Identifier
-
Mp00277:
Permutations
—catalanization⟶
Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
St000653: Permutations ⟶ ℤ
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 1
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[2,3,1] => [2,3,1] => [2,3,1] => [3,2,1] => 2
[3,1,2] => [2,3,1] => [2,3,1] => [3,2,1] => 2
[3,2,1] => [3,2,1] => [3,2,1] => [2,3,1] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 1
[1,3,2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => 1
[1,3,4,2] => [1,3,4,2] => [3,4,1,2] => [4,3,2,1] => 3
[1,4,2,3] => [1,3,4,2] => [3,4,1,2] => [4,3,2,1] => 3
[1,4,3,2] => [1,4,3,2] => [4,3,1,2] => [3,4,2,1] => 3
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => [2,4,1,3] => [4,2,1,3] => 2
[2,3,1,4] => [2,3,1,4] => [2,3,1,4] => [3,2,1,4] => 2
[2,3,4,1] => [2,3,4,1] => [2,3,4,1] => [4,2,3,1] => 3
[2,4,1,3] => [4,3,1,2] => [1,4,3,2] => [1,3,4,2] => 3
[2,4,3,1] => [2,4,3,1] => [4,2,3,1] => [2,3,4,1] => 3
[3,1,2,4] => [2,3,1,4] => [2,3,1,4] => [3,2,1,4] => 2
[3,1,4,2] => [2,3,4,1] => [2,3,4,1] => [4,2,3,1] => 3
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [2,3,1,4] => 2
[3,2,4,1] => [3,2,4,1] => [3,2,4,1] => [2,4,3,1] => 3
[3,4,1,2] => [4,3,2,1] => [4,3,2,1] => [3,4,1,2] => 2
[3,4,2,1] => [3,4,2,1] => [3,4,2,1] => [4,3,1,2] => 2
[4,1,2,3] => [2,3,4,1] => [2,3,4,1] => [4,2,3,1] => 3
[4,1,3,2] => [2,4,3,1] => [4,2,3,1] => [2,3,4,1] => 3
[4,2,1,3] => [3,2,4,1] => [3,2,4,1] => [2,4,3,1] => 3
[4,2,3,1] => [3,4,2,1] => [3,4,2,1] => [4,3,1,2] => 2
[4,3,1,2] => [3,4,2,1] => [3,4,2,1] => [4,3,1,2] => 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [3,4,1,2] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => [5,1,2,3,4] => 1
[1,2,4,3,5] => [1,2,4,3,5] => [4,1,2,3,5] => [4,1,2,3,5] => 1
[1,2,4,5,3] => [1,2,4,5,3] => [4,5,1,2,3] => [5,4,2,3,1] => 4
[1,2,5,3,4] => [1,2,4,5,3] => [4,5,1,2,3] => [5,4,2,3,1] => 4
[1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => [4,5,2,3,1] => 4
[1,3,2,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => 1
[1,3,2,5,4] => [1,3,2,5,4] => [3,5,1,2,4] => [5,3,2,1,4] => 3
[1,3,4,2,5] => [1,3,4,2,5] => [3,4,1,2,5] => [4,3,2,1,5] => 3
[1,3,4,5,2] => [1,3,4,5,2] => [3,4,5,1,2] => [5,4,3,2,1] => 4
[1,3,5,2,4] => [1,5,4,2,3] => [1,5,4,2,3] => [1,4,5,3,2] => 4
[1,3,5,4,2] => [1,3,5,4,2] => [5,3,4,1,2] => [3,5,4,2,1] => 4
[1,4,2,3,5] => [1,3,4,2,5] => [3,4,1,2,5] => [4,3,2,1,5] => 3
[1,4,2,5,3] => [1,3,4,5,2] => [3,4,5,1,2] => [5,4,3,2,1] => 4
[1,4,3,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => [3,4,2,1,5] => 3
[1,4,3,5,2] => [1,4,3,5,2] => [4,3,5,1,2] => [4,5,3,2,1] => 4
[1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,1,2] => [3,4,5,2,1] => 4
[1,4,5,3,2] => [1,4,5,3,2] => [4,5,3,1,2] => [4,3,5,2,1] => 4
[1,5,2,3,4] => [1,3,4,5,2] => [3,4,5,1,2] => [5,4,3,2,1] => 4
[1,5,2,4,3] => [1,3,5,4,2] => [5,3,4,1,2] => [3,5,4,2,1] => 4
[1,5,3,2,4] => [1,4,3,5,2] => [4,3,5,1,2] => [4,5,3,2,1] => 4
[1,5,3,4,2] => [1,4,5,3,2] => [4,5,3,1,2] => [4,3,5,2,1] => 4
[1,5,4,2,3] => [1,4,5,3,2] => [4,5,3,1,2] => [4,3,5,2,1] => 4
[1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => [3,4,5,2,1] => 4
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,5,1,3,4] => [5,2,1,3,4] => 2
[2,1,4,3,5] => [2,1,4,3,5] => [2,4,1,3,5] => [4,2,1,3,5] => 2
[2,1,4,5,3] => [2,1,4,5,3] => [2,4,5,1,3] => [5,2,4,3,1] => 4
[2,1,5,3,4] => [2,1,4,5,3] => [2,4,5,1,3] => [5,2,4,3,1] => 4
[2,1,5,4,3] => [2,1,5,4,3] => [5,2,4,1,3] => [2,4,5,3,1] => 4
[2,3,1,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[2,3,1,5,4] => [2,3,1,5,4] => [2,3,5,1,4] => [5,2,3,1,4] => 3
[2,3,4,1,5] => [2,3,4,1,5] => [2,3,4,1,5] => [4,2,3,1,5] => 3
[2,3,4,5,1] => [2,3,4,5,1] => [2,3,4,5,1] => [5,2,3,4,1] => 4
[2,3,5,1,4] => [2,5,4,1,3] => [5,4,2,1,3] => [4,5,1,3,2] => 4
[2,3,5,4,1] => [2,3,5,4,1] => [5,2,3,4,1] => [2,3,4,5,1] => 4
[2,4,1,3,5] => [4,3,1,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => 3
[2,4,1,5,3] => [4,3,1,5,2] => [1,4,3,5,2] => [1,3,5,4,2] => 4
[2,4,3,1,5] => [2,4,3,1,5] => [4,2,3,1,5] => [2,3,4,1,5] => 3
[2,4,3,5,1] => [2,4,3,5,1] => [4,2,3,5,1] => [2,3,5,4,1] => 4
[2,4,5,1,3] => [3,5,4,1,2] => [5,3,1,4,2] => [3,4,2,5,1] => 4
[2,4,5,3,1] => [2,4,5,3,1] => [4,5,2,3,1] => [5,4,1,2,3] => 2
[2,5,1,3,4] => [4,3,1,5,2] => [1,4,3,5,2] => [1,3,5,4,2] => 4
[2,5,1,4,3] => [5,3,1,4,2] => [1,3,5,4,2] => [1,4,3,5,2] => 4
[2,5,3,1,4] => [5,4,3,1,2] => [1,5,4,3,2] => [1,4,5,2,3] => 3
[2,5,3,4,1] => [2,4,5,3,1] => [4,5,2,3,1] => [5,4,1,2,3] => 2
[2,5,4,1,3] => [3,4,5,1,2] => [3,4,1,5,2] => [5,3,2,4,1] => 4
[2,5,4,3,1] => [2,5,4,3,1] => [5,4,2,3,1] => [4,5,1,2,3] => 2
[3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[3,1,2,5,4] => [2,3,1,5,4] => [2,3,5,1,4] => [5,2,3,1,4] => 3
[3,1,4,2,5] => [2,3,4,1,5] => [2,3,4,1,5] => [4,2,3,1,5] => 3
[3,1,4,5,2] => [2,3,4,5,1] => [2,3,4,5,1] => [5,2,3,4,1] => 4
[3,1,5,2,4] => [2,5,4,1,3] => [5,4,2,1,3] => [4,5,1,3,2] => 4
[3,1,5,4,2] => [2,3,5,4,1] => [5,2,3,4,1] => [2,3,4,5,1] => 4
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => 2
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,1,4] => [2,5,3,1,4] => 3
[3,2,4,1,5] => [3,2,4,1,5] => [3,2,4,1,5] => [2,4,3,1,5] => 3
[3,2,4,5,1] => [3,2,4,5,1] => [3,2,4,5,1] => [2,5,3,4,1] => 4
[3,2,5,1,4] => [5,2,4,1,3] => [5,2,1,4,3] => [2,4,1,5,3] => 4
[3,2,5,4,1] => [3,2,5,4,1] => [3,5,2,4,1] => [4,3,1,5,2] => 4
[3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => [3,4,1,2,5] => 2
[3,4,1,5,2] => [4,3,2,5,1] => [4,3,2,5,1] => [3,5,1,4,2] => 4
[3,4,2,1,5] => [3,4,2,1,5] => [3,4,2,1,5] => [4,3,1,2,5] => 2
[3,4,2,5,1] => [3,4,2,5,1] => [3,4,2,5,1] => [5,3,1,4,2] => 4
[3,4,5,1,2] => [3,5,4,2,1] => [5,3,4,2,1] => [3,5,4,1,2] => 3
[3,4,5,2,1] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,1,2] => 3
[3,5,1,2,4] => [4,3,5,1,2] => [4,3,1,5,2] => [3,5,2,4,1] => 4
[3,5,1,4,2] => [5,3,2,4,1] => [3,2,5,4,1] => [2,4,3,5,1] => 4
[3,5,2,1,4] => [3,4,5,1,2] => [3,4,1,5,2] => [5,3,2,4,1] => 4
>>> Load all 931 entries. <<<[3,5,2,4,1] => [5,4,2,3,1] => [2,5,4,3,1] => [4,2,5,1,3] => 3
[3,5,4,1,2] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,1,2] => 3
[3,5,4,2,1] => [3,5,4,2,1] => [5,3,4,2,1] => [3,5,4,1,2] => 3
[4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => [4,2,3,1,5] => 3
[4,1,2,5,3] => [2,3,4,5,1] => [2,3,4,5,1] => [5,2,3,4,1] => 4
[4,1,3,2,5] => [2,4,3,1,5] => [4,2,3,1,5] => [2,3,4,1,5] => 3
[4,1,3,5,2] => [2,4,3,5,1] => [4,2,3,5,1] => [2,3,5,4,1] => 4
[4,1,5,2,3] => [2,5,4,3,1] => [5,4,2,3,1] => [4,5,1,2,3] => 2
[4,1,5,3,2] => [2,4,5,3,1] => [4,5,2,3,1] => [5,4,1,2,3] => 2
[4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => [2,4,3,1,5] => 3
[4,2,1,5,3] => [3,2,4,5,1] => [3,2,4,5,1] => [2,5,3,4,1] => 4
[4,2,3,1,5] => [3,4,2,1,5] => [3,4,2,1,5] => [4,3,1,2,5] => 2
[4,2,3,5,1] => [3,4,2,5,1] => [3,4,2,5,1] => [5,3,1,4,2] => 4
[4,2,5,1,3] => [5,2,4,3,1] => [5,2,4,3,1] => [2,4,5,1,3] => 3
[4,2,5,3,1] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,1,2] => 3
[4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => [4,3,1,2,5] => 2
[4,3,1,5,2] => [3,4,2,5,1] => [3,4,2,5,1] => [5,3,1,4,2] => 4
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [3,4,1,2,5] => 2
[4,3,2,5,1] => [4,3,2,5,1] => [4,3,2,5,1] => [3,5,1,4,2] => 4
[4,3,5,1,2] => [5,3,4,2,1] => [3,5,4,2,1] => [5,3,4,1,2] => 3
[4,3,5,2,1] => [4,3,5,2,1] => [4,3,5,2,1] => [4,5,3,1,2] => 3
[4,5,1,2,3] => [4,3,5,2,1] => [4,3,5,2,1] => [4,5,3,1,2] => 3
[4,5,1,3,2] => [5,3,4,2,1] => [3,5,4,2,1] => [5,3,4,1,2] => 3
[4,5,2,1,3] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,1,2] => 3
[4,5,2,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => 3
[4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => 3
[4,5,3,2,1] => [4,5,3,2,1] => [4,5,3,2,1] => [4,3,5,1,2] => 3
[5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => [5,2,3,4,1] => 4
[5,1,2,4,3] => [2,3,5,4,1] => [5,2,3,4,1] => [2,3,4,5,1] => 4
[5,1,3,2,4] => [2,4,3,5,1] => [4,2,3,5,1] => [2,3,5,4,1] => 4
[5,1,3,4,2] => [2,4,5,3,1] => [4,5,2,3,1] => [5,4,1,2,3] => 2
[5,1,4,2,3] => [2,4,5,3,1] => [4,5,2,3,1] => [5,4,1,2,3] => 2
[5,1,4,3,2] => [2,5,4,3,1] => [5,4,2,3,1] => [4,5,1,2,3] => 2
[5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => [2,5,3,4,1] => 4
[5,2,1,4,3] => [3,2,5,4,1] => [3,5,2,4,1] => [4,3,1,5,2] => 4
[5,2,3,1,4] => [3,4,2,5,1] => [3,4,2,5,1] => [5,3,1,4,2] => 4
[5,2,3,4,1] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,1,2] => 3
[5,2,4,1,3] => [5,4,2,3,1] => [2,5,4,3,1] => [4,2,5,1,3] => 3
[5,2,4,3,1] => [3,5,4,2,1] => [5,3,4,2,1] => [3,5,4,1,2] => 3
[5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => [5,3,1,4,2] => 4
[5,3,1,4,2] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,1,2] => 3
[5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => [3,5,1,4,2] => 4
[5,3,2,4,1] => [4,3,5,2,1] => [4,3,5,2,1] => [4,5,3,1,2] => 3
[5,3,4,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => 3
[5,3,4,2,1] => [4,5,3,2,1] => [4,5,3,2,1] => [4,3,5,1,2] => 3
[5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => [5,4,3,1,2] => 3
[5,4,1,3,2] => [3,5,4,2,1] => [5,3,4,2,1] => [3,5,4,1,2] => 3
[5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => [4,5,3,1,2] => 3
[5,4,2,3,1] => [4,5,3,2,1] => [4,5,3,2,1] => [4,3,5,1,2] => 3
[5,4,3,1,2] => [4,5,3,2,1] => [4,5,3,2,1] => [4,3,5,1,2] => 3
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => 3
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => 1
[1,2,3,5,6,4] => [1,2,3,5,6,4] => [5,6,1,2,3,4] => [6,5,2,3,4,1] => 5
[1,2,3,6,4,5] => [1,2,3,5,6,4] => [5,6,1,2,3,4] => [6,5,2,3,4,1] => 5
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => [5,6,2,3,4,1] => 5
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => [6,4,2,3,1,5] => 4
[1,2,4,5,3,6] => [1,2,4,5,3,6] => [4,5,1,2,3,6] => [5,4,2,3,1,6] => 4
[1,2,4,5,6,3] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => 5
[1,2,4,6,3,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => [1,5,6,3,4,2] => 5
[1,2,4,6,5,3] => [1,2,4,6,5,3] => [6,4,5,1,2,3] => [4,6,5,3,2,1] => 5
[1,2,5,3,4,6] => [1,2,4,5,3,6] => [4,5,1,2,3,6] => [5,4,2,3,1,6] => 4
[1,2,5,3,6,4] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => 5
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => [4,5,2,3,1,6] => 4
[1,2,5,4,6,3] => [1,2,5,4,6,3] => [5,4,6,1,2,3] => [5,6,4,3,2,1] => 5
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 5
[1,2,5,6,4,3] => [1,2,5,6,4,3] => [5,6,4,1,2,3] => [5,4,6,3,2,1] => 5
[1,2,6,3,4,5] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => 5
[1,2,6,3,5,4] => [1,2,4,6,5,3] => [6,4,5,1,2,3] => [4,6,5,3,2,1] => 5
[1,2,6,4,3,5] => [1,2,5,4,6,3] => [5,4,6,1,2,3] => [5,6,4,3,2,1] => 5
[1,2,6,4,5,3] => [1,2,5,6,4,3] => [5,6,4,1,2,3] => [5,4,6,3,2,1] => 5
[1,2,6,5,3,4] => [1,2,5,6,4,3] => [5,6,4,1,2,3] => [5,4,6,3,2,1] => 5
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 5
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => [6,3,2,1,4,5] => 3
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => [5,3,2,1,4,6] => 3
[1,3,2,5,6,4] => [1,3,2,5,6,4] => [3,5,6,1,2,4] => [6,5,3,2,4,1] => 5
[1,3,2,6,4,5] => [1,3,2,5,6,4] => [3,5,6,1,2,4] => [6,5,3,2,4,1] => 5
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => [3,6,5,2,4,1] => 5
[1,3,4,2,5,6] => [1,3,4,2,5,6] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => 3
[1,3,4,2,6,5] => [1,3,4,2,6,5] => [3,4,6,1,2,5] => [6,4,3,2,1,5] => 4
[1,3,4,5,2,6] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => [5,4,3,2,1,6] => 4
[1,3,4,5,6,2] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => [6,5,3,4,2,1] => 5
[1,3,4,6,2,5] => [1,3,6,5,2,4] => [6,5,3,1,2,4] => [3,5,6,2,4,1] => 5
[1,3,4,6,5,2] => [1,3,4,6,5,2] => [6,3,4,5,1,2] => [3,6,4,5,2,1] => 5
[1,3,5,2,4,6] => [1,5,4,2,3,6] => [1,5,4,2,3,6] => [1,4,5,3,2,6] => 4
[1,3,5,2,6,4] => [1,5,4,2,6,3] => [1,5,4,6,2,3] => [1,5,6,4,3,2] => 5
[1,3,5,4,2,6] => [1,3,5,4,2,6] => [5,3,4,1,2,6] => [3,5,4,2,1,6] => 4
[1,3,5,4,6,2] => [1,3,5,4,6,2] => [5,3,4,6,1,2] => [3,6,5,4,2,1] => 5
[1,3,5,6,2,4] => [1,4,6,5,2,3] => [6,4,1,5,2,3] => [4,6,2,5,3,1] => 5
[1,3,5,6,4,2] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => 5
[1,3,6,2,4,5] => [1,5,4,2,6,3] => [1,5,4,6,2,3] => [1,5,6,4,3,2] => 5
[1,3,6,2,5,4] => [1,6,4,2,5,3] => [1,4,6,5,2,3] => [1,6,4,5,3,2] => 5
[1,3,6,4,2,5] => [1,6,5,4,2,3] => [1,6,5,4,2,3] => [1,4,5,6,3,2] => 5
[1,3,6,4,5,2] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => 5
[1,3,6,5,2,4] => [1,4,5,6,2,3] => [4,5,1,6,2,3] => [6,5,2,4,3,1] => 5
[1,3,6,5,4,2] => [1,3,6,5,4,2] => [6,5,3,4,1,2] => [3,4,5,6,2,1] => 5
[1,4,2,3,5,6] => [1,3,4,2,5,6] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => 3
[1,4,2,3,6,5] => [1,3,4,2,6,5] => [3,4,6,1,2,5] => [6,4,3,2,1,5] => 4
[1,4,2,5,3,6] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => [5,4,3,2,1,6] => 4
[1,4,2,5,6,3] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => [6,5,3,4,2,1] => 5
[1,4,2,6,3,5] => [1,3,6,5,2,4] => [6,5,3,1,2,4] => [3,5,6,2,4,1] => 5
[1,4,2,6,5,3] => [1,3,4,6,5,2] => [6,3,4,5,1,2] => [3,6,4,5,2,1] => 5
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => 3
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => [4,6,3,2,1,5] => 4
[1,4,3,5,2,6] => [1,4,3,5,2,6] => [4,3,5,1,2,6] => [4,5,3,2,1,6] => 4
[1,4,3,5,6,2] => [1,4,3,5,6,2] => [4,3,5,6,1,2] => [5,6,3,4,2,1] => 5
[1,4,3,6,2,5] => [1,6,3,5,2,4] => [6,5,1,3,2,4] => [5,6,2,1,4,3] => 5
[1,4,3,6,5,2] => [1,4,3,6,5,2] => [4,6,3,5,1,2] => [4,3,6,5,2,1] => 5
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [3,4,5,2,1,6] => 4
[1,4,5,2,6,3] => [1,5,4,3,6,2] => [5,4,3,6,1,2] => [3,5,6,4,2,1] => 5
[1,4,5,3,2,6] => [1,4,5,3,2,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => 4
[1,4,5,3,6,2] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => [5,3,6,4,2,1] => 5
[1,4,5,6,2,3] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => [4,6,5,1,3,2] => 5
[1,4,5,6,3,2] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => 5
[1,4,6,2,3,5] => [1,5,4,6,2,3] => [5,4,1,6,2,3] => [5,6,2,4,3,1] => 5
[1,4,6,2,5,3] => [1,6,4,3,5,2] => [4,3,6,5,1,2] => [4,6,3,5,2,1] => 5
[1,4,6,3,2,5] => [1,4,5,6,2,3] => [4,5,1,6,2,3] => [6,5,2,4,3,1] => 5
[1,4,6,3,5,2] => [1,6,5,3,4,2] => [3,6,5,4,1,2] => [5,3,4,6,2,1] => 5
[1,4,6,5,2,3] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => 5
[1,4,6,5,3,2] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => [4,6,5,1,3,2] => 5
[1,5,2,3,4,6] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => [5,4,3,2,1,6] => 4
[1,5,2,3,6,4] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => [6,5,3,4,2,1] => 5
[1,5,2,4,3,6] => [1,3,5,4,2,6] => [5,3,4,1,2,6] => [3,5,4,2,1,6] => 4
[1,5,2,4,6,3] => [1,3,5,4,6,2] => [5,3,4,6,1,2] => [3,6,5,4,2,1] => 5
[1,5,2,6,3,4] => [1,3,6,5,4,2] => [6,5,3,4,1,2] => [3,4,5,6,2,1] => 5
[1,5,2,6,4,3] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => 5
[1,5,3,2,4,6] => [1,4,3,5,2,6] => [4,3,5,1,2,6] => [4,5,3,2,1,6] => 4
[1,5,3,2,6,4] => [1,4,3,5,6,2] => [4,3,5,6,1,2] => [5,6,3,4,2,1] => 5
[1,5,3,4,2,6] => [1,4,5,3,2,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => 4
[1,5,3,4,6,2] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => [5,3,6,4,2,1] => 5
[1,5,3,6,2,4] => [1,6,3,5,4,2] => [6,3,5,4,1,2] => [3,5,4,6,2,1] => 5
[1,5,3,6,4,2] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => 5
[1,5,4,2,3,6] => [1,4,5,3,2,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => 4
[1,5,4,2,6,3] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => [5,3,6,4,2,1] => 5
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [3,4,5,2,1,6] => 4
[1,5,4,3,6,2] => [1,5,4,3,6,2] => [5,4,3,6,1,2] => [3,5,6,4,2,1] => 5
[1,5,4,6,2,3] => [1,6,4,5,3,2] => [4,6,5,3,1,2] => [6,4,5,1,3,2] => 5
[1,5,4,6,3,2] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => [5,6,4,1,3,2] => 5
[1,5,6,2,3,4] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => [5,6,4,1,3,2] => 5
[1,5,6,2,4,3] => [1,6,4,5,3,2] => [4,6,5,3,1,2] => [6,4,5,1,3,2] => 5
[1,5,6,3,2,4] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => 5
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [4,5,6,1,3,2] => 5
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [4,5,6,1,3,2] => 5
[1,5,6,4,3,2] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => 5
[1,6,2,3,4,5] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => [6,5,3,4,2,1] => 5
[1,6,2,3,5,4] => [1,3,4,6,5,2] => [6,3,4,5,1,2] => [3,6,4,5,2,1] => 5
[1,6,2,4,3,5] => [1,3,5,4,6,2] => [5,3,4,6,1,2] => [3,6,5,4,2,1] => 5
[1,6,2,4,5,3] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => 5
[1,6,2,5,3,4] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => 5
[1,6,2,5,4,3] => [1,3,6,5,4,2] => [6,5,3,4,1,2] => [3,4,5,6,2,1] => 5
[1,6,3,2,4,5] => [1,4,3,5,6,2] => [4,3,5,6,1,2] => [5,6,3,4,2,1] => 5
[1,6,3,2,5,4] => [1,4,3,6,5,2] => [4,6,3,5,1,2] => [4,3,6,5,2,1] => 5
[1,6,3,4,2,5] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => [5,3,6,4,2,1] => 5
[1,6,3,4,5,2] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => 5
[1,6,3,5,2,4] => [1,6,5,3,4,2] => [3,6,5,4,1,2] => [5,3,4,6,2,1] => 5
[1,6,3,5,4,2] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => [4,6,5,1,3,2] => 5
[1,6,4,2,3,5] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => [5,3,6,4,2,1] => 5
[1,6,4,2,5,3] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => 5
[1,6,4,3,2,5] => [1,5,4,3,6,2] => [5,4,3,6,1,2] => [3,5,6,4,2,1] => 5
[1,6,4,3,5,2] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => [5,6,4,1,3,2] => 5
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [4,5,6,1,3,2] => 5
[1,6,4,5,3,2] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => 5
[1,6,5,2,3,4] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => 5
[1,6,5,2,4,3] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => [4,6,5,1,3,2] => 5
[1,6,5,3,2,4] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => [5,6,4,1,3,2] => 5
[1,6,5,3,4,2] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => 5
[1,6,5,4,2,3] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => 5
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [4,5,6,1,3,2] => 5
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => 2
[2,1,3,5,6,4] => [2,1,3,5,6,4] => [2,5,6,1,3,4] => [6,2,5,3,4,1] => 5
[2,1,3,6,4,5] => [2,1,3,5,6,4] => [2,5,6,1,3,4] => [6,2,5,3,4,1] => 5
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,5,1,3,4] => [2,5,6,3,4,1] => 5
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,4,6,1,3,5] => [6,2,4,3,1,5] => 4
[2,1,4,5,3,6] => [2,1,4,5,3,6] => [2,4,5,1,3,6] => [5,2,4,3,1,6] => 4
[2,1,4,5,6,3] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => [6,2,5,4,3,1] => 5
[2,1,4,6,3,5] => [2,1,6,5,3,4] => [6,5,2,1,3,4] => [5,6,1,3,4,2] => 5
[2,1,4,6,5,3] => [2,1,4,6,5,3] => [6,2,4,5,1,3] => [2,4,6,5,3,1] => 5
[2,1,5,3,4,6] => [2,1,4,5,3,6] => [2,4,5,1,3,6] => [5,2,4,3,1,6] => 4
[2,1,5,3,6,4] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => [6,2,5,4,3,1] => 5
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [5,2,4,1,3,6] => [2,4,5,3,1,6] => 4
[2,1,5,4,6,3] => [2,1,5,4,6,3] => [5,2,4,6,1,3] => [2,5,6,4,3,1] => 5
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => [4,5,1,6,3,2] => 5
[2,1,5,6,4,3] => [2,1,5,6,4,3] => [5,6,2,4,1,3] => [5,4,1,6,3,2] => 5
[2,1,6,3,4,5] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => [6,2,5,4,3,1] => 5
[2,1,6,3,5,4] => [2,1,4,6,5,3] => [6,2,4,5,1,3] => [2,4,6,5,3,1] => 5
[2,1,6,4,3,5] => [2,1,5,4,6,3] => [5,2,4,6,1,3] => [2,5,6,4,3,1] => 5
[2,1,6,4,5,3] => [2,1,5,6,4,3] => [5,6,2,4,1,3] => [5,4,1,6,3,2] => 5
[2,1,6,5,3,4] => [2,1,5,6,4,3] => [5,6,2,4,1,3] => [5,4,1,6,3,2] => 5
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => [4,5,1,6,3,2] => 5
[2,3,1,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 2
[2,3,1,4,6,5] => [2,3,1,4,6,5] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => 3
[2,3,1,5,4,6] => [2,3,1,5,4,6] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => 3
[2,3,1,5,6,4] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => [6,2,3,5,4,1] => 5
[2,3,1,6,4,5] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => [6,2,3,5,4,1] => 5
[2,3,1,6,5,4] => [2,3,1,6,5,4] => [6,2,3,5,1,4] => [2,3,5,6,4,1] => 5
[2,3,4,1,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => 3
[2,3,4,1,6,5] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => 4
[2,3,4,5,1,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 4
[2,3,4,5,6,1] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 5
[2,3,4,6,1,5] => [2,3,6,5,1,4] => [6,5,2,3,1,4] => [5,6,1,2,4,3] => 5
[2,3,4,6,5,1] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => 5
[2,3,5,1,4,6] => [2,5,4,1,3,6] => [5,4,2,1,3,6] => [4,5,1,3,2,6] => 4
[2,3,5,1,6,4] => [2,5,4,1,6,3] => [5,4,2,6,1,3] => [5,6,1,4,3,2] => 5
[2,3,5,4,1,6] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => 4
[2,3,5,4,6,1] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [2,3,4,6,5,1] => 5
[2,3,5,6,1,4] => [2,4,6,5,1,3] => [6,4,5,2,1,3] => [4,6,5,2,3,1] => 5
[2,3,5,6,4,1] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [6,5,1,2,3,4] => 2
[2,3,6,1,4,5] => [2,5,4,1,6,3] => [5,4,2,6,1,3] => [5,6,1,4,3,2] => 5
[2,3,6,1,5,4] => [2,6,4,1,5,3] => [4,2,6,5,1,3] => [2,6,4,5,3,1] => 5
[2,3,6,4,1,5] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => [4,5,6,2,3,1] => 5
[2,3,6,4,5,1] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [6,5,1,2,3,4] => 2
[2,3,6,5,1,4] => [2,4,5,6,1,3] => [4,5,6,2,1,3] => [6,5,4,2,3,1] => 5
[2,3,6,5,4,1] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [5,6,1,2,3,4] => 2
[2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => 3
[2,4,1,3,6,5] => [4,3,1,2,6,5] => [1,4,3,6,2,5] => [1,3,6,4,2,5] => 4
[2,4,1,5,3,6] => [4,3,1,5,2,6] => [1,4,3,5,2,6] => [1,3,5,4,2,6] => 4
[2,4,1,5,6,3] => [4,3,1,5,6,2] => [1,4,3,5,6,2] => [1,3,6,4,5,2] => 5
[2,4,1,6,3,5] => [6,3,1,5,2,4] => [3,1,6,2,5,4] => [5,1,3,2,6,4] => 5
[2,4,1,6,5,3] => [4,3,1,6,5,2] => [1,4,6,3,5,2] => [1,5,4,2,6,3] => 5
[2,4,3,1,5,6] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => 3
[2,4,3,1,6,5] => [2,4,3,1,6,5] => [4,2,3,6,1,5] => [2,3,6,4,1,5] => 4
[2,4,3,5,1,6] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [2,3,5,4,1,6] => 4
[2,4,3,5,6,1] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [2,3,6,4,5,1] => 5
[2,4,3,6,1,5] => [2,6,3,5,1,4] => [6,2,5,3,1,4] => [2,5,6,1,4,3] => 5
[2,4,3,6,5,1] => [2,4,3,6,5,1] => [4,6,2,3,5,1] => [5,4,1,2,6,3] => 5
[2,4,5,1,3,6] => [3,5,4,1,2,6] => [5,3,1,4,2,6] => [3,4,2,5,1,6] => 4
[2,4,5,1,6,3] => [3,5,4,1,6,2] => [5,3,1,4,6,2] => [3,4,2,6,5,1] => 5
[2,4,5,3,1,6] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => [5,4,1,2,3,6] => 2
[2,4,5,3,6,1] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [6,4,1,2,5,3] => 5
[2,4,5,6,1,3] => [3,4,6,5,1,2] => [6,3,4,1,5,2] => [3,5,4,2,6,1] => 5
[2,4,5,6,3,1] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[2,4,6,1,3,5] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => 4
[2,4,6,1,5,3] => [3,6,4,1,5,2] => [3,1,6,4,5,2] => [4,1,3,5,6,2] => 5
[2,4,6,3,1,5] => [2,4,5,6,1,3] => [4,5,6,2,1,3] => [6,5,4,2,3,1] => 5
[2,4,6,3,5,1] => [2,6,5,3,4,1] => [2,6,5,3,4,1] => [5,2,6,1,3,4] => 3
[2,4,6,5,1,3] => [3,4,5,6,1,2] => [3,4,5,1,6,2] => [6,4,3,2,5,1] => 5
[2,4,6,5,3,1] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => 4
[2,5,1,3,4,6] => [4,3,1,5,2,6] => [1,4,3,5,2,6] => [1,3,5,4,2,6] => 4
[2,5,1,3,6,4] => [4,3,1,5,6,2] => [1,4,3,5,6,2] => [1,3,6,4,5,2] => 5
[2,5,1,4,3,6] => [5,3,1,4,2,6] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => 4
[2,5,1,4,6,3] => [5,3,1,4,6,2] => [1,3,5,4,6,2] => [1,4,3,6,5,2] => 5
[2,5,1,6,3,4] => [6,3,1,5,4,2] => [6,1,3,5,4,2] => [3,1,5,6,2,4] => 4
[2,5,1,6,4,3] => [5,3,1,6,4,2] => [1,3,5,6,4,2] => [1,6,3,5,2,4] => 4
[2,5,3,1,4,6] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => 3
[2,5,3,1,6,4] => [5,4,3,1,6,2] => [1,5,4,3,6,2] => [1,4,6,2,5,3] => 5
[2,5,3,4,1,6] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => [5,4,1,2,3,6] => 2
[2,5,3,4,6,1] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [6,4,1,2,5,3] => 5
[2,5,3,6,1,4] => [4,6,3,5,1,2] => [6,4,3,1,5,2] => [3,4,5,2,6,1] => 5
[2,5,3,6,4,1] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[2,5,4,1,3,6] => [3,4,5,1,2,6] => [3,4,1,5,2,6] => [5,3,2,4,1,6] => 4
[2,5,4,1,6,3] => [3,4,5,1,6,2] => [3,4,1,5,6,2] => [6,3,2,4,5,1] => 5
[2,5,4,3,1,6] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [4,5,1,2,3,6] => 2
[2,5,4,3,6,1] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [4,6,1,2,5,3] => 5
[2,5,4,6,1,3] => [3,6,4,5,1,2] => [3,6,4,1,5,2] => [5,3,4,2,6,1] => 5
[2,5,4,6,3,1] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [5,6,4,2,1,3] => 4
[2,5,6,1,3,4] => [6,5,4,1,3,2] => [6,1,5,4,3,2] => [4,1,5,6,2,3] => 4
[2,5,6,1,4,3] => [5,6,4,1,3,2] => [1,5,6,4,3,2] => [1,5,4,6,2,3] => 4
[2,5,6,3,1,4] => [3,4,5,6,1,2] => [3,4,5,1,6,2] => [6,4,3,2,5,1] => 5
[2,5,6,3,4,1] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [4,5,6,2,1,3] => 4
[2,5,6,4,1,3] => [3,6,5,4,1,2] => [6,5,3,1,4,2] => [3,5,6,2,1,4] => 4
[2,5,6,4,3,1] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [5,4,6,2,1,3] => 4
[2,6,1,3,4,5] => [4,3,1,5,6,2] => [1,4,3,5,6,2] => [1,3,6,4,5,2] => 5
[2,6,1,3,5,4] => [4,3,1,6,5,2] => [1,4,6,3,5,2] => [1,5,4,2,6,3] => 5
[2,6,1,4,3,5] => [5,3,1,4,6,2] => [1,3,5,4,6,2] => [1,4,3,6,5,2] => 5
[2,6,1,4,5,3] => [5,3,1,6,4,2] => [1,3,5,6,4,2] => [1,6,3,5,2,4] => 4
[2,6,1,5,3,4] => [5,3,1,6,4,2] => [1,3,5,6,4,2] => [1,6,3,5,2,4] => 4
[2,6,1,5,4,3] => [6,3,1,5,4,2] => [6,1,3,5,4,2] => [3,1,5,6,2,4] => 4
[2,6,3,1,4,5] => [5,4,3,1,6,2] => [1,5,4,3,6,2] => [1,4,6,2,5,3] => 5
[2,6,3,1,5,4] => [6,4,3,1,5,2] => [1,4,3,6,5,2] => [1,3,5,4,6,2] => 5
[2,6,3,4,1,5] => [6,4,5,3,1,2] => [4,1,6,5,3,2] => [6,1,4,5,2,3] => 4
[2,6,3,4,5,1] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[2,6,3,5,1,4] => [4,6,5,3,1,2] => [6,4,1,5,3,2] => [4,6,2,5,1,3] => 4
[2,6,3,5,4,1] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => 4
[2,6,4,1,3,5] => [3,4,5,1,6,2] => [3,4,1,5,6,2] => [6,3,2,4,5,1] => 5
[2,6,4,1,5,3] => [6,4,5,1,3,2] => [1,4,6,5,3,2] => [1,6,4,5,2,3] => 4
[2,6,4,3,1,5] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => 4
[2,6,4,3,5,1] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [5,6,4,2,1,3] => 4
[2,6,4,5,1,3] => [3,6,5,4,1,2] => [6,5,3,1,4,2] => [3,5,6,2,1,4] => 4
[2,6,4,5,3,1] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [5,4,6,2,1,3] => 4
[2,6,5,1,3,4] => [6,4,5,1,3,2] => [1,4,6,5,3,2] => [1,6,4,5,2,3] => 4
[2,6,5,1,4,3] => [5,4,6,1,3,2] => [1,5,4,6,3,2] => [1,5,6,4,2,3] => 4
[2,6,5,3,1,4] => [3,5,4,6,1,2] => [5,3,4,1,6,2] => [3,6,4,2,5,1] => 5
[2,6,5,3,4,1] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [5,4,6,2,1,3] => 4
[2,6,5,4,1,3] => [3,5,6,4,1,2] => [5,6,3,1,4,2] => [5,3,6,2,1,4] => 4
[2,6,5,4,3,1] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [4,5,6,2,1,3] => 4
[3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 2
[3,1,2,4,6,5] => [2,3,1,4,6,5] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => 3
[3,1,2,5,4,6] => [2,3,1,5,4,6] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => 3
[3,1,2,5,6,4] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => [6,2,3,5,4,1] => 5
[3,1,2,6,4,5] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => [6,2,3,5,4,1] => 5
[3,1,2,6,5,4] => [2,3,1,6,5,4] => [6,2,3,5,1,4] => [2,3,5,6,4,1] => 5
[3,1,4,2,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => 3
[3,1,4,2,6,5] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => 4
[3,1,4,5,2,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 4
[3,1,4,5,6,2] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 5
[3,1,4,6,2,5] => [2,3,6,5,1,4] => [6,5,2,3,1,4] => [5,6,1,2,4,3] => 5
[3,1,4,6,5,2] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => 5
[3,1,5,2,4,6] => [2,5,4,1,3,6] => [5,4,2,1,3,6] => [4,5,1,3,2,6] => 4
[3,1,5,2,6,4] => [2,5,4,1,6,3] => [5,4,2,6,1,3] => [5,6,1,4,3,2] => 5
[3,1,5,4,2,6] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => 4
[3,1,5,4,6,2] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [2,3,4,6,5,1] => 5
[3,1,5,6,2,4] => [2,4,6,5,1,3] => [6,4,5,2,1,3] => [4,6,5,2,3,1] => 5
[3,1,5,6,4,2] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [6,5,1,2,3,4] => 2
[3,1,6,2,4,5] => [2,5,4,1,6,3] => [5,4,2,6,1,3] => [5,6,1,4,3,2] => 5
[3,1,6,2,5,4] => [2,6,4,1,5,3] => [4,2,6,5,1,3] => [2,6,4,5,3,1] => 5
[3,1,6,4,2,5] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => [4,5,6,2,3,1] => 5
[3,1,6,4,5,2] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [6,5,1,2,3,4] => 2
[3,1,6,5,2,4] => [2,4,5,6,1,3] => [4,5,6,2,1,3] => [6,5,4,2,3,1] => 5
[3,1,6,5,4,2] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [5,6,1,2,3,4] => 2
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 2
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,6,1,4,5] => [2,6,3,1,4,5] => 3
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,5,1,4,6] => [2,5,3,1,4,6] => 3
[3,2,1,5,6,4] => [3,2,1,5,6,4] => [3,2,5,6,1,4] => [2,6,3,5,4,1] => 5
[3,2,1,6,4,5] => [3,2,1,5,6,4] => [3,2,5,6,1,4] => [2,6,3,5,4,1] => 5
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,6,2,5,1,4] => [5,3,1,6,4,2] => 5
[3,2,4,1,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [2,4,3,1,5,6] => 3
[3,2,4,1,6,5] => [3,2,4,1,6,5] => [3,2,4,6,1,5] => [2,6,3,4,1,5] => 4
[3,2,4,5,1,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [2,5,3,4,1,6] => 4
[3,2,4,5,6,1] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [2,6,3,4,5,1] => 5
[3,2,4,6,1,5] => [3,2,6,5,1,4] => [6,3,5,2,1,4] => [3,6,5,1,4,2] => 5
[3,2,4,6,5,1] => [3,2,4,6,5,1] => [3,6,2,4,5,1] => [4,3,1,5,6,2] => 5
[3,2,5,1,4,6] => [5,2,4,1,3,6] => [5,2,1,4,3,6] => [2,4,1,5,3,6] => 4
[3,2,5,1,6,4] => [5,2,4,1,6,3] => [5,2,1,4,6,3] => [2,4,1,6,5,3] => 5
[3,2,5,4,1,6] => [3,2,5,4,1,6] => [3,5,2,4,1,6] => [4,3,1,5,2,6] => 4
[3,2,5,4,6,1] => [3,2,5,4,6,1] => [3,5,2,4,6,1] => [4,3,1,6,5,2] => 5
[3,2,5,6,1,4] => [4,2,6,5,1,3] => [6,2,4,1,5,3] => [2,4,5,3,6,1] => 5
[3,2,5,6,4,1] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => [6,5,3,1,2,4] => 3
[3,2,6,1,4,5] => [5,2,4,1,6,3] => [5,2,1,4,6,3] => [2,4,1,6,5,3] => 5
[3,2,6,1,5,4] => [6,2,4,1,5,3] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => 5
[3,2,6,4,1,5] => [6,2,5,4,1,3] => [6,5,2,1,4,3] => [5,6,1,3,2,4] => 4
[3,2,6,4,5,1] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => [6,5,3,1,2,4] => 3
[3,2,6,5,1,4] => [4,2,5,6,1,3] => [2,4,5,1,6,3] => [6,2,4,3,5,1] => 5
[3,2,6,5,4,1] => [3,2,6,5,4,1] => [6,3,5,2,4,1] => [3,6,5,1,2,4] => 3
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [4,3,2,6,1,5] => [3,6,1,4,2,5] => 4
[3,4,1,5,2,6] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [3,5,1,4,2,6] => 4
[3,4,1,5,6,2] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [3,6,1,4,5,2] => 5
[3,4,1,6,2,5] => [6,3,2,5,1,4] => [3,6,2,1,5,4] => [5,3,1,2,6,4] => 5
[3,4,1,6,5,2] => [4,3,2,6,5,1] => [4,3,6,2,5,1] => [4,5,3,1,6,2] => 5
[3,4,2,1,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 2
[3,4,2,1,6,5] => [3,4,2,1,6,5] => [3,4,2,6,1,5] => [6,3,1,4,2,5] => 4
[3,4,2,5,1,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,3,1,4,2,6] => 4
[3,4,2,5,6,1] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,4,5,2] => 5
[3,4,2,6,1,5] => [3,6,2,5,1,4] => [3,6,5,2,1,4] => [6,3,5,1,4,2] => 5
[3,4,2,6,5,1] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => [5,4,3,1,6,2] => 5
[3,4,5,1,2,6] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => [3,5,4,1,2,6] => 3
[3,4,5,1,6,2] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [3,6,4,1,5,2] => 5
[3,4,5,2,1,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,3,1,2,6] => 3
[3,4,5,2,6,1] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[3,4,5,6,1,2] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 4
[3,4,5,6,2,1] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[3,4,6,1,2,5] => [6,5,4,2,1,3] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => 4
[3,4,6,1,5,2] => [3,6,4,2,5,1] => [3,6,4,2,5,1] => [5,3,4,1,6,2] => 5
[3,4,6,2,1,5] => [6,4,5,2,1,3] => [4,2,1,6,5,3] => [2,5,1,4,6,3] => 5
[3,4,6,2,5,1] => [3,6,5,2,4,1] => [6,5,3,2,4,1] => [3,5,6,1,2,4] => 3
[3,4,6,5,1,2] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[3,4,6,5,2,1] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 4
[3,5,1,2,4,6] => [4,3,5,1,2,6] => [4,3,1,5,2,6] => [3,5,2,4,1,6] => 4
[3,5,1,2,6,4] => [4,3,5,1,6,2] => [4,3,1,5,6,2] => [3,6,2,4,5,1] => 5
[3,5,1,4,2,6] => [5,3,2,4,1,6] => [3,2,5,4,1,6] => [2,4,3,5,1,6] => 4
[3,5,1,4,6,2] => [5,3,2,4,6,1] => [3,2,5,4,6,1] => [2,4,3,6,5,1] => 5
[3,5,1,6,2,4] => [6,3,4,5,1,2] => [3,4,1,6,5,2] => [5,3,2,4,6,1] => 5
[3,5,1,6,4,2] => [5,3,2,6,4,1] => [3,2,5,6,4,1] => [2,6,3,5,1,4] => 4
[3,5,2,1,4,6] => [3,4,5,1,2,6] => [3,4,1,5,2,6] => [5,3,2,4,1,6] => 4
[3,5,2,1,6,4] => [3,4,5,1,6,2] => [3,4,1,5,6,2] => [6,3,2,4,5,1] => 5
[3,5,2,4,1,6] => [5,4,2,3,1,6] => [2,5,4,3,1,6] => [4,2,5,1,3,6] => 3
[3,5,2,4,6,1] => [5,4,2,3,6,1] => [2,5,4,3,6,1] => [4,2,6,1,5,3] => 5
[3,5,2,6,1,4] => [3,6,4,5,1,2] => [3,6,4,1,5,2] => [5,3,4,2,6,1] => 5
[3,5,2,6,4,1] => [5,4,2,6,3,1] => [2,5,4,6,3,1] => [5,2,6,4,1,3] => 4
[3,5,4,1,2,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,3,1,2,6] => 3
[3,5,4,1,6,2] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[3,5,4,2,1,6] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => [3,5,4,1,2,6] => 3
[3,5,4,2,6,1] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [3,6,4,1,5,2] => 5
[3,5,4,6,1,2] => [3,6,4,5,2,1] => [3,6,4,5,2,1] => [6,3,4,5,1,2] => 4
[3,5,4,6,2,1] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [3,6,5,4,1,2] => 4
[3,5,6,1,2,4] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => 4
[3,5,6,1,4,2] => [5,6,4,2,3,1] => [5,2,6,4,3,1] => [2,5,4,6,1,3] => 4
[3,5,6,2,1,4] => [6,4,5,3,1,2] => [4,1,6,5,3,2] => [6,1,4,5,2,3] => 4
[3,5,6,2,4,1] => [4,6,5,2,3,1] => [6,4,2,5,3,1] => [4,6,1,5,2,3] => 4
[3,5,6,4,1,2] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 4
[3,5,6,4,2,1] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[3,6,1,2,4,5] => [4,3,5,1,6,2] => [4,3,1,5,6,2] => [3,6,2,4,5,1] => 5
[3,6,1,2,5,4] => [4,3,6,1,5,2] => [4,3,6,1,5,2] => [4,5,3,2,6,1] => 5
[3,6,1,4,2,5] => [5,3,6,4,1,2] => [3,5,1,6,4,2] => [6,3,2,5,1,4] => 4
[3,6,1,4,5,2] => [5,3,2,6,4,1] => [3,2,5,6,4,1] => [2,6,3,5,1,4] => 4
[3,6,1,5,2,4] => [5,3,4,6,1,2] => [3,5,4,1,6,2] => [6,3,4,2,5,1] => 5
[3,6,1,5,4,2] => [6,3,2,5,4,1] => [3,6,2,5,4,1] => [5,3,1,6,2,4] => 4
[3,6,2,1,4,5] => [3,4,5,1,6,2] => [3,4,1,5,6,2] => [6,3,2,4,5,1] => 5
[3,6,2,1,5,4] => [3,4,6,1,5,2] => [3,4,6,1,5,2] => [5,4,3,2,6,1] => 5
[3,6,2,4,1,5] => [5,4,6,3,1,2] => [5,4,1,6,3,2] => [5,6,2,4,1,3] => 4
[3,6,2,4,5,1] => [5,4,2,6,3,1] => [2,5,4,6,3,1] => [5,2,6,4,1,3] => 4
[3,6,2,5,1,4] => [5,6,4,3,1,2] => [5,1,6,4,3,2] => [5,1,4,6,2,3] => 4
[3,6,2,5,4,1] => [6,4,2,5,3,1] => [2,4,6,5,3,1] => [6,2,4,5,1,3] => 4
[3,6,4,1,2,5] => [3,4,5,6,1,2] => [3,4,5,1,6,2] => [6,4,3,2,5,1] => 5
[3,6,4,1,5,2] => [6,4,5,2,3,1] => [4,2,6,5,3,1] => [2,6,4,5,1,3] => 4
[3,6,4,2,1,5] => [3,5,4,6,1,2] => [5,3,4,1,6,2] => [3,6,4,2,5,1] => 5
[3,6,4,2,5,1] => [6,5,4,2,3,1] => [2,6,5,4,3,1] => [4,2,5,6,1,3] => 4
[3,6,4,5,1,2] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 4
[3,6,4,5,2,1] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[3,6,5,1,2,4] => [6,4,5,3,1,2] => [4,1,6,5,3,2] => [6,1,4,5,2,3] => 4
[3,6,5,1,4,2] => [5,4,6,2,3,1] => [5,4,2,6,3,1] => [5,6,1,4,2,3] => 4
[3,6,5,2,1,4] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => 4
[3,6,5,2,4,1] => [4,5,6,2,3,1] => [4,5,2,6,3,1] => [6,5,1,4,2,3] => 4
[3,6,5,4,1,2] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[3,6,5,4,2,1] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 4
[4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => 3
[4,1,2,3,6,5] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => 4
[4,1,2,5,3,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 4
[4,1,2,5,6,3] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 5
[4,1,2,6,3,5] => [2,3,6,5,1,4] => [6,5,2,3,1,4] => [5,6,1,2,4,3] => 5
[4,1,2,6,5,3] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => 5
[4,1,3,2,5,6] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => 3
[4,1,3,2,6,5] => [2,4,3,1,6,5] => [4,2,3,6,1,5] => [2,3,6,4,1,5] => 4
[4,1,3,5,2,6] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [2,3,5,4,1,6] => 4
[4,1,3,5,6,2] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [2,3,6,4,5,1] => 5
[4,1,3,6,2,5] => [2,6,3,5,1,4] => [6,2,5,3,1,4] => [2,5,6,1,4,3] => 5
[4,1,3,6,5,2] => [2,4,3,6,5,1] => [4,6,2,3,5,1] => [5,4,1,2,6,3] => 5
[4,1,5,2,3,6] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [4,5,1,2,3,6] => 2
[4,1,5,2,6,3] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [4,6,1,2,5,3] => 5
[4,1,5,3,2,6] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => [5,4,1,2,3,6] => 2
[4,1,5,3,6,2] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [6,4,1,2,5,3] => 5
[4,1,5,6,2,3] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => 4
[4,1,5,6,3,2] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[4,1,6,2,3,5] => [2,5,4,6,1,3] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 5
[4,1,6,2,5,3] => [2,6,4,3,5,1] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => 5
[4,1,6,3,2,5] => [2,4,5,6,1,3] => [4,5,6,2,1,3] => [6,5,4,2,3,1] => 5
[4,1,6,3,5,2] => [2,6,5,3,4,1] => [2,6,5,3,4,1] => [5,2,6,1,3,4] => 3
[4,1,6,5,2,3] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[4,1,6,5,3,2] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => 4
[4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [2,4,3,1,5,6] => 3
[4,2,1,3,6,5] => [3,2,4,1,6,5] => [3,2,4,6,1,5] => [2,6,3,4,1,5] => 4
[4,2,1,5,3,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [2,5,3,4,1,6] => 4
[4,2,1,5,6,3] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [2,6,3,4,5,1] => 5
[4,2,1,6,3,5] => [3,2,6,5,1,4] => [6,3,5,2,1,4] => [3,6,5,1,4,2] => 5
[4,2,1,6,5,3] => [3,2,4,6,5,1] => [3,6,2,4,5,1] => [4,3,1,5,6,2] => 5
[4,2,3,1,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 2
[4,2,3,1,6,5] => [3,4,2,1,6,5] => [3,4,2,6,1,5] => [6,3,1,4,2,5] => 4
[4,2,3,5,1,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,3,1,4,2,6] => 4
[4,2,3,5,6,1] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,4,5,2] => 5
[4,2,3,6,1,5] => [3,6,2,5,1,4] => [3,6,5,2,1,4] => [6,3,5,1,4,2] => 5
[4,2,3,6,5,1] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => [5,4,3,1,6,2] => 5
[4,2,5,1,3,6] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => 3
[4,2,5,1,6,3] => [5,2,4,3,6,1] => [5,2,4,3,6,1] => [2,4,6,1,5,3] => 5
[4,2,5,3,1,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,3,1,2,6] => 3
[4,2,5,3,6,1] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[4,2,5,6,1,3] => [4,2,6,5,3,1] => [6,2,4,5,3,1] => [2,4,6,5,1,3] => 4
[4,2,5,6,3,1] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[4,2,6,1,3,5] => [5,2,4,6,1,3] => [5,2,4,1,6,3] => [2,4,6,3,5,1] => 5
[4,2,6,1,5,3] => [6,2,4,3,5,1] => [4,2,3,6,5,1] => [2,3,5,4,6,1] => 5
[4,2,6,3,1,5] => [6,4,5,2,1,3] => [4,2,1,6,5,3] => [2,5,1,4,6,3] => 5
[4,2,6,3,5,1] => [3,6,5,2,4,1] => [6,5,3,2,4,1] => [3,5,6,1,2,4] => 3
[4,2,6,5,1,3] => [4,2,5,6,3,1] => [2,4,5,6,3,1] => [6,2,5,4,1,3] => 4
[4,2,6,5,3,1] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 4
[4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 2
[4,3,1,2,6,5] => [3,4,2,1,6,5] => [3,4,2,6,1,5] => [6,3,1,4,2,5] => 4
[4,3,1,5,2,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,3,1,4,2,6] => 4
[4,3,1,5,6,2] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,4,5,2] => 5
[4,3,1,6,2,5] => [3,6,2,5,1,4] => [3,6,5,2,1,4] => [6,3,5,1,4,2] => 5
[4,3,1,6,5,2] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => [5,4,3,1,6,2] => 5
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => 2
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,6,1,5] => [3,6,1,4,2,5] => 4
[4,3,2,5,1,6] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [3,5,1,4,2,6] => 4
[4,3,2,5,6,1] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [3,6,1,4,5,2] => 5
[4,3,2,6,1,5] => [6,3,2,5,1,4] => [3,6,2,1,5,4] => [5,3,1,2,6,4] => 5
[4,3,2,6,5,1] => [4,3,2,6,5,1] => [4,3,6,2,5,1] => [4,5,3,1,6,2] => 5
[4,3,5,1,2,6] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => [5,3,4,1,2,6] => 3
[4,3,5,1,6,2] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => [6,3,4,1,5,2] => 5
[4,3,5,2,1,6] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [4,5,3,1,2,6] => 3
[4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,6,3,1,5,2] => 5
[4,3,5,6,1,2] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => [4,3,6,5,1,2] => 4
[4,3,5,6,2,1] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,6,3,4,1,2] => 4
[4,3,6,1,2,5] => [5,6,4,2,1,3] => [5,2,1,6,4,3] => [2,6,1,5,3,4] => 4
[4,3,6,1,5,2] => [6,3,4,2,5,1] => [3,4,2,6,5,1] => [5,3,1,4,6,2] => 5
[4,3,6,2,1,5] => [4,6,5,2,1,3] => [6,4,2,1,5,3] => [4,5,1,3,6,2] => 5
[4,3,6,2,5,1] => [6,3,5,2,4,1] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => 4
[4,3,6,5,1,2] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,6,3,4,1,2] => 4
[4,3,6,5,2,1] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => [4,3,6,5,1,2] => 4
[4,5,1,2,3,6] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [4,5,3,1,2,6] => 3
[4,5,1,2,6,3] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,6,3,1,5,2] => 5
[4,5,1,3,2,6] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => [5,3,4,1,2,6] => 3
[4,5,1,3,6,2] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => [6,3,4,1,5,2] => 5
[4,5,1,6,2,3] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [6,4,3,5,1,2] => 4
[4,5,1,6,3,2] => [5,3,4,6,2,1] => [3,5,4,6,2,1] => [6,3,5,4,1,2] => 4
[4,5,2,1,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,3,1,2,6] => 3
[4,5,2,1,6,3] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => 3
[4,5,2,3,6,1] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [3,4,6,1,5,2] => 5
[4,5,2,6,1,3] => [3,6,4,5,2,1] => [3,6,4,5,2,1] => [6,3,4,5,1,2] => 4
[4,5,2,6,3,1] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,5,6,4,1,2] => 4
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => 3
[4,5,3,1,6,2] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [3,4,6,1,5,2] => 5
[4,5,3,2,1,6] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [4,3,5,1,2,6] => 3
[4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,3,6,1,5,2] => 5
[4,5,3,6,1,2] => [4,6,3,5,2,1] => [6,4,3,5,2,1] => [3,4,6,5,1,2] => 4
[4,5,3,6,2,1] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[4,5,6,2,1,3] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[4,5,6,2,3,1] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[4,5,6,3,1,2] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[4,5,6,3,2,1] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[4,6,1,2,3,5] => [4,3,5,6,1,2] => [4,3,5,1,6,2] => [4,6,3,2,5,1] => 5
[4,6,1,2,5,3] => [4,3,6,2,5,1] => [4,6,3,2,5,1] => [4,3,5,1,6,2] => 5
[4,6,1,3,2,5] => [5,3,4,6,1,2] => [3,5,4,1,6,2] => [6,3,4,2,5,1] => 5
[4,6,1,3,5,2] => [5,3,6,2,4,1] => [3,5,2,6,4,1] => [6,3,1,5,2,4] => 4
[4,6,1,5,2,3] => [5,3,4,6,2,1] => [3,5,4,6,2,1] => [6,3,5,4,1,2] => 4
[4,6,1,5,3,2] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [6,4,3,5,1,2] => 4
[4,6,2,1,3,5] => [3,4,5,6,1,2] => [3,4,5,1,6,2] => [6,4,3,2,5,1] => 5
[4,6,2,1,5,3] => [3,4,6,2,5,1] => [6,3,4,2,5,1] => [3,5,4,1,6,2] => 5
[4,6,2,3,1,5] => [5,4,3,6,1,2] => [5,4,3,1,6,2] => [3,4,6,2,5,1] => 5
[4,6,2,3,5,1] => [5,4,6,2,3,1] => [5,4,2,6,3,1] => [5,6,1,4,2,3] => 4
[4,6,2,5,1,3] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[4,6,2,5,3,1] => [6,4,3,5,2,1] => [4,3,6,5,2,1] => [4,6,3,5,1,2] => 4
[4,6,3,1,2,5] => [5,4,3,6,1,2] => [5,4,3,1,6,2] => [3,4,6,2,5,1] => 5
[4,6,3,1,5,2] => [5,4,6,2,3,1] => [5,4,2,6,3,1] => [5,6,1,4,2,3] => 4
[4,6,3,2,1,5] => [4,5,3,6,1,2] => [4,5,3,1,6,2] => [4,3,6,2,5,1] => 5
[4,6,3,2,5,1] => [4,5,6,2,3,1] => [4,5,2,6,3,1] => [6,5,1,4,2,3] => 4
[4,6,3,5,1,2] => [5,6,3,4,2,1] => [5,3,6,4,2,1] => [4,5,3,6,1,2] => 4
[4,6,3,5,2,1] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [5,3,4,6,1,2] => 4
[4,6,5,1,2,3] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[4,6,5,1,3,2] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[4,6,5,2,3,1] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[4,6,5,3,1,2] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[4,6,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 4
[5,1,2,3,6,4] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 5
[5,1,2,4,3,6] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => 4
[5,1,2,4,6,3] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [2,3,4,6,5,1] => 5
[5,1,2,6,3,4] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [5,6,1,2,3,4] => 2
[5,1,2,6,4,3] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [6,5,1,2,3,4] => 2
[5,1,3,2,4,6] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [2,3,5,4,1,6] => 4
[5,1,3,2,6,4] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [2,3,6,4,5,1] => 5
[5,1,3,4,2,6] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => [5,4,1,2,3,6] => 2
[5,1,3,4,6,2] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [6,4,1,2,5,3] => 5
[5,1,3,6,2,4] => [2,6,3,5,4,1] => [6,2,5,3,4,1] => [2,5,6,1,3,4] => 3
[5,1,3,6,4,2] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[5,1,4,2,3,6] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => [5,4,1,2,3,6] => 2
[5,1,4,2,6,3] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [6,4,1,2,5,3] => 5
[5,1,4,3,2,6] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [4,5,1,2,3,6] => 2
[5,1,4,3,6,2] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [4,6,1,2,5,3] => 5
[5,1,4,6,2,3] => [2,6,4,5,3,1] => [4,6,5,2,3,1] => [6,4,5,2,1,3] => 4
[5,1,4,6,3,2] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [5,6,4,2,1,3] => 4
[5,1,6,2,3,4] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [5,6,4,2,1,3] => 4
[5,1,6,2,4,3] => [2,6,4,5,3,1] => [4,6,5,2,3,1] => [6,4,5,2,1,3] => 4
[5,1,6,3,2,4] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[5,1,6,3,4,2] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [4,5,6,2,1,3] => 4
[5,1,6,4,2,3] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [4,5,6,2,1,3] => 4
[5,1,6,4,3,2] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [5,4,6,2,1,3] => 4
[5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [2,5,3,4,1,6] => 4
[5,2,1,3,6,4] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [2,6,3,4,5,1] => 5
[5,2,1,4,3,6] => [3,2,5,4,1,6] => [3,5,2,4,1,6] => [4,3,1,5,2,6] => 4
[5,2,1,4,6,3] => [3,2,5,4,6,1] => [3,5,2,4,6,1] => [4,3,1,6,5,2] => 5
[5,2,1,6,3,4] => [3,2,6,5,4,1] => [6,3,5,2,4,1] => [3,6,5,1,2,4] => 3
[5,2,1,6,4,3] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => [6,5,3,1,2,4] => 3
[5,2,3,1,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,3,1,4,2,6] => 4
[5,2,3,1,6,4] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,4,5,2] => 5
[5,2,3,4,1,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,3,1,2,6] => 3
[5,2,3,4,6,1] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[5,2,3,6,1,4] => [3,6,2,5,4,1] => [3,6,5,2,4,1] => [6,3,5,1,2,4] => 3
[5,2,3,6,4,1] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[5,2,4,1,3,6] => [5,4,2,3,1,6] => [2,5,4,3,1,6] => [4,2,5,1,3,6] => 3
[5,2,4,1,6,3] => [5,4,2,3,6,1] => [2,5,4,3,6,1] => [4,2,6,1,5,3] => 5
[5,2,4,3,1,6] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => [3,5,4,1,2,6] => 3
[5,2,4,3,6,1] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [3,6,4,1,5,2] => 5
[5,2,4,6,1,3] => [4,6,2,5,3,1] => [4,6,2,5,3,1] => [6,4,1,5,2,3] => 4
[5,2,4,6,3,1] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [3,6,5,4,1,2] => 4
[5,2,6,1,3,4] => [5,2,4,6,3,1] => [5,2,4,6,3,1] => [2,5,6,4,1,3] => 4
[5,2,6,1,4,3] => [6,2,4,5,3,1] => [2,6,4,5,3,1] => [4,2,6,5,1,3] => 4
[5,2,6,3,1,4] => [6,4,5,2,3,1] => [4,2,6,5,3,1] => [2,6,4,5,1,3] => 4
[5,2,6,3,4,1] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 4
[5,2,6,4,1,3] => [4,6,5,2,3,1] => [6,4,2,5,3,1] => [4,6,1,5,2,3] => 4
[5,2,6,4,3,1] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,3,1,4,2,6] => 4
[5,3,1,2,6,4] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,4,5,2] => 5
[5,3,1,4,2,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,3,1,2,6] => 3
[5,3,1,4,6,2] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[5,3,1,6,2,4] => [3,6,2,5,4,1] => [3,6,5,2,4,1] => [6,3,5,1,2,4] => 3
[5,3,1,6,4,2] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[5,3,2,1,4,6] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [3,5,1,4,2,6] => 4
[5,3,2,1,6,4] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [3,6,1,4,5,2] => 5
[5,3,2,4,1,6] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [4,5,3,1,2,6] => 3
[5,3,2,4,6,1] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,6,3,1,5,2] => 5
[5,3,2,6,1,4] => [6,3,2,5,4,1] => [3,6,2,5,4,1] => [5,3,1,6,2,4] => 4
[5,3,2,6,4,1] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,6,3,4,1,2] => 4
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => 3
[5,3,4,1,6,2] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [3,4,6,1,5,2] => 5
[5,3,4,2,1,6] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [4,3,5,1,2,6] => 3
[5,3,4,2,6,1] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,3,6,1,5,2] => 5
[5,3,4,6,1,2] => [4,6,3,5,2,1] => [6,4,3,5,2,1] => [3,4,6,5,1,2] => 4
[5,3,4,6,2,1] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[5,3,6,1,2,4] => [5,6,4,2,3,1] => [5,2,6,4,3,1] => [2,5,4,6,1,3] => 4
[5,3,6,1,4,2] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [6,4,3,5,1,2] => 4
[5,3,6,2,1,4] => [4,6,5,2,3,1] => [6,4,2,5,3,1] => [4,6,1,5,2,3] => 4
[5,3,6,2,4,1] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => [3,5,4,6,1,2] => 4
[5,3,6,4,1,2] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[5,3,6,4,2,1] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [5,4,3,1,2,6] => 3
[5,4,1,2,6,3] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[5,4,1,3,2,6] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => [3,5,4,1,2,6] => 3
[5,4,1,3,6,2] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [3,6,4,1,5,2] => 5
[5,4,1,6,2,3] => [3,6,4,5,2,1] => [3,6,4,5,2,1] => [6,3,4,5,1,2] => 4
[5,4,1,6,3,2] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [3,6,5,4,1,2] => 4
[5,4,2,1,3,6] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [4,5,3,1,2,6] => 3
[5,4,2,1,6,3] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,6,3,1,5,2] => 5
[5,4,2,3,1,6] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [4,3,5,1,2,6] => 3
[5,4,2,3,6,1] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,3,6,1,5,2] => 5
[5,4,2,6,1,3] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [6,4,3,5,1,2] => 4
[5,4,2,6,3,1] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[5,4,3,1,2,6] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [4,3,5,1,2,6] => 3
[5,4,3,1,6,2] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,3,6,1,5,2] => 5
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => 3
[5,4,3,2,6,1] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [3,4,6,1,5,2] => 5
[5,4,3,6,1,2] => [6,4,3,5,2,1] => [4,3,6,5,2,1] => [4,6,3,5,1,2] => 4
[5,4,3,6,2,1] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,5,6,4,1,2] => 4
[5,4,6,1,2,3] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[5,4,6,2,1,3] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[5,4,6,2,3,1] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[5,4,6,3,1,2] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[5,6,1,2,3,4] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,6,3,4,1,2] => 4
[5,6,1,2,4,3] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => [4,3,6,5,1,2] => 4
[5,6,1,3,2,4] => [5,3,4,6,2,1] => [3,5,4,6,2,1] => [6,3,5,4,1,2] => 4
[5,6,1,3,4,2] => [5,3,6,4,2,1] => [3,5,6,4,2,1] => [5,4,3,6,1,2] => 4
[5,6,1,4,2,3] => [5,3,6,4,2,1] => [3,5,6,4,2,1] => [5,4,3,6,1,2] => 4
[5,6,1,4,3,2] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => [3,5,4,6,1,2] => 4
[5,6,2,1,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[5,6,2,1,4,3] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 4
[5,6,2,3,1,4] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,5,6,4,1,2] => 4
[5,6,2,3,4,1] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[5,6,2,4,1,3] => [5,6,3,4,2,1] => [5,3,6,4,2,1] => [4,5,3,6,1,2] => 4
[5,6,2,4,3,1] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[5,6,3,1,2,4] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,5,6,4,1,2] => 4
[5,6,3,1,4,2] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[5,6,3,2,1,4] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[5,6,3,2,4,1] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[5,6,3,4,1,2] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[5,6,4,1,2,3] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[5,6,4,1,3,2] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[5,6,4,2,1,3] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 5
[6,1,2,3,5,4] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => 5
[6,1,2,4,3,5] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [2,3,4,6,5,1] => 5
[6,1,2,4,5,3] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [6,5,1,2,3,4] => 2
[6,1,2,5,3,4] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [6,5,1,2,3,4] => 2
[6,1,2,5,4,3] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [5,6,1,2,3,4] => 2
[6,1,3,2,4,5] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [2,3,6,4,5,1] => 5
[6,1,3,2,5,4] => [2,4,3,6,5,1] => [4,6,2,3,5,1] => [5,4,1,2,6,3] => 5
[6,1,3,4,2,5] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [6,4,1,2,5,3] => 5
[6,1,3,4,5,2] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[6,1,3,5,2,4] => [2,6,5,3,4,1] => [2,6,5,3,4,1] => [5,2,6,1,3,4] => 3
[6,1,3,5,4,2] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => 4
[6,1,4,2,3,5] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [6,4,1,2,5,3] => 5
[6,1,4,2,5,3] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[6,1,4,3,2,5] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [4,6,1,2,5,3] => 5
[6,1,4,3,5,2] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [5,6,4,2,1,3] => 4
[6,1,4,5,2,3] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [4,5,6,2,1,3] => 4
[6,1,4,5,3,2] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [5,4,6,2,1,3] => 4
[6,1,5,2,3,4] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => 4
[6,1,5,2,4,3] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => 4
[6,1,5,3,2,4] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [5,6,4,2,1,3] => 4
[6,1,5,3,4,2] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [5,4,6,2,1,3] => 4
[6,1,5,4,2,3] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [5,4,6,2,1,3] => 4
[6,1,5,4,3,2] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [4,5,6,2,1,3] => 4
[6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [2,6,3,4,5,1] => 5
[6,2,1,3,5,4] => [3,2,4,6,5,1] => [3,6,2,4,5,1] => [4,3,1,5,6,2] => 5
[6,2,1,4,3,5] => [3,2,5,4,6,1] => [3,5,2,4,6,1] => [4,3,1,6,5,2] => 5
[6,2,1,4,5,3] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => [6,5,3,1,2,4] => 3
[6,2,1,5,3,4] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => [6,5,3,1,2,4] => 3
[6,2,1,5,4,3] => [3,2,6,5,4,1] => [6,3,5,2,4,1] => [3,6,5,1,2,4] => 3
[6,2,3,1,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,4,5,2] => 5
[6,2,3,1,5,4] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => [5,4,3,1,6,2] => 5
[6,2,3,4,1,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[6,2,3,4,5,1] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[6,2,3,5,1,4] => [3,6,5,2,4,1] => [6,5,3,2,4,1] => [3,5,6,1,2,4] => 3
[6,2,3,5,4,1] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 4
[6,2,4,1,3,5] => [5,4,2,3,6,1] => [2,5,4,3,6,1] => [4,2,6,1,5,3] => 5
[6,2,4,1,5,3] => [5,4,2,6,3,1] => [2,5,4,6,3,1] => [5,2,6,4,1,3] => 4
[6,2,4,3,1,5] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [3,6,4,1,5,2] => 5
[6,2,4,3,5,1] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [3,6,5,4,1,2] => 4
[6,2,4,5,1,3] => [4,6,5,2,3,1] => [6,4,2,5,3,1] => [4,6,1,5,2,3] => 4
[6,2,4,5,3,1] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[6,2,5,1,3,4] => [5,4,2,6,3,1] => [2,5,4,6,3,1] => [5,2,6,4,1,3] => 4
[6,2,5,1,4,3] => [6,4,2,5,3,1] => [2,4,6,5,3,1] => [6,2,4,5,1,3] => 4
[6,2,5,3,1,4] => [6,5,4,2,3,1] => [2,6,5,4,3,1] => [4,2,5,6,1,3] => 4
[6,2,5,3,4,1] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[6,2,5,4,1,3] => [4,5,6,2,3,1] => [4,5,2,6,3,1] => [6,5,1,4,2,3] => 4
[6,2,5,4,3,1] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 4
[6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,3,1,4,5,2] => 5
[6,3,1,2,5,4] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => [5,4,3,1,6,2] => 5
[6,3,1,4,2,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[6,3,1,4,5,2] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[6,3,1,5,2,4] => [3,6,5,2,4,1] => [6,5,3,2,4,1] => [3,5,6,1,2,4] => 3
[6,3,1,5,4,2] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 4
[6,3,2,1,4,5] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [3,6,1,4,5,2] => 5
[6,3,2,1,5,4] => [4,3,2,6,5,1] => [4,3,6,2,5,1] => [4,5,3,1,6,2] => 5
[6,3,2,4,1,5] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,6,3,1,5,2] => 5
[6,3,2,4,5,1] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,6,3,4,1,2] => 4
[6,3,2,5,1,4] => [6,3,5,2,4,1] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => 4
[6,3,2,5,4,1] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => [4,3,6,5,1,2] => 4
[6,3,4,1,2,5] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [3,4,6,1,5,2] => 5
[6,3,4,1,5,2] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,5,6,4,1,2] => 4
[6,3,4,2,1,5] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,3,6,1,5,2] => 5
[6,3,4,2,5,1] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[6,3,4,5,1,2] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[6,3,4,5,2,1] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[6,3,5,1,2,4] => [5,4,6,2,3,1] => [5,4,2,6,3,1] => [5,6,1,4,2,3] => 4
[6,3,5,1,4,2] => [6,4,3,5,2,1] => [4,3,6,5,2,1] => [4,6,3,5,1,2] => 4
[6,3,5,2,1,4] => [4,5,6,2,3,1] => [4,5,2,6,3,1] => [6,5,1,4,2,3] => 4
[6,3,5,2,4,1] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [5,3,4,6,1,2] => 4
[6,3,5,4,1,2] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[6,3,5,4,2,1] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,4,3,1,5,2] => 5
[6,4,1,2,5,3] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[6,4,1,3,2,5] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [3,6,4,1,5,2] => 5
[6,4,1,3,5,2] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [3,6,5,4,1,2] => 4
[6,4,1,5,2,3] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 4
[6,4,1,5,3,2] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[6,4,2,1,3,5] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,6,3,1,5,2] => 5
[6,4,2,1,5,3] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,6,3,4,1,2] => 4
[6,4,2,3,1,5] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,3,6,1,5,2] => 5
[6,4,2,3,5,1] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[6,4,2,5,1,3] => [6,3,5,4,2,1] => [6,3,5,4,2,1] => [3,5,4,6,1,2] => 4
[6,4,2,5,3,1] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[6,4,3,1,2,5] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,3,6,1,5,2] => 5
[6,4,3,1,5,2] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[6,4,3,2,1,5] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [3,4,6,1,5,2] => 5
[6,4,3,2,5,1] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,5,6,4,1,2] => 4
[6,4,3,5,1,2] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[6,4,3,5,2,1] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[6,4,5,1,2,3] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[6,4,5,1,3,2] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [6,4,5,1,2,3] => 3
[6,4,5,2,1,3] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[6,4,5,3,2,1] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,5,3,4,1,2] => 4
[6,5,1,2,4,3] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 4
[6,5,1,3,2,4] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [3,6,5,4,1,2] => 4
[6,5,1,3,4,2] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[6,5,1,4,2,3] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,3,5,6,1,2] => 4
[6,5,1,4,3,2] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 4
[6,5,2,1,3,4] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,6,3,4,1,2] => 4
[6,5,2,1,4,3] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => [4,3,6,5,1,2] => 4
[6,5,2,3,1,4] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[6,5,2,3,4,1] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[6,5,2,4,1,3] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [5,3,4,6,1,2] => 4
[6,5,2,4,3,1] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[6,5,3,1,2,4] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [5,3,6,4,1,2] => 4
[6,5,3,1,4,2] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[6,5,3,2,1,4] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,5,6,4,1,2] => 4
[6,5,3,2,4,1] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[6,5,3,4,2,1] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[6,5,4,1,2,3] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[6,5,4,1,3,2] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [4,6,5,1,2,3] => 3
[6,5,4,2,1,3] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,6,4,1,2,3] => 3
[6,5,4,2,3,1] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[6,5,4,3,1,2] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 3
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,3,5,2,4,6,7] => [1,5,4,2,3,6,7] => [1,5,4,2,3,6,7] => [1,4,5,3,2,6,7] => 4
[1,3,5,7,2,4,6] => [1,7,6,5,2,3,4] => [1,2,7,6,5,3,4] => [1,2,5,6,7,4,3] => 6
[1,3,6,4,2,5,7] => [1,6,5,4,2,3,7] => [1,6,5,4,2,3,7] => [1,4,5,6,3,2,7] => 5
[2,4,1,3,5,6,7] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => 3
[2,4,1,3,5,7,6] => [4,3,1,2,5,7,6] => [1,4,3,7,2,5,6] => [1,3,7,4,2,5,6] => 4
[2,4,1,3,6,5,7] => [4,3,1,2,6,5,7] => [1,4,3,6,2,5,7] => [1,3,6,4,2,5,7] => 4
[2,4,1,3,6,7,5] => [4,3,1,2,6,7,5] => [1,4,3,6,7,2,5] => [1,3,7,4,6,5,2] => 6
[2,4,1,3,7,5,6] => [4,3,1,2,6,7,5] => [1,4,3,6,7,2,5] => [1,3,7,4,6,5,2] => 6
[2,4,1,5,3,6,7] => [4,3,1,5,2,6,7] => [1,4,3,5,2,6,7] => [1,3,5,4,2,6,7] => 4
[2,4,1,5,3,7,6] => [4,3,1,5,2,7,6] => [1,4,3,5,7,2,6] => [1,3,7,4,5,2,6] => 5
[2,4,1,5,6,3,7] => [4,3,1,5,6,2,7] => [1,4,3,5,6,2,7] => [1,3,6,4,5,2,7] => 5
[2,4,1,5,6,7,3] => [4,3,1,5,6,7,2] => [1,4,3,5,6,7,2] => [1,3,7,4,5,6,2] => 6
[2,4,1,7,3,6,5] => [7,3,1,5,2,6,4] => [1,7,3,2,5,6,4] => [1,3,5,2,6,7,4] => 6
[2,4,6,1,3,5,7] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => [1,2,5,6,3,4,7] => 4
[2,4,6,1,3,7,5] => [6,5,4,1,2,7,3] => [1,2,6,5,4,7,3] => [1,2,5,7,3,6,4] => 6
[2,4,7,1,3,5,6] => [6,5,4,1,2,7,3] => [1,2,6,5,4,7,3] => [1,2,5,7,3,6,4] => 6
[2,4,7,1,3,6,5] => [7,5,4,1,2,6,3] => [1,2,5,4,7,6,3] => [1,2,4,6,5,7,3] => 6
[2,5,1,3,4,6,7] => [4,3,1,5,2,6,7] => [1,4,3,5,2,6,7] => [1,3,5,4,2,6,7] => 4
[2,5,1,3,4,7,6] => [4,3,1,5,2,7,6] => [1,4,3,5,7,2,6] => [1,3,7,4,5,2,6] => 5
[2,5,1,3,6,4,7] => [4,3,1,5,6,2,7] => [1,4,3,5,6,2,7] => [1,3,6,4,5,2,7] => 5
[2,5,1,3,6,7,4] => [4,3,1,5,6,7,2] => [1,4,3,5,6,7,2] => [1,3,7,4,5,6,2] => 6
[2,5,1,4,3,6,7] => [5,3,1,4,2,6,7] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => 4
[2,5,1,4,3,7,6] => [5,3,1,4,2,7,6] => [1,3,5,4,7,2,6] => [1,4,3,7,5,2,6] => 5
[2,5,1,4,6,3,7] => [5,3,1,4,6,2,7] => [1,3,5,4,6,2,7] => [1,4,3,6,5,2,7] => 5
[2,5,1,4,6,7,3] => [5,3,1,4,6,7,2] => [1,3,5,4,6,7,2] => [1,4,3,7,5,6,2] => 6
[2,5,1,7,4,6,3] => [7,3,1,6,4,5,2] => [1,7,3,4,6,5,2] => [1,3,4,6,7,2,5] => 5
[2,5,3,1,4,6,7] => [5,4,3,1,2,6,7] => [1,5,4,3,2,6,7] => [1,4,5,2,3,6,7] => 3
[2,5,3,1,6,4,7] => [5,4,3,1,6,2,7] => [1,5,4,3,6,2,7] => [1,4,6,2,5,3,7] => 5
[2,5,3,7,1,4,6] => [7,6,3,5,1,2,4] => [1,7,3,2,6,5,4] => [1,3,6,2,7,4,5] => 5
[2,5,7,4,1,3,6] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => [1,2,5,6,7,3,4] => 5
[2,6,1,3,4,5,7] => [4,3,1,5,6,2,7] => [1,4,3,5,6,2,7] => [1,3,6,4,5,2,7] => 5
[2,6,1,3,4,7,5] => [4,3,1,5,6,7,2] => [1,4,3,5,6,7,2] => [1,3,7,4,5,6,2] => 6
[2,6,1,4,3,5,7] => [5,3,1,4,6,2,7] => [1,3,5,4,6,2,7] => [1,4,3,6,5,2,7] => 5
[2,6,1,4,3,7,5] => [5,3,1,4,6,7,2] => [1,3,5,4,6,7,2] => [1,4,3,7,5,6,2] => 6
[2,6,1,5,7,3,4] => [7,3,1,5,6,4,2] => [1,7,3,5,6,4,2] => [1,3,5,7,6,2,4] => 5
[2,6,1,7,3,5,4] => [7,3,1,5,6,4,2] => [1,7,3,5,6,4,2] => [1,3,5,7,6,2,4] => 5
[2,6,3,1,4,5,7] => [5,4,3,1,6,2,7] => [1,5,4,3,6,2,7] => [1,4,6,2,5,3,7] => 5
[2,6,3,1,5,4,7] => [6,4,3,1,5,2,7] => [1,4,3,6,5,2,7] => [1,3,5,4,6,2,7] => 5
[2,6,3,1,5,7,4] => [6,4,3,1,5,7,2] => [1,4,3,6,5,7,2] => [1,3,5,4,7,6,2] => 6
[2,6,3,1,7,5,4] => [6,4,3,1,7,5,2] => [1,4,3,6,7,5,2] => [1,3,7,4,6,2,5] => 5
[2,6,4,3,1,5,7] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [1,4,5,6,2,3,7] => 4
[2,6,4,3,1,7,5] => [6,5,4,3,1,7,2] => [1,6,5,4,3,7,2] => [1,4,5,7,2,6,3] => 6
[2,7,1,3,4,5,6] => [4,3,1,5,6,7,2] => [1,4,3,5,6,7,2] => [1,3,7,4,5,6,2] => 6
[2,7,1,4,3,5,6] => [5,3,1,4,6,7,2] => [1,3,5,4,6,7,2] => [1,4,3,7,5,6,2] => 6
[2,7,1,4,6,3,5] => [7,3,1,6,4,5,2] => [1,7,3,4,6,5,2] => [1,3,4,6,7,2,5] => 5
[2,7,3,1,5,4,6] => [6,4,3,1,5,7,2] => [1,4,3,6,5,7,2] => [1,3,5,4,7,6,2] => 6
[2,7,3,1,5,6,4] => [6,4,3,1,7,5,2] => [1,4,3,6,7,5,2] => [1,3,7,4,6,2,5] => 5
[2,7,3,1,6,4,5] => [6,4,3,1,7,5,2] => [1,4,3,6,7,5,2] => [1,3,7,4,6,2,5] => 5
[2,7,3,6,1,5,4] => [6,7,5,3,1,4,2] => [1,6,3,7,5,4,2] => [1,3,6,5,7,2,4] => 5
[2,7,4,3,1,5,6] => [6,5,4,3,1,7,2] => [1,6,5,4,3,7,2] => [1,4,5,7,2,6,3] => 6
[2,7,4,3,1,6,5] => [7,5,4,3,1,6,2] => [1,5,4,3,7,6,2] => [1,4,6,2,5,7,3] => 6
[3,5,6,1,2,4,7] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [1,4,5,6,2,3,7] => 4
[3,5,6,1,2,7,4] => [6,5,4,3,1,7,2] => [1,6,5,4,3,7,2] => [1,4,5,7,2,6,3] => 6
[3,5,7,1,2,4,6] => [6,5,4,7,1,2,3] => [1,6,5,4,2,7,3] => [1,4,5,7,3,6,2] => 6
[3,5,7,1,2,6,4] => [7,5,4,3,1,6,2] => [1,5,4,3,7,6,2] => [1,4,6,2,5,7,3] => 6
[3,6,5,2,1,4,7] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [1,4,5,6,2,3,7] => 4
[3,6,5,2,1,7,4] => [6,5,4,3,1,7,2] => [1,6,5,4,3,7,2] => [1,4,5,7,2,6,3] => 6
[3,7,5,2,1,4,6] => [6,5,4,3,1,7,2] => [1,6,5,4,3,7,2] => [1,4,5,7,2,6,3] => 6
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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:
1,1 1,2,3 1,3,9,11 1,4,18,44,53 1,5,30,124,263,297
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 3\ q^{2}$
$F_{4} = 1 + 3\ q + 9\ q^{2} + 11\ q^{3}$
$F_{5} = 1 + 4\ q + 18\ q^{2} + 44\ q^{3} + 53\ q^{4}$
$F_{6} = 1 + 5\ q + 30\ q^{2} + 124\ q^{3} + 263\ q^{4} + 297\ q^{5}$
Description
The last descent of a permutation.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is the largest index $0 \leq i < n$ such that $\pi(i) > \pi(i+1)$ where one considers $\pi(0) = n+1$.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is the largest index $0 \leq i < n$ such that $\pi(i) > \pi(i+1)$ where one considers $\pi(0) = n+1$.
Map
catalanization
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
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