Identifier
-
Mp00064:
Permutations
—reverse⟶
Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001508: Dyck paths ⟶ ℤ
Values
[1] => [1] => [1] => [1,0] => 0
[1,2] => [2,1] => [1,1] => [1,0,1,0] => 0
[2,1] => [1,2] => [2] => [1,1,0,0] => 1
[1,2,3] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
[1,3,2] => [2,3,1] => [2,1] => [1,1,0,0,1,0] => 1
[2,1,3] => [3,1,2] => [1,2] => [1,0,1,1,0,0] => 1
[2,3,1] => [1,3,2] => [2,1] => [1,1,0,0,1,0] => 1
[3,1,2] => [2,1,3] => [1,2] => [1,0,1,1,0,0] => 1
[3,2,1] => [1,2,3] => [3] => [1,1,1,0,0,0] => 1
[1,2,3,4] => [4,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,2,4,3] => [3,4,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,3,2,4] => [4,2,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,3,4,2] => [2,4,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,4,2,3] => [3,2,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,4,3,2] => [2,3,4,1] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,1,3,4] => [4,3,1,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[2,1,4,3] => [3,4,1,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[2,3,1,4] => [4,1,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[2,3,4,1] => [1,4,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[2,4,1,3] => [3,1,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[2,4,3,1] => [1,3,4,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[3,1,2,4] => [4,2,1,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[3,1,4,2] => [2,4,1,3] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[3,2,1,4] => [4,1,2,3] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[3,2,4,1] => [1,4,2,3] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[3,4,1,2] => [2,1,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[3,4,2,1] => [1,2,4,3] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[4,1,2,3] => [3,2,1,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[4,1,3,2] => [2,3,1,4] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[4,2,1,3] => [3,1,2,4] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[4,2,3,1] => [1,3,2,4] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[4,3,1,2] => [2,1,3,4] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[4,3,2,1] => [1,2,3,4] => [4] => [1,1,1,1,0,0,0,0] => 2
[1,2,3,4,5] => [5,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,2,3,5,4] => [4,5,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,2,4,3,5] => [5,3,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,2,4,5,3] => [3,5,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,2,5,3,4] => [4,3,5,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,2,5,4,3] => [3,4,5,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,3,2,4,5] => [5,4,2,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,3,2,5,4] => [4,5,2,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,3,4,2,5] => [5,2,4,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,3,4,5,2] => [2,5,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,3,5,2,4] => [4,2,5,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,3,5,4,2] => [2,4,5,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,4,2,3,5] => [5,3,2,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,4,2,5,3] => [3,5,2,4,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,4,3,2,5] => [5,2,3,4,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,4,3,5,2] => [2,5,3,4,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,4,5,2,3] => [3,2,5,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,4,5,3,2] => [2,3,5,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,5,2,3,4] => [4,3,2,5,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,5,2,4,3] => [3,4,2,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,5,3,2,4] => [4,2,3,5,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,5,3,4,2] => [2,4,3,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,5,4,2,3] => [3,2,4,5,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,5,4,3,2] => [2,3,4,5,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,3,4,5] => [5,4,3,1,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[2,1,3,5,4] => [4,5,3,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,4,3,5] => [5,3,4,1,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[2,1,4,5,3] => [3,5,4,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,5,3,4] => [4,3,5,1,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[2,1,5,4,3] => [3,4,5,1,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[2,3,1,4,5] => [5,4,1,3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[2,3,1,5,4] => [4,5,1,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,3,4,1,5] => [5,1,4,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[2,3,4,5,1] => [1,5,4,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[2,3,5,1,4] => [4,1,5,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[2,3,5,4,1] => [1,4,5,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,4,1,3,5] => [5,3,1,4,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[2,4,1,5,3] => [3,5,1,4,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,4,3,1,5] => [5,1,3,4,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,4,3,5,1] => [1,5,3,4,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,4,5,1,3] => [3,1,5,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[2,4,5,3,1] => [1,3,5,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,5,1,3,4] => [4,3,1,5,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[2,5,1,4,3] => [3,4,1,5,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,5,3,1,4] => [4,1,3,5,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,5,3,4,1] => [1,4,3,5,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,5,4,1,3] => [3,1,4,5,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,5,4,3,1] => [1,3,4,5,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,1,2,4,5] => [5,4,2,1,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[3,1,2,5,4] => [4,5,2,1,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,1,4,2,5] => [5,2,4,1,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,1,4,5,2] => [2,5,4,1,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,1,5,2,4] => [4,2,5,1,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,1,5,4,2] => [2,4,5,1,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[3,2,1,4,5] => [5,4,1,2,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[3,2,1,5,4] => [4,5,1,2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[3,2,4,1,5] => [5,1,4,2,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,2,4,5,1] => [1,5,4,2,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,2,5,1,4] => [4,1,5,2,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,2,5,4,1] => [1,4,5,2,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[3,4,1,2,5] => [5,2,1,4,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[3,4,1,5,2] => [2,5,1,4,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,4,2,1,5] => [5,1,2,4,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,4,2,5,1] => [1,5,2,4,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,4,5,1,2] => [2,1,5,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[3,4,5,2,1] => [1,2,5,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[3,5,1,2,4] => [4,2,1,5,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[3,5,1,4,2] => [2,4,1,5,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
>>> Load all 873 entries. <<<[3,5,2,1,4] => [4,1,2,5,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,5,2,4,1] => [1,4,2,5,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,5,4,1,2] => [2,1,4,5,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,5,4,2,1] => [1,2,4,5,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,1,2,3,5] => [5,3,2,1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[4,1,2,5,3] => [3,5,2,1,4] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[4,1,3,2,5] => [5,2,3,1,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[4,1,3,5,2] => [2,5,3,1,4] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[4,1,5,2,3] => [3,2,5,1,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[4,1,5,3,2] => [2,3,5,1,4] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[4,2,1,3,5] => [5,3,1,2,4] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[4,2,1,5,3] => [3,5,1,2,4] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[4,2,3,1,5] => [5,1,3,2,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[4,2,3,5,1] => [1,5,3,2,4] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[4,2,5,1,3] => [3,1,5,2,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[4,2,5,3,1] => [1,3,5,2,4] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[4,3,1,2,5] => [5,2,1,3,4] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[4,3,1,5,2] => [2,5,1,3,4] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[4,3,2,1,5] => [5,1,2,3,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[4,3,2,5,1] => [1,5,2,3,4] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[4,3,5,1,2] => [2,1,5,3,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[4,3,5,2,1] => [1,2,5,3,4] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[4,5,1,2,3] => [3,2,1,5,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[4,5,1,3,2] => [2,3,1,5,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[4,5,2,1,3] => [3,1,2,5,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,5,2,3,1] => [1,3,2,5,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[4,5,3,1,2] => [2,1,3,5,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,5,3,2,1] => [1,2,3,5,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[5,1,2,4,3] => [3,4,2,1,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[5,1,3,2,4] => [4,2,3,1,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[5,1,3,4,2] => [2,4,3,1,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[5,1,4,2,3] => [3,2,4,1,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[5,1,4,3,2] => [2,3,4,1,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[5,2,1,3,4] => [4,3,1,2,5] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[5,2,1,4,3] => [3,4,1,2,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[5,2,3,1,4] => [4,1,3,2,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[5,2,3,4,1] => [1,4,3,2,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[5,2,4,1,3] => [3,1,4,2,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[5,2,4,3,1] => [1,3,4,2,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[5,3,1,2,4] => [4,2,1,3,5] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[5,3,1,4,2] => [2,4,1,3,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[5,3,2,1,4] => [4,1,2,3,5] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[5,3,2,4,1] => [1,4,2,3,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[5,3,4,1,2] => [2,1,4,3,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[5,3,4,2,1] => [1,2,4,3,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[5,4,1,2,3] => [3,2,1,4,5] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[5,4,1,3,2] => [2,3,1,4,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[5,4,2,1,3] => [3,1,2,4,5] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[5,4,2,3,1] => [1,3,2,4,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[5,4,3,1,2] => [2,1,3,4,5] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[5,4,3,2,1] => [1,2,3,4,5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,2,3,4,6,5] => [5,6,4,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,3,5,4,6] => [6,4,5,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,3,5,6,4] => [4,6,5,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,3,6,4,5] => [5,4,6,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,3,6,5,4] => [4,5,6,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,2,4,3,6,5] => [5,6,3,4,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,2,4,5,3,6] => [6,3,5,4,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,4,5,6,3] => [3,6,5,4,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,4,6,3,5] => [5,3,6,4,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,4,6,5,3] => [3,5,6,4,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,5,3,4,6] => [6,4,3,5,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,2,5,3,6,4] => [4,6,3,5,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,2,5,4,3,6] => [6,3,4,5,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,2,5,4,6,3] => [3,6,4,5,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,2,5,6,3,4] => [4,3,6,5,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,5,6,4,3] => [3,4,6,5,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,6,3,4,5] => [5,4,3,6,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,2,6,3,5,4] => [4,5,3,6,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,2,6,4,3,5] => [5,3,4,6,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,2,6,4,5,3] => [3,5,4,6,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,2,6,5,3,4] => [4,3,5,6,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,2,6,5,4,3] => [3,4,5,6,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,3,2,4,5,6] => [6,5,4,2,3,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,3,2,4,6,5] => [5,6,4,2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,3,2,5,4,6] => [6,4,5,2,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,3,2,5,6,4] => [4,6,5,2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,3,2,6,4,5] => [5,4,6,2,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,3,2,6,5,4] => [4,5,6,2,3,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,3,4,2,5,6] => [6,5,2,4,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,3,4,2,6,5] => [5,6,2,4,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,4,5,2,6] => [6,2,5,4,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,3,4,5,6,2] => [2,6,5,4,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,3,4,6,2,5] => [5,2,6,4,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,3,4,6,5,2] => [2,5,6,4,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,3,5,2,4,6] => [6,4,2,5,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,3,5,2,6,4] => [4,6,2,5,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,5,4,2,6] => [6,2,4,5,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,3,5,4,6,2] => [2,6,4,5,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,5,6,2,4] => [4,2,6,5,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,3,5,6,4,2] => [2,4,6,5,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,3,6,2,4,5] => [5,4,2,6,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,3,6,2,5,4] => [4,5,2,6,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,6,4,2,5] => [5,2,4,6,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,3,6,4,5,2] => [2,5,4,6,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,6,5,2,4] => [4,2,5,6,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,3,6,5,4,2] => [2,4,5,6,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,4,2,3,5,6] => [6,5,3,2,4,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,4,2,3,6,5] => [5,6,3,2,4,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,4,2,5,3,6] => [6,3,5,2,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,4,2,5,6,3] => [3,6,5,2,4,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,4,2,6,3,5] => [5,3,6,2,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,4,2,6,5,3] => [3,5,6,2,4,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,4,3,2,5,6] => [6,5,2,3,4,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,4,3,2,6,5] => [5,6,2,3,4,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,4,3,5,2,6] => [6,2,5,3,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,4,3,5,6,2] => [2,6,5,3,4,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,4,3,6,2,5] => [5,2,6,3,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,4,3,6,5,2] => [2,5,6,3,4,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,4,5,2,3,6] => [6,3,2,5,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,4,5,2,6,3] => [3,6,2,5,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,4,5,3,2,6] => [6,2,3,5,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,4,5,3,6,2] => [2,6,3,5,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,4,5,6,2,3] => [3,2,6,5,4,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,4,5,6,3,2] => [2,3,6,5,4,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,4,6,2,3,5] => [5,3,2,6,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,4,6,2,5,3] => [3,5,2,6,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,4,6,3,2,5] => [5,2,3,6,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,4,6,3,5,2] => [2,5,3,6,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,4,6,5,2,3] => [3,2,5,6,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,4,6,5,3,2] => [2,3,5,6,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,5,2,3,4,6] => [6,4,3,2,5,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,5,2,3,6,4] => [4,6,3,2,5,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,5,2,4,3,6] => [6,3,4,2,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,5,2,4,6,3] => [3,6,4,2,5,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,5,2,6,3,4] => [4,3,6,2,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,5,2,6,4,3] => [3,4,6,2,5,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,5,3,2,4,6] => [6,4,2,3,5,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,5,3,2,6,4] => [4,6,2,3,5,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,5,3,4,2,6] => [6,2,4,3,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,5,3,4,6,2] => [2,6,4,3,5,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,5,3,6,2,4] => [4,2,6,3,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,5,3,6,4,2] => [2,4,6,3,5,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,5,4,2,3,6] => [6,3,2,4,5,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,5,4,2,6,3] => [3,6,2,4,5,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,5,4,3,2,6] => [6,2,3,4,5,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,5,4,3,6,2] => [2,6,3,4,5,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,5,4,6,2,3] => [3,2,6,4,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,5,4,6,3,2] => [2,3,6,4,5,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,5,6,2,3,4] => [4,3,2,6,5,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,5,6,2,4,3] => [3,4,2,6,5,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,5,6,3,2,4] => [4,2,3,6,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,5,6,3,4,2] => [2,4,3,6,5,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,5,6,4,2,3] => [3,2,4,6,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,5,6,4,3,2] => [2,3,4,6,5,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,6,2,3,4,5] => [5,4,3,2,6,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,6,2,3,5,4] => [4,5,3,2,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,6,2,4,3,5] => [5,3,4,2,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,6,2,4,5,3] => [3,5,4,2,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,6,2,5,3,4] => [4,3,5,2,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,6,2,5,4,3] => [3,4,5,2,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,6,3,2,4,5] => [5,4,2,3,6,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,6,3,2,5,4] => [4,5,2,3,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,6,3,4,2,5] => [5,2,4,3,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,6,3,4,5,2] => [2,5,4,3,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,6,3,5,2,4] => [4,2,5,3,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,6,3,5,4,2] => [2,4,5,3,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,6,4,2,3,5] => [5,3,2,4,6,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,6,4,2,5,3] => [3,5,2,4,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,6,4,3,2,5] => [5,2,3,4,6,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,6,4,3,5,2] => [2,5,3,4,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,6,4,5,2,3] => [3,2,5,4,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,6,4,5,3,2] => [2,3,5,4,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,6,5,2,3,4] => [4,3,2,5,6,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,6,5,2,4,3] => [3,4,2,5,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,6,5,3,2,4] => [4,2,3,5,6,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,6,5,3,4,2] => [2,4,3,5,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,6,5,4,2,3] => [3,2,4,5,6,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,6,5,4,3,2] => [2,3,4,5,6,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,1,3,4,5,6] => [6,5,4,3,1,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[2,1,3,4,6,5] => [5,6,4,3,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,3,5,4,6] => [6,4,5,3,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,3,5,6,4] => [4,6,5,3,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,3,6,4,5] => [5,4,6,3,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,3,6,5,4] => [4,5,6,3,1,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,1,4,3,5,6] => [6,5,3,4,1,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[2,1,4,3,6,5] => [5,6,3,4,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[2,1,4,5,3,6] => [6,3,5,4,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,4,5,6,3] => [3,6,5,4,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,4,6,3,5] => [5,3,6,4,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,4,6,5,3] => [3,5,6,4,1,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,1,5,3,4,6] => [6,4,3,5,1,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[2,1,5,3,6,4] => [4,6,3,5,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[2,1,5,4,3,6] => [6,3,4,5,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[2,1,5,4,6,3] => [3,6,4,5,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[2,1,5,6,3,4] => [4,3,6,5,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,5,6,4,3] => [3,4,6,5,1,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,1,6,3,4,5] => [5,4,3,6,1,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[2,1,6,3,5,4] => [4,5,3,6,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[2,1,6,4,3,5] => [5,3,4,6,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[2,1,6,4,5,3] => [3,5,4,6,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[2,1,6,5,3,4] => [4,3,5,6,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[2,1,6,5,4,3] => [3,4,5,6,1,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[2,3,1,4,5,6] => [6,5,4,1,3,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[2,3,1,4,6,5] => [5,6,4,1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,3,1,5,4,6] => [6,4,5,1,3,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,3,1,5,6,4] => [4,6,5,1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,3,1,6,4,5] => [5,4,6,1,3,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,3,1,6,5,4] => [4,5,6,1,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,3,4,1,5,6] => [6,5,1,4,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[2,3,4,1,6,5] => [5,6,1,4,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,3,4,5,1,6] => [6,1,5,4,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,3,4,5,6,1] => [1,6,5,4,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,3,4,6,1,5] => [5,1,6,4,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,3,4,6,5,1] => [1,5,6,4,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,3,5,1,4,6] => [6,4,1,5,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[2,3,5,1,6,4] => [4,6,1,5,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,3,5,4,1,6] => [6,1,4,5,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,3,5,4,6,1] => [1,6,4,5,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,3,5,6,1,4] => [4,1,6,5,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,3,5,6,4,1] => [1,4,6,5,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,3,6,1,4,5] => [5,4,1,6,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[2,3,6,1,5,4] => [4,5,1,6,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,3,6,4,1,5] => [5,1,4,6,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,3,6,4,5,1] => [1,5,4,6,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,3,6,5,1,4] => [4,1,5,6,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,3,6,5,4,1] => [1,4,5,6,3,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[2,4,1,3,5,6] => [6,5,3,1,4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[2,4,1,3,6,5] => [5,6,3,1,4,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,4,1,5,3,6] => [6,3,5,1,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,4,1,5,6,3] => [3,6,5,1,4,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,4,1,6,3,5] => [5,3,6,1,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,4,1,6,5,3] => [3,5,6,1,4,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,4,3,1,5,6] => [6,5,1,3,4,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,4,3,1,6,5] => [5,6,1,3,4,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,4,3,5,1,6] => [6,1,5,3,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,4,3,5,6,1] => [1,6,5,3,4,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,4,3,6,1,5] => [5,1,6,3,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,4,3,6,5,1] => [1,5,6,3,4,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,4,5,1,3,6] => [6,3,1,5,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[2,4,5,1,6,3] => [3,6,1,5,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,4,5,3,1,6] => [6,1,3,5,4,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,4,5,3,6,1] => [1,6,3,5,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,4,5,6,1,3] => [3,1,6,5,4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,4,5,6,3,1] => [1,3,6,5,4,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,4,6,1,3,5] => [5,3,1,6,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[2,4,6,1,5,3] => [3,5,1,6,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,4,6,3,1,5] => [5,1,3,6,4,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,4,6,3,5,1] => [1,5,3,6,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,4,6,5,1,3] => [3,1,5,6,4,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,4,6,5,3,1] => [1,3,5,6,4,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[2,5,1,3,4,6] => [6,4,3,1,5,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[2,5,1,3,6,4] => [4,6,3,1,5,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,5,1,4,3,6] => [6,3,4,1,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,5,1,4,6,3] => [3,6,4,1,5,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,5,1,6,3,4] => [4,3,6,1,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,5,1,6,4,3] => [3,4,6,1,5,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,5,3,1,4,6] => [6,4,1,3,5,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,5,3,1,6,4] => [4,6,1,3,5,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,3,4,1,6] => [6,1,4,3,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,5,3,4,6,1] => [1,6,4,3,5,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,5,3,6,1,4] => [4,1,6,3,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,5,3,6,4,1] => [1,4,6,3,5,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,5,4,1,3,6] => [6,3,1,4,5,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,5,4,1,6,3] => [3,6,1,4,5,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,4,3,1,6] => [6,1,3,4,5,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,5,4,3,6,1] => [1,6,3,4,5,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,5,4,6,1,3] => [3,1,6,4,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,5,4,6,3,1] => [1,3,6,4,5,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,5,6,1,3,4] => [4,3,1,6,5,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[2,5,6,1,4,3] => [3,4,1,6,5,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,5,6,3,1,4] => [4,1,3,6,5,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,5,6,3,4,1] => [1,4,3,6,5,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,5,6,4,1,3] => [3,1,4,6,5,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,5,6,4,3,1] => [1,3,4,6,5,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[2,6,1,3,4,5] => [5,4,3,1,6,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[2,6,1,3,5,4] => [4,5,3,1,6,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,6,1,4,3,5] => [5,3,4,1,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,6,1,4,5,3] => [3,5,4,1,6,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,6,1,5,3,4] => [4,3,5,1,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,6,1,5,4,3] => [3,4,5,1,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,6,3,1,4,5] => [5,4,1,3,6,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,6,3,1,5,4] => [4,5,1,3,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,6,3,4,1,5] => [5,1,4,3,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,6,3,4,5,1] => [1,5,4,3,6,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,6,3,5,1,4] => [4,1,5,3,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,6,3,5,4,1] => [1,4,5,3,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,6,4,1,3,5] => [5,3,1,4,6,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,6,4,1,5,3] => [3,5,1,4,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,6,4,3,1,5] => [5,1,3,4,6,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,6,4,3,5,1] => [1,5,3,4,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,6,4,5,1,3] => [3,1,5,4,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,6,4,5,3,1] => [1,3,5,4,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,6,5,1,3,4] => [4,3,1,5,6,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,6,5,1,4,3] => [3,4,1,5,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,6,5,3,1,4] => [4,1,3,5,6,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,6,5,3,4,1] => [1,4,3,5,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,6,5,4,1,3] => [3,1,4,5,6,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,6,5,4,3,1] => [1,3,4,5,6,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,1,2,4,5,6] => [6,5,4,2,1,3] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[3,1,2,4,6,5] => [5,6,4,2,1,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[3,1,2,5,4,6] => [6,4,5,2,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,1,2,5,6,4] => [4,6,5,2,1,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[3,1,2,6,4,5] => [5,4,6,2,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,1,2,6,5,4] => [4,5,6,2,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,1,4,2,5,6] => [6,5,2,4,1,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,1,4,2,6,5] => [5,6,2,4,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,1,4,5,2,6] => [6,2,5,4,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,1,4,5,6,2] => [2,6,5,4,1,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[3,1,4,6,2,5] => [5,2,6,4,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,1,4,6,5,2] => [2,5,6,4,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,1,5,2,4,6] => [6,4,2,5,1,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,1,5,2,6,4] => [4,6,2,5,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,1,5,4,2,6] => [6,2,4,5,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[3,1,5,4,6,2] => [2,6,4,5,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,1,5,6,2,4] => [4,2,6,5,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,1,5,6,4,2] => [2,4,6,5,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,1,6,2,4,5] => [5,4,2,6,1,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,1,6,2,5,4] => [4,5,2,6,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,1,6,4,2,5] => [5,2,4,6,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[3,1,6,4,5,2] => [2,5,4,6,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,1,6,5,2,4] => [4,2,5,6,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[3,1,6,5,4,2] => [2,4,5,6,1,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[3,2,1,4,5,6] => [6,5,4,1,2,3] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[3,2,1,4,6,5] => [5,6,4,1,2,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[3,2,1,5,4,6] => [6,4,5,1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[3,2,1,5,6,4] => [4,6,5,1,2,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[3,2,1,6,4,5] => [5,4,6,1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[3,2,1,6,5,4] => [4,5,6,1,2,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[3,2,4,1,5,6] => [6,5,1,4,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,2,4,1,6,5] => [5,6,1,4,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,2,4,5,1,6] => [6,1,5,4,2,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,2,4,5,6,1] => [1,6,5,4,2,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[3,2,4,6,1,5] => [5,1,6,4,2,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,2,4,6,5,1] => [1,5,6,4,2,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,5,1,4,6] => [6,4,1,5,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,2,5,1,6,4] => [4,6,1,5,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,2,5,4,1,6] => [6,1,4,5,2,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[3,2,5,4,6,1] => [1,6,4,5,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,2,5,6,1,4] => [4,1,6,5,2,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[3,2,5,6,4,1] => [1,4,6,5,2,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,6,1,4,5] => [5,4,1,6,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,2,6,1,5,4] => [4,5,1,6,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,2,6,4,1,5] => [5,1,4,6,2,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[3,2,6,4,5,1] => [1,5,4,6,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,2,6,5,1,4] => [4,1,5,6,2,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[3,2,6,5,4,1] => [1,4,5,6,2,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[3,4,1,2,5,6] => [6,5,2,1,4,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[3,4,1,2,6,5] => [5,6,2,1,4,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,4,1,5,2,6] => [6,2,5,1,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,4,1,5,6,2] => [2,6,5,1,4,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,4,1,6,2,5] => [5,2,6,1,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,4,1,6,5,2] => [2,5,6,1,4,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,4,2,1,5,6] => [6,5,1,2,4,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,4,2,1,6,5] => [5,6,1,2,4,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,4,2,5,1,6] => [6,1,5,2,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,4,2,5,6,1] => [1,6,5,2,4,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,4,2,6,1,5] => [5,1,6,2,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,4,2,6,5,1] => [1,5,6,2,4,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,4,5,1,2,6] => [6,2,1,5,4,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[3,4,5,1,6,2] => [2,6,1,5,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,4,5,2,1,6] => [6,1,2,5,4,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,4,5,2,6,1] => [1,6,2,5,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,4,5,6,1,2] => [2,1,6,5,4,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[3,4,5,6,2,1] => [1,2,6,5,4,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[3,4,6,1,2,5] => [5,2,1,6,4,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[3,4,6,1,5,2] => [2,5,1,6,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,4,6,2,1,5] => [5,1,2,6,4,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,4,6,2,5,1] => [1,5,2,6,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,4,6,5,1,2] => [2,1,5,6,4,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,4,6,5,2,1] => [1,2,5,6,4,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[3,5,1,2,4,6] => [6,4,2,1,5,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[3,5,1,2,6,4] => [4,6,2,1,5,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,5,1,4,2,6] => [6,2,4,1,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,5,1,4,6,2] => [2,6,4,1,5,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,5,1,6,2,4] => [4,2,6,1,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,5,1,6,4,2] => [2,4,6,1,5,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,2,1,4,6] => [6,4,1,2,5,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,5,2,1,6,4] => [4,6,1,2,5,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,5,2,4,1,6] => [6,1,4,2,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,5,2,4,6,1] => [1,6,4,2,5,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,5,2,6,1,4] => [4,1,6,2,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,5,2,6,4,1] => [1,4,6,2,5,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,4,1,2,6] => [6,2,1,4,5,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,5,4,1,6,2] => [2,6,1,4,5,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,5,4,2,1,6] => [6,1,2,4,5,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[3,5,4,2,6,1] => [1,6,2,4,5,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,5,4,6,1,2] => [2,1,6,4,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,5,4,6,2,1] => [1,2,6,4,5,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,5,6,1,2,4] => [4,2,1,6,5,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[3,5,6,1,4,2] => [2,4,1,6,5,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,5,6,2,1,4] => [4,1,2,6,5,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,5,6,2,4,1] => [1,4,2,6,5,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,5,6,4,1,2] => [2,1,4,6,5,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,5,6,4,2,1] => [1,2,4,6,5,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[3,6,1,2,4,5] => [5,4,2,1,6,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[3,6,1,2,5,4] => [4,5,2,1,6,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,6,1,4,2,5] => [5,2,4,1,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,6,1,4,5,2] => [2,5,4,1,6,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,6,1,5,2,4] => [4,2,5,1,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,6,1,5,4,2] => [2,4,5,1,6,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,6,2,1,4,5] => [5,4,1,2,6,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,6,2,1,5,4] => [4,5,1,2,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,6,2,4,1,5] => [5,1,4,2,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,6,2,4,5,1] => [1,5,4,2,6,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[3,6,2,5,1,4] => [4,1,5,2,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,6,2,5,4,1] => [1,4,5,2,6,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,6,4,1,2,5] => [5,2,1,4,6,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,6,4,1,5,2] => [2,5,1,4,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,6,4,2,1,5] => [5,1,2,4,6,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[3,6,4,2,5,1] => [1,5,2,4,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,6,4,5,1,2] => [2,1,5,4,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,6,4,5,2,1] => [1,2,5,4,6,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,6,5,1,2,4] => [4,2,1,5,6,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,6,5,1,4,2] => [2,4,1,5,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,6,5,2,1,4] => [4,1,2,5,6,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[3,6,5,2,4,1] => [1,4,2,5,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,6,5,4,1,2] => [2,1,4,5,6,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[3,6,5,4,2,1] => [1,2,4,5,6,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[4,1,2,3,5,6] => [6,5,3,2,1,4] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[4,1,2,3,6,5] => [5,6,3,2,1,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[4,1,2,5,3,6] => [6,3,5,2,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,1,2,5,6,3] => [3,6,5,2,1,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[4,1,2,6,3,5] => [5,3,6,2,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,1,2,6,5,3] => [3,5,6,2,1,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,1,3,2,5,6] => [6,5,2,3,1,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,1,3,2,6,5] => [5,6,2,3,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,1,3,5,2,6] => [6,2,5,3,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,1,3,5,6,2] => [2,6,5,3,1,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[4,1,3,6,2,5] => [5,2,6,3,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,1,3,6,5,2] => [2,5,6,3,1,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,1,5,2,3,6] => [6,3,2,5,1,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,1,5,2,6,3] => [3,6,2,5,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,1,5,3,2,6] => [6,2,3,5,1,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,1,5,3,6,2] => [2,6,3,5,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,1,5,6,2,3] => [3,2,6,5,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,1,5,6,3,2] => [2,3,6,5,1,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,1,6,2,3,5] => [5,3,2,6,1,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,1,6,2,5,3] => [3,5,2,6,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,1,6,3,2,5] => [5,2,3,6,1,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,1,6,3,5,2] => [2,5,3,6,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,1,6,5,2,3] => [3,2,5,6,1,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,1,6,5,3,2] => [2,3,5,6,1,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[4,2,1,3,5,6] => [6,5,3,1,2,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,2,1,3,6,5] => [5,6,3,1,2,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[4,2,1,5,3,6] => [6,3,5,1,2,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[4,2,1,5,6,3] => [3,6,5,1,2,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[4,2,1,6,3,5] => [5,3,6,1,2,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[4,2,1,6,5,3] => [3,5,6,1,2,4] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[4,2,3,1,5,6] => [6,5,1,3,2,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,2,3,1,6,5] => [5,6,1,3,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,2,3,5,1,6] => [6,1,5,3,2,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,2,3,5,6,1] => [1,6,5,3,2,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[4,2,3,6,1,5] => [5,1,6,3,2,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,2,3,6,5,1] => [1,5,6,3,2,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,2,5,1,3,6] => [6,3,1,5,2,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,2,5,1,6,3] => [3,6,1,5,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,2,5,3,1,6] => [6,1,3,5,2,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,2,5,3,6,1] => [1,6,3,5,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,2,5,6,1,3] => [3,1,6,5,2,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,2,5,6,3,1] => [1,3,6,5,2,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,2,6,1,3,5] => [5,3,1,6,2,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,2,6,1,5,3] => [3,5,1,6,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,2,6,3,1,5] => [5,1,3,6,2,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,2,6,3,5,1] => [1,5,3,6,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,2,6,5,1,3] => [3,1,5,6,2,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,2,6,5,3,1] => [1,3,5,6,2,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[4,3,1,2,5,6] => [6,5,2,1,3,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,3,1,2,6,5] => [5,6,2,1,3,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[4,3,1,5,2,6] => [6,2,5,1,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[4,3,1,5,6,2] => [2,6,5,1,3,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[4,3,1,6,2,5] => [5,2,6,1,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[4,3,1,6,5,2] => [2,5,6,1,3,4] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[4,3,2,1,5,6] => [6,5,1,2,3,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[4,3,2,1,6,5] => [5,6,1,2,3,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[4,3,2,5,1,6] => [6,1,5,2,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[4,3,2,5,6,1] => [1,6,5,2,3,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[4,3,2,6,1,5] => [5,1,6,2,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[4,3,2,6,5,1] => [1,5,6,2,3,4] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[4,3,5,1,2,6] => [6,2,1,5,3,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,3,5,1,6,2] => [2,6,1,5,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,3,5,2,1,6] => [6,1,2,5,3,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,3,5,2,6,1] => [1,6,2,5,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,3,5,6,1,2] => [2,1,6,5,3,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[4,3,5,6,2,1] => [1,2,6,5,3,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,3,6,1,2,5] => [5,2,1,6,3,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[4,3,6,1,5,2] => [2,5,1,6,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,3,6,2,1,5] => [5,1,2,6,3,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,3,6,2,5,1] => [1,5,2,6,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,3,6,5,1,2] => [2,1,5,6,3,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[4,3,6,5,2,1] => [1,2,5,6,3,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[4,5,1,2,3,6] => [6,3,2,1,5,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,5,1,2,6,3] => [3,6,2,1,5,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[4,5,1,3,2,6] => [6,2,3,1,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,5,1,3,6,2] => [2,6,3,1,5,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[4,5,1,6,2,3] => [3,2,6,1,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,5,1,6,3,2] => [2,3,6,1,5,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[4,5,2,1,3,6] => [6,3,1,2,5,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[4,5,2,1,6,3] => [3,6,1,2,5,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,5,2,3,1,6] => [6,1,3,2,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,5,2,3,6,1] => [1,6,3,2,5,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[4,5,2,6,1,3] => [3,1,6,2,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,5,2,6,3,1] => [1,3,6,2,5,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[4,5,3,1,2,6] => [6,2,1,3,5,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[4,5,3,1,6,2] => [2,6,1,3,5,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,5,3,2,1,6] => [6,1,2,3,5,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[4,5,3,2,6,1] => [1,6,2,3,5,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,5,3,6,1,2] => [2,1,6,3,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,5,3,6,2,1] => [1,2,6,3,5,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[4,5,6,1,3,2] => [2,3,1,6,5,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[4,5,6,2,1,3] => [3,1,2,6,5,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[4,5,6,2,3,1] => [1,3,2,6,5,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[4,5,6,3,1,2] => [2,1,3,6,5,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[4,5,6,3,2,1] => [1,2,3,6,5,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,6,1,2,3,5] => [5,3,2,1,6,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,6,1,2,5,3] => [3,5,2,1,6,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[4,6,1,3,2,5] => [5,2,3,1,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,6,1,3,5,2] => [2,5,3,1,6,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[4,6,1,5,2,3] => [3,2,5,1,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,6,1,5,3,2] => [2,3,5,1,6,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[4,6,2,1,3,5] => [5,3,1,2,6,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[4,6,2,1,5,3] => [3,5,1,2,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,6,2,3,1,5] => [5,1,3,2,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,6,2,3,5,1] => [1,5,3,2,6,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[4,6,2,5,1,3] => [3,1,5,2,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,6,2,5,3,1] => [1,3,5,2,6,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[4,6,3,1,2,5] => [5,2,1,3,6,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[4,6,3,1,5,2] => [2,5,1,3,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,6,3,2,1,5] => [5,1,2,3,6,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[4,6,3,2,5,1] => [1,5,2,3,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,6,3,5,1,2] => [2,1,5,3,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[4,6,3,5,2,1] => [1,2,5,3,6,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[4,6,5,1,2,3] => [3,2,1,5,6,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[4,6,5,1,3,2] => [2,3,1,5,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,6,5,2,1,3] => [3,1,2,5,6,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[4,6,5,2,3,1] => [1,3,2,5,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[4,6,5,3,1,2] => [2,1,3,5,6,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[4,6,5,3,2,1] => [1,2,3,5,6,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,1,2,3,4,6] => [6,4,3,2,1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,1,2,3,6,4] => [4,6,3,2,1,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[5,1,2,4,3,6] => [6,3,4,2,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,1,2,4,6,3] => [3,6,4,2,1,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[5,1,2,6,3,4] => [4,3,6,2,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,1,2,6,4,3] => [3,4,6,2,1,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[5,1,3,2,4,6] => [6,4,2,3,1,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,1,3,2,6,4] => [4,6,2,3,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,1,3,4,2,6] => [6,2,4,3,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,1,3,4,6,2] => [2,6,4,3,1,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[5,1,3,6,2,4] => [4,2,6,3,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,1,3,6,4,2] => [2,4,6,3,1,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[5,1,4,2,3,6] => [6,3,2,4,1,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,1,4,2,6,3] => [3,6,2,4,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,1,4,3,2,6] => [6,2,3,4,1,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,1,4,3,6,2] => [2,6,3,4,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,1,4,6,2,3] => [3,2,6,4,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,1,4,6,3,2] => [2,3,6,4,1,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[5,1,6,2,3,4] => [4,3,2,6,1,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,1,6,2,4,3] => [3,4,2,6,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,1,6,3,2,4] => [4,2,3,6,1,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,1,6,3,4,2] => [2,4,3,6,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,1,6,4,2,3] => [3,2,4,6,1,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,1,6,4,3,2] => [2,3,4,6,1,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[5,2,1,3,4,6] => [6,4,3,1,2,5] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[5,2,1,3,6,4] => [4,6,3,1,2,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,2,1,4,3,6] => [6,3,4,1,2,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,2,1,4,6,3] => [3,6,4,1,2,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,2,1,6,3,4] => [4,3,6,1,2,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,2,1,6,4,3] => [3,4,6,1,2,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[5,2,3,1,4,6] => [6,4,1,3,2,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,2,3,1,6,4] => [4,6,1,3,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,2,3,4,1,6] => [6,1,4,3,2,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,2,3,4,6,1] => [1,6,4,3,2,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[5,2,3,6,1,4] => [4,1,6,3,2,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,2,3,6,4,1] => [1,4,6,3,2,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[5,2,4,1,3,6] => [6,3,1,4,2,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,2,4,1,6,3] => [3,6,1,4,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,2,4,3,1,6] => [6,1,3,4,2,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,2,4,3,6,1] => [1,6,3,4,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,2,4,6,1,3] => [3,1,6,4,2,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,2,4,6,3,1] => [1,3,6,4,2,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[5,2,6,1,3,4] => [4,3,1,6,2,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,2,6,1,4,3] => [3,4,1,6,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,2,6,3,1,4] => [4,1,3,6,2,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,2,6,3,4,1] => [1,4,3,6,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,2,6,4,1,3] => [3,1,4,6,2,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,2,6,4,3,1] => [1,3,4,6,2,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[5,3,1,2,4,6] => [6,4,2,1,3,5] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[5,3,1,2,6,4] => [4,6,2,1,3,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,3,1,4,2,6] => [6,2,4,1,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,3,1,4,6,2] => [2,6,4,1,3,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,3,1,6,2,4] => [4,2,6,1,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,3,1,6,4,2] => [2,4,6,1,3,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[5,3,2,1,4,6] => [6,4,1,2,3,5] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[5,3,2,1,6,4] => [4,6,1,2,3,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[5,3,2,4,1,6] => [6,1,4,2,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,3,2,4,6,1] => [1,6,4,2,3,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,3,2,6,1,4] => [4,1,6,2,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,3,2,6,4,1] => [1,4,6,2,3,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[5,3,4,1,2,6] => [6,2,1,4,3,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,3,4,1,6,2] => [2,6,1,4,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,3,4,2,1,6] => [6,1,2,4,3,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,3,4,2,6,1] => [1,6,2,4,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,3,4,6,1,2] => [2,1,6,4,3,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[5,3,4,6,2,1] => [1,2,6,4,3,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[5,3,6,1,2,4] => [4,2,1,6,3,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,3,6,1,4,2] => [2,4,1,6,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,3,6,2,1,4] => [4,1,2,6,3,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,3,6,2,4,1] => [1,4,2,6,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,3,6,4,1,2] => [2,1,4,6,3,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,3,6,4,2,1] => [1,2,4,6,3,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[5,4,1,2,3,6] => [6,3,2,1,4,5] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[5,4,1,2,6,3] => [3,6,2,1,4,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,4,1,3,2,6] => [6,2,3,1,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,4,1,3,6,2] => [2,6,3,1,4,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,4,1,6,2,3] => [3,2,6,1,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,4,1,6,3,2] => [2,3,6,1,4,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[5,4,2,1,3,6] => [6,3,1,2,4,5] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[5,4,2,1,6,3] => [3,6,1,2,4,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[5,4,2,3,1,6] => [6,1,3,2,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,4,2,3,6,1] => [1,6,3,2,4,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[5,4,2,6,1,3] => [3,1,6,2,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,4,2,6,3,1] => [1,3,6,2,4,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[5,4,3,1,2,6] => [6,2,1,3,4,5] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[5,4,3,1,6,2] => [2,6,1,3,4,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[5,4,3,2,1,6] => [6,1,2,3,4,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[5,4,3,2,6,1] => [1,6,2,3,4,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[5,4,3,6,1,2] => [2,1,6,3,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[5,4,3,6,2,1] => [1,2,6,3,4,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[5,4,6,1,2,3] => [3,2,1,6,4,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[5,4,6,1,3,2] => [2,3,1,6,4,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,4,6,2,1,3] => [3,1,2,6,4,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,4,6,2,3,1] => [1,3,2,6,4,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[5,4,6,3,1,2] => [2,1,3,6,4,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[5,4,6,3,2,1] => [1,2,3,6,4,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[5,6,1,2,3,4] => [4,3,2,1,6,5] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[5,6,1,2,4,3] => [3,4,2,1,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[5,6,1,3,2,4] => [4,2,3,1,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[5,6,1,3,4,2] => [2,4,3,1,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[5,6,1,4,2,3] => [3,2,4,1,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[5,6,1,4,3,2] => [2,3,4,1,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[5,6,2,1,3,4] => [4,3,1,2,6,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[5,6,2,1,4,3] => [3,4,1,2,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[5,6,2,3,1,4] => [4,1,3,2,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[5,6,2,3,4,1] => [1,4,3,2,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[5,6,2,4,1,3] => [3,1,4,2,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[5,6,2,4,3,1] => [1,3,4,2,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[5,6,3,1,2,4] => [4,2,1,3,6,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[5,6,3,1,4,2] => [2,4,1,3,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[5,6,3,2,1,4] => [4,1,2,3,6,5] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[5,6,3,2,4,1] => [1,4,2,3,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[5,6,3,4,1,2] => [2,1,4,3,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[5,6,3,4,2,1] => [1,2,4,3,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[5,6,4,1,2,3] => [3,2,1,4,6,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[5,6,4,1,3,2] => [2,3,1,4,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[5,6,4,2,1,3] => [3,1,2,4,6,5] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[5,6,4,2,3,1] => [1,3,2,4,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[5,6,4,3,1,2] => [2,1,3,4,6,5] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[5,6,4,3,2,1] => [1,2,3,4,6,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[6,1,2,3,4,5] => [5,4,3,2,1,6] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[6,1,2,3,5,4] => [4,5,3,2,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[6,1,2,4,3,5] => [5,3,4,2,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,1,2,4,5,3] => [3,5,4,2,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[6,1,2,5,3,4] => [4,3,5,2,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,1,2,5,4,3] => [3,4,5,2,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[6,1,3,2,4,5] => [5,4,2,3,1,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,1,3,2,5,4] => [4,5,2,3,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,1,3,4,2,5] => [5,2,4,3,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,1,3,4,5,2] => [2,5,4,3,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[6,1,3,5,2,4] => [4,2,5,3,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,1,3,5,4,2] => [2,4,5,3,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[6,1,4,2,3,5] => [5,3,2,4,1,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,1,4,2,5,3] => [3,5,2,4,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,1,4,3,2,5] => [5,2,3,4,1,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,1,4,3,5,2] => [2,5,3,4,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,1,4,5,2,3] => [3,2,5,4,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,1,4,5,3,2] => [2,3,5,4,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[6,1,5,2,3,4] => [4,3,2,5,1,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,1,5,2,4,3] => [3,4,2,5,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,1,5,3,2,4] => [4,2,3,5,1,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,1,5,3,4,2] => [2,4,3,5,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,1,5,4,2,3] => [3,2,4,5,1,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,1,5,4,3,2] => [2,3,4,5,1,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[6,2,1,3,4,5] => [5,4,3,1,2,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[6,2,1,3,5,4] => [4,5,3,1,2,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,2,1,4,3,5] => [5,3,4,1,2,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,2,1,4,5,3] => [3,5,4,1,2,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,2,1,5,3,4] => [4,3,5,1,2,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,2,1,5,4,3] => [3,4,5,1,2,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,2,3,1,4,5] => [5,4,1,3,2,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,2,3,1,5,4] => [4,5,1,3,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,2,3,4,1,5] => [5,1,4,3,2,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,2,3,4,5,1] => [1,5,4,3,2,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[6,2,3,5,1,4] => [4,1,5,3,2,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,2,3,5,4,1] => [1,4,5,3,2,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[6,2,4,1,3,5] => [5,3,1,4,2,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,2,4,1,5,3] => [3,5,1,4,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,2,4,3,1,5] => [5,1,3,4,2,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,2,4,3,5,1] => [1,5,3,4,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,2,4,5,1,3] => [3,1,5,4,2,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,2,4,5,3,1] => [1,3,5,4,2,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[6,2,5,1,3,4] => [4,3,1,5,2,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,2,5,1,4,3] => [3,4,1,5,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,2,5,3,1,4] => [4,1,3,5,2,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,2,5,3,4,1] => [1,4,3,5,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,2,5,4,1,3] => [3,1,4,5,2,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,2,5,4,3,1] => [1,3,4,5,2,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[6,3,1,2,4,5] => [5,4,2,1,3,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[6,3,1,2,5,4] => [4,5,2,1,3,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,3,1,4,2,5] => [5,2,4,1,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,3,1,4,5,2] => [2,5,4,1,3,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,3,1,5,2,4] => [4,2,5,1,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,3,1,5,4,2] => [2,4,5,1,3,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,3,2,1,4,5] => [5,4,1,2,3,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[6,3,2,1,5,4] => [4,5,1,2,3,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,3,2,4,1,5] => [5,1,4,2,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,3,2,4,5,1] => [1,5,4,2,3,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,3,2,5,1,4] => [4,1,5,2,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,3,2,5,4,1] => [1,4,5,2,3,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,3,4,1,2,5] => [5,2,1,4,3,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,3,4,1,5,2] => [2,5,1,4,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,3,4,2,1,5] => [5,1,2,4,3,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,3,4,2,5,1] => [1,5,2,4,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,3,4,5,1,2] => [2,1,5,4,3,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[6,3,4,5,2,1] => [1,2,5,4,3,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[6,3,5,1,2,4] => [4,2,1,5,3,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,3,5,1,4,2] => [2,4,1,5,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,3,5,2,1,4] => [4,1,2,5,3,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,3,5,2,4,1] => [1,4,2,5,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,3,5,4,1,2] => [2,1,4,5,3,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,3,5,4,2,1] => [1,2,4,5,3,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[6,4,1,2,3,5] => [5,3,2,1,4,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[6,4,1,2,5,3] => [3,5,2,1,4,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,4,1,3,2,5] => [5,2,3,1,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,4,1,3,5,2] => [2,5,3,1,4,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,4,1,5,2,3] => [3,2,5,1,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,4,1,5,3,2] => [2,3,5,1,4,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,4,2,1,3,5] => [5,3,1,2,4,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[6,4,2,1,5,3] => [3,5,1,2,4,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,4,2,3,1,5] => [5,1,3,2,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,4,2,3,5,1] => [1,5,3,2,4,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,4,2,5,1,3] => [3,1,5,2,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,4,2,5,3,1] => [1,3,5,2,4,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,4,3,1,2,5] => [5,2,1,3,4,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[6,4,3,1,5,2] => [2,5,1,3,4,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,4,3,2,1,5] => [5,1,2,3,4,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[6,4,3,2,5,1] => [1,5,2,3,4,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,4,3,5,1,2] => [2,1,5,3,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,4,3,5,2,1] => [1,2,5,3,4,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,4,5,1,2,3] => [3,2,1,5,4,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[6,4,5,1,3,2] => [2,3,1,5,4,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,4,5,2,1,3] => [3,1,2,5,4,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,4,5,2,3,1] => [1,3,2,5,4,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[6,4,5,3,1,2] => [2,1,3,5,4,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[6,4,5,3,2,1] => [1,2,3,5,4,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[6,5,1,2,3,4] => [4,3,2,1,5,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[6,5,1,2,4,3] => [3,4,2,1,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,5,1,3,2,4] => [4,2,3,1,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,5,1,3,4,2] => [2,4,3,1,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,5,1,4,2,3] => [3,2,4,1,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,5,1,4,3,2] => [2,3,4,1,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,5,2,1,3,4] => [4,3,1,2,5,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[6,5,2,1,4,3] => [3,4,1,2,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,5,2,3,1,4] => [4,1,3,2,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,5,2,3,4,1] => [1,4,3,2,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[6,5,2,4,1,3] => [3,1,4,2,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,5,2,4,3,1] => [1,3,4,2,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,5,3,1,2,4] => [4,2,1,3,5,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[6,5,3,1,4,2] => [2,4,1,3,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,5,3,2,1,4] => [4,1,2,3,5,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[6,5,3,2,4,1] => [1,4,2,3,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,5,3,4,1,2] => [2,1,4,3,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[6,5,3,4,2,1] => [1,2,4,3,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[6,5,4,1,2,3] => [3,2,1,4,5,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[6,5,4,1,3,2] => [2,3,1,4,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,5,4,2,1,3] => [3,1,2,4,5,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[6,5,4,2,3,1] => [1,3,2,4,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[6,5,4,3,1,2] => [2,1,3,4,5,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[6,5,4,3,2,1] => [1,2,3,4,5,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,5 1,17,6 1,49,70 1,129,500,90
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 5\ q$
$F_{4} = 1 + 17\ q + 6\ q^{2}$
$F_{5} = 1 + 49\ q + 70\ q^{2}$
$F_{6} = 1 + 129\ q + 500\ q^{2} + 90\ q^{3}$
Description
The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary.
Given two lattice paths $U,L$ from $(0,0)$ to $(d,n-d)$, [1] describes a bijection between lattice paths weakly between $U$ and $L$ and subsets of $\{1,\dots,n\}$ such that the set of all such subsets gives the standard complex of the lattice path matroid $M[U,L]$.
This statistic gives the cardinality of the image of this bijection when a Dyck path is considered as a path weakly above the diagonal and relative to the diagonal boundary.
Given two lattice paths $U,L$ from $(0,0)$ to $(d,n-d)$, [1] describes a bijection between lattice paths weakly between $U$ and $L$ and subsets of $\{1,\dots,n\}$ such that the set of all such subsets gives the standard complex of the lattice path matroid $M[U,L]$.
This statistic gives the cardinality of the image of this bijection when a Dyck path is considered as a path weakly above the diagonal and relative to the diagonal boundary.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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