Identifier
-
Mp00319:
Parking functions
—to composition⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000548: Integer partitions ⟶ ℤ
Values
[1] => [1] => [1] => 1
[1,1] => [1,1] => [1,1] => 2
[1,2] => [1,2] => [2,1] => 3
[2,1] => [2,1] => [2,1] => 3
[1,1,1] => [1,1,1] => [1,1,1] => 3
[1,1,2] => [1,1,2] => [2,1,1] => 4
[1,2,1] => [1,2,1] => [2,1,1] => 4
[2,1,1] => [2,1,1] => [2,1,1] => 4
[1,1,3] => [1,1,3] => [3,1,1] => 5
[1,3,1] => [1,3,1] => [3,1,1] => 5
[3,1,1] => [3,1,1] => [3,1,1] => 5
[1,2,2] => [1,2,2] => [2,2,1] => 5
[2,1,2] => [2,1,2] => [2,2,1] => 5
[2,2,1] => [2,2,1] => [2,2,1] => 5
[1,2,3] => [1,2,3] => [3,2,1] => 6
[1,3,2] => [1,3,2] => [3,2,1] => 6
[2,1,3] => [2,1,3] => [3,2,1] => 6
[2,3,1] => [2,3,1] => [3,2,1] => 6
[3,1,2] => [3,1,2] => [3,2,1] => 6
[3,2,1] => [3,2,1] => [3,2,1] => 6
[1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[1,1,1,2] => [1,1,1,2] => [2,1,1,1] => 5
[1,1,2,1] => [1,1,2,1] => [2,1,1,1] => 5
[1,2,1,1] => [1,2,1,1] => [2,1,1,1] => 5
[2,1,1,1] => [2,1,1,1] => [2,1,1,1] => 5
[1,1,1,3] => [1,1,1,3] => [3,1,1,1] => 6
[1,1,3,1] => [1,1,3,1] => [3,1,1,1] => 6
[1,3,1,1] => [1,3,1,1] => [3,1,1,1] => 6
[3,1,1,1] => [3,1,1,1] => [3,1,1,1] => 6
[1,1,1,4] => [1,1,1,4] => [4,1,1,1] => 7
[1,1,4,1] => [1,1,4,1] => [4,1,1,1] => 7
[1,4,1,1] => [1,4,1,1] => [4,1,1,1] => 7
[4,1,1,1] => [4,1,1,1] => [4,1,1,1] => 7
[1,1,2,2] => [1,1,2,2] => [2,2,1,1] => 6
[1,2,1,2] => [1,2,1,2] => [2,2,1,1] => 6
[1,2,2,1] => [1,2,2,1] => [2,2,1,1] => 6
[2,1,1,2] => [2,1,1,2] => [2,2,1,1] => 6
[2,1,2,1] => [2,1,2,1] => [2,2,1,1] => 6
[2,2,1,1] => [2,2,1,1] => [2,2,1,1] => 6
[1,1,2,3] => [1,1,2,3] => [3,2,1,1] => 7
[1,1,3,2] => [1,1,3,2] => [3,2,1,1] => 7
[1,2,1,3] => [1,2,1,3] => [3,2,1,1] => 7
[1,2,3,1] => [1,2,3,1] => [3,2,1,1] => 7
[1,3,1,2] => [1,3,1,2] => [3,2,1,1] => 7
[1,3,2,1] => [1,3,2,1] => [3,2,1,1] => 7
[2,1,1,3] => [2,1,1,3] => [3,2,1,1] => 7
[2,1,3,1] => [2,1,3,1] => [3,2,1,1] => 7
[2,3,1,1] => [2,3,1,1] => [3,2,1,1] => 7
[3,1,1,2] => [3,1,1,2] => [3,2,1,1] => 7
[3,1,2,1] => [3,1,2,1] => [3,2,1,1] => 7
[3,2,1,1] => [3,2,1,1] => [3,2,1,1] => 7
[1,1,2,4] => [1,1,2,4] => [4,2,1,1] => 8
[1,1,4,2] => [1,1,4,2] => [4,2,1,1] => 8
[1,2,1,4] => [1,2,1,4] => [4,2,1,1] => 8
[1,2,4,1] => [1,2,4,1] => [4,2,1,1] => 8
[1,4,1,2] => [1,4,1,2] => [4,2,1,1] => 8
[1,4,2,1] => [1,4,2,1] => [4,2,1,1] => 8
[2,1,1,4] => [2,1,1,4] => [4,2,1,1] => 8
[2,1,4,1] => [2,1,4,1] => [4,2,1,1] => 8
[2,4,1,1] => [2,4,1,1] => [4,2,1,1] => 8
[4,1,1,2] => [4,1,1,2] => [4,2,1,1] => 8
[4,1,2,1] => [4,1,2,1] => [4,2,1,1] => 8
[4,2,1,1] => [4,2,1,1] => [4,2,1,1] => 8
[1,1,3,3] => [1,1,3,3] => [3,3,1,1] => 8
[1,3,1,3] => [1,3,1,3] => [3,3,1,1] => 8
[1,3,3,1] => [1,3,3,1] => [3,3,1,1] => 8
[3,1,1,3] => [3,1,1,3] => [3,3,1,1] => 8
[3,1,3,1] => [3,1,3,1] => [3,3,1,1] => 8
[3,3,1,1] => [3,3,1,1] => [3,3,1,1] => 8
[1,1,3,4] => [1,1,3,4] => [4,3,1,1] => 9
[1,1,4,3] => [1,1,4,3] => [4,3,1,1] => 9
[1,3,1,4] => [1,3,1,4] => [4,3,1,1] => 9
[1,3,4,1] => [1,3,4,1] => [4,3,1,1] => 9
[1,4,1,3] => [1,4,1,3] => [4,3,1,1] => 9
[1,4,3,1] => [1,4,3,1] => [4,3,1,1] => 9
[3,1,1,4] => [3,1,1,4] => [4,3,1,1] => 9
[3,1,4,1] => [3,1,4,1] => [4,3,1,1] => 9
[3,4,1,1] => [3,4,1,1] => [4,3,1,1] => 9
[4,1,1,3] => [4,1,1,3] => [4,3,1,1] => 9
[4,1,3,1] => [4,1,3,1] => [4,3,1,1] => 9
[4,3,1,1] => [4,3,1,1] => [4,3,1,1] => 9
[1,2,2,2] => [1,2,2,2] => [2,2,2,1] => 7
[2,1,2,2] => [2,1,2,2] => [2,2,2,1] => 7
[2,2,1,2] => [2,2,1,2] => [2,2,2,1] => 7
[2,2,2,1] => [2,2,2,1] => [2,2,2,1] => 7
[1,2,2,3] => [1,2,2,3] => [3,2,2,1] => 8
[1,2,3,2] => [1,2,3,2] => [3,2,2,1] => 8
[1,3,2,2] => [1,3,2,2] => [3,2,2,1] => 8
[2,1,2,3] => [2,1,2,3] => [3,2,2,1] => 8
[2,1,3,2] => [2,1,3,2] => [3,2,2,1] => 8
[2,2,1,3] => [2,2,1,3] => [3,2,2,1] => 8
[2,2,3,1] => [2,2,3,1] => [3,2,2,1] => 8
[2,3,1,2] => [2,3,1,2] => [3,2,2,1] => 8
[2,3,2,1] => [2,3,2,1] => [3,2,2,1] => 8
[3,1,2,2] => [3,1,2,2] => [3,2,2,1] => 8
[3,2,1,2] => [3,2,1,2] => [3,2,2,1] => 8
[3,2,2,1] => [3,2,2,1] => [3,2,2,1] => 8
[1,2,2,4] => [1,2,2,4] => [4,2,2,1] => 9
[1,2,4,2] => [1,2,4,2] => [4,2,2,1] => 9
[1,4,2,2] => [1,4,2,2] => [4,2,2,1] => 9
[2,1,2,4] => [2,1,2,4] => [4,2,2,1] => 9
>>> Load all 843 entries. <<<[2,1,4,2] => [2,1,4,2] => [4,2,2,1] => 9
[2,2,1,4] => [2,2,1,4] => [4,2,2,1] => 9
[2,2,4,1] => [2,2,4,1] => [4,2,2,1] => 9
[2,4,1,2] => [2,4,1,2] => [4,2,2,1] => 9
[2,4,2,1] => [2,4,2,1] => [4,2,2,1] => 9
[4,1,2,2] => [4,1,2,2] => [4,2,2,1] => 9
[4,2,1,2] => [4,2,1,2] => [4,2,2,1] => 9
[4,2,2,1] => [4,2,2,1] => [4,2,2,1] => 9
[1,2,3,3] => [1,2,3,3] => [3,3,2,1] => 9
[1,3,2,3] => [1,3,2,3] => [3,3,2,1] => 9
[1,3,3,2] => [1,3,3,2] => [3,3,2,1] => 9
[2,1,3,3] => [2,1,3,3] => [3,3,2,1] => 9
[2,3,1,3] => [2,3,1,3] => [3,3,2,1] => 9
[2,3,3,1] => [2,3,3,1] => [3,3,2,1] => 9
[3,1,2,3] => [3,1,2,3] => [3,3,2,1] => 9
[3,1,3,2] => [3,1,3,2] => [3,3,2,1] => 9
[3,2,1,3] => [3,2,1,3] => [3,3,2,1] => 9
[3,2,3,1] => [3,2,3,1] => [3,3,2,1] => 9
[3,3,1,2] => [3,3,1,2] => [3,3,2,1] => 9
[3,3,2,1] => [3,3,2,1] => [3,3,2,1] => 9
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 10
[1,2,4,3] => [1,2,4,3] => [4,3,2,1] => 10
[1,3,2,4] => [1,3,2,4] => [4,3,2,1] => 10
[1,3,4,2] => [1,3,4,2] => [4,3,2,1] => 10
[1,4,2,3] => [1,4,2,3] => [4,3,2,1] => 10
[1,4,3,2] => [1,4,3,2] => [4,3,2,1] => 10
[2,1,3,4] => [2,1,3,4] => [4,3,2,1] => 10
[2,1,4,3] => [2,1,4,3] => [4,3,2,1] => 10
[2,3,1,4] => [2,3,1,4] => [4,3,2,1] => 10
[2,3,4,1] => [2,3,4,1] => [4,3,2,1] => 10
[2,4,1,3] => [2,4,1,3] => [4,3,2,1] => 10
[2,4,3,1] => [2,4,3,1] => [4,3,2,1] => 10
[3,1,2,4] => [3,1,2,4] => [4,3,2,1] => 10
[3,1,4,2] => [3,1,4,2] => [4,3,2,1] => 10
[3,2,1,4] => [3,2,1,4] => [4,3,2,1] => 10
[3,2,4,1] => [3,2,4,1] => [4,3,2,1] => 10
[3,4,1,2] => [3,4,1,2] => [4,3,2,1] => 10
[3,4,2,1] => [3,4,2,1] => [4,3,2,1] => 10
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => 10
[4,1,3,2] => [4,1,3,2] => [4,3,2,1] => 10
[4,2,1,3] => [4,2,1,3] => [4,3,2,1] => 10
[4,2,3,1] => [4,2,3,1] => [4,3,2,1] => 10
[4,3,1,2] => [4,3,1,2] => [4,3,2,1] => 10
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 10
[1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[1,1,1,1,2] => [1,1,1,1,2] => [2,1,1,1,1] => 6
[1,1,1,2,1] => [1,1,1,2,1] => [2,1,1,1,1] => 6
[1,1,2,1,1] => [1,1,2,1,1] => [2,1,1,1,1] => 6
[1,2,1,1,1] => [1,2,1,1,1] => [2,1,1,1,1] => 6
[2,1,1,1,1] => [2,1,1,1,1] => [2,1,1,1,1] => 6
[1,1,1,1,3] => [1,1,1,1,3] => [3,1,1,1,1] => 7
[1,1,1,3,1] => [1,1,1,3,1] => [3,1,1,1,1] => 7
[1,1,3,1,1] => [1,1,3,1,1] => [3,1,1,1,1] => 7
[1,3,1,1,1] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[3,1,1,1,1] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[1,1,1,1,4] => [1,1,1,1,4] => [4,1,1,1,1] => 8
[1,1,1,4,1] => [1,1,1,4,1] => [4,1,1,1,1] => 8
[1,1,4,1,1] => [1,1,4,1,1] => [4,1,1,1,1] => 8
[1,4,1,1,1] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[4,1,1,1,1] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[1,1,1,1,5] => [1,1,1,1,5] => [5,1,1,1,1] => 9
[1,1,1,5,1] => [1,1,1,5,1] => [5,1,1,1,1] => 9
[1,1,5,1,1] => [1,1,5,1,1] => [5,1,1,1,1] => 9
[1,5,1,1,1] => [1,5,1,1,1] => [5,1,1,1,1] => 9
[5,1,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[1,1,1,2,2] => [1,1,1,2,2] => [2,2,1,1,1] => 7
[1,1,2,1,2] => [1,1,2,1,2] => [2,2,1,1,1] => 7
[1,1,2,2,1] => [1,1,2,2,1] => [2,2,1,1,1] => 7
[1,2,1,1,2] => [1,2,1,1,2] => [2,2,1,1,1] => 7
[1,2,1,2,1] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[1,2,2,1,1] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[2,1,1,1,2] => [2,1,1,1,2] => [2,2,1,1,1] => 7
[2,1,1,2,1] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[2,1,2,1,1] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[2,2,1,1,1] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[1,1,1,2,3] => [1,1,1,2,3] => [3,2,1,1,1] => 8
[1,1,1,3,2] => [1,1,1,3,2] => [3,2,1,1,1] => 8
[1,1,2,1,3] => [1,1,2,1,3] => [3,2,1,1,1] => 8
[1,1,2,3,1] => [1,1,2,3,1] => [3,2,1,1,1] => 8
[1,1,3,1,2] => [1,1,3,1,2] => [3,2,1,1,1] => 8
[1,1,3,2,1] => [1,1,3,2,1] => [3,2,1,1,1] => 8
[1,2,1,1,3] => [1,2,1,1,3] => [3,2,1,1,1] => 8
[1,2,1,3,1] => [1,2,1,3,1] => [3,2,1,1,1] => 8
[1,2,3,1,1] => [1,2,3,1,1] => [3,2,1,1,1] => 8
[1,3,1,1,2] => [1,3,1,1,2] => [3,2,1,1,1] => 8
[1,3,1,2,1] => [1,3,1,2,1] => [3,2,1,1,1] => 8
[1,3,2,1,1] => [1,3,2,1,1] => [3,2,1,1,1] => 8
[2,1,1,1,3] => [2,1,1,1,3] => [3,2,1,1,1] => 8
[2,1,1,3,1] => [2,1,1,3,1] => [3,2,1,1,1] => 8
[2,1,3,1,1] => [2,1,3,1,1] => [3,2,1,1,1] => 8
[2,3,1,1,1] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[3,1,1,1,2] => [3,1,1,1,2] => [3,2,1,1,1] => 8
[3,1,1,2,1] => [3,1,1,2,1] => [3,2,1,1,1] => 8
[3,1,2,1,1] => [3,1,2,1,1] => [3,2,1,1,1] => 8
[3,2,1,1,1] => [3,2,1,1,1] => [3,2,1,1,1] => 8
[1,1,1,2,4] => [1,1,1,2,4] => [4,2,1,1,1] => 9
[1,1,1,4,2] => [1,1,1,4,2] => [4,2,1,1,1] => 9
[1,1,2,1,4] => [1,1,2,1,4] => [4,2,1,1,1] => 9
[1,1,2,4,1] => [1,1,2,4,1] => [4,2,1,1,1] => 9
[1,1,4,1,2] => [1,1,4,1,2] => [4,2,1,1,1] => 9
[1,1,4,2,1] => [1,1,4,2,1] => [4,2,1,1,1] => 9
[1,2,1,1,4] => [1,2,1,1,4] => [4,2,1,1,1] => 9
[1,2,1,4,1] => [1,2,1,4,1] => [4,2,1,1,1] => 9
[1,2,4,1,1] => [1,2,4,1,1] => [4,2,1,1,1] => 9
[1,4,1,1,2] => [1,4,1,1,2] => [4,2,1,1,1] => 9
[1,4,1,2,1] => [1,4,1,2,1] => [4,2,1,1,1] => 9
[1,4,2,1,1] => [1,4,2,1,1] => [4,2,1,1,1] => 9
[2,1,1,1,4] => [2,1,1,1,4] => [4,2,1,1,1] => 9
[2,1,1,4,1] => [2,1,1,4,1] => [4,2,1,1,1] => 9
[2,1,4,1,1] => [2,1,4,1,1] => [4,2,1,1,1] => 9
[2,4,1,1,1] => [2,4,1,1,1] => [4,2,1,1,1] => 9
[4,1,1,1,2] => [4,1,1,1,2] => [4,2,1,1,1] => 9
[4,1,1,2,1] => [4,1,1,2,1] => [4,2,1,1,1] => 9
[4,1,2,1,1] => [4,1,2,1,1] => [4,2,1,1,1] => 9
[4,2,1,1,1] => [4,2,1,1,1] => [4,2,1,1,1] => 9
[1,1,1,2,5] => [1,1,1,2,5] => [5,2,1,1,1] => 10
[1,1,1,5,2] => [1,1,1,5,2] => [5,2,1,1,1] => 10
[1,1,2,1,5] => [1,1,2,1,5] => [5,2,1,1,1] => 10
[1,1,2,5,1] => [1,1,2,5,1] => [5,2,1,1,1] => 10
[1,1,5,1,2] => [1,1,5,1,2] => [5,2,1,1,1] => 10
[1,1,5,2,1] => [1,1,5,2,1] => [5,2,1,1,1] => 10
[1,2,1,1,5] => [1,2,1,1,5] => [5,2,1,1,1] => 10
[1,2,1,5,1] => [1,2,1,5,1] => [5,2,1,1,1] => 10
[1,2,5,1,1] => [1,2,5,1,1] => [5,2,1,1,1] => 10
[1,5,1,1,2] => [1,5,1,1,2] => [5,2,1,1,1] => 10
[1,5,1,2,1] => [1,5,1,2,1] => [5,2,1,1,1] => 10
[1,5,2,1,1] => [1,5,2,1,1] => [5,2,1,1,1] => 10
[2,1,1,1,5] => [2,1,1,1,5] => [5,2,1,1,1] => 10
[2,1,1,5,1] => [2,1,1,5,1] => [5,2,1,1,1] => 10
[2,1,5,1,1] => [2,1,5,1,1] => [5,2,1,1,1] => 10
[2,5,1,1,1] => [2,5,1,1,1] => [5,2,1,1,1] => 10
[5,1,1,1,2] => [5,1,1,1,2] => [5,2,1,1,1] => 10
[5,1,1,2,1] => [5,1,1,2,1] => [5,2,1,1,1] => 10
[5,1,2,1,1] => [5,1,2,1,1] => [5,2,1,1,1] => 10
[5,2,1,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => 10
[1,1,1,3,3] => [1,1,1,3,3] => [3,3,1,1,1] => 9
[1,1,3,1,3] => [1,1,3,1,3] => [3,3,1,1,1] => 9
[1,1,3,3,1] => [1,1,3,3,1] => [3,3,1,1,1] => 9
[1,3,1,1,3] => [1,3,1,1,3] => [3,3,1,1,1] => 9
[1,3,1,3,1] => [1,3,1,3,1] => [3,3,1,1,1] => 9
[1,3,3,1,1] => [1,3,3,1,1] => [3,3,1,1,1] => 9
[3,1,1,1,3] => [3,1,1,1,3] => [3,3,1,1,1] => 9
[3,1,1,3,1] => [3,1,1,3,1] => [3,3,1,1,1] => 9
[3,1,3,1,1] => [3,1,3,1,1] => [3,3,1,1,1] => 9
[3,3,1,1,1] => [3,3,1,1,1] => [3,3,1,1,1] => 9
[1,1,1,3,4] => [1,1,1,3,4] => [4,3,1,1,1] => 10
[1,1,1,4,3] => [1,1,1,4,3] => [4,3,1,1,1] => 10
[1,1,3,1,4] => [1,1,3,1,4] => [4,3,1,1,1] => 10
[1,1,3,4,1] => [1,1,3,4,1] => [4,3,1,1,1] => 10
[1,1,4,1,3] => [1,1,4,1,3] => [4,3,1,1,1] => 10
[1,1,4,3,1] => [1,1,4,3,1] => [4,3,1,1,1] => 10
[1,3,1,1,4] => [1,3,1,1,4] => [4,3,1,1,1] => 10
[1,3,1,4,1] => [1,3,1,4,1] => [4,3,1,1,1] => 10
[1,3,4,1,1] => [1,3,4,1,1] => [4,3,1,1,1] => 10
[1,4,1,1,3] => [1,4,1,1,3] => [4,3,1,1,1] => 10
[1,4,1,3,1] => [1,4,1,3,1] => [4,3,1,1,1] => 10
[1,4,3,1,1] => [1,4,3,1,1] => [4,3,1,1,1] => 10
[3,1,1,1,4] => [3,1,1,1,4] => [4,3,1,1,1] => 10
[3,1,1,4,1] => [3,1,1,4,1] => [4,3,1,1,1] => 10
[3,1,4,1,1] => [3,1,4,1,1] => [4,3,1,1,1] => 10
[3,4,1,1,1] => [3,4,1,1,1] => [4,3,1,1,1] => 10
[4,1,1,1,3] => [4,1,1,1,3] => [4,3,1,1,1] => 10
[4,1,1,3,1] => [4,1,1,3,1] => [4,3,1,1,1] => 10
[4,1,3,1,1] => [4,1,3,1,1] => [4,3,1,1,1] => 10
[4,3,1,1,1] => [4,3,1,1,1] => [4,3,1,1,1] => 10
[1,3,1,5,1] => [1,3,1,5,1] => [5,3,1,1,1] => 11
[1,5,1,3,1] => [1,5,1,3,1] => [5,3,1,1,1] => 11
[1,4,1,4,1] => [1,4,1,4,1] => [4,4,1,1,1] => 11
[1,1,4,1,5] => [1,1,4,1,5] => [5,4,1,1,1] => 12
[1,1,4,5,1] => [1,1,4,5,1] => [5,4,1,1,1] => 12
[1,5,4,1,1] => [1,5,4,1,1] => [5,4,1,1,1] => 12
[5,1,4,1,1] => [5,1,4,1,1] => [5,4,1,1,1] => 12
[1,1,2,2,2] => [1,1,2,2,2] => [2,2,2,1,1] => 8
[1,2,1,2,2] => [1,2,1,2,2] => [2,2,2,1,1] => 8
[1,2,2,1,2] => [1,2,2,1,2] => [2,2,2,1,1] => 8
[1,2,2,2,1] => [1,2,2,2,1] => [2,2,2,1,1] => 8
[2,1,1,2,2] => [2,1,1,2,2] => [2,2,2,1,1] => 8
[2,1,2,1,2] => [2,1,2,1,2] => [2,2,2,1,1] => 8
[2,1,2,2,1] => [2,1,2,2,1] => [2,2,2,1,1] => 8
[2,2,1,1,2] => [2,2,1,1,2] => [2,2,2,1,1] => 8
[2,2,1,2,1] => [2,2,1,2,1] => [2,2,2,1,1] => 8
[2,2,2,1,1] => [2,2,2,1,1] => [2,2,2,1,1] => 8
[1,1,2,2,3] => [1,1,2,2,3] => [3,2,2,1,1] => 9
[1,1,2,3,2] => [1,1,2,3,2] => [3,2,2,1,1] => 9
[1,1,3,2,2] => [1,1,3,2,2] => [3,2,2,1,1] => 9
[1,2,1,2,3] => [1,2,1,2,3] => [3,2,2,1,1] => 9
[1,2,1,3,2] => [1,2,1,3,2] => [3,2,2,1,1] => 9
[1,2,2,1,3] => [1,2,2,1,3] => [3,2,2,1,1] => 9
[1,2,2,3,1] => [1,2,2,3,1] => [3,2,2,1,1] => 9
[1,2,3,1,2] => [1,2,3,1,2] => [3,2,2,1,1] => 9
[1,2,3,2,1] => [1,2,3,2,1] => [3,2,2,1,1] => 9
[1,3,1,2,2] => [1,3,1,2,2] => [3,2,2,1,1] => 9
[1,3,2,1,2] => [1,3,2,1,2] => [3,2,2,1,1] => 9
[1,3,2,2,1] => [1,3,2,2,1] => [3,2,2,1,1] => 9
[2,1,1,2,3] => [2,1,1,2,3] => [3,2,2,1,1] => 9
[2,1,1,3,2] => [2,1,1,3,2] => [3,2,2,1,1] => 9
[2,1,2,1,3] => [2,1,2,1,3] => [3,2,2,1,1] => 9
[2,1,2,3,1] => [2,1,2,3,1] => [3,2,2,1,1] => 9
[2,1,3,1,2] => [2,1,3,1,2] => [3,2,2,1,1] => 9
[2,1,3,2,1] => [2,1,3,2,1] => [3,2,2,1,1] => 9
[2,2,1,1,3] => [2,2,1,1,3] => [3,2,2,1,1] => 9
[2,2,1,3,1] => [2,2,1,3,1] => [3,2,2,1,1] => 9
[2,2,3,1,1] => [2,2,3,1,1] => [3,2,2,1,1] => 9
[2,3,1,1,2] => [2,3,1,1,2] => [3,2,2,1,1] => 9
[2,3,1,2,1] => [2,3,1,2,1] => [3,2,2,1,1] => 9
[2,3,2,1,1] => [2,3,2,1,1] => [3,2,2,1,1] => 9
[3,1,1,2,2] => [3,1,1,2,2] => [3,2,2,1,1] => 9
[3,1,2,1,2] => [3,1,2,1,2] => [3,2,2,1,1] => 9
[3,1,2,2,1] => [3,1,2,2,1] => [3,2,2,1,1] => 9
[3,2,1,1,2] => [3,2,1,1,2] => [3,2,2,1,1] => 9
[3,2,1,2,1] => [3,2,1,2,1] => [3,2,2,1,1] => 9
[3,2,2,1,1] => [3,2,2,1,1] => [3,2,2,1,1] => 9
[1,1,2,2,4] => [1,1,2,2,4] => [4,2,2,1,1] => 10
[1,1,2,4,2] => [1,1,2,4,2] => [4,2,2,1,1] => 10
[1,1,4,2,2] => [1,1,4,2,2] => [4,2,2,1,1] => 10
[1,2,1,2,4] => [1,2,1,2,4] => [4,2,2,1,1] => 10
[1,2,1,4,2] => [1,2,1,4,2] => [4,2,2,1,1] => 10
[1,2,2,1,4] => [1,2,2,1,4] => [4,2,2,1,1] => 10
[1,2,2,4,1] => [1,2,2,4,1] => [4,2,2,1,1] => 10
[1,2,4,1,2] => [1,2,4,1,2] => [4,2,2,1,1] => 10
[1,2,4,2,1] => [1,2,4,2,1] => [4,2,2,1,1] => 10
[1,4,1,2,2] => [1,4,1,2,2] => [4,2,2,1,1] => 10
[1,4,2,1,2] => [1,4,2,1,2] => [4,2,2,1,1] => 10
[1,4,2,2,1] => [1,4,2,2,1] => [4,2,2,1,1] => 10
[2,1,1,2,4] => [2,1,1,2,4] => [4,2,2,1,1] => 10
[2,1,1,4,2] => [2,1,1,4,2] => [4,2,2,1,1] => 10
[2,1,2,1,4] => [2,1,2,1,4] => [4,2,2,1,1] => 10
[2,1,2,4,1] => [2,1,2,4,1] => [4,2,2,1,1] => 10
[2,1,4,1,2] => [2,1,4,1,2] => [4,2,2,1,1] => 10
[2,1,4,2,1] => [2,1,4,2,1] => [4,2,2,1,1] => 10
[2,2,1,1,4] => [2,2,1,1,4] => [4,2,2,1,1] => 10
[2,2,1,4,1] => [2,2,1,4,1] => [4,2,2,1,1] => 10
[2,2,4,1,1] => [2,2,4,1,1] => [4,2,2,1,1] => 10
[2,4,1,1,2] => [2,4,1,1,2] => [4,2,2,1,1] => 10
[2,4,1,2,1] => [2,4,1,2,1] => [4,2,2,1,1] => 10
[2,4,2,1,1] => [2,4,2,1,1] => [4,2,2,1,1] => 10
[4,1,1,2,2] => [4,1,1,2,2] => [4,2,2,1,1] => 10
[4,1,2,1,2] => [4,1,2,1,2] => [4,2,2,1,1] => 10
[4,1,2,2,1] => [4,1,2,2,1] => [4,2,2,1,1] => 10
[4,2,1,1,2] => [4,2,1,1,2] => [4,2,2,1,1] => 10
[4,2,1,2,1] => [4,2,1,2,1] => [4,2,2,1,1] => 10
[4,2,2,1,1] => [4,2,2,1,1] => [4,2,2,1,1] => 10
[1,2,5,2,1] => [1,2,5,2,1] => [5,2,2,1,1] => 11
[1,5,2,1,2] => [1,5,2,1,2] => [5,2,2,1,1] => 11
[2,1,2,5,1] => [2,1,2,5,1] => [5,2,2,1,1] => 11
[1,1,2,3,3] => [1,1,2,3,3] => [3,3,2,1,1] => 10
[1,1,3,2,3] => [1,1,3,2,3] => [3,3,2,1,1] => 10
[1,1,3,3,2] => [1,1,3,3,2] => [3,3,2,1,1] => 10
[1,2,1,3,3] => [1,2,1,3,3] => [3,3,2,1,1] => 10
[1,2,3,1,3] => [1,2,3,1,3] => [3,3,2,1,1] => 10
[1,2,3,3,1] => [1,2,3,3,1] => [3,3,2,1,1] => 10
[1,3,1,2,3] => [1,3,1,2,3] => [3,3,2,1,1] => 10
[1,3,1,3,2] => [1,3,1,3,2] => [3,3,2,1,1] => 10
[1,3,2,1,3] => [1,3,2,1,3] => [3,3,2,1,1] => 10
[1,3,2,3,1] => [1,3,2,3,1] => [3,3,2,1,1] => 10
[1,3,3,1,2] => [1,3,3,1,2] => [3,3,2,1,1] => 10
[1,3,3,2,1] => [1,3,3,2,1] => [3,3,2,1,1] => 10
[2,1,1,3,3] => [2,1,1,3,3] => [3,3,2,1,1] => 10
[2,1,3,1,3] => [2,1,3,1,3] => [3,3,2,1,1] => 10
[2,1,3,3,1] => [2,1,3,3,1] => [3,3,2,1,1] => 10
[2,3,1,1,3] => [2,3,1,1,3] => [3,3,2,1,1] => 10
[2,3,1,3,1] => [2,3,1,3,1] => [3,3,2,1,1] => 10
[2,3,3,1,1] => [2,3,3,1,1] => [3,3,2,1,1] => 10
[3,1,1,2,3] => [3,1,1,2,3] => [3,3,2,1,1] => 10
[3,1,1,3,2] => [3,1,1,3,2] => [3,3,2,1,1] => 10
[3,1,2,1,3] => [3,1,2,1,3] => [3,3,2,1,1] => 10
[3,1,2,3,1] => [3,1,2,3,1] => [3,3,2,1,1] => 10
[3,1,3,1,2] => [3,1,3,1,2] => [3,3,2,1,1] => 10
[3,1,3,2,1] => [3,1,3,2,1] => [3,3,2,1,1] => 10
[3,2,1,1,3] => [3,2,1,1,3] => [3,3,2,1,1] => 10
[3,2,1,3,1] => [3,2,1,3,1] => [3,3,2,1,1] => 10
[3,2,3,1,1] => [3,2,3,1,1] => [3,3,2,1,1] => 10
[3,3,1,1,2] => [3,3,1,1,2] => [3,3,2,1,1] => 10
[3,3,1,2,1] => [3,3,1,2,1] => [3,3,2,1,1] => 10
[3,3,2,1,1] => [3,3,2,1,1] => [3,3,2,1,1] => 10
[1,2,3,4,1] => [1,2,3,4,1] => [4,3,2,1,1] => 11
[1,4,3,2,1] => [1,4,3,2,1] => [4,3,2,1,1] => 11
[1,1,2,3,5] => [1,1,2,3,5] => [5,3,2,1,1] => 12
[1,1,2,5,3] => [1,1,2,5,3] => [5,3,2,1,1] => 12
[1,3,2,1,5] => [1,3,2,1,5] => [5,3,2,1,1] => 12
[1,3,2,5,1] => [1,3,2,5,1] => [5,3,2,1,1] => 12
[1,3,5,2,1] => [1,3,5,2,1] => [5,3,2,1,1] => 12
[1,5,2,1,3] => [1,5,2,1,3] => [5,3,2,1,1] => 12
[1,5,2,3,1] => [1,5,2,3,1] => [5,3,2,1,1] => 12
[1,5,3,2,1] => [1,5,3,2,1] => [5,3,2,1,1] => 12
[3,1,2,1,5] => [3,1,2,1,5] => [5,3,2,1,1] => 12
[3,1,2,5,1] => [3,1,2,5,1] => [5,3,2,1,1] => 12
[3,5,2,1,1] => [3,5,2,1,1] => [5,3,2,1,1] => 12
[5,1,2,1,3] => [5,1,2,1,3] => [5,3,2,1,1] => 12
[5,1,2,3,1] => [5,1,2,3,1] => [5,3,2,1,1] => 12
[5,3,2,1,1] => [5,3,2,1,1] => [5,3,2,1,1] => 12
[1,2,4,4,1] => [1,2,4,4,1] => [4,4,2,1,1] => 12
[1,4,2,4,1] => [1,4,2,4,1] => [4,4,2,1,1] => 12
[1,4,4,2,1] => [1,4,4,2,1] => [4,4,2,1,1] => 12
[1,2,5,4,1] => [1,2,5,4,1] => [5,4,2,1,1] => 13
[1,4,5,2,1] => [1,4,5,2,1] => [5,4,2,1,1] => 13
[1,1,4,3,3] => [1,1,4,3,3] => [4,3,3,1,1] => 12
[1,3,3,4,1] => [1,3,3,4,1] => [4,3,3,1,1] => 12
[1,3,4,1,3] => [1,3,4,1,3] => [4,3,3,1,1] => 12
[1,3,4,3,1] => [1,3,4,3,1] => [4,3,3,1,1] => 12
[1,4,3,3,1] => [1,4,3,3,1] => [4,3,3,1,1] => 12
[3,1,4,1,3] => [3,1,4,1,3] => [4,3,3,1,1] => 12
[3,1,4,3,1] => [3,1,4,3,1] => [4,3,3,1,1] => 12
[3,3,4,1,1] => [3,3,4,1,1] => [4,3,3,1,1] => 12
[1,4,3,4,1] => [1,4,3,4,1] => [4,4,3,1,1] => 13
[1,2,2,2,2] => [1,2,2,2,2] => [2,2,2,2,1] => 9
[2,1,2,2,2] => [2,1,2,2,2] => [2,2,2,2,1] => 9
[2,2,1,2,2] => [2,2,1,2,2] => [2,2,2,2,1] => 9
[2,2,2,1,2] => [2,2,2,1,2] => [2,2,2,2,1] => 9
[2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,2,1] => 9
[1,2,2,2,3] => [1,2,2,2,3] => [3,2,2,2,1] => 10
[1,2,2,3,2] => [1,2,2,3,2] => [3,2,2,2,1] => 10
[1,2,3,2,2] => [1,2,3,2,2] => [3,2,2,2,1] => 10
[1,3,2,2,2] => [1,3,2,2,2] => [3,2,2,2,1] => 10
[2,1,2,2,3] => [2,1,2,2,3] => [3,2,2,2,1] => 10
[2,1,2,3,2] => [2,1,2,3,2] => [3,2,2,2,1] => 10
[2,1,3,2,2] => [2,1,3,2,2] => [3,2,2,2,1] => 10
[2,2,1,2,3] => [2,2,1,2,3] => [3,2,2,2,1] => 10
[2,2,1,3,2] => [2,2,1,3,2] => [3,2,2,2,1] => 10
[2,2,2,1,3] => [2,2,2,1,3] => [3,2,2,2,1] => 10
[2,2,2,3,1] => [2,2,2,3,1] => [3,2,2,2,1] => 10
[2,2,3,1,2] => [2,2,3,1,2] => [3,2,2,2,1] => 10
[2,2,3,2,1] => [2,2,3,2,1] => [3,2,2,2,1] => 10
[2,3,1,2,2] => [2,3,1,2,2] => [3,2,2,2,1] => 10
[2,3,2,1,2] => [2,3,2,1,2] => [3,2,2,2,1] => 10
[2,3,2,2,1] => [2,3,2,2,1] => [3,2,2,2,1] => 10
[3,1,2,2,2] => [3,1,2,2,2] => [3,2,2,2,1] => 10
[3,2,1,2,2] => [3,2,1,2,2] => [3,2,2,2,1] => 10
[3,2,2,1,2] => [3,2,2,1,2] => [3,2,2,2,1] => 10
[3,2,2,2,1] => [3,2,2,2,1] => [3,2,2,2,1] => 10
[1,2,2,2,5] => [1,2,2,2,5] => [5,2,2,2,1] => 12
[1,2,5,2,2] => [1,2,5,2,2] => [5,2,2,2,1] => 12
[1,5,2,2,2] => [1,5,2,2,2] => [5,2,2,2,1] => 12
[2,2,5,2,1] => [2,2,5,2,1] => [5,2,2,2,1] => 12
[2,5,2,2,1] => [2,5,2,2,1] => [5,2,2,2,1] => 12
[5,2,2,2,1] => [5,2,2,2,1] => [5,2,2,2,1] => 12
[1,2,2,4,3] => [1,2,2,4,3] => [4,3,2,2,1] => 12
[1,2,3,4,2] => [1,2,3,4,2] => [4,3,2,2,1] => 12
[1,2,4,2,3] => [1,2,4,2,3] => [4,3,2,2,1] => 12
[1,2,4,3,2] => [1,2,4,3,2] => [4,3,2,2,1] => 12
[1,3,2,4,2] => [1,3,2,4,2] => [4,3,2,2,1] => 12
[1,3,4,2,2] => [1,3,4,2,2] => [4,3,2,2,1] => 12
[1,4,2,2,3] => [1,4,2,2,3] => [4,3,2,2,1] => 12
[1,4,2,3,2] => [1,4,2,3,2] => [4,3,2,2,1] => 12
[1,4,3,2,2] => [1,4,3,2,2] => [4,3,2,2,1] => 12
[2,2,3,4,1] => [2,2,3,4,1] => [4,3,2,2,1] => 12
[2,2,4,3,1] => [2,2,4,3,1] => [4,3,2,2,1] => 12
[2,3,2,4,1] => [2,3,2,4,1] => [4,3,2,2,1] => 12
[2,3,4,2,1] => [2,3,4,2,1] => [4,3,2,2,1] => 12
[2,4,2,3,1] => [2,4,2,3,1] => [4,3,2,2,1] => 12
[2,4,3,2,1] => [2,4,3,2,1] => [4,3,2,2,1] => 12
[3,2,2,4,1] => [3,2,2,4,1] => [4,3,2,2,1] => 12
[3,2,4,2,1] => [3,2,4,2,1] => [4,3,2,2,1] => 12
[3,4,2,2,1] => [3,4,2,2,1] => [4,3,2,2,1] => 12
[4,2,2,3,1] => [4,2,2,3,1] => [4,3,2,2,1] => 12
[4,2,3,2,1] => [4,2,3,2,1] => [4,3,2,2,1] => 12
[4,3,2,2,1] => [4,3,2,2,1] => [4,3,2,2,1] => 12
[1,2,3,3,3] => [1,2,3,3,3] => [3,3,3,2,1] => 12
[1,3,2,3,3] => [1,3,2,3,3] => [3,3,3,2,1] => 12
[1,3,3,2,3] => [1,3,3,2,3] => [3,3,3,2,1] => 12
[1,3,3,3,2] => [1,3,3,3,2] => [3,3,3,2,1] => 12
[2,3,3,3,1] => [2,3,3,3,1] => [3,3,3,2,1] => 12
[3,1,2,3,3] => [3,1,2,3,3] => [3,3,3,2,1] => 12
[3,2,3,3,1] => [3,2,3,3,1] => [3,3,3,2,1] => 12
[3,3,2,1,3] => [3,3,2,1,3] => [3,3,3,2,1] => 12
[3,3,2,3,1] => [3,3,2,3,1] => [3,3,3,2,1] => 12
[3,3,3,2,1] => [3,3,3,2,1] => [3,3,3,2,1] => 12
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[1,1,1,1,1,2] => [1,1,1,1,1,2] => [2,1,1,1,1,1] => 7
[1,1,1,1,2,1] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 7
[1,1,1,2,1,1] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 7
[1,1,2,1,1,1] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 7
[1,2,1,1,1,1] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 7
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 7
[1,1,1,1,1,3] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 8
[1,1,1,1,3,1] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 8
[1,1,1,3,1,1] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 8
[1,1,3,1,1,1] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 8
[1,3,1,1,1,1] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[3,1,1,1,1,1] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[1,1,1,1,1,4] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 9
[1,1,1,1,4,1] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 9
[1,1,1,4,1,1] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 9
[1,1,4,1,1,1] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 9
[1,4,1,1,1,1] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 9
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 9
[1,1,1,1,1,5] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 10
[1,1,1,1,5,1] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => 10
[1,1,1,5,1,1] => [1,1,1,5,1,1] => [5,1,1,1,1,1] => 10
[1,1,5,1,1,1] => [1,1,5,1,1,1] => [5,1,1,1,1,1] => 10
[1,5,1,1,1,1] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 10
[5,1,1,1,1,1] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 10
[1,1,1,1,1,6] => [1,1,1,1,1,6] => [6,1,1,1,1,1] => 11
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => 11
[1,1,1,1,2,2] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 8
[1,1,1,2,1,2] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => 8
[1,1,1,2,2,1] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => 8
[1,1,2,1,1,2] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 8
[1,1,2,1,2,1] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => 8
[1,1,2,2,1,1] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => 8
[1,2,1,1,1,2] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 8
[1,2,1,1,2,1] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 8
[1,2,1,2,1,1] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => 8
[1,2,2,1,1,1] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 8
[2,1,1,1,1,2] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 8
[2,1,1,1,2,1] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 8
[2,1,1,2,1,1] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 8
[2,1,2,1,1,1] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 8
[2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 8
[1,1,1,1,2,3] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => 9
[1,1,1,1,3,2] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => 9
[1,1,1,2,1,3] => [1,1,1,2,1,3] => [3,2,1,1,1,1] => 9
[1,1,1,2,3,1] => [1,1,1,2,3,1] => [3,2,1,1,1,1] => 9
[1,1,1,3,1,2] => [1,1,1,3,1,2] => [3,2,1,1,1,1] => 9
[1,1,1,3,2,1] => [1,1,1,3,2,1] => [3,2,1,1,1,1] => 9
[1,1,2,1,1,3] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => 9
[1,1,2,1,3,1] => [1,1,2,1,3,1] => [3,2,1,1,1,1] => 9
[1,1,2,3,1,1] => [1,1,2,3,1,1] => [3,2,1,1,1,1] => 9
[1,1,3,1,1,2] => [1,1,3,1,1,2] => [3,2,1,1,1,1] => 9
[1,1,3,1,2,1] => [1,1,3,1,2,1] => [3,2,1,1,1,1] => 9
[1,1,3,2,1,1] => [1,1,3,2,1,1] => [3,2,1,1,1,1] => 9
[1,2,1,1,1,3] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => 9
[1,2,1,1,3,1] => [1,2,1,1,3,1] => [3,2,1,1,1,1] => 9
[1,2,1,3,1,1] => [1,2,1,3,1,1] => [3,2,1,1,1,1] => 9
[1,2,3,1,1,1] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => 9
[1,3,1,1,1,2] => [1,3,1,1,1,2] => [3,2,1,1,1,1] => 9
[1,3,1,1,2,1] => [1,3,1,1,2,1] => [3,2,1,1,1,1] => 9
[1,3,1,2,1,1] => [1,3,1,2,1,1] => [3,2,1,1,1,1] => 9
[1,3,2,1,1,1] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => 9
[2,1,1,1,1,3] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 9
[2,1,1,1,3,1] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => 9
[2,1,1,3,1,1] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => 9
[2,1,3,1,1,1] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => 9
[2,3,1,1,1,1] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 9
[3,1,1,1,1,2] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 9
[3,1,1,1,2,1] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => 9
[3,1,1,2,1,1] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => 9
[3,1,2,1,1,1] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => 9
[3,2,1,1,1,1] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => 9
[1,1,1,1,2,4] => [1,1,1,1,2,4] => [4,2,1,1,1,1] => 10
[1,1,1,1,4,2] => [1,1,1,1,4,2] => [4,2,1,1,1,1] => 10
[1,1,1,2,1,4] => [1,1,1,2,1,4] => [4,2,1,1,1,1] => 10
[1,1,1,2,4,1] => [1,1,1,2,4,1] => [4,2,1,1,1,1] => 10
[1,1,1,4,1,2] => [1,1,1,4,1,2] => [4,2,1,1,1,1] => 10
[1,1,1,4,2,1] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => 10
[1,1,2,1,1,4] => [1,1,2,1,1,4] => [4,2,1,1,1,1] => 10
[1,1,2,1,4,1] => [1,1,2,1,4,1] => [4,2,1,1,1,1] => 10
[1,1,2,4,1,1] => [1,1,2,4,1,1] => [4,2,1,1,1,1] => 10
[1,1,4,1,1,2] => [1,1,4,1,1,2] => [4,2,1,1,1,1] => 10
[1,1,4,1,2,1] => [1,1,4,1,2,1] => [4,2,1,1,1,1] => 10
[1,1,4,2,1,1] => [1,1,4,2,1,1] => [4,2,1,1,1,1] => 10
[1,2,1,1,1,4] => [1,2,1,1,1,4] => [4,2,1,1,1,1] => 10
[1,2,1,1,4,1] => [1,2,1,1,4,1] => [4,2,1,1,1,1] => 10
[1,2,1,4,1,1] => [1,2,1,4,1,1] => [4,2,1,1,1,1] => 10
[1,2,4,1,1,1] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => 10
[1,4,1,1,1,2] => [1,4,1,1,1,2] => [4,2,1,1,1,1] => 10
[1,4,1,1,2,1] => [1,4,1,1,2,1] => [4,2,1,1,1,1] => 10
[1,4,1,2,1,1] => [1,4,1,2,1,1] => [4,2,1,1,1,1] => 10
[1,4,2,1,1,1] => [1,4,2,1,1,1] => [4,2,1,1,1,1] => 10
[2,1,1,1,1,4] => [2,1,1,1,1,4] => [4,2,1,1,1,1] => 10
[2,1,1,1,4,1] => [2,1,1,1,4,1] => [4,2,1,1,1,1] => 10
[2,1,1,4,1,1] => [2,1,1,4,1,1] => [4,2,1,1,1,1] => 10
[2,1,4,1,1,1] => [2,1,4,1,1,1] => [4,2,1,1,1,1] => 10
[2,4,1,1,1,1] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => 10
[4,1,1,1,1,2] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => 10
[4,1,1,1,2,1] => [4,1,1,1,2,1] => [4,2,1,1,1,1] => 10
[4,1,1,2,1,1] => [4,1,1,2,1,1] => [4,2,1,1,1,1] => 10
[4,1,2,1,1,1] => [4,1,2,1,1,1] => [4,2,1,1,1,1] => 10
[4,2,1,1,1,1] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => 10
[1,1,1,1,2,5] => [1,1,1,1,2,5] => [5,2,1,1,1,1] => 11
[1,1,1,1,5,2] => [1,1,1,1,5,2] => [5,2,1,1,1,1] => 11
[1,1,1,2,1,5] => [1,1,1,2,1,5] => [5,2,1,1,1,1] => 11
[1,1,2,1,1,5] => [1,1,2,1,1,5] => [5,2,1,1,1,1] => 11
[1,1,2,5,1,1] => [1,1,2,5,1,1] => [5,2,1,1,1,1] => 11
[1,1,5,2,1,1] => [1,1,5,2,1,1] => [5,2,1,1,1,1] => 11
[1,2,1,1,1,5] => [1,2,1,1,1,5] => [5,2,1,1,1,1] => 11
[1,5,1,1,1,2] => [1,5,1,1,1,2] => [5,2,1,1,1,1] => 11
[2,1,1,1,5,1] => [2,1,1,1,5,1] => [5,2,1,1,1,1] => 11
[2,5,1,1,1,1] => [2,5,1,1,1,1] => [5,2,1,1,1,1] => 11
[5,1,1,1,1,2] => [5,1,1,1,1,2] => [5,2,1,1,1,1] => 11
[5,1,1,1,2,1] => [5,1,1,1,2,1] => [5,2,1,1,1,1] => 11
[5,1,1,2,1,1] => [5,1,1,2,1,1] => [5,2,1,1,1,1] => 11
[5,1,2,1,1,1] => [5,1,2,1,1,1] => [5,2,1,1,1,1] => 11
[5,2,1,1,1,1] => [5,2,1,1,1,1] => [5,2,1,1,1,1] => 11
[1,6,1,1,1,2] => [1,6,1,1,1,2] => [6,2,1,1,1,1] => 12
[2,1,1,1,6,1] => [2,1,1,1,6,1] => [6,2,1,1,1,1] => 12
[1,1,1,1,3,3] => [1,1,1,1,3,3] => [3,3,1,1,1,1] => 10
[1,1,1,3,1,3] => [1,1,1,3,1,3] => [3,3,1,1,1,1] => 10
[1,1,1,3,3,1] => [1,1,1,3,3,1] => [3,3,1,1,1,1] => 10
[1,1,3,1,1,3] => [1,1,3,1,1,3] => [3,3,1,1,1,1] => 10
[1,1,3,1,3,1] => [1,1,3,1,3,1] => [3,3,1,1,1,1] => 10
[1,1,3,3,1,1] => [1,1,3,3,1,1] => [3,3,1,1,1,1] => 10
[1,3,1,1,1,3] => [1,3,1,1,1,3] => [3,3,1,1,1,1] => 10
[1,3,1,1,3,1] => [1,3,1,1,3,1] => [3,3,1,1,1,1] => 10
[1,3,1,3,1,1] => [1,3,1,3,1,1] => [3,3,1,1,1,1] => 10
[1,3,3,1,1,1] => [1,3,3,1,1,1] => [3,3,1,1,1,1] => 10
[3,1,1,1,1,3] => [3,1,1,1,1,3] => [3,3,1,1,1,1] => 10
[3,1,1,1,3,1] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => 10
[3,1,1,3,1,1] => [3,1,1,3,1,1] => [3,3,1,1,1,1] => 10
[3,1,3,1,1,1] => [3,1,3,1,1,1] => [3,3,1,1,1,1] => 10
[3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => 10
[1,1,1,1,3,4] => [1,1,1,1,3,4] => [4,3,1,1,1,1] => 11
[1,1,1,1,4,3] => [1,1,1,1,4,3] => [4,3,1,1,1,1] => 11
[1,1,1,3,1,4] => [1,1,1,3,1,4] => [4,3,1,1,1,1] => 11
[1,1,1,4,1,3] => [1,1,1,4,1,3] => [4,3,1,1,1,1] => 11
[1,1,3,1,1,4] => [1,1,3,1,1,4] => [4,3,1,1,1,1] => 11
[3,1,4,1,1,1] => [3,1,4,1,1,1] => [4,3,1,1,1,1] => 11
[3,4,1,1,1,1] => [3,4,1,1,1,1] => [4,3,1,1,1,1] => 11
[4,1,1,3,1,1] => [4,1,1,3,1,1] => [4,3,1,1,1,1] => 11
[4,1,3,1,1,1] => [4,1,3,1,1,1] => [4,3,1,1,1,1] => 11
[4,3,1,1,1,1] => [4,3,1,1,1,1] => [4,3,1,1,1,1] => 11
[1,1,1,1,4,4] => [1,1,1,1,4,4] => [4,4,1,1,1,1] => 12
[1,1,4,1,1,4] => [1,1,4,1,1,4] => [4,4,1,1,1,1] => 12
[1,1,4,4,1,1] => [1,1,4,4,1,1] => [4,4,1,1,1,1] => 12
[4,1,1,1,1,4] => [4,1,1,1,1,4] => [4,4,1,1,1,1] => 12
[4,1,1,4,1,1] => [4,1,1,4,1,1] => [4,4,1,1,1,1] => 12
[4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,4,1,1,1,1] => 12
[1,1,1,2,2,2] => [1,1,1,2,2,2] => [2,2,2,1,1,1] => 9
[1,1,2,1,2,2] => [1,1,2,1,2,2] => [2,2,2,1,1,1] => 9
[1,1,2,2,1,2] => [1,1,2,2,1,2] => [2,2,2,1,1,1] => 9
[1,1,2,2,2,1] => [1,1,2,2,2,1] => [2,2,2,1,1,1] => 9
[1,2,1,1,2,2] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => 9
[1,2,1,2,1,2] => [1,2,1,2,1,2] => [2,2,2,1,1,1] => 9
[1,2,1,2,2,1] => [1,2,1,2,2,1] => [2,2,2,1,1,1] => 9
[1,2,2,1,1,2] => [1,2,2,1,1,2] => [2,2,2,1,1,1] => 9
[1,2,2,1,2,1] => [1,2,2,1,2,1] => [2,2,2,1,1,1] => 9
[1,2,2,2,1,1] => [1,2,2,2,1,1] => [2,2,2,1,1,1] => 9
[2,1,1,1,2,2] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => 9
[2,1,1,2,1,2] => [2,1,1,2,1,2] => [2,2,2,1,1,1] => 9
[2,1,1,2,2,1] => [2,1,1,2,2,1] => [2,2,2,1,1,1] => 9
[2,1,2,1,1,2] => [2,1,2,1,1,2] => [2,2,2,1,1,1] => 9
[2,1,2,1,2,1] => [2,1,2,1,2,1] => [2,2,2,1,1,1] => 9
[2,1,2,2,1,1] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => 9
[2,2,1,1,1,2] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => 9
[2,2,1,1,2,1] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => 9
[2,2,1,2,1,1] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => 9
[2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => 9
[1,1,1,2,2,3] => [1,1,1,2,2,3] => [3,2,2,1,1,1] => 10
[1,1,1,2,3,2] => [1,1,1,2,3,2] => [3,2,2,1,1,1] => 10
[1,1,1,3,2,2] => [1,1,1,3,2,2] => [3,2,2,1,1,1] => 10
[1,1,2,1,2,3] => [1,1,2,1,2,3] => [3,2,2,1,1,1] => 10
[1,1,2,1,3,2] => [1,1,2,1,3,2] => [3,2,2,1,1,1] => 10
[1,1,2,2,1,3] => [1,1,2,2,1,3] => [3,2,2,1,1,1] => 10
[1,1,2,2,3,1] => [1,1,2,2,3,1] => [3,2,2,1,1,1] => 10
[1,1,2,3,1,2] => [1,1,2,3,1,2] => [3,2,2,1,1,1] => 10
[1,1,2,3,2,1] => [1,1,2,3,2,1] => [3,2,2,1,1,1] => 10
[1,1,3,1,2,2] => [1,1,3,1,2,2] => [3,2,2,1,1,1] => 10
[1,1,3,2,1,2] => [1,1,3,2,1,2] => [3,2,2,1,1,1] => 10
[1,1,3,2,2,1] => [1,1,3,2,2,1] => [3,2,2,1,1,1] => 10
[1,2,1,1,2,3] => [1,2,1,1,2,3] => [3,2,2,1,1,1] => 10
[1,2,1,1,3,2] => [1,2,1,1,3,2] => [3,2,2,1,1,1] => 10
[1,2,1,2,1,3] => [1,2,1,2,1,3] => [3,2,2,1,1,1] => 10
[1,2,1,2,3,1] => [1,2,1,2,3,1] => [3,2,2,1,1,1] => 10
[1,2,1,3,1,2] => [1,2,1,3,1,2] => [3,2,2,1,1,1] => 10
[1,2,1,3,2,1] => [1,2,1,3,2,1] => [3,2,2,1,1,1] => 10
[1,2,2,1,1,3] => [1,2,2,1,1,3] => [3,2,2,1,1,1] => 10
[1,2,2,1,3,1] => [1,2,2,1,3,1] => [3,2,2,1,1,1] => 10
[1,2,2,3,1,1] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => 10
[1,2,3,1,1,2] => [1,2,3,1,1,2] => [3,2,2,1,1,1] => 10
[1,2,3,1,2,1] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => 10
[1,2,3,2,1,1] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => 10
[1,3,1,1,2,2] => [1,3,1,1,2,2] => [3,2,2,1,1,1] => 10
[1,3,1,2,1,2] => [1,3,1,2,1,2] => [3,2,2,1,1,1] => 10
[1,3,1,2,2,1] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => 10
[1,3,2,1,1,2] => [1,3,2,1,1,2] => [3,2,2,1,1,1] => 10
[1,3,2,1,2,1] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => 10
[1,3,2,2,1,1] => [1,3,2,2,1,1] => [3,2,2,1,1,1] => 10
[2,1,1,1,2,3] => [2,1,1,1,2,3] => [3,2,2,1,1,1] => 10
[2,1,1,1,3,2] => [2,1,1,1,3,2] => [3,2,2,1,1,1] => 10
[2,1,1,2,1,3] => [2,1,1,2,1,3] => [3,2,2,1,1,1] => 10
[2,1,1,2,3,1] => [2,1,1,2,3,1] => [3,2,2,1,1,1] => 10
[2,1,1,3,1,2] => [2,1,1,3,1,2] => [3,2,2,1,1,1] => 10
[2,1,1,3,2,1] => [2,1,1,3,2,1] => [3,2,2,1,1,1] => 10
[2,1,2,1,1,3] => [2,1,2,1,1,3] => [3,2,2,1,1,1] => 10
[2,1,2,1,3,1] => [2,1,2,1,3,1] => [3,2,2,1,1,1] => 10
[2,1,2,3,1,1] => [2,1,2,3,1,1] => [3,2,2,1,1,1] => 10
[2,1,3,1,1,2] => [2,1,3,1,1,2] => [3,2,2,1,1,1] => 10
[2,1,3,1,2,1] => [2,1,3,1,2,1] => [3,2,2,1,1,1] => 10
[2,1,3,2,1,1] => [2,1,3,2,1,1] => [3,2,2,1,1,1] => 10
[2,2,1,1,1,3] => [2,2,1,1,1,3] => [3,2,2,1,1,1] => 10
[2,2,1,1,3,1] => [2,2,1,1,3,1] => [3,2,2,1,1,1] => 10
[2,2,1,3,1,1] => [2,2,1,3,1,1] => [3,2,2,1,1,1] => 10
[2,2,3,1,1,1] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => 10
[2,3,1,1,1,2] => [2,3,1,1,1,2] => [3,2,2,1,1,1] => 10
[2,3,1,1,2,1] => [2,3,1,1,2,1] => [3,2,2,1,1,1] => 10
[2,3,1,2,1,1] => [2,3,1,2,1,1] => [3,2,2,1,1,1] => 10
[2,3,2,1,1,1] => [2,3,2,1,1,1] => [3,2,2,1,1,1] => 10
[3,1,1,1,2,2] => [3,1,1,1,2,2] => [3,2,2,1,1,1] => 10
[3,1,1,2,1,2] => [3,1,1,2,1,2] => [3,2,2,1,1,1] => 10
[3,1,1,2,2,1] => [3,1,1,2,2,1] => [3,2,2,1,1,1] => 10
[3,1,2,1,1,2] => [3,1,2,1,1,2] => [3,2,2,1,1,1] => 10
[3,1,2,1,2,1] => [3,1,2,1,2,1] => [3,2,2,1,1,1] => 10
[3,1,2,2,1,1] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => 10
[3,2,1,1,1,2] => [3,2,1,1,1,2] => [3,2,2,1,1,1] => 10
[3,2,1,1,2,1] => [3,2,1,1,2,1] => [3,2,2,1,1,1] => 10
[3,2,1,2,1,1] => [3,2,1,2,1,1] => [3,2,2,1,1,1] => 10
[3,2,2,1,1,1] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => 10
[1,1,1,2,2,4] => [1,1,1,2,2,4] => [4,2,2,1,1,1] => 11
[1,1,1,2,4,2] => [1,1,1,2,4,2] => [4,2,2,1,1,1] => 11
[1,1,1,4,2,2] => [1,1,1,4,2,2] => [4,2,2,1,1,1] => 11
[1,1,2,1,2,4] => [1,1,2,1,2,4] => [4,2,2,1,1,1] => 11
[1,1,2,1,4,2] => [1,1,2,1,4,2] => [4,2,2,1,1,1] => 11
[1,1,2,2,1,4] => [1,1,2,2,1,4] => [4,2,2,1,1,1] => 11
[1,1,2,2,4,1] => [1,1,2,2,4,1] => [4,2,2,1,1,1] => 11
[1,2,1,1,2,4] => [1,2,1,1,2,4] => [4,2,2,1,1,1] => 11
[1,2,1,1,4,2] => [1,2,1,1,4,2] => [4,2,2,1,1,1] => 11
[1,2,1,2,1,4] => [1,2,1,2,1,4] => [4,2,2,1,1,1] => 11
[1,2,2,1,1,4] => [1,2,2,1,1,4] => [4,2,2,1,1,1] => 11
[1,4,2,1,1,2] => [1,4,2,1,1,2] => [4,2,2,1,1,1] => 11
[1,4,2,2,1,1] => [1,4,2,2,1,1] => [4,2,2,1,1,1] => 11
[2,1,1,2,4,1] => [2,1,1,2,4,1] => [4,2,2,1,1,1] => 11
[2,2,4,1,1,1] => [2,2,4,1,1,1] => [4,2,2,1,1,1] => 11
[2,4,1,1,2,1] => [2,4,1,1,2,1] => [4,2,2,1,1,1] => 11
[2,4,1,2,1,1] => [2,4,1,2,1,1] => [4,2,2,1,1,1] => 11
[2,4,2,1,1,1] => [2,4,2,1,1,1] => [4,2,2,1,1,1] => 11
[4,1,1,2,2,1] => [4,1,1,2,2,1] => [4,2,2,1,1,1] => 11
[4,1,2,1,2,1] => [4,1,2,1,2,1] => [4,2,2,1,1,1] => 11
[4,1,2,2,1,1] => [4,1,2,2,1,1] => [4,2,2,1,1,1] => 11
[4,2,1,1,2,1] => [4,2,1,1,2,1] => [4,2,2,1,1,1] => 11
[4,2,1,2,1,1] => [4,2,1,2,1,1] => [4,2,2,1,1,1] => 11
[4,2,2,1,1,1] => [4,2,2,1,1,1] => [4,2,2,1,1,1] => 11
[1,1,1,2,3,3] => [1,1,1,2,3,3] => [3,3,2,1,1,1] => 11
[1,1,1,3,2,3] => [1,1,1,3,2,3] => [3,3,2,1,1,1] => 11
[1,1,1,3,3,2] => [1,1,1,3,3,2] => [3,3,2,1,1,1] => 11
[1,1,2,1,3,3] => [1,1,2,1,3,3] => [3,3,2,1,1,1] => 11
[1,1,2,3,1,3] => [1,1,2,3,1,3] => [3,3,2,1,1,1] => 11
[1,1,3,1,2,3] => [1,1,3,1,2,3] => [3,3,2,1,1,1] => 11
[1,1,3,1,3,2] => [1,1,3,1,3,2] => [3,3,2,1,1,1] => 11
[1,1,3,2,1,3] => [1,1,3,2,1,3] => [3,3,2,1,1,1] => 11
[1,2,1,1,3,3] => [1,2,1,1,3,3] => [3,3,2,1,1,1] => 11
[1,2,1,3,1,3] => [1,2,1,3,1,3] => [3,3,2,1,1,1] => 11
[2,3,1,3,1,1] => [2,3,1,3,1,1] => [3,3,2,1,1,1] => 11
[2,3,3,1,1,1] => [2,3,3,1,1,1] => [3,3,2,1,1,1] => 11
[3,1,2,3,1,1] => [3,1,2,3,1,1] => [3,3,2,1,1,1] => 11
[3,1,3,1,2,1] => [3,1,3,1,2,1] => [3,3,2,1,1,1] => 11
[3,1,3,2,1,1] => [3,1,3,2,1,1] => [3,3,2,1,1,1] => 11
[3,2,1,3,1,1] => [3,2,1,3,1,1] => [3,3,2,1,1,1] => 11
[3,2,3,1,1,1] => [3,2,3,1,1,1] => [3,3,2,1,1,1] => 11
[3,3,1,1,2,1] => [3,3,1,1,2,1] => [3,3,2,1,1,1] => 11
[3,3,1,2,1,1] => [3,3,1,2,1,1] => [3,3,2,1,1,1] => 11
[3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,3,2,1,1,1] => 11
[1,1,2,1,3,4] => [1,1,2,1,3,4] => [4,3,2,1,1,1] => 12
[1,1,3,1,2,4] => [1,1,3,1,2,4] => [4,3,2,1,1,1] => 12
[1,1,4,2,1,3] => [1,1,4,2,1,3] => [4,3,2,1,1,1] => 12
[1,1,4,3,1,2] => [1,1,4,3,1,2] => [4,3,2,1,1,1] => 12
[2,1,1,1,3,4] => [2,1,1,1,3,4] => [4,3,2,1,1,1] => 12
[2,1,3,1,1,4] => [2,1,3,1,1,4] => [4,3,2,1,1,1] => 12
[2,1,3,4,1,1] => [2,1,3,4,1,1] => [4,3,2,1,1,1] => 12
[3,1,1,1,2,4] => [3,1,1,1,2,4] => [4,3,2,1,1,1] => 12
[3,1,2,1,1,4] => [3,1,2,1,1,4] => [4,3,2,1,1,1] => 12
[3,1,2,4,1,1] => [3,1,2,4,1,1] => [4,3,2,1,1,1] => 12
[4,1,1,2,1,3] => [4,1,1,2,1,3] => [4,3,2,1,1,1] => 12
[4,1,1,3,1,2] => [4,1,1,3,1,2] => [4,3,2,1,1,1] => 12
[4,2,1,1,1,3] => [4,2,1,1,1,3] => [4,3,2,1,1,1] => 12
[4,2,1,3,1,1] => [4,2,1,3,1,1] => [4,3,2,1,1,1] => 12
[4,3,1,1,1,2] => [4,3,1,1,1,2] => [4,3,2,1,1,1] => 12
[4,3,1,2,1,1] => [4,3,1,2,1,1] => [4,3,2,1,1,1] => 12
[1,1,2,2,2,2] => [1,1,2,2,2,2] => [2,2,2,2,1,1] => 10
[1,2,1,2,2,2] => [1,2,1,2,2,2] => [2,2,2,2,1,1] => 10
[1,2,2,1,2,2] => [1,2,2,1,2,2] => [2,2,2,2,1,1] => 10
[1,2,2,2,1,2] => [1,2,2,2,1,2] => [2,2,2,2,1,1] => 10
[1,2,2,2,2,1] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 10
[2,1,1,2,2,2] => [2,1,1,2,2,2] => [2,2,2,2,1,1] => 10
[2,1,2,1,2,2] => [2,1,2,1,2,2] => [2,2,2,2,1,1] => 10
[2,1,2,2,1,2] => [2,1,2,2,1,2] => [2,2,2,2,1,1] => 10
[2,1,2,2,2,1] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => 10
[2,2,1,1,2,2] => [2,2,1,1,2,2] => [2,2,2,2,1,1] => 10
[2,2,1,2,1,2] => [2,2,1,2,1,2] => [2,2,2,2,1,1] => 10
[2,2,1,2,2,1] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => 10
[2,2,2,1,1,2] => [2,2,2,1,1,2] => [2,2,2,2,1,1] => 10
[2,2,2,1,2,1] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => 10
[2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => 10
[1,1,2,2,2,3] => [1,1,2,2,2,3] => [3,2,2,2,1,1] => 11
[1,1,2,2,3,2] => [1,1,2,2,3,2] => [3,2,2,2,1,1] => 11
[1,1,2,3,2,2] => [1,1,2,3,2,2] => [3,2,2,2,1,1] => 11
[1,1,3,2,2,2] => [1,1,3,2,2,2] => [3,2,2,2,1,1] => 11
[1,2,1,2,2,3] => [1,2,1,2,2,3] => [3,2,2,2,1,1] => 11
[1,2,1,2,3,2] => [1,2,1,2,3,2] => [3,2,2,2,1,1] => 11
[1,2,1,3,2,2] => [1,2,1,3,2,2] => [3,2,2,2,1,1] => 11
[1,2,2,1,2,3] => [1,2,2,1,2,3] => [3,2,2,2,1,1] => 11
[1,2,2,1,3,2] => [1,2,2,1,3,2] => [3,2,2,2,1,1] => 11
[1,2,2,2,1,3] => [1,2,2,2,1,3] => [3,2,2,2,1,1] => 11
[2,2,2,3,1,1] => [2,2,2,3,1,1] => [3,2,2,2,1,1] => 11
[2,2,3,1,2,1] => [2,2,3,1,2,1] => [3,2,2,2,1,1] => 11
[2,2,3,2,1,1] => [2,2,3,2,1,1] => [3,2,2,2,1,1] => 11
[2,3,1,2,2,1] => [2,3,1,2,2,1] => [3,2,2,2,1,1] => 11
[2,3,2,1,2,1] => [2,3,2,1,2,1] => [3,2,2,2,1,1] => 11
[2,3,2,2,1,1] => [2,3,2,2,1,1] => [3,2,2,2,1,1] => 11
[3,1,2,2,2,1] => [3,1,2,2,2,1] => [3,2,2,2,1,1] => 11
[3,2,1,2,2,1] => [3,2,1,2,2,1] => [3,2,2,2,1,1] => 11
[3,2,2,1,2,1] => [3,2,2,1,2,1] => [3,2,2,2,1,1] => 11
[3,2,2,2,1,1] => [3,2,2,2,1,1] => [3,2,2,2,1,1] => 11
[1,1,2,2,2,4] => [1,1,2,2,2,4] => [4,2,2,2,1,1] => 12
[1,2,2,4,2,1] => [1,2,2,4,2,1] => [4,2,2,2,1,1] => 12
[1,2,4,2,2,1] => [1,2,4,2,2,1] => [4,2,2,2,1,1] => 12
[1,4,2,2,2,1] => [1,4,2,2,2,1] => [4,2,2,2,1,1] => 12
[2,1,2,1,2,4] => [2,1,2,1,2,4] => [4,2,2,2,1,1] => 12
[4,2,1,2,1,2] => [4,2,1,2,1,2] => [4,2,2,2,1,1] => 12
[1,1,2,2,3,3] => [1,1,2,2,3,3] => [3,3,2,2,1,1] => 12
[1,1,2,3,2,3] => [1,1,2,3,2,3] => [3,3,2,2,1,1] => 12
[1,1,3,2,2,3] => [1,1,3,2,2,3] => [3,3,2,2,1,1] => 12
[1,1,3,3,2,2] => [1,1,3,3,2,2] => [3,3,2,2,1,1] => 12
[1,2,2,3,3,1] => [1,2,2,3,3,1] => [3,3,2,2,1,1] => 12
[1,2,3,2,3,1] => [1,2,3,2,3,1] => [3,3,2,2,1,1] => 12
[1,2,3,3,2,1] => [1,2,3,3,2,1] => [3,3,2,2,1,1] => 12
[1,3,2,2,3,1] => [1,3,2,2,3,1] => [3,3,2,2,1,1] => 12
[1,3,2,3,2,1] => [1,3,2,3,2,1] => [3,3,2,2,1,1] => 12
[1,3,3,2,2,1] => [1,3,3,2,2,1] => [3,3,2,2,1,1] => 12
[2,1,1,2,3,3] => [2,1,1,2,3,3] => [3,3,2,2,1,1] => 12
[2,1,3,2,1,3] => [2,1,3,2,1,3] => [3,3,2,2,1,1] => 12
[2,1,3,3,1,2] => [2,1,3,3,1,2] => [3,3,2,2,1,1] => 12
[2,2,1,1,3,3] => [2,2,1,1,3,3] => [3,3,2,2,1,1] => 12
[2,2,3,1,1,3] => [2,2,3,1,1,3] => [3,3,2,2,1,1] => 12
[2,2,3,3,1,1] => [2,2,3,3,1,1] => [3,3,2,2,1,1] => 12
[3,1,1,2,2,3] => [3,1,1,2,2,3] => [3,3,2,2,1,1] => 12
[3,1,1,3,2,2] => [3,1,1,3,2,2] => [3,3,2,2,1,1] => 12
[3,1,2,2,1,3] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => 12
[3,1,2,3,1,2] => [3,1,2,3,1,2] => [3,3,2,2,1,1] => 12
[3,2,1,1,2,3] => [3,2,1,1,2,3] => [3,3,2,2,1,1] => 12
[3,2,2,1,1,3] => [3,2,2,1,1,3] => [3,3,2,2,1,1] => 12
[3,2,2,3,1,1] => [3,2,2,3,1,1] => [3,3,2,2,1,1] => 12
[3,3,1,1,2,2] => [3,3,1,1,2,2] => [3,3,2,2,1,1] => 12
[3,3,2,1,1,2] => [3,3,2,1,1,2] => [3,3,2,2,1,1] => 12
[3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,3,2,2,1,1] => 12
[1,2,2,2,2,2] => [1,2,2,2,2,2] => [2,2,2,2,2,1] => 11
[2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,2,1] => 11
[1,2,2,2,2,3] => [1,2,2,2,2,3] => [3,2,2,2,2,1] => 12
[1,2,2,2,3,2] => [1,2,2,2,3,2] => [3,2,2,2,2,1] => 12
[1,2,2,3,2,2] => [1,2,2,3,2,2] => [3,2,2,2,2,1] => 12
[1,2,3,2,2,2] => [1,2,3,2,2,2] => [3,2,2,2,2,1] => 12
[1,3,2,2,2,2] => [1,3,2,2,2,2] => [3,2,2,2,2,1] => 12
[2,1,2,2,2,3] => [2,1,2,2,2,3] => [3,2,2,2,2,1] => 12
[2,1,2,3,2,2] => [2,1,2,3,2,2] => [3,2,2,2,2,1] => 12
[2,2,2,1,2,3] => [2,2,2,1,2,3] => [3,2,2,2,2,1] => 12
[2,2,2,2,3,1] => [2,2,2,2,3,1] => [3,2,2,2,2,1] => 12
[2,2,2,3,2,1] => [2,2,2,3,2,1] => [3,2,2,2,2,1] => 12
[2,2,3,2,1,2] => [2,2,3,2,1,2] => [3,2,2,2,2,1] => 12
[2,2,3,2,2,1] => [2,2,3,2,2,1] => [3,2,2,2,2,1] => 12
[2,3,2,2,2,1] => [2,3,2,2,2,1] => [3,2,2,2,2,1] => 12
[3,2,1,2,2,2] => [3,2,1,2,2,2] => [3,2,2,2,2,1] => 12
[3,2,2,2,1,2] => [3,2,2,2,1,2] => [3,2,2,2,2,1] => 12
[3,2,2,2,2,1] => [3,2,2,2,2,1] => [3,2,2,2,2,1] => 12
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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:
1,2 1,3,6,6 1,4,10,20,30,36,24
$F_{1} = q$
$F_{2} = q^{2} + 2\ q^{3}$
$F_{3} = q^{3} + 3\ q^{4} + 6\ q^{5} + 6\ q^{6}$
$F_{4} = q^{4} + 4\ q^{5} + 10\ q^{6} + 20\ q^{7} + 30\ q^{8} + 36\ q^{9} + 24\ q^{10}$
Description
The number of different non-empty partial sums of an integer partition.
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Description
Return the parking function interpreted as an integer composition.
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to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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