Identifier
-
Mp00320:
Parking functions
—reverse⟶
Parking functions
St001935: Parking functions ⟶ ℤ
Values
[1] => [1] => 0
[1,1] => [1,1] => 0
[1,2] => [2,1] => 0
[2,1] => [1,2] => 1
[1,1,1] => [1,1,1] => 0
[1,1,2] => [2,1,1] => 0
[1,2,1] => [1,2,1] => 1
[2,1,1] => [1,1,2] => 1
[1,1,3] => [3,1,1] => 0
[1,3,1] => [1,3,1] => 1
[3,1,1] => [1,1,3] => 1
[1,2,2] => [2,2,1] => 0
[2,1,2] => [2,1,2] => 1
[2,2,1] => [1,2,2] => 1
[1,2,3] => [3,2,1] => 0
[1,3,2] => [2,3,1] => 1
[2,1,3] => [3,1,2] => 1
[2,3,1] => [1,3,2] => 1
[3,1,2] => [2,1,3] => 1
[3,2,1] => [1,2,3] => 2
[1,1,1,1] => [1,1,1,1] => 0
[1,1,1,2] => [2,1,1,1] => 0
[1,1,2,1] => [1,2,1,1] => 1
[1,2,1,1] => [1,1,2,1] => 1
[2,1,1,1] => [1,1,1,2] => 1
[1,1,1,3] => [3,1,1,1] => 0
[1,1,3,1] => [1,3,1,1] => 1
[1,3,1,1] => [1,1,3,1] => 1
[3,1,1,1] => [1,1,1,3] => 1
[1,1,1,4] => [4,1,1,1] => 0
[1,1,4,1] => [1,4,1,1] => 1
[1,4,1,1] => [1,1,4,1] => 1
[4,1,1,1] => [1,1,1,4] => 1
[1,1,2,2] => [2,2,1,1] => 0
[1,2,1,2] => [2,1,2,1] => 1
[1,2,2,1] => [1,2,2,1] => 1
[2,1,1,2] => [2,1,1,2] => 1
[2,1,2,1] => [1,2,1,2] => 2
[2,2,1,1] => [1,1,2,2] => 1
[1,1,2,3] => [3,2,1,1] => 0
[1,1,3,2] => [2,3,1,1] => 1
[1,2,1,3] => [3,1,2,1] => 1
[1,2,3,1] => [1,3,2,1] => 1
[1,3,1,2] => [2,1,3,1] => 1
[1,3,2,1] => [1,2,3,1] => 2
[2,1,1,3] => [3,1,1,2] => 1
[2,1,3,1] => [1,3,1,2] => 2
[2,3,1,1] => [1,1,3,2] => 1
[3,1,1,2] => [2,1,1,3] => 1
[3,1,2,1] => [1,2,1,3] => 2
[3,2,1,1] => [1,1,2,3] => 2
[1,1,2,4] => [4,2,1,1] => 0
[1,1,4,2] => [2,4,1,1] => 1
[1,2,1,4] => [4,1,2,1] => 1
[1,2,4,1] => [1,4,2,1] => 1
[1,4,1,2] => [2,1,4,1] => 1
[1,4,2,1] => [1,2,4,1] => 2
[2,1,1,4] => [4,1,1,2] => 1
[2,1,4,1] => [1,4,1,2] => 2
[2,4,1,1] => [1,1,4,2] => 1
[4,1,1,2] => [2,1,1,4] => 1
[4,1,2,1] => [1,2,1,4] => 2
[4,2,1,1] => [1,1,2,4] => 2
[1,1,3,3] => [3,3,1,1] => 0
[1,3,1,3] => [3,1,3,1] => 1
[1,3,3,1] => [1,3,3,1] => 1
[3,1,1,3] => [3,1,1,3] => 1
[3,1,3,1] => [1,3,1,3] => 2
[3,3,1,1] => [1,1,3,3] => 1
[1,1,3,4] => [4,3,1,1] => 0
[1,1,4,3] => [3,4,1,1] => 1
[1,3,1,4] => [4,1,3,1] => 1
[1,3,4,1] => [1,4,3,1] => 1
[1,4,1,3] => [3,1,4,1] => 1
[1,4,3,1] => [1,3,4,1] => 2
[3,1,1,4] => [4,1,1,3] => 1
[3,1,4,1] => [1,4,1,3] => 2
[3,4,1,1] => [1,1,4,3] => 1
[4,1,1,3] => [3,1,1,4] => 1
[4,1,3,1] => [1,3,1,4] => 2
[4,3,1,1] => [1,1,3,4] => 2
[1,2,2,2] => [2,2,2,1] => 0
[2,1,2,2] => [2,2,1,2] => 1
[2,2,1,2] => [2,1,2,2] => 1
[2,2,2,1] => [1,2,2,2] => 1
[1,2,2,3] => [3,2,2,1] => 0
[1,2,3,2] => [2,3,2,1] => 1
[1,3,2,2] => [2,2,3,1] => 1
[2,1,2,3] => [3,2,1,2] => 1
[2,1,3,2] => [2,3,1,2] => 2
[2,2,1,3] => [3,1,2,2] => 1
[2,2,3,1] => [1,3,2,2] => 1
[2,3,1,2] => [2,1,3,2] => 1
[2,3,2,1] => [1,2,3,2] => 2
[3,1,2,2] => [2,2,1,3] => 1
[3,2,1,2] => [2,1,2,3] => 2
[3,2,2,1] => [1,2,2,3] => 2
[1,2,2,4] => [4,2,2,1] => 0
[1,2,4,2] => [2,4,2,1] => 1
[1,4,2,2] => [2,2,4,1] => 1
[2,1,2,4] => [4,2,1,2] => 1
>>> Load all 1200 entries. <<<[2,1,4,2] => [2,4,1,2] => 2
[2,2,1,4] => [4,1,2,2] => 1
[2,2,4,1] => [1,4,2,2] => 1
[2,4,1,2] => [2,1,4,2] => 1
[2,4,2,1] => [1,2,4,2] => 2
[4,1,2,2] => [2,2,1,4] => 1
[4,2,1,2] => [2,1,2,4] => 2
[4,2,2,1] => [1,2,2,4] => 2
[1,2,3,3] => [3,3,2,1] => 0
[1,3,2,3] => [3,2,3,1] => 1
[1,3,3,2] => [2,3,3,1] => 1
[2,1,3,3] => [3,3,1,2] => 1
[2,3,1,3] => [3,1,3,2] => 1
[2,3,3,1] => [1,3,3,2] => 1
[3,1,2,3] => [3,2,1,3] => 1
[3,1,3,2] => [2,3,1,3] => 2
[3,2,1,3] => [3,1,2,3] => 2
[3,2,3,1] => [1,3,2,3] => 2
[3,3,1,2] => [2,1,3,3] => 1
[3,3,2,1] => [1,2,3,3] => 2
[1,2,3,4] => [4,3,2,1] => 0
[1,2,4,3] => [3,4,2,1] => 1
[1,3,2,4] => [4,2,3,1] => 1
[1,3,4,2] => [2,4,3,1] => 1
[1,4,2,3] => [3,2,4,1] => 1
[1,4,3,2] => [2,3,4,1] => 2
[2,1,3,4] => [4,3,1,2] => 1
[2,1,4,3] => [3,4,1,2] => 2
[2,3,1,4] => [4,1,3,2] => 1
[2,3,4,1] => [1,4,3,2] => 1
[2,4,1,3] => [3,1,4,2] => 1
[2,4,3,1] => [1,3,4,2] => 2
[3,1,2,4] => [4,2,1,3] => 1
[3,1,4,2] => [2,4,1,3] => 2
[3,2,1,4] => [4,1,2,3] => 2
[3,2,4,1] => [1,4,2,3] => 2
[3,4,1,2] => [2,1,4,3] => 1
[3,4,2,1] => [1,2,4,3] => 2
[4,1,2,3] => [3,2,1,4] => 1
[4,1,3,2] => [2,3,1,4] => 2
[4,2,1,3] => [3,1,2,4] => 2
[4,2,3,1] => [1,3,2,4] => 2
[4,3,1,2] => [2,1,3,4] => 2
[4,3,2,1] => [1,2,3,4] => 3
[1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,2] => [2,1,1,1,1] => 0
[1,1,1,2,1] => [1,2,1,1,1] => 1
[1,1,2,1,1] => [1,1,2,1,1] => 1
[1,2,1,1,1] => [1,1,1,2,1] => 1
[2,1,1,1,1] => [1,1,1,1,2] => 1
[1,1,1,1,3] => [3,1,1,1,1] => 0
[1,1,1,3,1] => [1,3,1,1,1] => 1
[1,1,3,1,1] => [1,1,3,1,1] => 1
[1,3,1,1,1] => [1,1,1,3,1] => 1
[3,1,1,1,1] => [1,1,1,1,3] => 1
[1,1,1,1,4] => [4,1,1,1,1] => 0
[1,1,1,4,1] => [1,4,1,1,1] => 1
[1,1,4,1,1] => [1,1,4,1,1] => 1
[1,4,1,1,1] => [1,1,1,4,1] => 1
[4,1,1,1,1] => [1,1,1,1,4] => 1
[1,1,1,1,5] => [5,1,1,1,1] => 0
[1,1,1,5,1] => [1,5,1,1,1] => 1
[1,1,5,1,1] => [1,1,5,1,1] => 1
[1,5,1,1,1] => [1,1,1,5,1] => 1
[5,1,1,1,1] => [1,1,1,1,5] => 1
[1,1,1,2,2] => [2,2,1,1,1] => 0
[1,1,2,1,2] => [2,1,2,1,1] => 1
[1,1,2,2,1] => [1,2,2,1,1] => 1
[1,2,1,1,2] => [2,1,1,2,1] => 1
[1,2,1,2,1] => [1,2,1,2,1] => 2
[1,2,2,1,1] => [1,1,2,2,1] => 1
[2,1,1,1,2] => [2,1,1,1,2] => 1
[2,1,1,2,1] => [1,2,1,1,2] => 2
[2,1,2,1,1] => [1,1,2,1,2] => 2
[2,2,1,1,1] => [1,1,1,2,2] => 1
[1,1,1,2,3] => [3,2,1,1,1] => 0
[1,1,1,3,2] => [2,3,1,1,1] => 1
[1,1,2,1,3] => [3,1,2,1,1] => 1
[1,1,2,3,1] => [1,3,2,1,1] => 1
[1,1,3,1,2] => [2,1,3,1,1] => 1
[1,1,3,2,1] => [1,2,3,1,1] => 2
[1,2,1,1,3] => [3,1,1,2,1] => 1
[1,2,1,3,1] => [1,3,1,2,1] => 2
[1,2,3,1,1] => [1,1,3,2,1] => 1
[1,3,1,1,2] => [2,1,1,3,1] => 1
[1,3,1,2,1] => [1,2,1,3,1] => 2
[1,3,2,1,1] => [1,1,2,3,1] => 2
[2,1,1,1,3] => [3,1,1,1,2] => 1
[2,1,1,3,1] => [1,3,1,1,2] => 2
[2,1,3,1,1] => [1,1,3,1,2] => 2
[2,3,1,1,1] => [1,1,1,3,2] => 1
[3,1,1,1,2] => [2,1,1,1,3] => 1
[3,1,1,2,1] => [1,2,1,1,3] => 2
[3,1,2,1,1] => [1,1,2,1,3] => 2
[3,2,1,1,1] => [1,1,1,2,3] => 2
[1,1,1,2,4] => [4,2,1,1,1] => 0
[1,1,1,4,2] => [2,4,1,1,1] => 1
[1,1,2,1,4] => [4,1,2,1,1] => 1
[1,1,2,4,1] => [1,4,2,1,1] => 1
[1,1,4,1,2] => [2,1,4,1,1] => 1
[1,1,4,2,1] => [1,2,4,1,1] => 2
[1,2,1,1,4] => [4,1,1,2,1] => 1
[1,2,1,4,1] => [1,4,1,2,1] => 2
[1,2,4,1,1] => [1,1,4,2,1] => 1
[1,4,1,1,2] => [2,1,1,4,1] => 1
[1,4,1,2,1] => [1,2,1,4,1] => 2
[1,4,2,1,1] => [1,1,2,4,1] => 2
[2,1,1,1,4] => [4,1,1,1,2] => 1
[2,1,1,4,1] => [1,4,1,1,2] => 2
[2,1,4,1,1] => [1,1,4,1,2] => 2
[2,4,1,1,1] => [1,1,1,4,2] => 1
[4,1,1,1,2] => [2,1,1,1,4] => 1
[4,1,1,2,1] => [1,2,1,1,4] => 2
[4,1,2,1,1] => [1,1,2,1,4] => 2
[4,2,1,1,1] => [1,1,1,2,4] => 2
[1,1,1,2,5] => [5,2,1,1,1] => 0
[1,1,1,5,2] => [2,5,1,1,1] => 1
[1,1,2,1,5] => [5,1,2,1,1] => 1
[1,1,2,5,1] => [1,5,2,1,1] => 1
[1,1,5,1,2] => [2,1,5,1,1] => 1
[1,1,5,2,1] => [1,2,5,1,1] => 2
[1,2,1,1,5] => [5,1,1,2,1] => 1
[1,2,1,5,1] => [1,5,1,2,1] => 2
[1,2,5,1,1] => [1,1,5,2,1] => 1
[1,5,1,1,2] => [2,1,1,5,1] => 1
[1,5,1,2,1] => [1,2,1,5,1] => 2
[1,5,2,1,1] => [1,1,2,5,1] => 2
[2,1,1,1,5] => [5,1,1,1,2] => 1
[2,1,1,5,1] => [1,5,1,1,2] => 2
[2,1,5,1,1] => [1,1,5,1,2] => 2
[2,5,1,1,1] => [1,1,1,5,2] => 1
[5,1,1,1,2] => [2,1,1,1,5] => 1
[5,1,1,2,1] => [1,2,1,1,5] => 2
[5,1,2,1,1] => [1,1,2,1,5] => 2
[5,2,1,1,1] => [1,1,1,2,5] => 2
[1,1,1,3,3] => [3,3,1,1,1] => 0
[1,1,3,1,3] => [3,1,3,1,1] => 1
[1,1,3,3,1] => [1,3,3,1,1] => 1
[1,3,1,1,3] => [3,1,1,3,1] => 1
[1,3,1,3,1] => [1,3,1,3,1] => 2
[1,3,3,1,1] => [1,1,3,3,1] => 1
[3,1,1,1,3] => [3,1,1,1,3] => 1
[3,1,1,3,1] => [1,3,1,1,3] => 2
[3,1,3,1,1] => [1,1,3,1,3] => 2
[3,3,1,1,1] => [1,1,1,3,3] => 1
[1,1,1,3,4] => [4,3,1,1,1] => 0
[1,1,1,4,3] => [3,4,1,1,1] => 1
[1,1,3,1,4] => [4,1,3,1,1] => 1
[1,1,3,4,1] => [1,4,3,1,1] => 1
[1,1,4,1,3] => [3,1,4,1,1] => 1
[1,1,4,3,1] => [1,3,4,1,1] => 2
[1,3,1,1,4] => [4,1,1,3,1] => 1
[1,3,1,4,1] => [1,4,1,3,1] => 2
[1,3,4,1,1] => [1,1,4,3,1] => 1
[1,4,1,1,3] => [3,1,1,4,1] => 1
[1,4,1,3,1] => [1,3,1,4,1] => 2
[1,4,3,1,1] => [1,1,3,4,1] => 2
[3,1,1,1,4] => [4,1,1,1,3] => 1
[3,1,1,4,1] => [1,4,1,1,3] => 2
[3,1,4,1,1] => [1,1,4,1,3] => 2
[3,4,1,1,1] => [1,1,1,4,3] => 1
[4,1,1,1,3] => [3,1,1,1,4] => 1
[4,1,1,3,1] => [1,3,1,1,4] => 2
[4,1,3,1,1] => [1,1,3,1,4] => 2
[4,3,1,1,1] => [1,1,1,3,4] => 2
[1,1,1,3,5] => [5,3,1,1,1] => 0
[1,1,1,5,3] => [3,5,1,1,1] => 1
[1,1,3,1,5] => [5,1,3,1,1] => 1
[1,1,3,5,1] => [1,5,3,1,1] => 1
[1,1,5,1,3] => [3,1,5,1,1] => 1
[1,1,5,3,1] => [1,3,5,1,1] => 2
[1,3,1,1,5] => [5,1,1,3,1] => 1
[1,3,1,5,1] => [1,5,1,3,1] => 2
[1,3,5,1,1] => [1,1,5,3,1] => 1
[1,5,1,1,3] => [3,1,1,5,1] => 1
[1,5,1,3,1] => [1,3,1,5,1] => 2
[1,5,3,1,1] => [1,1,3,5,1] => 2
[3,1,1,1,5] => [5,1,1,1,3] => 1
[3,1,1,5,1] => [1,5,1,1,3] => 2
[3,1,5,1,1] => [1,1,5,1,3] => 2
[3,5,1,1,1] => [1,1,1,5,3] => 1
[5,1,1,1,3] => [3,1,1,1,5] => 1
[5,1,1,3,1] => [1,3,1,1,5] => 2
[5,1,3,1,1] => [1,1,3,1,5] => 2
[5,3,1,1,1] => [1,1,1,3,5] => 2
[1,1,1,4,4] => [4,4,1,1,1] => 0
[1,1,4,1,4] => [4,1,4,1,1] => 1
[1,1,4,4,1] => [1,4,4,1,1] => 1
[1,4,1,1,4] => [4,1,1,4,1] => 1
[1,4,1,4,1] => [1,4,1,4,1] => 2
[1,4,4,1,1] => [1,1,4,4,1] => 1
[4,1,1,1,4] => [4,1,1,1,4] => 1
[4,1,1,4,1] => [1,4,1,1,4] => 2
[4,1,4,1,1] => [1,1,4,1,4] => 2
[4,4,1,1,1] => [1,1,1,4,4] => 1
[1,1,1,4,5] => [5,4,1,1,1] => 0
[1,1,1,5,4] => [4,5,1,1,1] => 1
[1,1,4,1,5] => [5,1,4,1,1] => 1
[1,1,4,5,1] => [1,5,4,1,1] => 1
[1,1,5,1,4] => [4,1,5,1,1] => 1
[1,1,5,4,1] => [1,4,5,1,1] => 2
[1,4,1,1,5] => [5,1,1,4,1] => 1
[1,4,1,5,1] => [1,5,1,4,1] => 2
[1,4,5,1,1] => [1,1,5,4,1] => 1
[1,5,1,1,4] => [4,1,1,5,1] => 1
[1,5,1,4,1] => [1,4,1,5,1] => 2
[1,5,4,1,1] => [1,1,4,5,1] => 2
[4,1,1,1,5] => [5,1,1,1,4] => 1
[4,1,1,5,1] => [1,5,1,1,4] => 2
[4,1,5,1,1] => [1,1,5,1,4] => 2
[4,5,1,1,1] => [1,1,1,5,4] => 1
[5,1,1,1,4] => [4,1,1,1,5] => 1
[5,1,1,4,1] => [1,4,1,1,5] => 2
[5,1,4,1,1] => [1,1,4,1,5] => 2
[5,4,1,1,1] => [1,1,1,4,5] => 2
[1,1,2,2,2] => [2,2,2,1,1] => 0
[1,2,1,2,2] => [2,2,1,2,1] => 1
[1,2,2,1,2] => [2,1,2,2,1] => 1
[1,2,2,2,1] => [1,2,2,2,1] => 1
[2,1,1,2,2] => [2,2,1,1,2] => 1
[2,1,2,1,2] => [2,1,2,1,2] => 2
[2,1,2,2,1] => [1,2,2,1,2] => 2
[2,2,1,1,2] => [2,1,1,2,2] => 1
[2,2,1,2,1] => [1,2,1,2,2] => 2
[2,2,2,1,1] => [1,1,2,2,2] => 1
[1,1,2,2,3] => [3,2,2,1,1] => 0
[1,1,2,3,2] => [2,3,2,1,1] => 1
[1,1,3,2,2] => [2,2,3,1,1] => 1
[1,2,1,2,3] => [3,2,1,2,1] => 1
[1,2,1,3,2] => [2,3,1,2,1] => 2
[1,2,2,1,3] => [3,1,2,2,1] => 1
[1,2,2,3,1] => [1,3,2,2,1] => 1
[1,2,3,1,2] => [2,1,3,2,1] => 1
[1,2,3,2,1] => [1,2,3,2,1] => 2
[1,3,1,2,2] => [2,2,1,3,1] => 1
[1,3,2,1,2] => [2,1,2,3,1] => 2
[1,3,2,2,1] => [1,2,2,3,1] => 2
[2,1,1,2,3] => [3,2,1,1,2] => 1
[2,1,1,3,2] => [2,3,1,1,2] => 2
[2,1,2,1,3] => [3,1,2,1,2] => 2
[2,1,2,3,1] => [1,3,2,1,2] => 2
[2,1,3,1,2] => [2,1,3,1,2] => 2
[2,1,3,2,1] => [1,2,3,1,2] => 3
[2,2,1,1,3] => [3,1,1,2,2] => 1
[2,2,1,3,1] => [1,3,1,2,2] => 2
[2,2,3,1,1] => [1,1,3,2,2] => 1
[2,3,1,1,2] => [2,1,1,3,2] => 1
[2,3,1,2,1] => [1,2,1,3,2] => 2
[2,3,2,1,1] => [1,1,2,3,2] => 2
[3,1,1,2,2] => [2,2,1,1,3] => 1
[3,1,2,1,2] => [2,1,2,1,3] => 2
[3,1,2,2,1] => [1,2,2,1,3] => 2
[3,2,1,1,2] => [2,1,1,2,3] => 2
[3,2,1,2,1] => [1,2,1,2,3] => 3
[3,2,2,1,1] => [1,1,2,2,3] => 2
[1,1,2,2,4] => [4,2,2,1,1] => 0
[1,1,2,4,2] => [2,4,2,1,1] => 1
[1,1,4,2,2] => [2,2,4,1,1] => 1
[1,2,1,2,4] => [4,2,1,2,1] => 1
[1,2,1,4,2] => [2,4,1,2,1] => 2
[1,2,2,1,4] => [4,1,2,2,1] => 1
[1,2,2,4,1] => [1,4,2,2,1] => 1
[1,2,4,1,2] => [2,1,4,2,1] => 1
[1,2,4,2,1] => [1,2,4,2,1] => 2
[1,4,1,2,2] => [2,2,1,4,1] => 1
[1,4,2,1,2] => [2,1,2,4,1] => 2
[1,4,2,2,1] => [1,2,2,4,1] => 2
[2,1,1,2,4] => [4,2,1,1,2] => 1
[2,1,1,4,2] => [2,4,1,1,2] => 2
[2,1,2,1,4] => [4,1,2,1,2] => 2
[2,1,2,4,1] => [1,4,2,1,2] => 2
[2,1,4,1,2] => [2,1,4,1,2] => 2
[2,1,4,2,1] => [1,2,4,1,2] => 3
[2,2,1,1,4] => [4,1,1,2,2] => 1
[2,2,1,4,1] => [1,4,1,2,2] => 2
[2,2,4,1,1] => [1,1,4,2,2] => 1
[2,4,1,1,2] => [2,1,1,4,2] => 1
[2,4,1,2,1] => [1,2,1,4,2] => 2
[2,4,2,1,1] => [1,1,2,4,2] => 2
[4,1,1,2,2] => [2,2,1,1,4] => 1
[4,1,2,1,2] => [2,1,2,1,4] => 2
[4,1,2,2,1] => [1,2,2,1,4] => 2
[4,2,1,1,2] => [2,1,1,2,4] => 2
[4,2,1,2,1] => [1,2,1,2,4] => 3
[4,2,2,1,1] => [1,1,2,2,4] => 2
[1,1,2,2,5] => [5,2,2,1,1] => 0
[1,1,2,5,2] => [2,5,2,1,1] => 1
[1,1,5,2,2] => [2,2,5,1,1] => 1
[1,2,1,2,5] => [5,2,1,2,1] => 1
[1,2,1,5,2] => [2,5,1,2,1] => 2
[1,2,2,1,5] => [5,1,2,2,1] => 1
[1,2,2,5,1] => [1,5,2,2,1] => 1
[1,2,5,1,2] => [2,1,5,2,1] => 1
[1,2,5,2,1] => [1,2,5,2,1] => 2
[1,5,1,2,2] => [2,2,1,5,1] => 1
[1,5,2,1,2] => [2,1,2,5,1] => 2
[1,5,2,2,1] => [1,2,2,5,1] => 2
[2,1,1,2,5] => [5,2,1,1,2] => 1
[2,1,1,5,2] => [2,5,1,1,2] => 2
[2,1,2,1,5] => [5,1,2,1,2] => 2
[2,1,2,5,1] => [1,5,2,1,2] => 2
[2,1,5,1,2] => [2,1,5,1,2] => 2
[2,1,5,2,1] => [1,2,5,1,2] => 3
[2,2,1,1,5] => [5,1,1,2,2] => 1
[2,2,1,5,1] => [1,5,1,2,2] => 2
[2,2,5,1,1] => [1,1,5,2,2] => 1
[2,5,1,1,2] => [2,1,1,5,2] => 1
[2,5,1,2,1] => [1,2,1,5,2] => 2
[2,5,2,1,1] => [1,1,2,5,2] => 2
[5,1,1,2,2] => [2,2,1,1,5] => 1
[5,1,2,1,2] => [2,1,2,1,5] => 2
[5,1,2,2,1] => [1,2,2,1,5] => 2
[5,2,1,1,2] => [2,1,1,2,5] => 2
[5,2,1,2,1] => [1,2,1,2,5] => 3
[5,2,2,1,1] => [1,1,2,2,5] => 2
[1,1,2,3,3] => [3,3,2,1,1] => 0
[1,1,3,2,3] => [3,2,3,1,1] => 1
[1,1,3,3,2] => [2,3,3,1,1] => 1
[1,2,1,3,3] => [3,3,1,2,1] => 1
[1,2,3,1,3] => [3,1,3,2,1] => 1
[1,2,3,3,1] => [1,3,3,2,1] => 1
[1,3,1,2,3] => [3,2,1,3,1] => 1
[1,3,1,3,2] => [2,3,1,3,1] => 2
[1,3,2,1,3] => [3,1,2,3,1] => 2
[1,3,2,3,1] => [1,3,2,3,1] => 2
[1,3,3,1,2] => [2,1,3,3,1] => 1
[1,3,3,2,1] => [1,2,3,3,1] => 2
[2,1,1,3,3] => [3,3,1,1,2] => 1
[2,1,3,1,3] => [3,1,3,1,2] => 2
[2,1,3,3,1] => [1,3,3,1,2] => 2
[2,3,1,1,3] => [3,1,1,3,2] => 1
[2,3,1,3,1] => [1,3,1,3,2] => 2
[2,3,3,1,1] => [1,1,3,3,2] => 1
[3,1,1,2,3] => [3,2,1,1,3] => 1
[3,1,1,3,2] => [2,3,1,1,3] => 2
[3,1,2,1,3] => [3,1,2,1,3] => 2
[3,1,2,3,1] => [1,3,2,1,3] => 2
[3,1,3,1,2] => [2,1,3,1,3] => 2
[3,1,3,2,1] => [1,2,3,1,3] => 3
[3,2,1,1,3] => [3,1,1,2,3] => 2
[3,2,1,3,1] => [1,3,1,2,3] => 3
[3,2,3,1,1] => [1,1,3,2,3] => 2
[3,3,1,1,2] => [2,1,1,3,3] => 1
[3,3,1,2,1] => [1,2,1,3,3] => 2
[3,3,2,1,1] => [1,1,2,3,3] => 2
[1,1,2,3,4] => [4,3,2,1,1] => 0
[1,1,2,4,3] => [3,4,2,1,1] => 1
[1,1,3,2,4] => [4,2,3,1,1] => 1
[1,1,3,4,2] => [2,4,3,1,1] => 1
[1,1,4,2,3] => [3,2,4,1,1] => 1
[1,1,4,3,2] => [2,3,4,1,1] => 2
[1,2,1,3,4] => [4,3,1,2,1] => 1
[1,2,1,4,3] => [3,4,1,2,1] => 2
[1,2,3,1,4] => [4,1,3,2,1] => 1
[1,2,3,4,1] => [1,4,3,2,1] => 1
[1,2,4,1,3] => [3,1,4,2,1] => 1
[1,2,4,3,1] => [1,3,4,2,1] => 2
[1,3,1,2,4] => [4,2,1,3,1] => 1
[1,3,1,4,2] => [2,4,1,3,1] => 2
[1,3,2,1,4] => [4,1,2,3,1] => 2
[1,3,2,4,1] => [1,4,2,3,1] => 2
[1,3,4,1,2] => [2,1,4,3,1] => 1
[1,3,4,2,1] => [1,2,4,3,1] => 2
[1,4,1,2,3] => [3,2,1,4,1] => 1
[1,4,1,3,2] => [2,3,1,4,1] => 2
[1,4,2,1,3] => [3,1,2,4,1] => 2
[1,4,2,3,1] => [1,3,2,4,1] => 2
[1,4,3,1,2] => [2,1,3,4,1] => 2
[1,4,3,2,1] => [1,2,3,4,1] => 3
[2,1,1,3,4] => [4,3,1,1,2] => 1
[2,1,1,4,3] => [3,4,1,1,2] => 2
[2,1,3,1,4] => [4,1,3,1,2] => 2
[2,1,3,4,1] => [1,4,3,1,2] => 2
[2,1,4,1,3] => [3,1,4,1,2] => 2
[2,1,4,3,1] => [1,3,4,1,2] => 3
[2,3,1,1,4] => [4,1,1,3,2] => 1
[2,3,1,4,1] => [1,4,1,3,2] => 2
[2,3,4,1,1] => [1,1,4,3,2] => 1
[2,4,1,1,3] => [3,1,1,4,2] => 1
[2,4,1,3,1] => [1,3,1,4,2] => 2
[2,4,3,1,1] => [1,1,3,4,2] => 2
[3,1,1,2,4] => [4,2,1,1,3] => 1
[3,1,1,4,2] => [2,4,1,1,3] => 2
[3,1,2,1,4] => [4,1,2,1,3] => 2
[3,1,2,4,1] => [1,4,2,1,3] => 2
[3,1,4,1,2] => [2,1,4,1,3] => 2
[3,1,4,2,1] => [1,2,4,1,3] => 3
[3,2,1,1,4] => [4,1,1,2,3] => 2
[3,2,1,4,1] => [1,4,1,2,3] => 3
[3,2,4,1,1] => [1,1,4,2,3] => 2
[3,4,1,1,2] => [2,1,1,4,3] => 1
[3,4,1,2,1] => [1,2,1,4,3] => 2
[3,4,2,1,1] => [1,1,2,4,3] => 2
[4,1,1,2,3] => [3,2,1,1,4] => 1
[4,1,1,3,2] => [2,3,1,1,4] => 2
[4,1,2,1,3] => [3,1,2,1,4] => 2
[4,1,2,3,1] => [1,3,2,1,4] => 2
[4,1,3,1,2] => [2,1,3,1,4] => 2
[4,1,3,2,1] => [1,2,3,1,4] => 3
[4,2,1,1,3] => [3,1,1,2,4] => 2
[4,2,1,3,1] => [1,3,1,2,4] => 3
[4,2,3,1,1] => [1,1,3,2,4] => 2
[4,3,1,1,2] => [2,1,1,3,4] => 2
[4,3,1,2,1] => [1,2,1,3,4] => 3
[4,3,2,1,1] => [1,1,2,3,4] => 3
[1,1,2,3,5] => [5,3,2,1,1] => 0
[1,1,2,5,3] => [3,5,2,1,1] => 1
[1,1,3,2,5] => [5,2,3,1,1] => 1
[1,1,3,5,2] => [2,5,3,1,1] => 1
[1,1,5,2,3] => [3,2,5,1,1] => 1
[1,1,5,3,2] => [2,3,5,1,1] => 2
[1,2,1,3,5] => [5,3,1,2,1] => 1
[1,2,1,5,3] => [3,5,1,2,1] => 2
[1,2,3,1,5] => [5,1,3,2,1] => 1
[1,2,3,5,1] => [1,5,3,2,1] => 1
[1,2,5,1,3] => [3,1,5,2,1] => 1
[1,2,5,3,1] => [1,3,5,2,1] => 2
[1,3,1,2,5] => [5,2,1,3,1] => 1
[1,3,1,5,2] => [2,5,1,3,1] => 2
[1,3,2,1,5] => [5,1,2,3,1] => 2
[1,3,2,5,1] => [1,5,2,3,1] => 2
[1,3,5,1,2] => [2,1,5,3,1] => 1
[1,3,5,2,1] => [1,2,5,3,1] => 2
[1,5,1,2,3] => [3,2,1,5,1] => 1
[1,5,1,3,2] => [2,3,1,5,1] => 2
[1,5,2,1,3] => [3,1,2,5,1] => 2
[1,5,2,3,1] => [1,3,2,5,1] => 2
[1,5,3,1,2] => [2,1,3,5,1] => 2
[1,5,3,2,1] => [1,2,3,5,1] => 3
[2,1,1,3,5] => [5,3,1,1,2] => 1
[2,1,1,5,3] => [3,5,1,1,2] => 2
[2,1,3,1,5] => [5,1,3,1,2] => 2
[2,1,3,5,1] => [1,5,3,1,2] => 2
[2,1,5,1,3] => [3,1,5,1,2] => 2
[2,1,5,3,1] => [1,3,5,1,2] => 3
[2,3,1,1,5] => [5,1,1,3,2] => 1
[2,3,1,5,1] => [1,5,1,3,2] => 2
[2,3,5,1,1] => [1,1,5,3,2] => 1
[2,5,1,1,3] => [3,1,1,5,2] => 1
[2,5,1,3,1] => [1,3,1,5,2] => 2
[2,5,3,1,1] => [1,1,3,5,2] => 2
[3,1,1,2,5] => [5,2,1,1,3] => 1
[3,1,1,5,2] => [2,5,1,1,3] => 2
[3,1,2,1,5] => [5,1,2,1,3] => 2
[3,1,2,5,1] => [1,5,2,1,3] => 2
[3,1,5,1,2] => [2,1,5,1,3] => 2
[3,1,5,2,1] => [1,2,5,1,3] => 3
[3,2,1,1,5] => [5,1,1,2,3] => 2
[3,2,1,5,1] => [1,5,1,2,3] => 3
[3,2,5,1,1] => [1,1,5,2,3] => 2
[3,5,1,1,2] => [2,1,1,5,3] => 1
[3,5,1,2,1] => [1,2,1,5,3] => 2
[3,5,2,1,1] => [1,1,2,5,3] => 2
[5,1,1,2,3] => [3,2,1,1,5] => 1
[5,1,1,3,2] => [2,3,1,1,5] => 2
[5,1,2,1,3] => [3,1,2,1,5] => 2
[5,1,2,3,1] => [1,3,2,1,5] => 2
[5,1,3,1,2] => [2,1,3,1,5] => 2
[5,1,3,2,1] => [1,2,3,1,5] => 3
[5,2,1,1,3] => [3,1,1,2,5] => 2
[5,2,1,3,1] => [1,3,1,2,5] => 3
[5,2,3,1,1] => [1,1,3,2,5] => 2
[5,3,1,1,2] => [2,1,1,3,5] => 2
[5,3,1,2,1] => [1,2,1,3,5] => 3
[5,3,2,1,1] => [1,1,2,3,5] => 3
[1,1,2,4,4] => [4,4,2,1,1] => 0
[1,1,4,2,4] => [4,2,4,1,1] => 1
[1,1,4,4,2] => [2,4,4,1,1] => 1
[1,2,1,4,4] => [4,4,1,2,1] => 1
[1,2,4,1,4] => [4,1,4,2,1] => 1
[1,2,4,4,1] => [1,4,4,2,1] => 1
[1,4,1,2,4] => [4,2,1,4,1] => 1
[1,4,1,4,2] => [2,4,1,4,1] => 2
[1,4,2,1,4] => [4,1,2,4,1] => 2
[1,4,2,4,1] => [1,4,2,4,1] => 2
[1,4,4,1,2] => [2,1,4,4,1] => 1
[1,4,4,2,1] => [1,2,4,4,1] => 2
[2,1,1,4,4] => [4,4,1,1,2] => 1
[2,1,4,1,4] => [4,1,4,1,2] => 2
[2,1,4,4,1] => [1,4,4,1,2] => 2
[2,4,1,1,4] => [4,1,1,4,2] => 1
[2,4,1,4,1] => [1,4,1,4,2] => 2
[2,4,4,1,1] => [1,1,4,4,2] => 1
[4,1,1,2,4] => [4,2,1,1,4] => 1
[4,1,1,4,2] => [2,4,1,1,4] => 2
[4,1,2,1,4] => [4,1,2,1,4] => 2
[4,1,2,4,1] => [1,4,2,1,4] => 2
[4,1,4,1,2] => [2,1,4,1,4] => 2
[4,1,4,2,1] => [1,2,4,1,4] => 3
[4,2,1,1,4] => [4,1,1,2,4] => 2
[4,2,1,4,1] => [1,4,1,2,4] => 3
[4,2,4,1,1] => [1,1,4,2,4] => 2
[4,4,1,1,2] => [2,1,1,4,4] => 1
[4,4,1,2,1] => [1,2,1,4,4] => 2
[4,4,2,1,1] => [1,1,2,4,4] => 2
[1,1,2,4,5] => [5,4,2,1,1] => 0
[1,1,2,5,4] => [4,5,2,1,1] => 1
[1,1,4,2,5] => [5,2,4,1,1] => 1
[1,1,4,5,2] => [2,5,4,1,1] => 1
[1,1,5,2,4] => [4,2,5,1,1] => 1
[1,1,5,4,2] => [2,4,5,1,1] => 2
[1,2,1,4,5] => [5,4,1,2,1] => 1
[1,2,1,5,4] => [4,5,1,2,1] => 2
[1,2,4,1,5] => [5,1,4,2,1] => 1
[1,2,4,5,1] => [1,5,4,2,1] => 1
[1,2,5,1,4] => [4,1,5,2,1] => 1
[1,2,5,4,1] => [1,4,5,2,1] => 2
[1,4,1,2,5] => [5,2,1,4,1] => 1
[1,4,1,5,2] => [2,5,1,4,1] => 2
[1,4,2,1,5] => [5,1,2,4,1] => 2
[1,4,2,5,1] => [1,5,2,4,1] => 2
[1,4,5,1,2] => [2,1,5,4,1] => 1
[1,4,5,2,1] => [1,2,5,4,1] => 2
[1,5,1,2,4] => [4,2,1,5,1] => 1
[1,5,1,4,2] => [2,4,1,5,1] => 2
[1,5,2,1,4] => [4,1,2,5,1] => 2
[1,5,2,4,1] => [1,4,2,5,1] => 2
[1,5,4,1,2] => [2,1,4,5,1] => 2
[1,5,4,2,1] => [1,2,4,5,1] => 3
[2,1,1,4,5] => [5,4,1,1,2] => 1
[2,1,1,5,4] => [4,5,1,1,2] => 2
[2,1,4,1,5] => [5,1,4,1,2] => 2
[2,1,4,5,1] => [1,5,4,1,2] => 2
[2,1,5,1,4] => [4,1,5,1,2] => 2
[2,1,5,4,1] => [1,4,5,1,2] => 3
[2,4,1,1,5] => [5,1,1,4,2] => 1
[2,4,1,5,1] => [1,5,1,4,2] => 2
[2,4,5,1,1] => [1,1,5,4,2] => 1
[2,5,1,1,4] => [4,1,1,5,2] => 1
[2,5,1,4,1] => [1,4,1,5,2] => 2
[2,5,4,1,1] => [1,1,4,5,2] => 2
[4,1,1,2,5] => [5,2,1,1,4] => 1
[4,1,1,5,2] => [2,5,1,1,4] => 2
[4,1,2,1,5] => [5,1,2,1,4] => 2
[4,1,2,5,1] => [1,5,2,1,4] => 2
[4,1,5,1,2] => [2,1,5,1,4] => 2
[4,1,5,2,1] => [1,2,5,1,4] => 3
[4,2,1,1,5] => [5,1,1,2,4] => 2
[4,2,1,5,1] => [1,5,1,2,4] => 3
[4,2,5,1,1] => [1,1,5,2,4] => 2
[4,5,1,1,2] => [2,1,1,5,4] => 1
[4,5,1,2,1] => [1,2,1,5,4] => 2
[4,5,2,1,1] => [1,1,2,5,4] => 2
[5,1,1,2,4] => [4,2,1,1,5] => 1
[5,1,1,4,2] => [2,4,1,1,5] => 2
[5,1,2,1,4] => [4,1,2,1,5] => 2
[5,1,2,4,1] => [1,4,2,1,5] => 2
[5,1,4,1,2] => [2,1,4,1,5] => 2
[5,1,4,2,1] => [1,2,4,1,5] => 3
[5,2,1,1,4] => [4,1,1,2,5] => 2
[5,2,1,4,1] => [1,4,1,2,5] => 3
[5,2,4,1,1] => [1,1,4,2,5] => 2
[5,4,1,1,2] => [2,1,1,4,5] => 2
[5,4,1,2,1] => [1,2,1,4,5] => 3
[5,4,2,1,1] => [1,1,2,4,5] => 3
[1,1,3,3,3] => [3,3,3,1,1] => 0
[1,3,1,3,3] => [3,3,1,3,1] => 1
[1,3,3,1,3] => [3,1,3,3,1] => 1
[1,3,3,3,1] => [1,3,3,3,1] => 1
[3,1,1,3,3] => [3,3,1,1,3] => 1
[3,1,3,1,3] => [3,1,3,1,3] => 2
[3,1,3,3,1] => [1,3,3,1,3] => 2
[3,3,1,1,3] => [3,1,1,3,3] => 1
[3,3,1,3,1] => [1,3,1,3,3] => 2
[3,3,3,1,1] => [1,1,3,3,3] => 1
[1,1,3,3,4] => [4,3,3,1,1] => 0
[1,1,3,4,3] => [3,4,3,1,1] => 1
[1,1,4,3,3] => [3,3,4,1,1] => 1
[1,3,1,3,4] => [4,3,1,3,1] => 1
[1,3,1,4,3] => [3,4,1,3,1] => 2
[1,3,3,1,4] => [4,1,3,3,1] => 1
[1,3,3,4,1] => [1,4,3,3,1] => 1
[1,3,4,1,3] => [3,1,4,3,1] => 1
[1,3,4,3,1] => [1,3,4,3,1] => 2
[1,4,1,3,3] => [3,3,1,4,1] => 1
[1,4,3,1,3] => [3,1,3,4,1] => 2
[1,4,3,3,1] => [1,3,3,4,1] => 2
[3,1,1,3,4] => [4,3,1,1,3] => 1
[3,1,1,4,3] => [3,4,1,1,3] => 2
[3,1,3,1,4] => [4,1,3,1,3] => 2
[3,1,3,4,1] => [1,4,3,1,3] => 2
[3,1,4,1,3] => [3,1,4,1,3] => 2
[3,1,4,3,1] => [1,3,4,1,3] => 3
[3,3,1,1,4] => [4,1,1,3,3] => 1
[3,3,1,4,1] => [1,4,1,3,3] => 2
[3,3,4,1,1] => [1,1,4,3,3] => 1
[3,4,1,1,3] => [3,1,1,4,3] => 1
[3,4,1,3,1] => [1,3,1,4,3] => 2
[3,4,3,1,1] => [1,1,3,4,3] => 2
[4,1,1,3,3] => [3,3,1,1,4] => 1
[4,1,3,1,3] => [3,1,3,1,4] => 2
[4,1,3,3,1] => [1,3,3,1,4] => 2
[4,3,1,1,3] => [3,1,1,3,4] => 2
[4,3,1,3,1] => [1,3,1,3,4] => 3
[4,3,3,1,1] => [1,1,3,3,4] => 2
[1,1,3,3,5] => [5,3,3,1,1] => 0
[1,1,3,5,3] => [3,5,3,1,1] => 1
[1,1,5,3,3] => [3,3,5,1,1] => 1
[1,3,1,3,5] => [5,3,1,3,1] => 1
[1,3,1,5,3] => [3,5,1,3,1] => 2
[1,3,3,1,5] => [5,1,3,3,1] => 1
[1,3,3,5,1] => [1,5,3,3,1] => 1
[1,3,5,1,3] => [3,1,5,3,1] => 1
[1,3,5,3,1] => [1,3,5,3,1] => 2
[1,5,1,3,3] => [3,3,1,5,1] => 1
[1,5,3,1,3] => [3,1,3,5,1] => 2
[1,5,3,3,1] => [1,3,3,5,1] => 2
[3,1,1,3,5] => [5,3,1,1,3] => 1
[3,1,1,5,3] => [3,5,1,1,3] => 2
[3,1,3,1,5] => [5,1,3,1,3] => 2
[3,1,3,5,1] => [1,5,3,1,3] => 2
[3,1,5,1,3] => [3,1,5,1,3] => 2
[3,1,5,3,1] => [1,3,5,1,3] => 3
[3,3,1,1,5] => [5,1,1,3,3] => 1
[3,3,1,5,1] => [1,5,1,3,3] => 2
[3,3,5,1,1] => [1,1,5,3,3] => 1
[3,5,1,1,3] => [3,1,1,5,3] => 1
[3,5,1,3,1] => [1,3,1,5,3] => 2
[3,5,3,1,1] => [1,1,3,5,3] => 2
[5,1,1,3,3] => [3,3,1,1,5] => 1
[5,1,3,1,3] => [3,1,3,1,5] => 2
[5,1,3,3,1] => [1,3,3,1,5] => 2
[5,3,1,1,3] => [3,1,1,3,5] => 2
[5,3,1,3,1] => [1,3,1,3,5] => 3
[5,3,3,1,1] => [1,1,3,3,5] => 2
[1,1,3,4,4] => [4,4,3,1,1] => 0
[1,1,4,3,4] => [4,3,4,1,1] => 1
[1,1,4,4,3] => [3,4,4,1,1] => 1
[1,3,1,4,4] => [4,4,1,3,1] => 1
[1,3,4,1,4] => [4,1,4,3,1] => 1
[1,3,4,4,1] => [1,4,4,3,1] => 1
[1,4,1,3,4] => [4,3,1,4,1] => 1
[1,4,1,4,3] => [3,4,1,4,1] => 2
[1,4,3,1,4] => [4,1,3,4,1] => 2
[1,4,3,4,1] => [1,4,3,4,1] => 2
[1,4,4,1,3] => [3,1,4,4,1] => 1
[1,4,4,3,1] => [1,3,4,4,1] => 2
[3,1,1,4,4] => [4,4,1,1,3] => 1
[3,1,4,1,4] => [4,1,4,1,3] => 2
[3,1,4,4,1] => [1,4,4,1,3] => 2
[3,4,1,1,4] => [4,1,1,4,3] => 1
[3,4,1,4,1] => [1,4,1,4,3] => 2
[3,4,4,1,1] => [1,1,4,4,3] => 1
[4,1,1,3,4] => [4,3,1,1,4] => 1
[4,1,1,4,3] => [3,4,1,1,4] => 2
[4,1,3,1,4] => [4,1,3,1,4] => 2
[4,1,3,4,1] => [1,4,3,1,4] => 2
[4,1,4,1,3] => [3,1,4,1,4] => 2
[4,1,4,3,1] => [1,3,4,1,4] => 3
[4,3,1,1,4] => [4,1,1,3,4] => 2
[4,3,1,4,1] => [1,4,1,3,4] => 3
[4,3,4,1,1] => [1,1,4,3,4] => 2
[4,4,1,1,3] => [3,1,1,4,4] => 1
[4,4,1,3,1] => [1,3,1,4,4] => 2
[4,4,3,1,1] => [1,1,3,4,4] => 2
[1,1,3,4,5] => [5,4,3,1,1] => 0
[1,1,3,5,4] => [4,5,3,1,1] => 1
[1,1,4,3,5] => [5,3,4,1,1] => 1
[1,1,4,5,3] => [3,5,4,1,1] => 1
[1,1,5,3,4] => [4,3,5,1,1] => 1
[1,1,5,4,3] => [3,4,5,1,1] => 2
[1,3,1,4,5] => [5,4,1,3,1] => 1
[1,3,1,5,4] => [4,5,1,3,1] => 2
[1,3,4,1,5] => [5,1,4,3,1] => 1
[1,3,4,5,1] => [1,5,4,3,1] => 1
[1,3,5,1,4] => [4,1,5,3,1] => 1
[1,3,5,4,1] => [1,4,5,3,1] => 2
[1,4,1,3,5] => [5,3,1,4,1] => 1
[1,4,1,5,3] => [3,5,1,4,1] => 2
[1,4,3,1,5] => [5,1,3,4,1] => 2
[1,4,3,5,1] => [1,5,3,4,1] => 2
[1,4,5,1,3] => [3,1,5,4,1] => 1
[1,4,5,3,1] => [1,3,5,4,1] => 2
[1,5,1,3,4] => [4,3,1,5,1] => 1
[1,5,1,4,3] => [3,4,1,5,1] => 2
[1,5,3,1,4] => [4,1,3,5,1] => 2
[1,5,3,4,1] => [1,4,3,5,1] => 2
[1,5,4,1,3] => [3,1,4,5,1] => 2
[1,5,4,3,1] => [1,3,4,5,1] => 3
[3,1,1,4,5] => [5,4,1,1,3] => 1
[3,1,1,5,4] => [4,5,1,1,3] => 2
[3,1,4,1,5] => [5,1,4,1,3] => 2
[3,1,4,5,1] => [1,5,4,1,3] => 2
[3,1,5,1,4] => [4,1,5,1,3] => 2
[3,1,5,4,1] => [1,4,5,1,3] => 3
[3,4,1,1,5] => [5,1,1,4,3] => 1
[3,4,1,5,1] => [1,5,1,4,3] => 2
[3,4,5,1,1] => [1,1,5,4,3] => 1
[3,5,1,1,4] => [4,1,1,5,3] => 1
[3,5,1,4,1] => [1,4,1,5,3] => 2
[3,5,4,1,1] => [1,1,4,5,3] => 2
[4,1,1,3,5] => [5,3,1,1,4] => 1
[4,1,1,5,3] => [3,5,1,1,4] => 2
[4,1,3,1,5] => [5,1,3,1,4] => 2
[4,1,3,5,1] => [1,5,3,1,4] => 2
[4,1,5,1,3] => [3,1,5,1,4] => 2
[4,1,5,3,1] => [1,3,5,1,4] => 3
[4,3,1,1,5] => [5,1,1,3,4] => 2
[4,3,1,5,1] => [1,5,1,3,4] => 3
[4,3,5,1,1] => [1,1,5,3,4] => 2
[4,5,1,1,3] => [3,1,1,5,4] => 1
[4,5,1,3,1] => [1,3,1,5,4] => 2
[4,5,3,1,1] => [1,1,3,5,4] => 2
[5,1,1,3,4] => [4,3,1,1,5] => 1
[5,1,1,4,3] => [3,4,1,1,5] => 2
[5,1,3,1,4] => [4,1,3,1,5] => 2
[5,1,3,4,1] => [1,4,3,1,5] => 2
[5,1,4,1,3] => [3,1,4,1,5] => 2
[5,1,4,3,1] => [1,3,4,1,5] => 3
[5,3,1,1,4] => [4,1,1,3,5] => 2
[5,3,1,4,1] => [1,4,1,3,5] => 3
[5,3,4,1,1] => [1,1,4,3,5] => 2
[5,4,1,1,3] => [3,1,1,4,5] => 2
[5,4,1,3,1] => [1,3,1,4,5] => 3
[5,4,3,1,1] => [1,1,3,4,5] => 3
[1,2,2,2,2] => [2,2,2,2,1] => 0
[2,1,2,2,2] => [2,2,2,1,2] => 1
[2,2,1,2,2] => [2,2,1,2,2] => 1
[2,2,2,1,2] => [2,1,2,2,2] => 1
[2,2,2,2,1] => [1,2,2,2,2] => 1
[1,2,2,2,3] => [3,2,2,2,1] => 0
[1,2,2,3,2] => [2,3,2,2,1] => 1
[1,2,3,2,2] => [2,2,3,2,1] => 1
[1,3,2,2,2] => [2,2,2,3,1] => 1
[2,1,2,2,3] => [3,2,2,1,2] => 1
[2,1,2,3,2] => [2,3,2,1,2] => 2
[2,1,3,2,2] => [2,2,3,1,2] => 2
[2,2,1,2,3] => [3,2,1,2,2] => 1
[2,2,1,3,2] => [2,3,1,2,2] => 2
[2,2,2,1,3] => [3,1,2,2,2] => 1
[2,2,2,3,1] => [1,3,2,2,2] => 1
[2,2,3,1,2] => [2,1,3,2,2] => 1
[2,2,3,2,1] => [1,2,3,2,2] => 2
[2,3,1,2,2] => [2,2,1,3,2] => 1
[2,3,2,1,2] => [2,1,2,3,2] => 2
[2,3,2,2,1] => [1,2,2,3,2] => 2
[3,1,2,2,2] => [2,2,2,1,3] => 1
[3,2,1,2,2] => [2,2,1,2,3] => 2
[3,2,2,1,2] => [2,1,2,2,3] => 2
[3,2,2,2,1] => [1,2,2,2,3] => 2
[1,2,2,2,4] => [4,2,2,2,1] => 0
[1,2,2,4,2] => [2,4,2,2,1] => 1
[1,2,4,2,2] => [2,2,4,2,1] => 1
[1,4,2,2,2] => [2,2,2,4,1] => 1
[2,1,2,2,4] => [4,2,2,1,2] => 1
[2,1,2,4,2] => [2,4,2,1,2] => 2
[2,1,4,2,2] => [2,2,4,1,2] => 2
[2,2,1,2,4] => [4,2,1,2,2] => 1
[2,2,1,4,2] => [2,4,1,2,2] => 2
[2,2,2,1,4] => [4,1,2,2,2] => 1
[2,2,2,4,1] => [1,4,2,2,2] => 1
[2,2,4,1,2] => [2,1,4,2,2] => 1
[2,2,4,2,1] => [1,2,4,2,2] => 2
[2,4,1,2,2] => [2,2,1,4,2] => 1
[2,4,2,1,2] => [2,1,2,4,2] => 2
[2,4,2,2,1] => [1,2,2,4,2] => 2
[4,1,2,2,2] => [2,2,2,1,4] => 1
[4,2,1,2,2] => [2,2,1,2,4] => 2
[4,2,2,1,2] => [2,1,2,2,4] => 2
[4,2,2,2,1] => [1,2,2,2,4] => 2
[1,2,2,2,5] => [5,2,2,2,1] => 0
[1,2,2,5,2] => [2,5,2,2,1] => 1
[1,2,5,2,2] => [2,2,5,2,1] => 1
[1,5,2,2,2] => [2,2,2,5,1] => 1
[2,1,2,2,5] => [5,2,2,1,2] => 1
[2,1,2,5,2] => [2,5,2,1,2] => 2
[2,1,5,2,2] => [2,2,5,1,2] => 2
[2,2,1,2,5] => [5,2,1,2,2] => 1
[2,2,1,5,2] => [2,5,1,2,2] => 2
[2,2,2,1,5] => [5,1,2,2,2] => 1
[2,2,2,5,1] => [1,5,2,2,2] => 1
[2,2,5,1,2] => [2,1,5,2,2] => 1
[2,2,5,2,1] => [1,2,5,2,2] => 2
[2,5,1,2,2] => [2,2,1,5,2] => 1
[2,5,2,1,2] => [2,1,2,5,2] => 2
[2,5,2,2,1] => [1,2,2,5,2] => 2
[5,1,2,2,2] => [2,2,2,1,5] => 1
[5,2,1,2,2] => [2,2,1,2,5] => 2
[5,2,2,1,2] => [2,1,2,2,5] => 2
[5,2,2,2,1] => [1,2,2,2,5] => 2
[1,2,2,3,3] => [3,3,2,2,1] => 0
[1,2,3,2,3] => [3,2,3,2,1] => 1
[1,2,3,3,2] => [2,3,3,2,1] => 1
[1,3,2,2,3] => [3,2,2,3,1] => 1
[1,3,2,3,2] => [2,3,2,3,1] => 2
[1,3,3,2,2] => [2,2,3,3,1] => 1
[2,1,2,3,3] => [3,3,2,1,2] => 1
[2,1,3,2,3] => [3,2,3,1,2] => 2
[2,1,3,3,2] => [2,3,3,1,2] => 2
[2,2,1,3,3] => [3,3,1,2,2] => 1
[2,2,3,1,3] => [3,1,3,2,2] => 1
[2,2,3,3,1] => [1,3,3,2,2] => 1
[2,3,1,2,3] => [3,2,1,3,2] => 1
[2,3,1,3,2] => [2,3,1,3,2] => 2
[2,3,2,1,3] => [3,1,2,3,2] => 2
[2,3,2,3,1] => [1,3,2,3,2] => 2
[2,3,3,1,2] => [2,1,3,3,2] => 1
[2,3,3,2,1] => [1,2,3,3,2] => 2
[3,1,2,2,3] => [3,2,2,1,3] => 1
[3,1,2,3,2] => [2,3,2,1,3] => 2
[3,1,3,2,2] => [2,2,3,1,3] => 2
[3,2,1,2,3] => [3,2,1,2,3] => 2
[3,2,1,3,2] => [2,3,1,2,3] => 3
[3,2,2,1,3] => [3,1,2,2,3] => 2
[3,2,2,3,1] => [1,3,2,2,3] => 2
[3,2,3,1,2] => [2,1,3,2,3] => 2
[3,2,3,2,1] => [1,2,3,2,3] => 3
[3,3,1,2,2] => [2,2,1,3,3] => 1
[3,3,2,1,2] => [2,1,2,3,3] => 2
[3,3,2,2,1] => [1,2,2,3,3] => 2
[1,2,2,3,4] => [4,3,2,2,1] => 0
[1,2,2,4,3] => [3,4,2,2,1] => 1
[1,2,3,2,4] => [4,2,3,2,1] => 1
[1,2,3,4,2] => [2,4,3,2,1] => 1
[1,2,4,2,3] => [3,2,4,2,1] => 1
[1,2,4,3,2] => [2,3,4,2,1] => 2
[1,3,2,2,4] => [4,2,2,3,1] => 1
[1,3,2,4,2] => [2,4,2,3,1] => 2
[1,3,4,2,2] => [2,2,4,3,1] => 1
[1,4,2,2,3] => [3,2,2,4,1] => 1
[1,4,2,3,2] => [2,3,2,4,1] => 2
[1,4,3,2,2] => [2,2,3,4,1] => 2
[2,1,2,3,4] => [4,3,2,1,2] => 1
[2,1,2,4,3] => [3,4,2,1,2] => 2
[2,1,3,2,4] => [4,2,3,1,2] => 2
[2,1,3,4,2] => [2,4,3,1,2] => 2
[2,1,4,2,3] => [3,2,4,1,2] => 2
[2,1,4,3,2] => [2,3,4,1,2] => 3
[2,2,1,3,4] => [4,3,1,2,2] => 1
[2,2,1,4,3] => [3,4,1,2,2] => 2
[2,2,3,1,4] => [4,1,3,2,2] => 1
[2,2,3,4,1] => [1,4,3,2,2] => 1
[2,2,4,1,3] => [3,1,4,2,2] => 1
[2,2,4,3,1] => [1,3,4,2,2] => 2
[2,3,1,2,4] => [4,2,1,3,2] => 1
[2,3,1,4,2] => [2,4,1,3,2] => 2
[2,3,2,1,4] => [4,1,2,3,2] => 2
[2,3,2,4,1] => [1,4,2,3,2] => 2
[2,3,4,1,2] => [2,1,4,3,2] => 1
[2,3,4,2,1] => [1,2,4,3,2] => 2
[2,4,1,2,3] => [3,2,1,4,2] => 1
[2,4,1,3,2] => [2,3,1,4,2] => 2
[2,4,2,1,3] => [3,1,2,4,2] => 2
[2,4,2,3,1] => [1,3,2,4,2] => 2
[2,4,3,1,2] => [2,1,3,4,2] => 2
[2,4,3,2,1] => [1,2,3,4,2] => 3
[3,1,2,2,4] => [4,2,2,1,3] => 1
[3,1,2,4,2] => [2,4,2,1,3] => 2
[3,1,4,2,2] => [2,2,4,1,3] => 2
[3,2,1,2,4] => [4,2,1,2,3] => 2
[3,2,1,4,2] => [2,4,1,2,3] => 3
[3,2,2,1,4] => [4,1,2,2,3] => 2
[3,2,2,4,1] => [1,4,2,2,3] => 2
[3,2,4,1,2] => [2,1,4,2,3] => 2
[3,2,4,2,1] => [1,2,4,2,3] => 3
[3,4,1,2,2] => [2,2,1,4,3] => 1
[3,4,2,1,2] => [2,1,2,4,3] => 2
[3,4,2,2,1] => [1,2,2,4,3] => 2
[4,1,2,2,3] => [3,2,2,1,4] => 1
[4,1,2,3,2] => [2,3,2,1,4] => 2
[4,1,3,2,2] => [2,2,3,1,4] => 2
[4,2,1,2,3] => [3,2,1,2,4] => 2
[4,2,1,3,2] => [2,3,1,2,4] => 3
[4,2,2,1,3] => [3,1,2,2,4] => 2
[4,2,2,3,1] => [1,3,2,2,4] => 2
[4,2,3,1,2] => [2,1,3,2,4] => 2
[4,2,3,2,1] => [1,2,3,2,4] => 3
[4,3,1,2,2] => [2,2,1,3,4] => 2
[4,3,2,1,2] => [2,1,2,3,4] => 3
[4,3,2,2,1] => [1,2,2,3,4] => 3
[1,2,2,3,5] => [5,3,2,2,1] => 0
[1,2,2,5,3] => [3,5,2,2,1] => 1
[1,2,3,2,5] => [5,2,3,2,1] => 1
[1,2,3,5,2] => [2,5,3,2,1] => 1
[1,2,5,2,3] => [3,2,5,2,1] => 1
[1,2,5,3,2] => [2,3,5,2,1] => 2
[1,3,2,2,5] => [5,2,2,3,1] => 1
[1,3,2,5,2] => [2,5,2,3,1] => 2
[1,3,5,2,2] => [2,2,5,3,1] => 1
[1,5,2,2,3] => [3,2,2,5,1] => 1
[1,5,2,3,2] => [2,3,2,5,1] => 2
[1,5,3,2,2] => [2,2,3,5,1] => 2
[2,1,2,3,5] => [5,3,2,1,2] => 1
[2,1,2,5,3] => [3,5,2,1,2] => 2
[2,1,3,2,5] => [5,2,3,1,2] => 2
[2,1,3,5,2] => [2,5,3,1,2] => 2
[2,1,5,2,3] => [3,2,5,1,2] => 2
[2,1,5,3,2] => [2,3,5,1,2] => 3
[2,2,1,3,5] => [5,3,1,2,2] => 1
[2,2,1,5,3] => [3,5,1,2,2] => 2
[2,2,3,1,5] => [5,1,3,2,2] => 1
[2,2,3,5,1] => [1,5,3,2,2] => 1
[2,2,5,1,3] => [3,1,5,2,2] => 1
[2,2,5,3,1] => [1,3,5,2,2] => 2
[2,3,1,2,5] => [5,2,1,3,2] => 1
[2,3,1,5,2] => [2,5,1,3,2] => 2
[2,3,2,1,5] => [5,1,2,3,2] => 2
[2,3,2,5,1] => [1,5,2,3,2] => 2
[2,3,5,1,2] => [2,1,5,3,2] => 1
[2,3,5,2,1] => [1,2,5,3,2] => 2
[2,5,1,2,3] => [3,2,1,5,2] => 1
[2,5,1,3,2] => [2,3,1,5,2] => 2
[2,5,2,1,3] => [3,1,2,5,2] => 2
[2,5,2,3,1] => [1,3,2,5,2] => 2
[2,5,3,1,2] => [2,1,3,5,2] => 2
[2,5,3,2,1] => [1,2,3,5,2] => 3
[3,1,2,2,5] => [5,2,2,1,3] => 1
[3,1,2,5,2] => [2,5,2,1,3] => 2
[3,1,5,2,2] => [2,2,5,1,3] => 2
[3,2,1,2,5] => [5,2,1,2,3] => 2
[3,2,1,5,2] => [2,5,1,2,3] => 3
[3,2,2,1,5] => [5,1,2,2,3] => 2
[3,2,2,5,1] => [1,5,2,2,3] => 2
[3,2,5,1,2] => [2,1,5,2,3] => 2
[3,2,5,2,1] => [1,2,5,2,3] => 3
[3,5,1,2,2] => [2,2,1,5,3] => 1
[3,5,2,1,2] => [2,1,2,5,3] => 2
[3,5,2,2,1] => [1,2,2,5,3] => 2
[5,1,2,2,3] => [3,2,2,1,5] => 1
[5,1,2,3,2] => [2,3,2,1,5] => 2
[5,1,3,2,2] => [2,2,3,1,5] => 2
[5,2,1,2,3] => [3,2,1,2,5] => 2
[5,2,1,3,2] => [2,3,1,2,5] => 3
[5,2,2,1,3] => [3,1,2,2,5] => 2
[5,2,2,3,1] => [1,3,2,2,5] => 2
[5,2,3,1,2] => [2,1,3,2,5] => 2
[5,2,3,2,1] => [1,2,3,2,5] => 3
[5,3,1,2,2] => [2,2,1,3,5] => 2
[5,3,2,1,2] => [2,1,2,3,5] => 3
[5,3,2,2,1] => [1,2,2,3,5] => 3
[1,2,2,4,4] => [4,4,2,2,1] => 0
[1,2,4,2,4] => [4,2,4,2,1] => 1
[1,2,4,4,2] => [2,4,4,2,1] => 1
[1,4,2,2,4] => [4,2,2,4,1] => 1
[1,4,2,4,2] => [2,4,2,4,1] => 2
[1,4,4,2,2] => [2,2,4,4,1] => 1
[2,1,2,4,4] => [4,4,2,1,2] => 1
[2,1,4,2,4] => [4,2,4,1,2] => 2
[2,1,4,4,2] => [2,4,4,1,2] => 2
[2,2,1,4,4] => [4,4,1,2,2] => 1
[2,2,4,1,4] => [4,1,4,2,2] => 1
[2,2,4,4,1] => [1,4,4,2,2] => 1
[2,4,1,2,4] => [4,2,1,4,2] => 1
[2,4,1,4,2] => [2,4,1,4,2] => 2
[2,4,2,1,4] => [4,1,2,4,2] => 2
[2,4,2,4,1] => [1,4,2,4,2] => 2
[2,4,4,1,2] => [2,1,4,4,2] => 1
[2,4,4,2,1] => [1,2,4,4,2] => 2
[4,1,2,2,4] => [4,2,2,1,4] => 1
[4,1,2,4,2] => [2,4,2,1,4] => 2
[4,1,4,2,2] => [2,2,4,1,4] => 2
[4,2,1,2,4] => [4,2,1,2,4] => 2
[4,2,1,4,2] => [2,4,1,2,4] => 3
[4,2,2,1,4] => [4,1,2,2,4] => 2
[4,2,2,4,1] => [1,4,2,2,4] => 2
[4,2,4,1,2] => [2,1,4,2,4] => 2
[4,2,4,2,1] => [1,2,4,2,4] => 3
[4,4,1,2,2] => [2,2,1,4,4] => 1
[4,4,2,1,2] => [2,1,2,4,4] => 2
[4,4,2,2,1] => [1,2,2,4,4] => 2
[1,2,2,4,5] => [5,4,2,2,1] => 0
[1,2,2,5,4] => [4,5,2,2,1] => 1
[1,2,4,2,5] => [5,2,4,2,1] => 1
[1,2,4,5,2] => [2,5,4,2,1] => 1
[1,2,5,2,4] => [4,2,5,2,1] => 1
[1,2,5,4,2] => [2,4,5,2,1] => 2
[1,4,2,2,5] => [5,2,2,4,1] => 1
[1,4,2,5,2] => [2,5,2,4,1] => 2
[1,4,5,2,2] => [2,2,5,4,1] => 1
[1,5,2,2,4] => [4,2,2,5,1] => 1
[1,5,2,4,2] => [2,4,2,5,1] => 2
[1,5,4,2,2] => [2,2,4,5,1] => 2
[2,1,2,4,5] => [5,4,2,1,2] => 1
[2,1,2,5,4] => [4,5,2,1,2] => 2
[2,1,4,2,5] => [5,2,4,1,2] => 2
[2,1,4,5,2] => [2,5,4,1,2] => 2
[2,1,5,2,4] => [4,2,5,1,2] => 2
[2,1,5,4,2] => [2,4,5,1,2] => 3
[2,2,1,4,5] => [5,4,1,2,2] => 1
[2,2,1,5,4] => [4,5,1,2,2] => 2
[2,2,4,1,5] => [5,1,4,2,2] => 1
[2,2,4,5,1] => [1,5,4,2,2] => 1
[2,2,5,1,4] => [4,1,5,2,2] => 1
[2,2,5,4,1] => [1,4,5,2,2] => 2
[2,4,1,2,5] => [5,2,1,4,2] => 1
[2,4,1,5,2] => [2,5,1,4,2] => 2
[2,4,2,1,5] => [5,1,2,4,2] => 2
[2,4,2,5,1] => [1,5,2,4,2] => 2
[2,4,5,1,2] => [2,1,5,4,2] => 1
[2,4,5,2,1] => [1,2,5,4,2] => 2
[2,5,1,2,4] => [4,2,1,5,2] => 1
[2,5,1,4,2] => [2,4,1,5,2] => 2
[2,5,2,1,4] => [4,1,2,5,2] => 2
[2,5,2,4,1] => [1,4,2,5,2] => 2
[2,5,4,1,2] => [2,1,4,5,2] => 2
[2,5,4,2,1] => [1,2,4,5,2] => 3
[4,1,2,2,5] => [5,2,2,1,4] => 1
[4,1,2,5,2] => [2,5,2,1,4] => 2
[4,1,5,2,2] => [2,2,5,1,4] => 2
[4,2,1,2,5] => [5,2,1,2,4] => 2
[4,2,1,5,2] => [2,5,1,2,4] => 3
[4,2,2,1,5] => [5,1,2,2,4] => 2
[4,2,2,5,1] => [1,5,2,2,4] => 2
[4,2,5,1,2] => [2,1,5,2,4] => 2
[4,2,5,2,1] => [1,2,5,2,4] => 3
[4,5,1,2,2] => [2,2,1,5,4] => 1
[4,5,2,1,2] => [2,1,2,5,4] => 2
[4,5,2,2,1] => [1,2,2,5,4] => 2
[5,1,2,2,4] => [4,2,2,1,5] => 1
[5,1,2,4,2] => [2,4,2,1,5] => 2
[5,1,4,2,2] => [2,2,4,1,5] => 2
[5,2,1,2,4] => [4,2,1,2,5] => 2
[5,2,1,4,2] => [2,4,1,2,5] => 3
[5,2,2,1,4] => [4,1,2,2,5] => 2
[5,2,2,4,1] => [1,4,2,2,5] => 2
[5,2,4,1,2] => [2,1,4,2,5] => 2
[5,2,4,2,1] => [1,2,4,2,5] => 3
[5,4,1,2,2] => [2,2,1,4,5] => 2
[5,4,2,1,2] => [2,1,2,4,5] => 3
[5,4,2,2,1] => [1,2,2,4,5] => 3
[1,2,3,3,3] => [3,3,3,2,1] => 0
[1,3,2,3,3] => [3,3,2,3,1] => 1
[1,3,3,2,3] => [3,2,3,3,1] => 1
[1,3,3,3,2] => [2,3,3,3,1] => 1
[2,1,3,3,3] => [3,3,3,1,2] => 1
[2,3,1,3,3] => [3,3,1,3,2] => 1
[2,3,3,1,3] => [3,1,3,3,2] => 1
[2,3,3,3,1] => [1,3,3,3,2] => 1
[3,1,2,3,3] => [3,3,2,1,3] => 1
[3,1,3,2,3] => [3,2,3,1,3] => 2
[3,1,3,3,2] => [2,3,3,1,3] => 2
[3,2,1,3,3] => [3,3,1,2,3] => 2
[3,2,3,1,3] => [3,1,3,2,3] => 2
[3,2,3,3,1] => [1,3,3,2,3] => 2
[3,3,1,2,3] => [3,2,1,3,3] => 1
[3,3,1,3,2] => [2,3,1,3,3] => 2
[3,3,2,1,3] => [3,1,2,3,3] => 2
[3,3,2,3,1] => [1,3,2,3,3] => 2
[3,3,3,1,2] => [2,1,3,3,3] => 1
[3,3,3,2,1] => [1,2,3,3,3] => 2
[1,2,3,4,3] => [3,4,3,2,1] => 1
[1,2,4,3,3] => [3,3,4,2,1] => 1
[1,3,2,3,4] => [4,3,2,3,1] => 1
[1,3,2,4,3] => [3,4,2,3,1] => 2
[1,3,3,2,4] => [4,2,3,3,1] => 1
[1,3,3,4,2] => [2,4,3,3,1] => 1
[1,3,4,2,3] => [3,2,4,3,1] => 1
[1,3,4,3,2] => [2,3,4,3,1] => 2
[1,4,2,3,3] => [3,3,2,4,1] => 1
[1,4,3,2,3] => [3,2,3,4,1] => 2
[1,4,3,3,2] => [2,3,3,4,1] => 2
[2,1,3,3,4] => [4,3,3,1,2] => 1
[2,1,3,4,3] => [3,4,3,1,2] => 2
[2,1,4,3,3] => [3,3,4,1,2] => 2
[2,3,1,3,4] => [4,3,1,3,2] => 1
[2,3,1,4,3] => [3,4,1,3,2] => 2
[2,3,3,1,4] => [4,1,3,3,2] => 1
[2,3,3,4,1] => [1,4,3,3,2] => 1
[2,3,4,1,3] => [3,1,4,3,2] => 1
[2,3,4,3,1] => [1,3,4,3,2] => 2
[2,4,1,3,3] => [3,3,1,4,2] => 1
[2,4,3,1,3] => [3,1,3,4,2] => 2
[2,4,3,3,1] => [1,3,3,4,2] => 2
[3,1,2,3,4] => [4,3,2,1,3] => 1
[3,1,2,4,3] => [3,4,2,1,3] => 2
[3,1,3,2,4] => [4,2,3,1,3] => 2
[3,1,3,4,2] => [2,4,3,1,3] => 2
[3,1,4,2,3] => [3,2,4,1,3] => 2
[3,1,4,3,2] => [2,3,4,1,3] => 3
[3,2,1,3,4] => [4,3,1,2,3] => 2
[3,2,1,4,3] => [3,4,1,2,3] => 3
[3,2,3,1,4] => [4,1,3,2,3] => 2
[3,2,3,4,1] => [1,4,3,2,3] => 2
[3,2,4,1,3] => [3,1,4,2,3] => 2
[3,2,4,3,1] => [1,3,4,2,3] => 3
[3,3,1,2,4] => [4,2,1,3,3] => 1
[3,3,1,4,2] => [2,4,1,3,3] => 2
[3,3,2,1,4] => [4,1,2,3,3] => 2
[3,3,2,4,1] => [1,4,2,3,3] => 2
[3,3,4,1,2] => [2,1,4,3,3] => 1
[3,3,4,2,1] => [1,2,4,3,3] => 2
[3,4,1,2,3] => [3,2,1,4,3] => 1
[3,4,1,3,2] => [2,3,1,4,3] => 2
[3,4,2,1,3] => [3,1,2,4,3] => 2
[3,4,2,3,1] => [1,3,2,4,3] => 2
[3,4,3,1,2] => [2,1,3,4,3] => 2
[3,4,3,2,1] => [1,2,3,4,3] => 3
[4,1,2,3,3] => [3,3,2,1,4] => 1
[4,1,3,2,3] => [3,2,3,1,4] => 2
[4,1,3,3,2] => [2,3,3,1,4] => 2
[4,2,1,3,3] => [3,3,1,2,4] => 2
[4,2,3,1,3] => [3,1,3,2,4] => 2
[4,2,3,3,1] => [1,3,3,2,4] => 2
[4,3,1,2,3] => [3,2,1,3,4] => 2
[4,3,1,3,2] => [2,3,1,3,4] => 3
[4,3,2,1,3] => [3,1,2,3,4] => 3
[4,3,2,3,1] => [1,3,2,3,4] => 3
[4,3,3,1,2] => [2,1,3,3,4] => 2
[4,3,3,2,1] => [1,2,3,3,4] => 3
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 5,10,1 14,73,37,1
$F_{1} = 1$
$F_{2} = 2 + q$
$F_{3} = 5 + 10\ q + q^{2}$
$F_{4} = 14 + 73\ q + 37\ q^{2} + q^{3}$
Description
The number of ascents in a parking function.
This is the number of indices $i$ such that $p_i > p_{i+1}$.
This is the number of indices $i$ such that $p_i > p_{i+1}$.
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reverse
Description
Return the reversal of a parking function.
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