,2,4,5,3] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,4,5,1,3] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[2,4,5,3,1] => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 4
[2,5,1,3,4] => [1,2,5,4,3] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,5,1,4,3] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[2,5,3,1,4] => [1,2,5,4,3] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 2
[2,5,3,4,1] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[2,5,4,1,3] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[2,5,4,3,1] => [1,2,5,3,4] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 3
[3,1,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,1,2,5,4] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,1,4,2,5] => [1,3,4,2,5] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[3,1,4,5,2] => [1,3,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1,5,2,4] => [1,3,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1,5,4,2] => [1,3,5,2,4] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,2,1,5,4] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,2,4,1,5] => [1,3,4,2,5] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[3,2,4,5,1] => [1,3,4,5,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,2,5,1,4] => [1,3,5,4,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,2,5,4,1] => [1,3,5,2,4] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,4,1,2,5] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,4,1,5,2] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,4,2,1,5] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,4,2,5,1] => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,4,5,1,2] => [1,3,5,2,4] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,4,5,2,1] => [1,3,5,2,4] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,1,2,4] => [1,3,2,5,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 3
[3,5,1,4,2] => [1,3,2,5,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 3
>>> Load all 873 entries. <<<[3,5,2,1,4] => [1,3,2,5,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 3
[3,5,2,4,1] => [1,3,2,5,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 3
[3,5,4,1,2] => [1,3,4,2,5] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[3,5,4,2,1] => [1,3,4,2,5] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[4,1,2,3,5] => [1,4,3,2,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[4,1,2,5,3] => [1,4,5,3,2] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[4,1,3,2,5] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,1,3,5,2] => [1,4,5,2,3] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,1,5,2,3] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,1,5,3,2] => [1,4,3,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[4,2,1,3,5] => [1,4,3,2,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[4,2,1,5,3] => [1,4,5,3,2] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[4,2,3,1,5] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,2,3,5,1] => [1,4,5,2,3] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,2,5,1,3] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,2,5,3,1] => [1,4,3,5,2] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[4,3,1,2,5] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,3,1,5,2] => [1,4,5,2,3] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,3,2,1,5] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,3,2,5,1] => [1,4,5,2,3] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[4,3,5,1,2] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,3,5,2,1] => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[4,5,1,2,3] => [1,4,2,5,3] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[4,5,1,3,2] => [1,4,3,2,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[4,5,2,1,3] => [1,4,2,5,3] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[4,5,2,3,1] => [1,4,3,2,5] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[4,5,3,1,2] => [1,4,2,5,3] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[4,5,3,2,1] => [1,4,2,5,3] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[5,1,2,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,1,2,4,3] => [1,5,3,2,4] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,3,2,4] => [1,5,4,2,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,1,3,4,2] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,1,4,2,3] => [1,5,3,4,2] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,1,4,3,2] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,2,1,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,1,4,3] => [1,5,3,2,4] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,3,1,4] => [1,5,4,2,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,2,3,4,1] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,2,4,1,3] => [1,5,3,4,2] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 1
[5,2,4,3,1] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,3,1,2,4] => [1,5,4,2,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,3,1,4,2] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,3,2,1,4] => [1,5,4,2,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,3,2,4,1] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,3,4,1,2] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,3,4,2,1] => [1,5,2,3,4] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 3
[5,4,1,2,3] => [1,5,3,2,4] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,1,3,2] => [1,5,2,4,3] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[5,4,2,1,3] => [1,5,3,2,4] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,2,3,1] => [1,5,2,4,3] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[5,4,3,1,2] => [1,5,2,4,3] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[5,4,3,2,1] => [1,5,2,4,3] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,3,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,3,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,3,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,3,6,4,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,2,3,6,5,4] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,2,4,3,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,4,3,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,4,5,3,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,4,5,6,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,2,4,6,3,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,2,4,6,5,3] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,2,5,3,4,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,2,5,3,6,4] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,2,5,4,3,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,2,5,4,6,3] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,2,5,6,3,4] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,2,5,6,4,3] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,2,6,3,5,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,2,6,4,5,3] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,2,6,5,3,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,2,6,5,4,3] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,3,2,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,2,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,2,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,2,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,2,6,4,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,3,2,6,5,4] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,3,4,2,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,4,2,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,4,5,2,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,4,5,6,2] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,3,4,6,2,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,3,4,6,5,2] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,3,5,2,4,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,3,5,2,6,4] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,3,5,4,2,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,3,5,4,6,2] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,3,5,6,2,4] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,3,5,6,4,2] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,3,6,2,4,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,3,6,2,5,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,3,6,4,2,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,3,6,4,5,2] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,3,6,5,2,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,3,6,5,4,2] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,4,2,3,5,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,2,3,6,5] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,2,5,3,6] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,4,2,5,6,3] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,4,2,6,3,5] => [1,2,4,6,5,3] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,4,2,6,5,3] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,4,3,2,5,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,3,2,6,5] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,3,5,2,6] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,4,3,5,6,2] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,4,3,6,2,5] => [1,2,4,6,5,3] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,4,3,6,5,2] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,4,5,2,3,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,5,2,6,3] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,5,3,2,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,5,3,6,2] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,4,5,6,2,3] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,4,5,6,3,2] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,4,6,2,3,5] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,4,6,2,5,3] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,4,6,3,2,5] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,4,6,3,5,2] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,4,6,5,2,3] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,4,6,5,3,2] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,5,2,3,4,6] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,5,2,3,6,4] => [1,2,5,6,4,3] => [2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,5,2,4,3,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,2,4,6,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,5,2,6,3,4] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,2,6,4,3] => [1,2,5,4,6,3] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,5,3,2,4,6] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,5,3,2,6,4] => [1,2,5,6,4,3] => [2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,5,3,4,2,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,3,4,6,2] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,5,3,6,2,4] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,3,6,4,2] => [1,2,5,4,6,3] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,5,4,2,3,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,4,2,6,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,5,4,3,2,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,4,3,6,2] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,5,4,6,2,3] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,4,6,3,2] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,5,6,2,3,4] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,5,6,2,4,3] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,5,6,3,2,4] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,5,6,3,4,2] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,5,6,4,2,3] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,5,6,4,3,2] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,6,2,3,4,5] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,6,2,3,5,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,6,2,4,3,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,6,2,4,5,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,2,5,3,4] => [1,2,6,4,5,3] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,6,2,5,4,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,3,2,4,5] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,2,5,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,6,3,4,2,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,6,3,4,5,2] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,3,5,2,4] => [1,2,6,4,5,3] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,6,3,5,4,2] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,4,2,3,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,6,4,2,5,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,4,3,2,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,6,4,3,5,2] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,4,5,2,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,4,5,3,2] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,6,5,2,3,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,6,5,2,4,3] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,6,5,3,2,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,6,5,3,4,2] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,6,5,4,2,3] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,6,5,4,3,2] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,1,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,3,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,3,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,3,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,3,6,4,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,1,3,6,5,4] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,1,4,3,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,4,3,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,4,5,3,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,4,5,6,3] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,1,4,6,3,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,1,4,6,5,3] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,1,5,3,4,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,1,5,3,6,4] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,1,5,4,3,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,1,5,4,6,3] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,1,5,6,3,4] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,1,5,6,4,3] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,1,6,3,4,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,1,6,3,5,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,1,6,4,3,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,1,6,4,5,3] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,1,6,5,3,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,1,6,5,4,3] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,3,1,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,1,4,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,1,5,4,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,1,5,6,4] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,1,6,4,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,3,1,6,5,4] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,3,4,1,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,4,1,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,4,5,1,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[2,3,4,6,1,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,3,4,6,5,1] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[2,3,5,1,4,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,5,1,6,4] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,5,4,1,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,5,4,6,1] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,5,6,1,4] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,5,6,4,1] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,6,1,4,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,6,1,5,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,3,6,4,1,5] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 3
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,3,6,5,1,4] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,4,1,3,5,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,1,3,6,5] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,1,5,3,6] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,4,1,5,6,3] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,4,1,6,3,5] => [1,2,4,6,5,3] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,4,1,6,5,3] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,4,3,1,5,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,3,1,6,5] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,3,5,1,6] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,4,3,5,6,1] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,4,3,6,1,5] => [1,2,4,6,5,3] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,4,3,6,5,1] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,4,5,1,3,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,5,1,6,3] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,5,3,1,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,5,3,6,1] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,5,6,1,3] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,4,5,6,3,1] => [1,2,4,6,3,5] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,4,6,1,3,5] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[2,4,6,1,5,3] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[2,4,6,3,1,5] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[2,4,6,3,5,1] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[2,4,6,5,1,3] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,4,6,5,3,1] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,5,1,3,4,6] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,5,1,3,6,4] => [1,2,5,6,4,3] => [2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,5,1,4,3,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,1,4,6,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,1,6,3,4] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,1,6,4,3] => [1,2,5,4,6,3] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,5,3,1,4,6] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,5,3,1,6,4] => [1,2,5,6,4,3] => [2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,5,3,4,1,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,3,4,6,1] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,3,6,1,4] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,3,6,4,1] => [1,2,5,4,6,3] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,5,4,1,3,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,4,1,6,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,4,3,1,6] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,4,3,6,1] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,5,4,6,1,3] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,4,6,3,1] => [1,2,5,3,4,6] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,5,6,1,3,4] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,5,6,1,4,3] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,5,6,3,1,4] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,5,6,3,4,1] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5
[2,5,6,4,1,3] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,5,6,4,3,1] => [1,2,5,3,6,4] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,6,1,3,4,5] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,1,3,5,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,6,1,4,3,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,6,1,4,5,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,1,5,3,4] => [1,2,6,4,5,3] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,1,5,4,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,3,1,4,5] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,1,5,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,6,3,4,1,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,6,3,4,5,1] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,3,5,1,4] => [1,2,6,4,5,3] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,6,3,5,4,1] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,4,1,3,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,6,4,1,5,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,4,3,1,5] => [1,2,6,5,3,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[2,6,4,3,5,1] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,4,5,1,3] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,4,5,3,1] => [1,2,6,3,4,5] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[2,6,5,1,3,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,6,5,1,4,3] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,6,5,3,1,4] => [1,2,6,4,3,5] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[2,6,5,3,4,1] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,6,5,4,1,3] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[2,6,5,4,3,1] => [1,2,6,3,5,4] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[3,1,2,4,5,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,1,2,4,6,5] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,1,2,5,4,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,1,2,5,6,4] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,1,2,6,4,5] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,1,2,6,5,4] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,1,4,2,5,6] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,1,4,2,6,5] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,1,4,5,2,6] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,1,4,5,6,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,4,6,2,5] => [1,3,4,6,5,2] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,4,6,5,2] => [1,3,4,6,2,5] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,1,5,2,4,6] => [1,3,5,4,2,6] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,1,5,2,6,4] => [1,3,5,6,4,2] => [6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,5,4,2,6] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,1,5,4,6,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,1,5,6,2,4] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,1,5,6,4,2] => [1,3,5,4,6,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,6,2,4,5] => [1,3,6,5,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,6,2,5,4] => [1,3,6,4,2,5] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,1,6,4,2,5] => [1,3,6,5,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,1,6,4,5,2] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,1,6,5,2,4] => [1,3,6,4,5,2] => [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,6,5,4,2] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,2,1,4,5,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,2,1,4,6,5] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,2,1,5,4,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,2,1,5,6,4] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,2,1,6,4,5] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,2,1,6,5,4] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,2,4,1,5,6] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,2,4,1,6,5] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,2,4,5,1,6] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,2,4,5,6,1] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,4,6,1,5] => [1,3,4,6,5,2] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,4,6,5,1] => [1,3,4,6,2,5] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,2,5,1,4,6] => [1,3,5,4,2,6] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,2,5,1,6,4] => [1,3,5,6,4,2] => [6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,5,4,1,6] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,2,5,4,6,1] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,2,5,6,1,4] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,2,5,6,4,1] => [1,3,5,4,6,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,6,1,4,5] => [1,3,6,5,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,6,1,5,4] => [1,3,6,4,2,5] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,2,6,4,1,5] => [1,3,6,5,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,2,6,4,5,1] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,2,6,5,1,4] => [1,3,6,4,5,2] => [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,6,5,4,1] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,4,1,2,5,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,1,2,6,5] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,1,5,2,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,1,5,6,2] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,1,6,2,5] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,4,1,6,5,2] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,4,2,1,5,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,2,1,6,5] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,2,5,1,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,2,5,6,1] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[3,4,2,6,1,5] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,4,2,6,5,1] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[3,4,5,1,2,6] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,4,5,1,6,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,4,5,2,1,6] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,4,5,2,6,1] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,4,5,6,1,2] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,4,5,6,2,1] => [1,3,5,2,4,6] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[3,4,6,1,2,5] => [1,3,6,5,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,4,6,1,5,2] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,4,6,2,1,5] => [1,3,6,5,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[3,4,6,2,5,1] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,4,6,5,1,2] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,4,6,5,2,1] => [1,3,6,2,4,5] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[3,5,1,2,4,6] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,1,2,6,4] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,5,1,4,2,6] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,1,4,6,2] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,5,1,6,2,4] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,1,6,4,2] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,2,1,4,6] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,2,1,6,4] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,5,2,4,1,6] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,2,4,6,1] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,5,2,6,1,4] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,2,6,4,1] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[3,5,4,1,2,6] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,5,4,1,6,2] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,5,4,2,1,6] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,5,4,2,6,1] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[3,5,4,6,1,2] => [1,3,4,6,2,5] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,5,4,6,2,1] => [1,3,4,6,2,5] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,5,6,1,2,4] => [1,3,6,4,2,5] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,5,6,1,4,2] => [1,3,6,2,5,4] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,5,6,2,1,4] => [1,3,6,4,2,5] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,5,6,2,4,1] => [1,3,6,2,5,4] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,5,6,4,1,2] => [1,3,6,2,5,4] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,5,6,4,2,1] => [1,3,6,2,5,4] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,6,1,2,4,5] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,6,1,2,5,4] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,1,4,2,5] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,6,1,4,5,2] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,1,5,2,4] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,1,5,4,2] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,2,1,4,5] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,6,2,1,5,4] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,2,4,1,5] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,6,2,4,5,1] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,2,5,1,4] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,2,5,4,1] => [1,3,2,6,4,5] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[3,6,4,1,2,5] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[3,6,4,1,5,2] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[3,6,4,2,1,5] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[3,6,4,2,5,1] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[3,6,4,5,1,2] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,6,4,5,2,1] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,6,5,1,2,4] => [1,3,5,2,6,4] => [4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,6,5,1,4,2] => [1,3,5,4,2,6] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,6,5,2,1,4] => [1,3,5,2,6,4] => [4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,6,5,2,4,1] => [1,3,5,4,2,6] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,6,5,4,1,2] => [1,3,5,2,6,4] => [4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,6,5,4,2,1] => [1,3,5,2,6,4] => [4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[4,1,2,3,5,6] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,1,2,3,6,5] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,1,2,5,3,6] => [1,4,5,3,2,6] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,1,2,5,6,3] => [1,4,5,6,3,2] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,2,6,3,5] => [1,4,6,5,3,2] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,2,6,5,3] => [1,4,6,3,2,5] => [5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,1,3,2,5,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,1,3,2,6,5] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,1,3,5,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,1,3,5,6,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,1,3,6,2,5] => [1,4,6,5,2,3] => [5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,1,3,6,5,2] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,1,5,2,3,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,1,5,2,6,3] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,1,5,3,2,6] => [1,4,3,5,2,6] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,1,5,3,6,2] => [1,4,3,5,6,2] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,5,6,2,3] => [1,4,6,3,5,2] => [6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,5,6,3,2] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,1,6,2,3,5] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,1,6,2,5,3] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,1,6,3,2,5] => [1,4,3,6,5,2] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,6,3,5,2] => [1,4,3,6,2,5] => [5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,1,6,5,2,3] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,1,6,5,3,2] => [1,4,5,3,6,2] => [6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,1,3,5,6] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,2,1,3,6,5] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,2,1,5,3,6] => [1,4,5,3,2,6] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,2,1,5,6,3] => [1,4,5,6,3,2] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,1,6,3,5] => [1,4,6,5,3,2] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,1,6,5,3] => [1,4,6,3,2,5] => [5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,2,3,1,5,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,2,3,1,6,5] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,2,3,5,1,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,2,3,5,6,1] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,2,3,6,1,5] => [1,4,6,5,2,3] => [5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,2,3,6,5,1] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,2,5,1,3,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,2,5,1,6,3] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,2,5,3,1,6] => [1,4,3,5,2,6] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,2,5,3,6,1] => [1,4,3,5,6,2] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,5,6,1,3] => [1,4,6,3,5,2] => [6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,5,6,3,1] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,2,6,1,3,5] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,2,6,1,5,3] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,2,6,3,1,5] => [1,4,3,6,5,2] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,6,3,5,1] => [1,4,3,6,2,5] => [5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,2,6,5,1,3] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,2,6,5,3,1] => [1,4,5,3,6,2] => [6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,3,1,2,5,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,1,2,6,5] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,1,5,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,3,1,5,6,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,3,1,6,2,5] => [1,4,6,5,2,3] => [5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,3,1,6,5,2] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,3,2,1,5,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,2,1,6,5] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,2,5,1,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,3,2,5,6,1] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,3,2,6,1,5] => [1,4,6,5,2,3] => [5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,3,2,6,5,1] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,3,5,1,2,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,5,1,6,2] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,5,2,1,6] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,5,2,6,1] => [1,4,2,3,5,6] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[4,3,5,6,1,2] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,3,5,6,2,1] => [1,4,6,2,3,5] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[4,3,6,1,2,5] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,3,6,1,5,2] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,3,6,2,1,5] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,3,6,2,5,1] => [1,4,2,3,6,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[4,3,6,5,1,2] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,3,6,5,2,1] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,5,1,2,3,6] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,1,2,6,3] => [1,4,2,5,6,3] => [3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,5,1,3,2,6] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,5,1,3,6,2] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,5,1,6,2,3] => [1,4,6,3,2,5] => [5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,5,1,6,3,2] => [1,4,6,2,5,3] => [4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,5,2,1,3,6] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,2,1,6,3] => [1,4,2,5,6,3] => [3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,5,2,3,1,6] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,5,2,3,6,1] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,5,2,6,1,3] => [1,4,6,3,2,5] => [5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,5,2,6,3,1] => [1,4,6,2,5,3] => [4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,5,3,1,2,6] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,3,1,6,2] => [1,4,2,5,6,3] => [3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,5,3,2,1,6] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,3,2,6,1] => [1,4,2,5,6,3] => [3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,5,3,6,1,2] => [1,4,6,2,5,3] => [4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,5,3,6,2,1] => [1,4,6,2,5,3] => [4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,5,6,1,2,3] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,6,1,3,2] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,6,2,1,3] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,6,2,3,1] => [1,4,2,5,3,6] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[4,5,6,3,1,2] => [1,4,3,6,2,5] => [5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,5,6,3,2,1] => [1,4,3,6,2,5] => [5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[4,6,1,2,3,5] => [1,4,2,6,5,3] => [3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,6,1,2,5,3] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,1,3,2,5] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[4,6,1,3,5,2] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[4,6,1,5,2,3] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,1,5,3,2] => [1,4,5,3,2,6] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,6,2,1,3,5] => [1,4,2,6,5,3] => [3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,6,2,1,5,3] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,2,3,1,5] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[4,6,2,3,5,1] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[4,6,2,5,1,3] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,2,5,3,1] => [1,4,5,3,2,6] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,6,3,1,2,5] => [1,4,2,6,5,3] => [3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,6,3,1,5,2] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,3,2,1,5] => [1,4,2,6,5,3] => [3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,6,3,2,5,1] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,3,5,1,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,3,5,2,1] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,6,5,1,2,3] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,5,1,3,2] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,5,2,1,3] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,5,2,3,1] => [1,4,2,6,3,5] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,6,5,3,1,2] => [1,4,3,5,2,6] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,6,5,3,2,1] => [1,4,3,5,2,6] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,1,2,3,4,6] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,1,2,3,6,4] => [1,5,6,4,3,2] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,1,2,4,3,6] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,1,2,4,6,3] => [1,5,6,3,2,4] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,1,2,6,3,4] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,1,2,6,4,3] => [1,5,4,6,3,2] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,1,3,2,4,6] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,1,3,2,6,4] => [1,5,6,4,2,3] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,1,3,4,2,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,1,3,4,6,2] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,1,3,6,2,4] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,1,3,6,4,2] => [1,5,4,6,2,3] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,1,4,2,3,6] => [1,5,3,4,2,6] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,1,4,2,6,3] => [1,5,6,3,4,2] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,1,4,3,2,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,1,4,3,6,2] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,1,4,6,2,3] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,1,4,6,3,2] => [1,5,3,4,6,2] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,1,6,2,3,4] => [1,5,3,6,4,2] => [6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,1,6,2,4,3] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,1,6,3,2,4] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,1,6,3,4,2] => [1,5,4,3,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,1,6,4,2,3] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,1,6,4,3,2] => [1,5,3,6,2,4] => [5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,2,1,3,4,6] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,2,1,3,6,4] => [1,5,6,4,3,2] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,2,1,4,3,6] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,2,1,4,6,3] => [1,5,6,3,2,4] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,2,1,6,3,4] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,2,1,6,4,3] => [1,5,4,6,3,2] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,2,3,1,4,6] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,2,3,1,6,4] => [1,5,6,4,2,3] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,2,3,4,1,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,2,3,4,6,1] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,2,3,6,1,4] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,2,3,6,4,1] => [1,5,4,6,2,3] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,2,4,1,3,6] => [1,5,3,4,2,6] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,2,4,1,6,3] => [1,5,6,3,4,2] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,2,4,3,1,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,2,4,3,6,1] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,2,4,6,1,3] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,2,4,6,3,1] => [1,5,3,4,6,2] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,2,6,1,3,4] => [1,5,3,6,4,2] => [6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,2,6,1,4,3] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,2,6,3,1,4] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,2,6,3,4,1] => [1,5,4,3,6,2] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,2,6,4,1,3] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,2,6,4,3,1] => [1,5,3,6,2,4] => [5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,3,1,2,4,6] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,3,1,2,6,4] => [1,5,6,4,2,3] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,3,1,4,2,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,1,4,6,2] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,3,1,6,2,4] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,1,6,4,2] => [1,5,4,6,2,3] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,3,2,1,4,6] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,3,2,1,6,4] => [1,5,6,4,2,3] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,3,2,4,1,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,2,4,6,1] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,3,2,6,1,4] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,2,6,4,1] => [1,5,4,6,2,3] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[5,3,4,1,2,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,4,1,6,2] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,3,4,2,1,6] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,4,2,6,1] => [1,5,6,2,3,4] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[5,3,4,6,1,2] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,4,6,2,1] => [1,5,2,3,4,6] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[5,3,6,1,2,4] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,3,6,1,4,2] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,3,6,2,1,4] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,3,6,2,4,1] => [1,5,4,2,3,6] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[5,3,6,4,1,2] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,3,6,4,2,1] => [1,5,2,3,6,4] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[5,4,1,2,3,6] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,4,1,2,6,3] => [1,5,6,3,2,4] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,4,1,3,2,6] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,1,3,6,2] => [1,5,6,2,4,3] => [4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,4,1,6,2,3] => [1,5,2,4,6,3] => [3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,4,1,6,3,2] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,4,2,1,3,6] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,4,2,1,6,3] => [1,5,6,3,2,4] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,4,2,3,1,6] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,2,3,6,1] => [1,5,6,2,4,3] => [4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,4,2,6,1,3] => [1,5,2,4,6,3] => [3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,4,2,6,3,1] => [1,5,3,2,4,6] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[5,4,3,1,2,6] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,3,1,6,2] => [1,5,6,2,4,3] => [4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,4,3,2,1,6] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,3,2,6,1] => [1,5,6,2,4,3] => [4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,4,3,6,1,2] => [1,5,2,4,6,3] => [3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,4,3,6,2,1] => [1,5,2,4,6,3] => [3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,4,6,1,2,3] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,6,1,3,2] => [1,5,3,6,2,4] => [5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,4,6,2,1,3] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,6,2,3,1] => [1,5,3,6,2,4] => [5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,4,6,3,1,2] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,6,3,2,1] => [1,5,2,4,3,6] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,6,1,2,3,4] => [1,5,3,2,6,4] => [4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[5,6,1,2,4,3] => [1,5,4,2,6,3] => [4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,6,1,3,2,4] => [1,5,2,6,4,3] => [3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,6,1,3,4,2] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,6,1,4,2,3] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,6,1,4,3,2] => [1,5,3,2,6,4] => [4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[5,6,2,1,3,4] => [1,5,3,2,6,4] => [4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[5,6,2,1,4,3] => [1,5,4,2,6,3] => [4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,6,2,3,1,4] => [1,5,2,6,4,3] => [3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,6,2,3,4,1] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,6,2,4,1,3] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,6,2,4,3,1] => [1,5,3,2,6,4] => [4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[5,6,3,1,2,4] => [1,5,2,6,4,3] => [3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,6,3,1,4,2] => [1,5,4,2,6,3] => [4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,6,3,2,1,4] => [1,5,2,6,4,3] => [3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,6,3,2,4,1] => [1,5,4,2,6,3] => [4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[5,6,3,4,1,2] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,6,3,4,2,1] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,6,4,1,2,3] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,6,4,1,3,2] => [1,5,3,4,2,6] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,6,4,2,1,3] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,6,4,2,3,1] => [1,5,3,4,2,6] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,6,4,3,1,2] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,6,4,3,2,1] => [1,5,2,6,3,4] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,1,2,3,4,5] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,2,3,5,4] => [1,6,4,3,2,5] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,1,2,4,3,5] => [1,6,5,3,2,4] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,1,2,4,5,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,1,2,5,3,4] => [1,6,4,5,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,2,5,4,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,1,3,2,4,5] => [1,6,5,4,2,3] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,1,3,2,5,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,1,3,4,2,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,1,3,4,5,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,1,3,5,2,4] => [1,6,4,5,2,3] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,1,3,5,4,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,1,4,2,3,5] => [1,6,5,3,4,2] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,2,5,3] => [1,6,3,4,2,5] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,1,4,3,2,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,1,4,3,5,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,1,4,5,2,3] => [1,6,3,4,5,2] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,4,5,3,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,1,5,2,3,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,1,5,2,4,3] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,3,2,4] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1,5,3,4,2] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,1,5,4,2,3] => [1,6,3,5,2,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,1,5,4,3,2] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,2,1,3,4,5] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,3,5,4] => [1,6,4,3,2,5] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,2,1,4,3,5] => [1,6,5,3,2,4] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,2,1,4,5,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,2,1,5,3,4] => [1,6,4,5,3,2] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,1,5,4,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,2,3,1,4,5] => [1,6,5,4,2,3] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,2,3,1,5,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,2,3,4,1,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,2,3,4,5,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,2,3,5,1,4] => [1,6,4,5,2,3] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,2,3,5,4,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,2,4,1,3,5] => [1,6,5,3,4,2] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,1,5,3] => [1,6,3,4,2,5] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,2,4,3,1,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,2,4,3,5,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,2,4,5,1,3] => [1,6,3,4,5,2] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,4,5,3,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,2,5,1,3,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,2,5,1,4,3] => [1,6,3,5,4,2] => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,3,1,4] => [1,6,4,3,5,2] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,2,5,3,4,1] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,2,5,4,1,3] => [1,6,3,5,2,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,2,5,4,3,1] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,3,1,2,4,5] => [1,6,5,4,2,3] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,3,1,2,5,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,3,1,4,2,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,3,1,4,5,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,1,5,2,4] => [1,6,4,5,2,3] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,3,1,5,4,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,2,1,4,5] => [1,6,5,4,2,3] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,3,2,1,5,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,3,2,4,1,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,3,2,4,5,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,2,5,1,4] => [1,6,4,5,2,3] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[6,3,2,5,4,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,4,1,2,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,3,4,1,5,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,4,2,1,5] => [1,6,5,2,3,4] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,3,4,2,5,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,4,5,1,2] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,4,5,2,1] => [1,6,2,3,4,5] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[6,3,5,1,2,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,3,5,1,4,2] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,3,5,2,1,4] => [1,6,4,2,3,5] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 4
[6,3,5,2,4,1] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,3,5,4,1,2] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,3,5,4,2,1] => [1,6,2,3,5,4] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[6,4,1,2,3,5] => [1,6,5,3,2,4] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,4,1,2,5,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,4,1,3,2,5] => [1,6,5,2,4,3] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,4,1,3,5,2] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,4,1,5,2,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,4,1,5,3,2] => [1,6,2,4,5,3] => [3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,4,2,1,3,5] => [1,6,5,3,2,4] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,4,2,1,5,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,4,2,3,1,5] => [1,6,5,2,4,3] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,4,2,3,5,1] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,4,2,5,1,3] => [1,6,3,2,4,5] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[6,4,2,5,3,1] => [1,6,2,4,5,3] => [3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,4,3,1,2,5] => [1,6,5,2,4,3] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,4,3,1,5,2] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,4,3,2,1,5] => [1,6,5,2,4,3] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,4,3,2,5,1] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,4,3,5,1,2] => [1,6,2,4,5,3] => [3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,4,3,5,2,1] => [1,6,2,4,5,3] => [3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,4,5,1,2,3] => [1,6,3,5,2,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,4,5,1,3,2] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,4,5,2,1,3] => [1,6,3,5,2,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[6,4,5,2,3,1] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,4,5,3,1,2] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,4,5,3,2,1] => [1,6,2,4,3,5] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[6,5,1,2,3,4] => [1,6,4,2,5,3] => [4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,5,1,2,4,3] => [1,6,3,2,5,4] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[6,5,1,3,2,4] => [1,6,4,3,2,5] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,5,1,3,4,2] => [1,6,2,5,4,3] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,5,1,4,2,3] => [1,6,3,2,5,4] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[6,5,1,4,3,2] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,5,2,1,3,4] => [1,6,4,2,5,3] => [4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,5,2,1,4,3] => [1,6,3,2,5,4] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[6,5,2,3,1,4] => [1,6,4,3,2,5] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,5,2,3,4,1] => [1,6,2,5,4,3] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,5,2,4,1,3] => [1,6,3,2,5,4] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[6,5,2,4,3,1] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,5,3,1,2,4] => [1,6,4,2,5,3] => [4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,5,3,1,4,2] => [1,6,2,5,4,3] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,5,3,2,1,4] => [1,6,4,2,5,3] => [4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[6,5,3,2,4,1] => [1,6,2,5,4,3] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,5,3,4,1,2] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,5,3,4,2,1] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,5,4,1,2,3] => [1,6,3,4,2,5] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,5,4,1,3,2] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,5,4,2,1,3] => [1,6,3,4,2,5] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[6,5,4,2,3,1] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,5,4,3,1,2] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[6,5,4,3,2,1] => [1,6,2,5,3,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
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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:
2,4 4,8,12 12,24,36,48 48,96,144,192,240
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 2\ q + 4\ q^{2}$
$F_{4} = 4\ q + 8\ q^{2} + 12\ q^{3}$
$F_{5} = 12\ q + 24\ q^{2} + 36\ q^{3} + 48\ q^{4}$
$F_{6} = 48\ q + 96\ q^{2} + 144\ q^{3} + 192\ q^{4} + 240\ q^{5}$
Description
The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
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.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
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