Identifier
-
Mp00302:
Parking functions
—insertion tableau⟶
Semistandard tableaux
St000103: Semistandard tableaux ⟶ ℤ
Values
[1] => [[1]] => 1
[1,1] => [[1,1]] => 2
[1,2] => [[1,2]] => 3
[2,1] => [[1],[2]] => 3
[1,1,1] => [[1,1,1]] => 3
[1,1,2] => [[1,1,2]] => 4
[1,2,1] => [[1,1],[2]] => 4
[2,1,1] => [[1,1],[2]] => 4
[1,1,3] => [[1,1,3]] => 5
[1,3,1] => [[1,1],[3]] => 5
[3,1,1] => [[1,1],[3]] => 5
[1,2,2] => [[1,2,2]] => 5
[2,1,2] => [[1,2],[2]] => 5
[2,2,1] => [[1,2],[2]] => 5
[1,2,3] => [[1,2,3]] => 6
[1,3,2] => [[1,2],[3]] => 6
[2,1,3] => [[1,3],[2]] => 6
[2,3,1] => [[1,3],[2]] => 6
[3,1,2] => [[1,2],[3]] => 6
[3,2,1] => [[1],[2],[3]] => 6
[1,1,1,1] => [[1,1,1,1]] => 4
[1,1,1,2] => [[1,1,1,2]] => 5
[1,1,2,1] => [[1,1,1],[2]] => 5
[1,2,1,1] => [[1,1,1],[2]] => 5
[2,1,1,1] => [[1,1,1],[2]] => 5
[1,1,1,3] => [[1,1,1,3]] => 6
[1,1,3,1] => [[1,1,1],[3]] => 6
[1,3,1,1] => [[1,1,1],[3]] => 6
[3,1,1,1] => [[1,1,1],[3]] => 6
[1,1,1,4] => [[1,1,1,4]] => 7
[1,1,4,1] => [[1,1,1],[4]] => 7
[1,4,1,1] => [[1,1,1],[4]] => 7
[4,1,1,1] => [[1,1,1],[4]] => 7
[1,1,2,2] => [[1,1,2,2]] => 6
[1,2,1,2] => [[1,1,2],[2]] => 6
[1,2,2,1] => [[1,1,2],[2]] => 6
[2,1,1,2] => [[1,1,2],[2]] => 6
[2,1,2,1] => [[1,1],[2,2]] => 6
[2,2,1,1] => [[1,1],[2,2]] => 6
[1,1,2,3] => [[1,1,2,3]] => 7
[1,1,3,2] => [[1,1,2],[3]] => 7
[1,2,1,3] => [[1,1,3],[2]] => 7
[1,2,3,1] => [[1,1,3],[2]] => 7
[1,3,1,2] => [[1,1,2],[3]] => 7
[1,3,2,1] => [[1,1],[2],[3]] => 7
[2,1,1,3] => [[1,1,3],[2]] => 7
[2,1,3,1] => [[1,1],[2,3]] => 7
[2,3,1,1] => [[1,1],[2,3]] => 7
[3,1,1,2] => [[1,1,2],[3]] => 7
[3,1,2,1] => [[1,1],[2],[3]] => 7
[3,2,1,1] => [[1,1],[2],[3]] => 7
[1,1,2,4] => [[1,1,2,4]] => 8
[1,1,4,2] => [[1,1,2],[4]] => 8
[1,2,1,4] => [[1,1,4],[2]] => 8
[1,2,4,1] => [[1,1,4],[2]] => 8
[1,4,1,2] => [[1,1,2],[4]] => 8
[1,4,2,1] => [[1,1],[2],[4]] => 8
[2,1,1,4] => [[1,1,4],[2]] => 8
[2,1,4,1] => [[1,1],[2,4]] => 8
[2,4,1,1] => [[1,1],[2,4]] => 8
[4,1,1,2] => [[1,1,2],[4]] => 8
[4,1,2,1] => [[1,1],[2],[4]] => 8
[4,2,1,1] => [[1,1],[2],[4]] => 8
[1,1,3,3] => [[1,1,3,3]] => 8
[1,3,1,3] => [[1,1,3],[3]] => 8
[1,3,3,1] => [[1,1,3],[3]] => 8
[3,1,1,3] => [[1,1,3],[3]] => 8
[3,1,3,1] => [[1,1],[3,3]] => 8
[3,3,1,1] => [[1,1],[3,3]] => 8
[1,1,3,4] => [[1,1,3,4]] => 9
[1,1,4,3] => [[1,1,3],[4]] => 9
[1,3,1,4] => [[1,1,4],[3]] => 9
[1,3,4,1] => [[1,1,4],[3]] => 9
[1,4,1,3] => [[1,1,3],[4]] => 9
[1,4,3,1] => [[1,1],[3],[4]] => 9
[3,1,1,4] => [[1,1,4],[3]] => 9
[3,1,4,1] => [[1,1],[3,4]] => 9
[3,4,1,1] => [[1,1],[3,4]] => 9
[4,1,1,3] => [[1,1,3],[4]] => 9
[4,1,3,1] => [[1,1],[3],[4]] => 9
[4,3,1,1] => [[1,1],[3],[4]] => 9
[1,2,2,2] => [[1,2,2,2]] => 7
[2,1,2,2] => [[1,2,2],[2]] => 7
[2,2,1,2] => [[1,2,2],[2]] => 7
[2,2,2,1] => [[1,2,2],[2]] => 7
[1,2,2,3] => [[1,2,2,3]] => 8
[1,2,3,2] => [[1,2,2],[3]] => 8
[1,3,2,2] => [[1,2,2],[3]] => 8
[2,1,2,3] => [[1,2,3],[2]] => 8
[2,1,3,2] => [[1,2],[2,3]] => 8
[2,2,1,3] => [[1,2,3],[2]] => 8
[2,2,3,1] => [[1,2,3],[2]] => 8
[2,3,1,2] => [[1,2],[2,3]] => 8
[2,3,2,1] => [[1,2],[2],[3]] => 8
[3,1,2,2] => [[1,2,2],[3]] => 8
[3,2,1,2] => [[1,2],[2],[3]] => 8
[3,2,2,1] => [[1,2],[2],[3]] => 8
[1,2,2,4] => [[1,2,2,4]] => 9
[1,2,4,2] => [[1,2,2],[4]] => 9
[1,4,2,2] => [[1,2,2],[4]] => 9
[2,1,2,4] => [[1,2,4],[2]] => 9
>>> Load all 1441 entries. <<<[2,1,4,2] => [[1,2],[2,4]] => 9
[2,2,1,4] => [[1,2,4],[2]] => 9
[2,2,4,1] => [[1,2,4],[2]] => 9
[2,4,1,2] => [[1,2],[2,4]] => 9
[2,4,2,1] => [[1,2],[2],[4]] => 9
[4,1,2,2] => [[1,2,2],[4]] => 9
[4,2,1,2] => [[1,2],[2],[4]] => 9
[4,2,2,1] => [[1,2],[2],[4]] => 9
[1,2,3,3] => [[1,2,3,3]] => 9
[1,3,2,3] => [[1,2,3],[3]] => 9
[1,3,3,2] => [[1,2,3],[3]] => 9
[2,1,3,3] => [[1,3,3],[2]] => 9
[2,3,1,3] => [[1,3,3],[2]] => 9
[2,3,3,1] => [[1,3,3],[2]] => 9
[3,1,2,3] => [[1,2,3],[3]] => 9
[3,1,3,2] => [[1,2],[3,3]] => 9
[3,2,1,3] => [[1,3],[2],[3]] => 9
[3,2,3,1] => [[1,3],[2],[3]] => 9
[3,3,1,2] => [[1,2],[3,3]] => 9
[3,3,2,1] => [[1,3],[2],[3]] => 9
[1,2,3,4] => [[1,2,3,4]] => 10
[1,2,4,3] => [[1,2,3],[4]] => 10
[1,3,2,4] => [[1,2,4],[3]] => 10
[1,3,4,2] => [[1,2,4],[3]] => 10
[1,4,2,3] => [[1,2,3],[4]] => 10
[1,4,3,2] => [[1,2],[3],[4]] => 10
[2,1,3,4] => [[1,3,4],[2]] => 10
[2,1,4,3] => [[1,3],[2,4]] => 10
[2,3,1,4] => [[1,3,4],[2]] => 10
[2,3,4,1] => [[1,3,4],[2]] => 10
[2,4,1,3] => [[1,3],[2,4]] => 10
[2,4,3,1] => [[1,3],[2],[4]] => 10
[3,1,2,4] => [[1,2,4],[3]] => 10
[3,1,4,2] => [[1,2],[3,4]] => 10
[3,2,1,4] => [[1,4],[2],[3]] => 10
[3,2,4,1] => [[1,4],[2],[3]] => 10
[3,4,1,2] => [[1,2],[3,4]] => 10
[3,4,2,1] => [[1,4],[2],[3]] => 10
[4,1,2,3] => [[1,2,3],[4]] => 10
[4,1,3,2] => [[1,2],[3],[4]] => 10
[4,2,1,3] => [[1,3],[2],[4]] => 10
[4,2,3,1] => [[1,3],[2],[4]] => 10
[4,3,1,2] => [[1,2],[3],[4]] => 10
[4,3,2,1] => [[1],[2],[3],[4]] => 10
[1,1,1,1,1] => [[1,1,1,1,1]] => 5
[1,1,1,1,2] => [[1,1,1,1,2]] => 6
[1,1,1,2,1] => [[1,1,1,1],[2]] => 6
[1,1,2,1,1] => [[1,1,1,1],[2]] => 6
[1,2,1,1,1] => [[1,1,1,1],[2]] => 6
[2,1,1,1,1] => [[1,1,1,1],[2]] => 6
[1,1,1,1,3] => [[1,1,1,1,3]] => 7
[1,1,1,3,1] => [[1,1,1,1],[3]] => 7
[1,1,3,1,1] => [[1,1,1,1],[3]] => 7
[1,3,1,1,1] => [[1,1,1,1],[3]] => 7
[3,1,1,1,1] => [[1,1,1,1],[3]] => 7
[1,1,1,1,4] => [[1,1,1,1,4]] => 8
[1,1,1,4,1] => [[1,1,1,1],[4]] => 8
[1,1,4,1,1] => [[1,1,1,1],[4]] => 8
[1,4,1,1,1] => [[1,1,1,1],[4]] => 8
[4,1,1,1,1] => [[1,1,1,1],[4]] => 8
[1,1,1,1,5] => [[1,1,1,1,5]] => 9
[1,1,1,5,1] => [[1,1,1,1],[5]] => 9
[1,1,5,1,1] => [[1,1,1,1],[5]] => 9
[1,5,1,1,1] => [[1,1,1,1],[5]] => 9
[5,1,1,1,1] => [[1,1,1,1],[5]] => 9
[1,1,1,2,2] => [[1,1,1,2,2]] => 7
[1,1,2,1,2] => [[1,1,1,2],[2]] => 7
[1,1,2,2,1] => [[1,1,1,2],[2]] => 7
[1,2,1,1,2] => [[1,1,1,2],[2]] => 7
[1,2,1,2,1] => [[1,1,1],[2,2]] => 7
[1,2,2,1,1] => [[1,1,1],[2,2]] => 7
[2,1,1,1,2] => [[1,1,1,2],[2]] => 7
[2,1,1,2,1] => [[1,1,1],[2,2]] => 7
[2,1,2,1,1] => [[1,1,1],[2,2]] => 7
[2,2,1,1,1] => [[1,1,1],[2,2]] => 7
[1,1,1,2,3] => [[1,1,1,2,3]] => 8
[1,1,1,3,2] => [[1,1,1,2],[3]] => 8
[1,1,2,1,3] => [[1,1,1,3],[2]] => 8
[1,1,2,3,1] => [[1,1,1,3],[2]] => 8
[1,1,3,1,2] => [[1,1,1,2],[3]] => 8
[1,1,3,2,1] => [[1,1,1],[2],[3]] => 8
[1,2,1,1,3] => [[1,1,1,3],[2]] => 8
[1,2,1,3,1] => [[1,1,1],[2,3]] => 8
[1,2,3,1,1] => [[1,1,1],[2,3]] => 8
[1,3,1,1,2] => [[1,1,1,2],[3]] => 8
[1,3,1,2,1] => [[1,1,1],[2],[3]] => 8
[1,3,2,1,1] => [[1,1,1],[2],[3]] => 8
[2,1,1,1,3] => [[1,1,1,3],[2]] => 8
[2,1,1,3,1] => [[1,1,1],[2,3]] => 8
[2,1,3,1,1] => [[1,1,1],[2,3]] => 8
[2,3,1,1,1] => [[1,1,1],[2,3]] => 8
[3,1,1,1,2] => [[1,1,1,2],[3]] => 8
[3,1,1,2,1] => [[1,1,1],[2],[3]] => 8
[3,1,2,1,1] => [[1,1,1],[2],[3]] => 8
[3,2,1,1,1] => [[1,1,1],[2],[3]] => 8
[1,1,1,2,4] => [[1,1,1,2,4]] => 9
[1,1,1,4,2] => [[1,1,1,2],[4]] => 9
[1,1,2,1,4] => [[1,1,1,4],[2]] => 9
[1,1,2,4,1] => [[1,1,1,4],[2]] => 9
[1,1,4,1,2] => [[1,1,1,2],[4]] => 9
[1,1,4,2,1] => [[1,1,1],[2],[4]] => 9
[1,2,1,1,4] => [[1,1,1,4],[2]] => 9
[1,2,1,4,1] => [[1,1,1],[2,4]] => 9
[1,2,4,1,1] => [[1,1,1],[2,4]] => 9
[1,4,1,1,2] => [[1,1,1,2],[4]] => 9
[1,4,1,2,1] => [[1,1,1],[2],[4]] => 9
[1,4,2,1,1] => [[1,1,1],[2],[4]] => 9
[2,1,1,1,4] => [[1,1,1,4],[2]] => 9
[2,1,1,4,1] => [[1,1,1],[2,4]] => 9
[2,1,4,1,1] => [[1,1,1],[2,4]] => 9
[2,4,1,1,1] => [[1,1,1],[2,4]] => 9
[4,1,1,1,2] => [[1,1,1,2],[4]] => 9
[4,1,1,2,1] => [[1,1,1],[2],[4]] => 9
[4,1,2,1,1] => [[1,1,1],[2],[4]] => 9
[4,2,1,1,1] => [[1,1,1],[2],[4]] => 9
[1,1,1,2,5] => [[1,1,1,2,5]] => 10
[1,1,1,5,2] => [[1,1,1,2],[5]] => 10
[1,1,2,1,5] => [[1,1,1,5],[2]] => 10
[1,1,2,5,1] => [[1,1,1,5],[2]] => 10
[1,1,5,1,2] => [[1,1,1,2],[5]] => 10
[1,1,5,2,1] => [[1,1,1],[2],[5]] => 10
[1,2,1,1,5] => [[1,1,1,5],[2]] => 10
[1,2,1,5,1] => [[1,1,1],[2,5]] => 10
[1,2,5,1,1] => [[1,1,1],[2,5]] => 10
[1,5,1,1,2] => [[1,1,1,2],[5]] => 10
[1,5,1,2,1] => [[1,1,1],[2],[5]] => 10
[1,5,2,1,1] => [[1,1,1],[2],[5]] => 10
[2,1,1,1,5] => [[1,1,1,5],[2]] => 10
[2,1,1,5,1] => [[1,1,1],[2,5]] => 10
[2,1,5,1,1] => [[1,1,1],[2,5]] => 10
[2,5,1,1,1] => [[1,1,1],[2,5]] => 10
[5,1,1,1,2] => [[1,1,1,2],[5]] => 10
[5,1,1,2,1] => [[1,1,1],[2],[5]] => 10
[5,1,2,1,1] => [[1,1,1],[2],[5]] => 10
[5,2,1,1,1] => [[1,1,1],[2],[5]] => 10
[1,1,1,3,3] => [[1,1,1,3,3]] => 9
[1,1,3,1,3] => [[1,1,1,3],[3]] => 9
[1,1,3,3,1] => [[1,1,1,3],[3]] => 9
[1,3,1,1,3] => [[1,1,1,3],[3]] => 9
[1,3,1,3,1] => [[1,1,1],[3,3]] => 9
[1,3,3,1,1] => [[1,1,1],[3,3]] => 9
[3,1,1,1,3] => [[1,1,1,3],[3]] => 9
[3,1,1,3,1] => [[1,1,1],[3,3]] => 9
[3,1,3,1,1] => [[1,1,1],[3,3]] => 9
[3,3,1,1,1] => [[1,1,1],[3,3]] => 9
[1,1,1,3,4] => [[1,1,1,3,4]] => 10
[1,1,1,4,3] => [[1,1,1,3],[4]] => 10
[1,1,3,1,4] => [[1,1,1,4],[3]] => 10
[1,1,3,4,1] => [[1,1,1,4],[3]] => 10
[1,1,4,1,3] => [[1,1,1,3],[4]] => 10
[1,1,4,3,1] => [[1,1,1],[3],[4]] => 10
[1,3,1,1,4] => [[1,1,1,4],[3]] => 10
[1,3,1,4,1] => [[1,1,1],[3,4]] => 10
[1,3,4,1,1] => [[1,1,1],[3,4]] => 10
[1,4,1,1,3] => [[1,1,1,3],[4]] => 10
[1,4,1,3,1] => [[1,1,1],[3],[4]] => 10
[1,4,3,1,1] => [[1,1,1],[3],[4]] => 10
[3,1,1,1,4] => [[1,1,1,4],[3]] => 10
[3,1,1,4,1] => [[1,1,1],[3,4]] => 10
[3,1,4,1,1] => [[1,1,1],[3,4]] => 10
[3,4,1,1,1] => [[1,1,1],[3,4]] => 10
[4,1,1,1,3] => [[1,1,1,3],[4]] => 10
[4,1,1,3,1] => [[1,1,1],[3],[4]] => 10
[4,1,3,1,1] => [[1,1,1],[3],[4]] => 10
[4,3,1,1,1] => [[1,1,1],[3],[4]] => 10
[1,1,1,3,5] => [[1,1,1,3,5]] => 11
[1,1,1,5,3] => [[1,1,1,3],[5]] => 11
[1,1,3,1,5] => [[1,1,1,5],[3]] => 11
[1,1,3,5,1] => [[1,1,1,5],[3]] => 11
[1,1,5,1,3] => [[1,1,1,3],[5]] => 11
[1,1,5,3,1] => [[1,1,1],[3],[5]] => 11
[1,3,1,1,5] => [[1,1,1,5],[3]] => 11
[1,3,1,5,1] => [[1,1,1],[3,5]] => 11
[1,3,5,1,1] => [[1,1,1],[3,5]] => 11
[1,5,1,1,3] => [[1,1,1,3],[5]] => 11
[1,5,1,3,1] => [[1,1,1],[3],[5]] => 11
[1,5,3,1,1] => [[1,1,1],[3],[5]] => 11
[3,1,1,1,5] => [[1,1,1,5],[3]] => 11
[3,1,1,5,1] => [[1,1,1],[3,5]] => 11
[3,1,5,1,1] => [[1,1,1],[3,5]] => 11
[3,5,1,1,1] => [[1,1,1],[3,5]] => 11
[5,1,1,1,3] => [[1,1,1,3],[5]] => 11
[5,1,1,3,1] => [[1,1,1],[3],[5]] => 11
[5,1,3,1,1] => [[1,1,1],[3],[5]] => 11
[5,3,1,1,1] => [[1,1,1],[3],[5]] => 11
[1,1,1,4,4] => [[1,1,1,4,4]] => 11
[1,1,4,1,4] => [[1,1,1,4],[4]] => 11
[1,1,4,4,1] => [[1,1,1,4],[4]] => 11
[1,4,1,1,4] => [[1,1,1,4],[4]] => 11
[1,4,1,4,1] => [[1,1,1],[4,4]] => 11
[1,4,4,1,1] => [[1,1,1],[4,4]] => 11
[4,1,1,1,4] => [[1,1,1,4],[4]] => 11
[4,1,1,4,1] => [[1,1,1],[4,4]] => 11
[4,1,4,1,1] => [[1,1,1],[4,4]] => 11
[4,4,1,1,1] => [[1,1,1],[4,4]] => 11
[1,1,1,4,5] => [[1,1,1,4,5]] => 12
[1,1,1,5,4] => [[1,1,1,4],[5]] => 12
[1,1,4,1,5] => [[1,1,1,5],[4]] => 12
[1,1,4,5,1] => [[1,1,1,5],[4]] => 12
[1,1,5,1,4] => [[1,1,1,4],[5]] => 12
[1,1,5,4,1] => [[1,1,1],[4],[5]] => 12
[1,4,1,1,5] => [[1,1,1,5],[4]] => 12
[1,4,1,5,1] => [[1,1,1],[4,5]] => 12
[1,4,5,1,1] => [[1,1,1],[4,5]] => 12
[1,5,1,1,4] => [[1,1,1,4],[5]] => 12
[1,5,1,4,1] => [[1,1,1],[4],[5]] => 12
[1,5,4,1,1] => [[1,1,1],[4],[5]] => 12
[4,1,1,1,5] => [[1,1,1,5],[4]] => 12
[4,1,1,5,1] => [[1,1,1],[4,5]] => 12
[4,1,5,1,1] => [[1,1,1],[4,5]] => 12
[4,5,1,1,1] => [[1,1,1],[4,5]] => 12
[5,1,1,1,4] => [[1,1,1,4],[5]] => 12
[5,1,1,4,1] => [[1,1,1],[4],[5]] => 12
[5,1,4,1,1] => [[1,1,1],[4],[5]] => 12
[5,4,1,1,1] => [[1,1,1],[4],[5]] => 12
[1,1,2,2,2] => [[1,1,2,2,2]] => 8
[1,2,1,2,2] => [[1,1,2,2],[2]] => 8
[1,2,2,1,2] => [[1,1,2,2],[2]] => 8
[1,2,2,2,1] => [[1,1,2,2],[2]] => 8
[2,1,1,2,2] => [[1,1,2,2],[2]] => 8
[2,1,2,1,2] => [[1,1,2],[2,2]] => 8
[2,1,2,2,1] => [[1,1,2],[2,2]] => 8
[2,2,1,1,2] => [[1,1,2],[2,2]] => 8
[2,2,1,2,1] => [[1,1,2],[2,2]] => 8
[2,2,2,1,1] => [[1,1,2],[2,2]] => 8
[1,1,2,2,3] => [[1,1,2,2,3]] => 9
[1,1,2,3,2] => [[1,1,2,2],[3]] => 9
[1,1,3,2,2] => [[1,1,2,2],[3]] => 9
[1,2,1,2,3] => [[1,1,2,3],[2]] => 9
[1,2,1,3,2] => [[1,1,2],[2,3]] => 9
[1,2,2,1,3] => [[1,1,2,3],[2]] => 9
[1,2,2,3,1] => [[1,1,2,3],[2]] => 9
[1,2,3,1,2] => [[1,1,2],[2,3]] => 9
[1,2,3,2,1] => [[1,1,2],[2],[3]] => 9
[1,3,1,2,2] => [[1,1,2,2],[3]] => 9
[1,3,2,1,2] => [[1,1,2],[2],[3]] => 9
[1,3,2,2,1] => [[1,1,2],[2],[3]] => 9
[2,1,1,2,3] => [[1,1,2,3],[2]] => 9
[2,1,1,3,2] => [[1,1,2],[2,3]] => 9
[2,1,2,1,3] => [[1,1,3],[2,2]] => 9
[2,1,2,3,1] => [[1,1,3],[2,2]] => 9
[2,1,3,1,2] => [[1,1,2],[2,3]] => 9
[2,1,3,2,1] => [[1,1],[2,2],[3]] => 9
[2,2,1,1,3] => [[1,1,3],[2,2]] => 9
[2,2,1,3,1] => [[1,1,3],[2,2]] => 9
[2,2,3,1,1] => [[1,1,3],[2,2]] => 9
[2,3,1,1,2] => [[1,1,2],[2,3]] => 9
[2,3,1,2,1] => [[1,1],[2,2],[3]] => 9
[2,3,2,1,1] => [[1,1],[2,2],[3]] => 9
[3,1,1,2,2] => [[1,1,2,2],[3]] => 9
[3,1,2,1,2] => [[1,1,2],[2],[3]] => 9
[3,1,2,2,1] => [[1,1,2],[2],[3]] => 9
[3,2,1,1,2] => [[1,1,2],[2],[3]] => 9
[3,2,1,2,1] => [[1,1],[2,2],[3]] => 9
[3,2,2,1,1] => [[1,1],[2,2],[3]] => 9
[1,1,2,2,4] => [[1,1,2,2,4]] => 10
[1,1,2,4,2] => [[1,1,2,2],[4]] => 10
[1,1,4,2,2] => [[1,1,2,2],[4]] => 10
[1,2,1,2,4] => [[1,1,2,4],[2]] => 10
[1,2,1,4,2] => [[1,1,2],[2,4]] => 10
[1,2,2,1,4] => [[1,1,2,4],[2]] => 10
[1,2,2,4,1] => [[1,1,2,4],[2]] => 10
[1,2,4,1,2] => [[1,1,2],[2,4]] => 10
[1,2,4,2,1] => [[1,1,2],[2],[4]] => 10
[1,4,1,2,2] => [[1,1,2,2],[4]] => 10
[1,4,2,1,2] => [[1,1,2],[2],[4]] => 10
[1,4,2,2,1] => [[1,1,2],[2],[4]] => 10
[2,1,1,2,4] => [[1,1,2,4],[2]] => 10
[2,1,1,4,2] => [[1,1,2],[2,4]] => 10
[2,1,2,1,4] => [[1,1,4],[2,2]] => 10
[2,1,2,4,1] => [[1,1,4],[2,2]] => 10
[2,1,4,1,2] => [[1,1,2],[2,4]] => 10
[2,1,4,2,1] => [[1,1],[2,2],[4]] => 10
[2,2,1,1,4] => [[1,1,4],[2,2]] => 10
[2,2,1,4,1] => [[1,1,4],[2,2]] => 10
[2,2,4,1,1] => [[1,1,4],[2,2]] => 10
[2,4,1,1,2] => [[1,1,2],[2,4]] => 10
[2,4,1,2,1] => [[1,1],[2,2],[4]] => 10
[2,4,2,1,1] => [[1,1],[2,2],[4]] => 10
[4,1,1,2,2] => [[1,1,2,2],[4]] => 10
[4,1,2,1,2] => [[1,1,2],[2],[4]] => 10
[4,1,2,2,1] => [[1,1,2],[2],[4]] => 10
[4,2,1,1,2] => [[1,1,2],[2],[4]] => 10
[4,2,1,2,1] => [[1,1],[2,2],[4]] => 10
[4,2,2,1,1] => [[1,1],[2,2],[4]] => 10
[1,1,2,2,5] => [[1,1,2,2,5]] => 11
[1,1,2,5,2] => [[1,1,2,2],[5]] => 11
[1,1,5,2,2] => [[1,1,2,2],[5]] => 11
[1,2,1,2,5] => [[1,1,2,5],[2]] => 11
[1,2,1,5,2] => [[1,1,2],[2,5]] => 11
[1,2,2,1,5] => [[1,1,2,5],[2]] => 11
[1,2,2,5,1] => [[1,1,2,5],[2]] => 11
[1,2,5,1,2] => [[1,1,2],[2,5]] => 11
[1,2,5,2,1] => [[1,1,2],[2],[5]] => 11
[1,5,1,2,2] => [[1,1,2,2],[5]] => 11
[1,5,2,1,2] => [[1,1,2],[2],[5]] => 11
[1,5,2,2,1] => [[1,1,2],[2],[5]] => 11
[2,1,1,2,5] => [[1,1,2,5],[2]] => 11
[2,1,1,5,2] => [[1,1,2],[2,5]] => 11
[2,1,2,1,5] => [[1,1,5],[2,2]] => 11
[2,1,2,5,1] => [[1,1,5],[2,2]] => 11
[2,1,5,1,2] => [[1,1,2],[2,5]] => 11
[2,1,5,2,1] => [[1,1],[2,2],[5]] => 11
[2,2,1,1,5] => [[1,1,5],[2,2]] => 11
[2,2,1,5,1] => [[1,1,5],[2,2]] => 11
[2,2,5,1,1] => [[1,1,5],[2,2]] => 11
[2,5,1,1,2] => [[1,1,2],[2,5]] => 11
[2,5,1,2,1] => [[1,1],[2,2],[5]] => 11
[2,5,2,1,1] => [[1,1],[2,2],[5]] => 11
[5,1,1,2,2] => [[1,1,2,2],[5]] => 11
[5,1,2,1,2] => [[1,1,2],[2],[5]] => 11
[5,1,2,2,1] => [[1,1,2],[2],[5]] => 11
[5,2,1,1,2] => [[1,1,2],[2],[5]] => 11
[5,2,1,2,1] => [[1,1],[2,2],[5]] => 11
[5,2,2,1,1] => [[1,1],[2,2],[5]] => 11
[1,1,2,3,3] => [[1,1,2,3,3]] => 10
[1,1,3,2,3] => [[1,1,2,3],[3]] => 10
[1,1,3,3,2] => [[1,1,2,3],[3]] => 10
[1,2,1,3,3] => [[1,1,3,3],[2]] => 10
[1,2,3,1,3] => [[1,1,3,3],[2]] => 10
[1,2,3,3,1] => [[1,1,3,3],[2]] => 10
[1,3,1,2,3] => [[1,1,2,3],[3]] => 10
[1,3,1,3,2] => [[1,1,2],[3,3]] => 10
[1,3,2,1,3] => [[1,1,3],[2],[3]] => 10
[1,3,2,3,1] => [[1,1,3],[2],[3]] => 10
[1,3,3,1,2] => [[1,1,2],[3,3]] => 10
[1,3,3,2,1] => [[1,1,3],[2],[3]] => 10
[2,1,1,3,3] => [[1,1,3,3],[2]] => 10
[2,1,3,1,3] => [[1,1,3],[2,3]] => 10
[2,1,3,3,1] => [[1,1,3],[2,3]] => 10
[2,3,1,1,3] => [[1,1,3],[2,3]] => 10
[2,3,1,3,1] => [[1,1,3],[2,3]] => 10
[2,3,3,1,1] => [[1,1,3],[2,3]] => 10
[3,1,1,2,3] => [[1,1,2,3],[3]] => 10
[3,1,1,3,2] => [[1,1,2],[3,3]] => 10
[3,1,2,1,3] => [[1,1,3],[2],[3]] => 10
[3,1,2,3,1] => [[1,1,3],[2],[3]] => 10
[3,1,3,1,2] => [[1,1,2],[3,3]] => 10
[3,1,3,2,1] => [[1,1],[2,3],[3]] => 10
[3,2,1,1,3] => [[1,1,3],[2],[3]] => 10
[3,2,1,3,1] => [[1,1],[2,3],[3]] => 10
[3,2,3,1,1] => [[1,1],[2,3],[3]] => 10
[3,3,1,1,2] => [[1,1,2],[3,3]] => 10
[3,3,1,2,1] => [[1,1],[2,3],[3]] => 10
[3,3,2,1,1] => [[1,1],[2,3],[3]] => 10
[1,1,2,3,4] => [[1,1,2,3,4]] => 11
[1,1,2,4,3] => [[1,1,2,3],[4]] => 11
[1,1,3,2,4] => [[1,1,2,4],[3]] => 11
[1,1,3,4,2] => [[1,1,2,4],[3]] => 11
[1,1,4,2,3] => [[1,1,2,3],[4]] => 11
[1,1,4,3,2] => [[1,1,2],[3],[4]] => 11
[1,2,1,3,4] => [[1,1,3,4],[2]] => 11
[1,2,1,4,3] => [[1,1,3],[2,4]] => 11
[1,2,3,1,4] => [[1,1,3,4],[2]] => 11
[1,2,3,4,1] => [[1,1,3,4],[2]] => 11
[1,2,4,1,3] => [[1,1,3],[2,4]] => 11
[1,2,4,3,1] => [[1,1,3],[2],[4]] => 11
[1,3,1,2,4] => [[1,1,2,4],[3]] => 11
[1,3,1,4,2] => [[1,1,2],[3,4]] => 11
[1,3,2,1,4] => [[1,1,4],[2],[3]] => 11
[1,3,2,4,1] => [[1,1,4],[2],[3]] => 11
[1,3,4,1,2] => [[1,1,2],[3,4]] => 11
[1,3,4,2,1] => [[1,1,4],[2],[3]] => 11
[1,4,1,2,3] => [[1,1,2,3],[4]] => 11
[1,4,1,3,2] => [[1,1,2],[3],[4]] => 11
[1,4,2,1,3] => [[1,1,3],[2],[4]] => 11
[1,4,2,3,1] => [[1,1,3],[2],[4]] => 11
[1,4,3,1,2] => [[1,1,2],[3],[4]] => 11
[1,4,3,2,1] => [[1,1],[2],[3],[4]] => 11
[2,1,1,3,4] => [[1,1,3,4],[2]] => 11
[2,1,1,4,3] => [[1,1,3],[2,4]] => 11
[2,1,3,1,4] => [[1,1,4],[2,3]] => 11
[2,1,3,4,1] => [[1,1,4],[2,3]] => 11
[2,1,4,1,3] => [[1,1,3],[2,4]] => 11
[2,1,4,3,1] => [[1,1],[2,3],[4]] => 11
[2,3,1,1,4] => [[1,1,4],[2,3]] => 11
[2,3,1,4,1] => [[1,1,4],[2,3]] => 11
[2,3,4,1,1] => [[1,1,4],[2,3]] => 11
[2,4,1,1,3] => [[1,1,3],[2,4]] => 11
[2,4,1,3,1] => [[1,1],[2,3],[4]] => 11
[2,4,3,1,1] => [[1,1],[2,3],[4]] => 11
[3,1,1,2,4] => [[1,1,2,4],[3]] => 11
[3,1,1,4,2] => [[1,1,2],[3,4]] => 11
[3,1,2,1,4] => [[1,1,4],[2],[3]] => 11
[3,1,2,4,1] => [[1,1,4],[2],[3]] => 11
[3,1,4,1,2] => [[1,1,2],[3,4]] => 11
[3,1,4,2,1] => [[1,1],[2,4],[3]] => 11
[3,2,1,1,4] => [[1,1,4],[2],[3]] => 11
[3,2,1,4,1] => [[1,1],[2,4],[3]] => 11
[3,2,4,1,1] => [[1,1],[2,4],[3]] => 11
[3,4,1,1,2] => [[1,1,2],[3,4]] => 11
[3,4,1,2,1] => [[1,1],[2,4],[3]] => 11
[3,4,2,1,1] => [[1,1],[2,4],[3]] => 11
[4,1,1,2,3] => [[1,1,2,3],[4]] => 11
[4,1,1,3,2] => [[1,1,2],[3],[4]] => 11
[4,1,2,1,3] => [[1,1,3],[2],[4]] => 11
[4,1,2,3,1] => [[1,1,3],[2],[4]] => 11
[4,1,3,1,2] => [[1,1,2],[3],[4]] => 11
[4,1,3,2,1] => [[1,1],[2],[3],[4]] => 11
[4,2,1,1,3] => [[1,1,3],[2],[4]] => 11
[4,2,1,3,1] => [[1,1],[2,3],[4]] => 11
[4,2,3,1,1] => [[1,1],[2,3],[4]] => 11
[4,3,1,1,2] => [[1,1,2],[3],[4]] => 11
[4,3,1,2,1] => [[1,1],[2],[3],[4]] => 11
[4,3,2,1,1] => [[1,1],[2],[3],[4]] => 11
[1,1,2,3,5] => [[1,1,2,3,5]] => 12
[1,1,2,5,3] => [[1,1,2,3],[5]] => 12
[1,1,3,2,5] => [[1,1,2,5],[3]] => 12
[1,1,3,5,2] => [[1,1,2,5],[3]] => 12
[1,1,5,2,3] => [[1,1,2,3],[5]] => 12
[1,1,5,3,2] => [[1,1,2],[3],[5]] => 12
[1,2,1,3,5] => [[1,1,3,5],[2]] => 12
[1,2,1,5,3] => [[1,1,3],[2,5]] => 12
[1,2,3,1,5] => [[1,1,3,5],[2]] => 12
[1,2,3,5,1] => [[1,1,3,5],[2]] => 12
[1,2,5,1,3] => [[1,1,3],[2,5]] => 12
[1,2,5,3,1] => [[1,1,3],[2],[5]] => 12
[1,3,1,2,5] => [[1,1,2,5],[3]] => 12
[1,3,1,5,2] => [[1,1,2],[3,5]] => 12
[1,3,2,1,5] => [[1,1,5],[2],[3]] => 12
[1,3,2,5,1] => [[1,1,5],[2],[3]] => 12
[1,3,5,1,2] => [[1,1,2],[3,5]] => 12
[1,3,5,2,1] => [[1,1,5],[2],[3]] => 12
[1,5,1,2,3] => [[1,1,2,3],[5]] => 12
[1,5,1,3,2] => [[1,1,2],[3],[5]] => 12
[1,5,2,1,3] => [[1,1,3],[2],[5]] => 12
[1,5,2,3,1] => [[1,1,3],[2],[5]] => 12
[1,5,3,1,2] => [[1,1,2],[3],[5]] => 12
[1,5,3,2,1] => [[1,1],[2],[3],[5]] => 12
[2,1,1,3,5] => [[1,1,3,5],[2]] => 12
[2,1,1,5,3] => [[1,1,3],[2,5]] => 12
[2,1,3,1,5] => [[1,1,5],[2,3]] => 12
[2,1,3,5,1] => [[1,1,5],[2,3]] => 12
[2,1,5,1,3] => [[1,1,3],[2,5]] => 12
[2,1,5,3,1] => [[1,1],[2,3],[5]] => 12
[2,3,1,1,5] => [[1,1,5],[2,3]] => 12
[2,3,1,5,1] => [[1,1,5],[2,3]] => 12
[2,3,5,1,1] => [[1,1,5],[2,3]] => 12
[2,5,1,1,3] => [[1,1,3],[2,5]] => 12
[2,5,1,3,1] => [[1,1],[2,3],[5]] => 12
[2,5,3,1,1] => [[1,1],[2,3],[5]] => 12
[3,1,1,2,5] => [[1,1,2,5],[3]] => 12
[3,1,1,5,2] => [[1,1,2],[3,5]] => 12
[3,1,2,1,5] => [[1,1,5],[2],[3]] => 12
[3,1,2,5,1] => [[1,1,5],[2],[3]] => 12
[3,1,5,1,2] => [[1,1,2],[3,5]] => 12
[3,1,5,2,1] => [[1,1],[2,5],[3]] => 12
[3,2,1,1,5] => [[1,1,5],[2],[3]] => 12
[3,2,1,5,1] => [[1,1],[2,5],[3]] => 12
[3,2,5,1,1] => [[1,1],[2,5],[3]] => 12
[3,5,1,1,2] => [[1,1,2],[3,5]] => 12
[3,5,1,2,1] => [[1,1],[2,5],[3]] => 12
[3,5,2,1,1] => [[1,1],[2,5],[3]] => 12
[5,1,1,2,3] => [[1,1,2,3],[5]] => 12
[5,1,1,3,2] => [[1,1,2],[3],[5]] => 12
[5,1,2,1,3] => [[1,1,3],[2],[5]] => 12
[5,1,2,3,1] => [[1,1,3],[2],[5]] => 12
[5,1,3,1,2] => [[1,1,2],[3],[5]] => 12
[5,1,3,2,1] => [[1,1],[2],[3],[5]] => 12
[5,2,1,1,3] => [[1,1,3],[2],[5]] => 12
[5,2,1,3,1] => [[1,1],[2,3],[5]] => 12
[5,2,3,1,1] => [[1,1],[2,3],[5]] => 12
[5,3,1,1,2] => [[1,1,2],[3],[5]] => 12
[5,3,1,2,1] => [[1,1],[2],[3],[5]] => 12
[5,3,2,1,1] => [[1,1],[2],[3],[5]] => 12
[1,1,2,4,4] => [[1,1,2,4,4]] => 12
[1,1,4,2,4] => [[1,1,2,4],[4]] => 12
[1,1,4,4,2] => [[1,1,2,4],[4]] => 12
[1,2,1,4,4] => [[1,1,4,4],[2]] => 12
[1,2,4,1,4] => [[1,1,4,4],[2]] => 12
[1,2,4,4,1] => [[1,1,4,4],[2]] => 12
[1,4,1,2,4] => [[1,1,2,4],[4]] => 12
[1,4,1,4,2] => [[1,1,2],[4,4]] => 12
[1,4,2,1,4] => [[1,1,4],[2],[4]] => 12
[1,4,2,4,1] => [[1,1,4],[2],[4]] => 12
[1,4,4,1,2] => [[1,1,2],[4,4]] => 12
[1,4,4,2,1] => [[1,1,4],[2],[4]] => 12
[2,1,1,4,4] => [[1,1,4,4],[2]] => 12
[2,1,4,1,4] => [[1,1,4],[2,4]] => 12
[2,1,4,4,1] => [[1,1,4],[2,4]] => 12
[2,4,1,1,4] => [[1,1,4],[2,4]] => 12
[2,4,1,4,1] => [[1,1,4],[2,4]] => 12
[2,4,4,1,1] => [[1,1,4],[2,4]] => 12
[4,1,1,2,4] => [[1,1,2,4],[4]] => 12
[4,1,1,4,2] => [[1,1,2],[4,4]] => 12
[4,1,2,1,4] => [[1,1,4],[2],[4]] => 12
[4,1,2,4,1] => [[1,1,4],[2],[4]] => 12
[4,1,4,1,2] => [[1,1,2],[4,4]] => 12
[4,1,4,2,1] => [[1,1],[2,4],[4]] => 12
[4,2,1,1,4] => [[1,1,4],[2],[4]] => 12
[4,2,1,4,1] => [[1,1],[2,4],[4]] => 12
[4,2,4,1,1] => [[1,1],[2,4],[4]] => 12
[4,4,1,1,2] => [[1,1,2],[4,4]] => 12
[4,4,1,2,1] => [[1,1],[2,4],[4]] => 12
[4,4,2,1,1] => [[1,1],[2,4],[4]] => 12
[1,1,2,4,5] => [[1,1,2,4,5]] => 13
[1,1,2,5,4] => [[1,1,2,4],[5]] => 13
[1,1,4,2,5] => [[1,1,2,5],[4]] => 13
[1,1,4,5,2] => [[1,1,2,5],[4]] => 13
[1,1,5,2,4] => [[1,1,2,4],[5]] => 13
[1,1,5,4,2] => [[1,1,2],[4],[5]] => 13
[1,2,1,4,5] => [[1,1,4,5],[2]] => 13
[1,2,1,5,4] => [[1,1,4],[2,5]] => 13
[1,2,4,1,5] => [[1,1,4,5],[2]] => 13
[1,2,4,5,1] => [[1,1,4,5],[2]] => 13
[1,2,5,1,4] => [[1,1,4],[2,5]] => 13
[1,2,5,4,1] => [[1,1,4],[2],[5]] => 13
[1,4,1,2,5] => [[1,1,2,5],[4]] => 13
[1,4,1,5,2] => [[1,1,2],[4,5]] => 13
[1,4,2,1,5] => [[1,1,5],[2],[4]] => 13
[1,4,2,5,1] => [[1,1,5],[2],[4]] => 13
[1,4,5,1,2] => [[1,1,2],[4,5]] => 13
[1,4,5,2,1] => [[1,1,5],[2],[4]] => 13
[1,5,1,2,4] => [[1,1,2,4],[5]] => 13
[1,5,1,4,2] => [[1,1,2],[4],[5]] => 13
[1,5,2,1,4] => [[1,1,4],[2],[5]] => 13
[1,5,2,4,1] => [[1,1,4],[2],[5]] => 13
[1,5,4,1,2] => [[1,1,2],[4],[5]] => 13
[1,5,4,2,1] => [[1,1],[2],[4],[5]] => 13
[2,1,1,4,5] => [[1,1,4,5],[2]] => 13
[2,1,1,5,4] => [[1,1,4],[2,5]] => 13
[2,1,4,1,5] => [[1,1,5],[2,4]] => 13
[2,1,4,5,1] => [[1,1,5],[2,4]] => 13
[2,1,5,1,4] => [[1,1,4],[2,5]] => 13
[2,1,5,4,1] => [[1,1],[2,4],[5]] => 13
[2,4,1,1,5] => [[1,1,5],[2,4]] => 13
[2,4,1,5,1] => [[1,1,5],[2,4]] => 13
[2,4,5,1,1] => [[1,1,5],[2,4]] => 13
[2,5,1,1,4] => [[1,1,4],[2,5]] => 13
[2,5,1,4,1] => [[1,1],[2,4],[5]] => 13
[2,5,4,1,1] => [[1,1],[2,4],[5]] => 13
[4,1,1,2,5] => [[1,1,2,5],[4]] => 13
[4,1,1,5,2] => [[1,1,2],[4,5]] => 13
[4,1,2,1,5] => [[1,1,5],[2],[4]] => 13
[4,1,2,5,1] => [[1,1,5],[2],[4]] => 13
[4,1,5,1,2] => [[1,1,2],[4,5]] => 13
[4,1,5,2,1] => [[1,1],[2,5],[4]] => 13
[4,2,1,1,5] => [[1,1,5],[2],[4]] => 13
[4,2,1,5,1] => [[1,1],[2,5],[4]] => 13
[4,2,5,1,1] => [[1,1],[2,5],[4]] => 13
[4,5,1,1,2] => [[1,1,2],[4,5]] => 13
[4,5,1,2,1] => [[1,1],[2,5],[4]] => 13
[4,5,2,1,1] => [[1,1],[2,5],[4]] => 13
[5,1,1,2,4] => [[1,1,2,4],[5]] => 13
[5,1,1,4,2] => [[1,1,2],[4],[5]] => 13
[5,1,2,1,4] => [[1,1,4],[2],[5]] => 13
[5,1,2,4,1] => [[1,1,4],[2],[5]] => 13
[5,1,4,1,2] => [[1,1,2],[4],[5]] => 13
[5,1,4,2,1] => [[1,1],[2],[4],[5]] => 13
[5,2,1,1,4] => [[1,1,4],[2],[5]] => 13
[5,2,1,4,1] => [[1,1],[2,4],[5]] => 13
[5,2,4,1,1] => [[1,1],[2,4],[5]] => 13
[5,4,1,1,2] => [[1,1,2],[4],[5]] => 13
[5,4,1,2,1] => [[1,1],[2],[4],[5]] => 13
[5,4,2,1,1] => [[1,1],[2],[4],[5]] => 13
[1,1,3,3,3] => [[1,1,3,3,3]] => 11
[1,3,1,3,3] => [[1,1,3,3],[3]] => 11
[1,3,3,1,3] => [[1,1,3,3],[3]] => 11
[1,3,3,3,1] => [[1,1,3,3],[3]] => 11
[3,1,1,3,3] => [[1,1,3,3],[3]] => 11
[3,1,3,1,3] => [[1,1,3],[3,3]] => 11
[3,1,3,3,1] => [[1,1,3],[3,3]] => 11
[3,3,1,1,3] => [[1,1,3],[3,3]] => 11
[3,3,1,3,1] => [[1,1,3],[3,3]] => 11
[3,3,3,1,1] => [[1,1,3],[3,3]] => 11
[1,1,3,3,4] => [[1,1,3,3,4]] => 12
[1,1,3,4,3] => [[1,1,3,3],[4]] => 12
[1,1,4,3,3] => [[1,1,3,3],[4]] => 12
[1,3,1,3,4] => [[1,1,3,4],[3]] => 12
[1,3,1,4,3] => [[1,1,3],[3,4]] => 12
[1,3,3,1,4] => [[1,1,3,4],[3]] => 12
[1,3,3,4,1] => [[1,1,3,4],[3]] => 12
[1,3,4,1,3] => [[1,1,3],[3,4]] => 12
[1,3,4,3,1] => [[1,1,3],[3],[4]] => 12
[1,4,1,3,3] => [[1,1,3,3],[4]] => 12
[1,4,3,1,3] => [[1,1,3],[3],[4]] => 12
[1,4,3,3,1] => [[1,1,3],[3],[4]] => 12
[3,1,1,3,4] => [[1,1,3,4],[3]] => 12
[3,1,1,4,3] => [[1,1,3],[3,4]] => 12
[3,1,3,1,4] => [[1,1,4],[3,3]] => 12
[3,1,3,4,1] => [[1,1,4],[3,3]] => 12
[3,1,4,1,3] => [[1,1,3],[3,4]] => 12
[3,1,4,3,1] => [[1,1],[3,3],[4]] => 12
[3,3,1,1,4] => [[1,1,4],[3,3]] => 12
[3,3,1,4,1] => [[1,1,4],[3,3]] => 12
[3,3,4,1,1] => [[1,1,4],[3,3]] => 12
[3,4,1,1,3] => [[1,1,3],[3,4]] => 12
[3,4,1,3,1] => [[1,1],[3,3],[4]] => 12
[3,4,3,1,1] => [[1,1],[3,3],[4]] => 12
[4,1,1,3,3] => [[1,1,3,3],[4]] => 12
[4,1,3,1,3] => [[1,1,3],[3],[4]] => 12
[4,1,3,3,1] => [[1,1,3],[3],[4]] => 12
[4,3,1,1,3] => [[1,1,3],[3],[4]] => 12
[4,3,1,3,1] => [[1,1],[3,3],[4]] => 12
[4,3,3,1,1] => [[1,1],[3,3],[4]] => 12
[1,1,3,3,5] => [[1,1,3,3,5]] => 13
[1,1,3,5,3] => [[1,1,3,3],[5]] => 13
[1,1,5,3,3] => [[1,1,3,3],[5]] => 13
[1,3,1,3,5] => [[1,1,3,5],[3]] => 13
[1,3,1,5,3] => [[1,1,3],[3,5]] => 13
[1,3,3,1,5] => [[1,1,3,5],[3]] => 13
[1,3,3,5,1] => [[1,1,3,5],[3]] => 13
[1,3,5,1,3] => [[1,1,3],[3,5]] => 13
[1,3,5,3,1] => [[1,1,3],[3],[5]] => 13
[1,5,1,3,3] => [[1,1,3,3],[5]] => 13
[1,5,3,1,3] => [[1,1,3],[3],[5]] => 13
[1,5,3,3,1] => [[1,1,3],[3],[5]] => 13
[3,1,1,3,5] => [[1,1,3,5],[3]] => 13
[3,1,1,5,3] => [[1,1,3],[3,5]] => 13
[3,1,3,1,5] => [[1,1,5],[3,3]] => 13
[3,1,3,5,1] => [[1,1,5],[3,3]] => 13
[3,1,5,1,3] => [[1,1,3],[3,5]] => 13
[3,1,5,3,1] => [[1,1],[3,3],[5]] => 13
[3,3,1,1,5] => [[1,1,5],[3,3]] => 13
[3,3,1,5,1] => [[1,1,5],[3,3]] => 13
[3,3,5,1,1] => [[1,1,5],[3,3]] => 13
[3,5,1,1,3] => [[1,1,3],[3,5]] => 13
[3,5,1,3,1] => [[1,1],[3,3],[5]] => 13
[3,5,3,1,1] => [[1,1],[3,3],[5]] => 13
[5,1,1,3,3] => [[1,1,3,3],[5]] => 13
[5,1,3,1,3] => [[1,1,3],[3],[5]] => 13
[5,1,3,3,1] => [[1,1,3],[3],[5]] => 13
[5,3,1,1,3] => [[1,1,3],[3],[5]] => 13
[5,3,1,3,1] => [[1,1],[3,3],[5]] => 13
[5,3,3,1,1] => [[1,1],[3,3],[5]] => 13
[1,1,3,4,4] => [[1,1,3,4,4]] => 13
[1,1,4,3,4] => [[1,1,3,4],[4]] => 13
[1,1,4,4,3] => [[1,1,3,4],[4]] => 13
[1,3,1,4,4] => [[1,1,4,4],[3]] => 13
[1,3,4,1,4] => [[1,1,4,4],[3]] => 13
[1,3,4,4,1] => [[1,1,4,4],[3]] => 13
[1,4,1,3,4] => [[1,1,3,4],[4]] => 13
[1,4,1,4,3] => [[1,1,3],[4,4]] => 13
[1,4,3,1,4] => [[1,1,4],[3],[4]] => 13
[1,4,3,4,1] => [[1,1,4],[3],[4]] => 13
[1,4,4,1,3] => [[1,1,3],[4,4]] => 13
[1,4,4,3,1] => [[1,1,4],[3],[4]] => 13
[3,1,1,4,4] => [[1,1,4,4],[3]] => 13
[3,1,4,1,4] => [[1,1,4],[3,4]] => 13
[3,1,4,4,1] => [[1,1,4],[3,4]] => 13
[3,4,1,1,4] => [[1,1,4],[3,4]] => 13
[3,4,1,4,1] => [[1,1,4],[3,4]] => 13
[3,4,4,1,1] => [[1,1,4],[3,4]] => 13
[4,1,1,3,4] => [[1,1,3,4],[4]] => 13
[4,1,1,4,3] => [[1,1,3],[4,4]] => 13
[4,1,3,1,4] => [[1,1,4],[3],[4]] => 13
[4,1,3,4,1] => [[1,1,4],[3],[4]] => 13
[4,1,4,1,3] => [[1,1,3],[4,4]] => 13
[4,1,4,3,1] => [[1,1],[3,4],[4]] => 13
[4,3,1,1,4] => [[1,1,4],[3],[4]] => 13
[4,3,1,4,1] => [[1,1],[3,4],[4]] => 13
[4,3,4,1,1] => [[1,1],[3,4],[4]] => 13
[4,4,1,1,3] => [[1,1,3],[4,4]] => 13
[4,4,1,3,1] => [[1,1],[3,4],[4]] => 13
[4,4,3,1,1] => [[1,1],[3,4],[4]] => 13
[1,1,3,4,5] => [[1,1,3,4,5]] => 14
[1,1,3,5,4] => [[1,1,3,4],[5]] => 14
[1,1,4,3,5] => [[1,1,3,5],[4]] => 14
[1,1,4,5,3] => [[1,1,3,5],[4]] => 14
[1,1,5,3,4] => [[1,1,3,4],[5]] => 14
[1,1,5,4,3] => [[1,1,3],[4],[5]] => 14
[1,3,1,4,5] => [[1,1,4,5],[3]] => 14
[1,3,1,5,4] => [[1,1,4],[3,5]] => 14
[1,3,4,1,5] => [[1,1,4,5],[3]] => 14
[1,3,4,5,1] => [[1,1,4,5],[3]] => 14
[1,3,5,1,4] => [[1,1,4],[3,5]] => 14
[1,3,5,4,1] => [[1,1,4],[3],[5]] => 14
[1,4,1,3,5] => [[1,1,3,5],[4]] => 14
[1,4,1,5,3] => [[1,1,3],[4,5]] => 14
[1,4,3,1,5] => [[1,1,5],[3],[4]] => 14
[1,4,3,5,1] => [[1,1,5],[3],[4]] => 14
[1,4,5,1,3] => [[1,1,3],[4,5]] => 14
[1,4,5,3,1] => [[1,1,5],[3],[4]] => 14
[1,5,1,3,4] => [[1,1,3,4],[5]] => 14
[1,5,1,4,3] => [[1,1,3],[4],[5]] => 14
[1,5,3,1,4] => [[1,1,4],[3],[5]] => 14
[1,5,3,4,1] => [[1,1,4],[3],[5]] => 14
[1,5,4,1,3] => [[1,1,3],[4],[5]] => 14
[1,5,4,3,1] => [[1,1],[3],[4],[5]] => 14
[3,1,1,4,5] => [[1,1,4,5],[3]] => 14
[3,1,1,5,4] => [[1,1,4],[3,5]] => 14
[3,1,4,1,5] => [[1,1,5],[3,4]] => 14
[3,1,4,5,1] => [[1,1,5],[3,4]] => 14
[3,1,5,1,4] => [[1,1,4],[3,5]] => 14
[3,1,5,4,1] => [[1,1],[3,4],[5]] => 14
[3,4,1,1,5] => [[1,1,5],[3,4]] => 14
[3,4,1,5,1] => [[1,1,5],[3,4]] => 14
[3,4,5,1,1] => [[1,1,5],[3,4]] => 14
[3,5,1,1,4] => [[1,1,4],[3,5]] => 14
[3,5,1,4,1] => [[1,1],[3,4],[5]] => 14
[3,5,4,1,1] => [[1,1],[3,4],[5]] => 14
[4,1,1,3,5] => [[1,1,3,5],[4]] => 14
[4,1,1,5,3] => [[1,1,3],[4,5]] => 14
[4,1,3,1,5] => [[1,1,5],[3],[4]] => 14
[4,1,3,5,1] => [[1,1,5],[3],[4]] => 14
[4,1,5,1,3] => [[1,1,3],[4,5]] => 14
[4,1,5,3,1] => [[1,1],[3,5],[4]] => 14
[4,3,1,1,5] => [[1,1,5],[3],[4]] => 14
[4,3,1,5,1] => [[1,1],[3,5],[4]] => 14
[4,3,5,1,1] => [[1,1],[3,5],[4]] => 14
[4,5,1,1,3] => [[1,1,3],[4,5]] => 14
[4,5,1,3,1] => [[1,1],[3,5],[4]] => 14
[4,5,3,1,1] => [[1,1],[3,5],[4]] => 14
[5,1,1,3,4] => [[1,1,3,4],[5]] => 14
[5,1,1,4,3] => [[1,1,3],[4],[5]] => 14
[5,1,3,1,4] => [[1,1,4],[3],[5]] => 14
[5,1,3,4,1] => [[1,1,4],[3],[5]] => 14
[5,1,4,1,3] => [[1,1,3],[4],[5]] => 14
[5,1,4,3,1] => [[1,1],[3],[4],[5]] => 14
[5,3,1,1,4] => [[1,1,4],[3],[5]] => 14
[5,3,1,4,1] => [[1,1],[3,4],[5]] => 14
[5,3,4,1,1] => [[1,1],[3,4],[5]] => 14
[5,4,1,1,3] => [[1,1,3],[4],[5]] => 14
[5,4,1,3,1] => [[1,1],[3],[4],[5]] => 14
[5,4,3,1,1] => [[1,1],[3],[4],[5]] => 14
[1,2,2,2,2] => [[1,2,2,2,2]] => 9
[2,1,2,2,2] => [[1,2,2,2],[2]] => 9
[2,2,1,2,2] => [[1,2,2,2],[2]] => 9
[2,2,2,1,2] => [[1,2,2,2],[2]] => 9
[2,2,2,2,1] => [[1,2,2,2],[2]] => 9
[1,2,2,2,3] => [[1,2,2,2,3]] => 10
[1,2,2,3,2] => [[1,2,2,2],[3]] => 10
[1,2,3,2,2] => [[1,2,2,2],[3]] => 10
[1,3,2,2,2] => [[1,2,2,2],[3]] => 10
[2,1,2,2,3] => [[1,2,2,3],[2]] => 10
[2,1,2,3,2] => [[1,2,2],[2,3]] => 10
[2,1,3,2,2] => [[1,2,2],[2,3]] => 10
[2,2,1,2,3] => [[1,2,2,3],[2]] => 10
[2,2,1,3,2] => [[1,2,2],[2,3]] => 10
[2,2,2,1,3] => [[1,2,2,3],[2]] => 10
[2,2,2,3,1] => [[1,2,2,3],[2]] => 10
[2,2,3,1,2] => [[1,2,2],[2,3]] => 10
[2,2,3,2,1] => [[1,2,2],[2],[3]] => 10
[2,3,1,2,2] => [[1,2,2],[2,3]] => 10
[2,3,2,1,2] => [[1,2,2],[2],[3]] => 10
[2,3,2,2,1] => [[1,2,2],[2],[3]] => 10
[3,1,2,2,2] => [[1,2,2,2],[3]] => 10
[3,2,1,2,2] => [[1,2,2],[2],[3]] => 10
[3,2,2,1,2] => [[1,2,2],[2],[3]] => 10
[3,2,2,2,1] => [[1,2,2],[2],[3]] => 10
[1,2,2,2,4] => [[1,2,2,2,4]] => 11
[1,2,2,4,2] => [[1,2,2,2],[4]] => 11
[1,2,4,2,2] => [[1,2,2,2],[4]] => 11
[1,4,2,2,2] => [[1,2,2,2],[4]] => 11
[2,1,2,2,4] => [[1,2,2,4],[2]] => 11
[2,1,2,4,2] => [[1,2,2],[2,4]] => 11
[2,1,4,2,2] => [[1,2,2],[2,4]] => 11
[2,2,1,2,4] => [[1,2,2,4],[2]] => 11
[2,2,1,4,2] => [[1,2,2],[2,4]] => 11
[2,2,2,1,4] => [[1,2,2,4],[2]] => 11
[2,2,2,4,1] => [[1,2,2,4],[2]] => 11
[2,2,4,1,2] => [[1,2,2],[2,4]] => 11
[2,2,4,2,1] => [[1,2,2],[2],[4]] => 11
[2,4,1,2,2] => [[1,2,2],[2,4]] => 11
[2,4,2,1,2] => [[1,2,2],[2],[4]] => 11
[2,4,2,2,1] => [[1,2,2],[2],[4]] => 11
[4,1,2,2,2] => [[1,2,2,2],[4]] => 11
[4,2,1,2,2] => [[1,2,2],[2],[4]] => 11
[4,2,2,1,2] => [[1,2,2],[2],[4]] => 11
[4,2,2,2,1] => [[1,2,2],[2],[4]] => 11
[1,2,2,2,5] => [[1,2,2,2,5]] => 12
[1,2,2,5,2] => [[1,2,2,2],[5]] => 12
[1,2,5,2,2] => [[1,2,2,2],[5]] => 12
[1,5,2,2,2] => [[1,2,2,2],[5]] => 12
[2,1,2,2,5] => [[1,2,2,5],[2]] => 12
[2,1,2,5,2] => [[1,2,2],[2,5]] => 12
[2,1,5,2,2] => [[1,2,2],[2,5]] => 12
[2,2,1,2,5] => [[1,2,2,5],[2]] => 12
[2,2,1,5,2] => [[1,2,2],[2,5]] => 12
[2,2,2,1,5] => [[1,2,2,5],[2]] => 12
[2,2,2,5,1] => [[1,2,2,5],[2]] => 12
[2,2,5,1,2] => [[1,2,2],[2,5]] => 12
[2,2,5,2,1] => [[1,2,2],[2],[5]] => 12
[2,5,1,2,2] => [[1,2,2],[2,5]] => 12
[2,5,2,1,2] => [[1,2,2],[2],[5]] => 12
[2,5,2,2,1] => [[1,2,2],[2],[5]] => 12
[5,1,2,2,2] => [[1,2,2,2],[5]] => 12
[5,2,1,2,2] => [[1,2,2],[2],[5]] => 12
[5,2,2,1,2] => [[1,2,2],[2],[5]] => 12
[5,2,2,2,1] => [[1,2,2],[2],[5]] => 12
[1,2,2,3,3] => [[1,2,2,3,3]] => 11
[1,2,3,2,3] => [[1,2,2,3],[3]] => 11
[1,2,3,3,2] => [[1,2,2,3],[3]] => 11
[1,3,2,2,3] => [[1,2,2,3],[3]] => 11
[1,3,2,3,2] => [[1,2,2],[3,3]] => 11
[1,3,3,2,2] => [[1,2,2],[3,3]] => 11
[2,1,2,3,3] => [[1,2,3,3],[2]] => 11
[2,1,3,2,3] => [[1,2,3],[2,3]] => 11
[2,1,3,3,2] => [[1,2,3],[2,3]] => 11
[2,2,1,3,3] => [[1,2,3,3],[2]] => 11
[2,2,3,1,3] => [[1,2,3,3],[2]] => 11
[2,2,3,3,1] => [[1,2,3,3],[2]] => 11
[2,3,1,2,3] => [[1,2,3],[2,3]] => 11
[2,3,1,3,2] => [[1,2,3],[2,3]] => 11
[2,3,2,1,3] => [[1,2,3],[2],[3]] => 11
[2,3,2,3,1] => [[1,2,3],[2],[3]] => 11
[2,3,3,1,2] => [[1,2,3],[2,3]] => 11
[2,3,3,2,1] => [[1,2,3],[2],[3]] => 11
[3,1,2,2,3] => [[1,2,2,3],[3]] => 11
[3,1,2,3,2] => [[1,2,2],[3,3]] => 11
[3,1,3,2,2] => [[1,2,2],[3,3]] => 11
[3,2,1,2,3] => [[1,2,3],[2],[3]] => 11
[3,2,1,3,2] => [[1,2],[2,3],[3]] => 11
[3,2,2,1,3] => [[1,2,3],[2],[3]] => 11
[3,2,2,3,1] => [[1,2,3],[2],[3]] => 11
[3,2,3,1,2] => [[1,2],[2,3],[3]] => 11
[3,2,3,2,1] => [[1,2],[2,3],[3]] => 11
[3,3,1,2,2] => [[1,2,2],[3,3]] => 11
[3,3,2,1,2] => [[1,2],[2,3],[3]] => 11
[3,3,2,2,1] => [[1,2],[2,3],[3]] => 11
[1,2,2,3,4] => [[1,2,2,3,4]] => 12
[1,2,2,4,3] => [[1,2,2,3],[4]] => 12
[1,2,3,2,4] => [[1,2,2,4],[3]] => 12
[1,2,3,4,2] => [[1,2,2,4],[3]] => 12
[1,2,4,2,3] => [[1,2,2,3],[4]] => 12
[1,2,4,3,2] => [[1,2,2],[3],[4]] => 12
[1,3,2,2,4] => [[1,2,2,4],[3]] => 12
[1,3,2,4,2] => [[1,2,2],[3,4]] => 12
[1,3,4,2,2] => [[1,2,2],[3,4]] => 12
[1,4,2,2,3] => [[1,2,2,3],[4]] => 12
[1,4,2,3,2] => [[1,2,2],[3],[4]] => 12
[1,4,3,2,2] => [[1,2,2],[3],[4]] => 12
[2,1,2,3,4] => [[1,2,3,4],[2]] => 12
[2,1,2,4,3] => [[1,2,3],[2,4]] => 12
[2,1,3,2,4] => [[1,2,4],[2,3]] => 12
[2,1,3,4,2] => [[1,2,4],[2,3]] => 12
[2,1,4,2,3] => [[1,2,3],[2,4]] => 12
[2,1,4,3,2] => [[1,2],[2,3],[4]] => 12
[2,2,1,3,4] => [[1,2,3,4],[2]] => 12
[2,2,1,4,3] => [[1,2,3],[2,4]] => 12
[2,2,3,1,4] => [[1,2,3,4],[2]] => 12
[2,2,3,4,1] => [[1,2,3,4],[2]] => 12
[2,2,4,1,3] => [[1,2,3],[2,4]] => 12
[2,2,4,3,1] => [[1,2,3],[2],[4]] => 12
[2,3,1,2,4] => [[1,2,4],[2,3]] => 12
[2,3,1,4,2] => [[1,2,4],[2,3]] => 12
[2,3,2,1,4] => [[1,2,4],[2],[3]] => 12
[2,3,2,4,1] => [[1,2,4],[2],[3]] => 12
[2,3,4,1,2] => [[1,2,4],[2,3]] => 12
[2,3,4,2,1] => [[1,2,4],[2],[3]] => 12
[2,4,1,2,3] => [[1,2,3],[2,4]] => 12
[2,4,1,3,2] => [[1,2],[2,3],[4]] => 12
[2,4,2,1,3] => [[1,2,3],[2],[4]] => 12
[2,4,2,3,1] => [[1,2,3],[2],[4]] => 12
[2,4,3,1,2] => [[1,2],[2,3],[4]] => 12
[2,4,3,2,1] => [[1,2],[2],[3],[4]] => 12
[3,1,2,2,4] => [[1,2,2,4],[3]] => 12
[3,1,2,4,2] => [[1,2,2],[3,4]] => 12
[3,1,4,2,2] => [[1,2,2],[3,4]] => 12
[3,2,1,2,4] => [[1,2,4],[2],[3]] => 12
[3,2,1,4,2] => [[1,2],[2,4],[3]] => 12
[3,2,2,1,4] => [[1,2,4],[2],[3]] => 12
[3,2,2,4,1] => [[1,2,4],[2],[3]] => 12
[3,2,4,1,2] => [[1,2],[2,4],[3]] => 12
[3,2,4,2,1] => [[1,2],[2,4],[3]] => 12
[3,4,1,2,2] => [[1,2,2],[3,4]] => 12
[3,4,2,1,2] => [[1,2],[2,4],[3]] => 12
[3,4,2,2,1] => [[1,2],[2,4],[3]] => 12
[4,1,2,2,3] => [[1,2,2,3],[4]] => 12
[4,1,2,3,2] => [[1,2,2],[3],[4]] => 12
[4,1,3,2,2] => [[1,2,2],[3],[4]] => 12
[4,2,1,2,3] => [[1,2,3],[2],[4]] => 12
[4,2,1,3,2] => [[1,2],[2,3],[4]] => 12
[4,2,2,1,3] => [[1,2,3],[2],[4]] => 12
[4,2,2,3,1] => [[1,2,3],[2],[4]] => 12
[4,2,3,1,2] => [[1,2],[2,3],[4]] => 12
[4,2,3,2,1] => [[1,2],[2],[3],[4]] => 12
[4,3,1,2,2] => [[1,2,2],[3],[4]] => 12
[4,3,2,1,2] => [[1,2],[2],[3],[4]] => 12
[4,3,2,2,1] => [[1,2],[2],[3],[4]] => 12
[1,2,2,3,5] => [[1,2,2,3,5]] => 13
[1,2,2,5,3] => [[1,2,2,3],[5]] => 13
[1,2,3,2,5] => [[1,2,2,5],[3]] => 13
[1,2,3,5,2] => [[1,2,2,5],[3]] => 13
[1,2,5,2,3] => [[1,2,2,3],[5]] => 13
[1,2,5,3,2] => [[1,2,2],[3],[5]] => 13
[1,3,2,2,5] => [[1,2,2,5],[3]] => 13
[1,3,2,5,2] => [[1,2,2],[3,5]] => 13
[1,3,5,2,2] => [[1,2,2],[3,5]] => 13
[1,5,2,2,3] => [[1,2,2,3],[5]] => 13
[1,5,2,3,2] => [[1,2,2],[3],[5]] => 13
[1,5,3,2,2] => [[1,2,2],[3],[5]] => 13
[2,1,2,3,5] => [[1,2,3,5],[2]] => 13
[2,1,2,5,3] => [[1,2,3],[2,5]] => 13
[2,1,3,2,5] => [[1,2,5],[2,3]] => 13
[2,1,3,5,2] => [[1,2,5],[2,3]] => 13
[2,1,5,2,3] => [[1,2,3],[2,5]] => 13
[2,1,5,3,2] => [[1,2],[2,3],[5]] => 13
[2,2,1,3,5] => [[1,2,3,5],[2]] => 13
[2,2,1,5,3] => [[1,2,3],[2,5]] => 13
[2,2,3,1,5] => [[1,2,3,5],[2]] => 13
[2,2,3,5,1] => [[1,2,3,5],[2]] => 13
[2,2,5,1,3] => [[1,2,3],[2,5]] => 13
[2,2,5,3,1] => [[1,2,3],[2],[5]] => 13
[2,3,1,2,5] => [[1,2,5],[2,3]] => 13
[2,3,1,5,2] => [[1,2,5],[2,3]] => 13
[2,3,2,1,5] => [[1,2,5],[2],[3]] => 13
[2,3,2,5,1] => [[1,2,5],[2],[3]] => 13
[2,3,5,1,2] => [[1,2,5],[2,3]] => 13
[2,3,5,2,1] => [[1,2,5],[2],[3]] => 13
[2,5,1,2,3] => [[1,2,3],[2,5]] => 13
[2,5,1,3,2] => [[1,2],[2,3],[5]] => 13
[2,5,2,1,3] => [[1,2,3],[2],[5]] => 13
[2,5,2,3,1] => [[1,2,3],[2],[5]] => 13
[2,5,3,1,2] => [[1,2],[2,3],[5]] => 13
[2,5,3,2,1] => [[1,2],[2],[3],[5]] => 13
[3,1,2,2,5] => [[1,2,2,5],[3]] => 13
[3,1,2,5,2] => [[1,2,2],[3,5]] => 13
[3,1,5,2,2] => [[1,2,2],[3,5]] => 13
[3,2,1,2,5] => [[1,2,5],[2],[3]] => 13
[3,2,1,5,2] => [[1,2],[2,5],[3]] => 13
[3,2,2,1,5] => [[1,2,5],[2],[3]] => 13
[3,2,2,5,1] => [[1,2,5],[2],[3]] => 13
[3,2,5,1,2] => [[1,2],[2,5],[3]] => 13
[3,2,5,2,1] => [[1,2],[2,5],[3]] => 13
[3,5,1,2,2] => [[1,2,2],[3,5]] => 13
[3,5,2,1,2] => [[1,2],[2,5],[3]] => 13
[3,5,2,2,1] => [[1,2],[2,5],[3]] => 13
[5,1,2,2,3] => [[1,2,2,3],[5]] => 13
[5,1,2,3,2] => [[1,2,2],[3],[5]] => 13
[5,1,3,2,2] => [[1,2,2],[3],[5]] => 13
[5,2,1,2,3] => [[1,2,3],[2],[5]] => 13
[5,2,1,3,2] => [[1,2],[2,3],[5]] => 13
[5,2,2,1,3] => [[1,2,3],[2],[5]] => 13
[5,2,2,3,1] => [[1,2,3],[2],[5]] => 13
[5,2,3,1,2] => [[1,2],[2,3],[5]] => 13
[5,2,3,2,1] => [[1,2],[2],[3],[5]] => 13
[5,3,1,2,2] => [[1,2,2],[3],[5]] => 13
[5,3,2,1,2] => [[1,2],[2],[3],[5]] => 13
[5,3,2,2,1] => [[1,2],[2],[3],[5]] => 13
[1,2,2,4,4] => [[1,2,2,4,4]] => 13
[1,2,4,2,4] => [[1,2,2,4],[4]] => 13
[1,2,4,4,2] => [[1,2,2,4],[4]] => 13
[1,4,2,2,4] => [[1,2,2,4],[4]] => 13
[1,4,2,4,2] => [[1,2,2],[4,4]] => 13
[1,4,4,2,2] => [[1,2,2],[4,4]] => 13
[2,1,2,4,4] => [[1,2,4,4],[2]] => 13
[2,1,4,2,4] => [[1,2,4],[2,4]] => 13
[2,1,4,4,2] => [[1,2,4],[2,4]] => 13
[2,2,1,4,4] => [[1,2,4,4],[2]] => 13
[2,2,4,1,4] => [[1,2,4,4],[2]] => 13
[2,2,4,4,1] => [[1,2,4,4],[2]] => 13
[2,4,1,2,4] => [[1,2,4],[2,4]] => 13
[2,4,1,4,2] => [[1,2,4],[2,4]] => 13
[2,4,2,1,4] => [[1,2,4],[2],[4]] => 13
[2,4,2,4,1] => [[1,2,4],[2],[4]] => 13
[2,4,4,1,2] => [[1,2,4],[2,4]] => 13
[2,4,4,2,1] => [[1,2,4],[2],[4]] => 13
[4,1,2,2,4] => [[1,2,2,4],[4]] => 13
[4,1,2,4,2] => [[1,2,2],[4,4]] => 13
[4,1,4,2,2] => [[1,2,2],[4,4]] => 13
[4,2,1,2,4] => [[1,2,4],[2],[4]] => 13
[4,2,1,4,2] => [[1,2],[2,4],[4]] => 13
[4,2,2,1,4] => [[1,2,4],[2],[4]] => 13
[4,2,2,4,1] => [[1,2,4],[2],[4]] => 13
[4,2,4,1,2] => [[1,2],[2,4],[4]] => 13
[4,2,4,2,1] => [[1,2],[2,4],[4]] => 13
[4,4,1,2,2] => [[1,2,2],[4,4]] => 13
[4,4,2,1,2] => [[1,2],[2,4],[4]] => 13
[4,4,2,2,1] => [[1,2],[2,4],[4]] => 13
[1,2,2,4,5] => [[1,2,2,4,5]] => 14
[1,2,2,5,4] => [[1,2,2,4],[5]] => 14
[1,2,4,2,5] => [[1,2,2,5],[4]] => 14
[1,2,4,5,2] => [[1,2,2,5],[4]] => 14
[1,2,5,2,4] => [[1,2,2,4],[5]] => 14
[1,2,5,4,2] => [[1,2,2],[4],[5]] => 14
[1,4,2,2,5] => [[1,2,2,5],[4]] => 14
[1,4,2,5,2] => [[1,2,2],[4,5]] => 14
[1,4,5,2,2] => [[1,2,2],[4,5]] => 14
[1,5,2,2,4] => [[1,2,2,4],[5]] => 14
[1,5,2,4,2] => [[1,2,2],[4],[5]] => 14
[1,5,4,2,2] => [[1,2,2],[4],[5]] => 14
[2,1,2,4,5] => [[1,2,4,5],[2]] => 14
[2,1,2,5,4] => [[1,2,4],[2,5]] => 14
[2,1,4,2,5] => [[1,2,5],[2,4]] => 14
[2,1,4,5,2] => [[1,2,5],[2,4]] => 14
[2,1,5,2,4] => [[1,2,4],[2,5]] => 14
[2,1,5,4,2] => [[1,2],[2,4],[5]] => 14
[2,2,1,4,5] => [[1,2,4,5],[2]] => 14
[2,2,1,5,4] => [[1,2,4],[2,5]] => 14
[2,2,4,1,5] => [[1,2,4,5],[2]] => 14
[2,2,4,5,1] => [[1,2,4,5],[2]] => 14
[2,2,5,1,4] => [[1,2,4],[2,5]] => 14
[2,2,5,4,1] => [[1,2,4],[2],[5]] => 14
[2,4,1,2,5] => [[1,2,5],[2,4]] => 14
[2,4,1,5,2] => [[1,2,5],[2,4]] => 14
[2,4,2,1,5] => [[1,2,5],[2],[4]] => 14
[2,4,2,5,1] => [[1,2,5],[2],[4]] => 14
[2,4,5,1,2] => [[1,2,5],[2,4]] => 14
[2,4,5,2,1] => [[1,2,5],[2],[4]] => 14
[2,5,1,2,4] => [[1,2,4],[2,5]] => 14
[2,5,1,4,2] => [[1,2],[2,4],[5]] => 14
[2,5,2,1,4] => [[1,2,4],[2],[5]] => 14
[2,5,2,4,1] => [[1,2,4],[2],[5]] => 14
[2,5,4,1,2] => [[1,2],[2,4],[5]] => 14
[2,5,4,2,1] => [[1,2],[2],[4],[5]] => 14
[4,1,2,2,5] => [[1,2,2,5],[4]] => 14
[4,1,2,5,2] => [[1,2,2],[4,5]] => 14
[4,1,5,2,2] => [[1,2,2],[4,5]] => 14
[4,2,1,2,5] => [[1,2,5],[2],[4]] => 14
[4,2,1,5,2] => [[1,2],[2,5],[4]] => 14
[4,2,2,1,5] => [[1,2,5],[2],[4]] => 14
[4,2,2,5,1] => [[1,2,5],[2],[4]] => 14
[4,2,5,1,2] => [[1,2],[2,5],[4]] => 14
[4,2,5,2,1] => [[1,2],[2,5],[4]] => 14
[4,5,1,2,2] => [[1,2,2],[4,5]] => 14
[4,5,2,1,2] => [[1,2],[2,5],[4]] => 14
[4,5,2,2,1] => [[1,2],[2,5],[4]] => 14
[5,1,2,2,4] => [[1,2,2,4],[5]] => 14
[5,1,2,4,2] => [[1,2,2],[4],[5]] => 14
[5,1,4,2,2] => [[1,2,2],[4],[5]] => 14
[5,2,1,2,4] => [[1,2,4],[2],[5]] => 14
[5,2,1,4,2] => [[1,2],[2,4],[5]] => 14
[5,2,2,1,4] => [[1,2,4],[2],[5]] => 14
[5,2,2,4,1] => [[1,2,4],[2],[5]] => 14
[5,2,4,1,2] => [[1,2],[2,4],[5]] => 14
[5,2,4,2,1] => [[1,2],[2],[4],[5]] => 14
[5,4,1,2,2] => [[1,2,2],[4],[5]] => 14
[5,4,2,1,2] => [[1,2],[2],[4],[5]] => 14
[5,4,2,2,1] => [[1,2],[2],[4],[5]] => 14
[1,2,3,3,3] => [[1,2,3,3,3]] => 12
[1,3,2,3,3] => [[1,2,3,3],[3]] => 12
[1,3,3,2,3] => [[1,2,3,3],[3]] => 12
[1,3,3,3,2] => [[1,2,3,3],[3]] => 12
[2,1,3,3,3] => [[1,3,3,3],[2]] => 12
[2,3,1,3,3] => [[1,3,3,3],[2]] => 12
[2,3,3,1,3] => [[1,3,3,3],[2]] => 12
[2,3,3,3,1] => [[1,3,3,3],[2]] => 12
[3,1,2,3,3] => [[1,2,3,3],[3]] => 12
[3,1,3,2,3] => [[1,2,3],[3,3]] => 12
[3,1,3,3,2] => [[1,2,3],[3,3]] => 12
[3,2,1,3,3] => [[1,3,3],[2],[3]] => 12
[3,2,3,1,3] => [[1,3,3],[2],[3]] => 12
[3,2,3,3,1] => [[1,3,3],[2],[3]] => 12
[3,3,1,2,3] => [[1,2,3],[3,3]] => 12
[3,3,1,3,2] => [[1,2,3],[3,3]] => 12
[3,3,2,1,3] => [[1,3,3],[2],[3]] => 12
[3,3,2,3,1] => [[1,3,3],[2],[3]] => 12
[3,3,3,1,2] => [[1,2,3],[3,3]] => 12
[3,3,3,2,1] => [[1,3,3],[2],[3]] => 12
[1,2,3,3,4] => [[1,2,3,3,4]] => 13
[1,2,3,4,3] => [[1,2,3,3],[4]] => 13
[1,2,4,3,3] => [[1,2,3,3],[4]] => 13
[1,3,2,3,4] => [[1,2,3,4],[3]] => 13
[1,3,2,4,3] => [[1,2,3],[3,4]] => 13
[1,3,3,2,4] => [[1,2,3,4],[3]] => 13
[1,3,3,4,2] => [[1,2,3,4],[3]] => 13
[1,3,4,2,3] => [[1,2,3],[3,4]] => 13
[1,3,4,3,2] => [[1,2,3],[3],[4]] => 13
[1,4,2,3,3] => [[1,2,3,3],[4]] => 13
[1,4,3,2,3] => [[1,2,3],[3],[4]] => 13
[1,4,3,3,2] => [[1,2,3],[3],[4]] => 13
[2,1,3,3,4] => [[1,3,3,4],[2]] => 13
[2,1,3,4,3] => [[1,3,3],[2,4]] => 13
[2,1,4,3,3] => [[1,3,3],[2,4]] => 13
[2,3,1,3,4] => [[1,3,3,4],[2]] => 13
[2,3,1,4,3] => [[1,3,3],[2,4]] => 13
[2,3,3,1,4] => [[1,3,3,4],[2]] => 13
[2,3,3,4,1] => [[1,3,3,4],[2]] => 13
[2,3,4,1,3] => [[1,3,3],[2,4]] => 13
[2,3,4,3,1] => [[1,3,3],[2],[4]] => 13
[2,4,1,3,3] => [[1,3,3],[2,4]] => 13
[2,4,3,1,3] => [[1,3,3],[2],[4]] => 13
[2,4,3,3,1] => [[1,3,3],[2],[4]] => 13
[3,1,2,3,4] => [[1,2,3,4],[3]] => 13
[3,1,2,4,3] => [[1,2,3],[3,4]] => 13
[3,1,3,2,4] => [[1,2,4],[3,3]] => 13
[3,1,3,4,2] => [[1,2,4],[3,3]] => 13
[3,1,4,2,3] => [[1,2,3],[3,4]] => 13
[3,1,4,3,2] => [[1,2],[3,3],[4]] => 13
[3,2,1,3,4] => [[1,3,4],[2],[3]] => 13
[3,2,1,4,3] => [[1,3],[2,4],[3]] => 13
[3,2,3,1,4] => [[1,3,4],[2],[3]] => 13
[3,2,3,4,1] => [[1,3,4],[2],[3]] => 13
[3,2,4,1,3] => [[1,3],[2,4],[3]] => 13
[3,2,4,3,1] => [[1,3],[2,4],[3]] => 13
[3,3,1,2,4] => [[1,2,4],[3,3]] => 13
[3,3,1,4,2] => [[1,2,4],[3,3]] => 13
[3,3,2,1,4] => [[1,3,4],[2],[3]] => 13
[3,3,2,4,1] => [[1,3,4],[2],[3]] => 13
[3,3,4,1,2] => [[1,2,4],[3,3]] => 13
[3,3,4,2,1] => [[1,3,4],[2],[3]] => 13
[3,4,1,2,3] => [[1,2,3],[3,4]] => 13
[3,4,1,3,2] => [[1,2],[3,3],[4]] => 13
[3,4,2,1,3] => [[1,3],[2,4],[3]] => 13
[3,4,2,3,1] => [[1,3],[2,4],[3]] => 13
[3,4,3,1,2] => [[1,2],[3,3],[4]] => 13
[3,4,3,2,1] => [[1,3],[2],[3],[4]] => 13
[4,1,2,3,3] => [[1,2,3,3],[4]] => 13
[4,1,3,2,3] => [[1,2,3],[3],[4]] => 13
[4,1,3,3,2] => [[1,2,3],[3],[4]] => 13
[4,2,1,3,3] => [[1,3,3],[2],[4]] => 13
[4,2,3,1,3] => [[1,3,3],[2],[4]] => 13
[4,2,3,3,1] => [[1,3,3],[2],[4]] => 13
[4,3,1,2,3] => [[1,2,3],[3],[4]] => 13
[4,3,1,3,2] => [[1,2],[3,3],[4]] => 13
[4,3,2,1,3] => [[1,3],[2],[3],[4]] => 13
[4,3,2,3,1] => [[1,3],[2],[3],[4]] => 13
[4,3,3,1,2] => [[1,2],[3,3],[4]] => 13
[4,3,3,2,1] => [[1,3],[2],[3],[4]] => 13
[1,2,3,3,5] => [[1,2,3,3,5]] => 14
[1,2,3,5,3] => [[1,2,3,3],[5]] => 14
[1,2,5,3,3] => [[1,2,3,3],[5]] => 14
[1,3,2,3,5] => [[1,2,3,5],[3]] => 14
[1,3,2,5,3] => [[1,2,3],[3,5]] => 14
[1,3,3,2,5] => [[1,2,3,5],[3]] => 14
[1,3,3,5,2] => [[1,2,3,5],[3]] => 14
[1,3,5,2,3] => [[1,2,3],[3,5]] => 14
[1,3,5,3,2] => [[1,2,3],[3],[5]] => 14
[1,5,2,3,3] => [[1,2,3,3],[5]] => 14
[1,5,3,2,3] => [[1,2,3],[3],[5]] => 14
[1,5,3,3,2] => [[1,2,3],[3],[5]] => 14
[2,1,3,3,5] => [[1,3,3,5],[2]] => 14
[2,1,3,5,3] => [[1,3,3],[2,5]] => 14
[2,1,5,3,3] => [[1,3,3],[2,5]] => 14
[2,3,1,3,5] => [[1,3,3,5],[2]] => 14
[2,3,1,5,3] => [[1,3,3],[2,5]] => 14
[2,3,3,1,5] => [[1,3,3,5],[2]] => 14
[2,3,3,5,1] => [[1,3,3,5],[2]] => 14
[2,3,5,1,3] => [[1,3,3],[2,5]] => 14
[2,3,5,3,1] => [[1,3,3],[2],[5]] => 14
[2,5,1,3,3] => [[1,3,3],[2,5]] => 14
[2,5,3,1,3] => [[1,3,3],[2],[5]] => 14
[2,5,3,3,1] => [[1,3,3],[2],[5]] => 14
[3,1,2,3,5] => [[1,2,3,5],[3]] => 14
[3,1,2,5,3] => [[1,2,3],[3,5]] => 14
[3,1,3,2,5] => [[1,2,5],[3,3]] => 14
[3,1,3,5,2] => [[1,2,5],[3,3]] => 14
[3,1,5,2,3] => [[1,2,3],[3,5]] => 14
[3,1,5,3,2] => [[1,2],[3,3],[5]] => 14
[3,2,1,3,5] => [[1,3,5],[2],[3]] => 14
[3,2,1,5,3] => [[1,3],[2,5],[3]] => 14
[3,2,3,1,5] => [[1,3,5],[2],[3]] => 14
[3,2,3,5,1] => [[1,3,5],[2],[3]] => 14
[3,2,5,1,3] => [[1,3],[2,5],[3]] => 14
[3,2,5,3,1] => [[1,3],[2,5],[3]] => 14
[3,3,1,2,5] => [[1,2,5],[3,3]] => 14
[3,3,1,5,2] => [[1,2,5],[3,3]] => 14
[3,3,2,1,5] => [[1,3,5],[2],[3]] => 14
[3,3,2,5,1] => [[1,3,5],[2],[3]] => 14
[3,3,5,1,2] => [[1,2,5],[3,3]] => 14
[3,3,5,2,1] => [[1,3,5],[2],[3]] => 14
[3,5,1,2,3] => [[1,2,3],[3,5]] => 14
[3,5,1,3,2] => [[1,2],[3,3],[5]] => 14
[3,5,2,1,3] => [[1,3],[2,5],[3]] => 14
[3,5,2,3,1] => [[1,3],[2,5],[3]] => 14
[3,5,3,1,2] => [[1,2],[3,3],[5]] => 14
[3,5,3,2,1] => [[1,3],[2],[3],[5]] => 14
[5,1,2,3,3] => [[1,2,3,3],[5]] => 14
[5,1,3,2,3] => [[1,2,3],[3],[5]] => 14
[5,1,3,3,2] => [[1,2,3],[3],[5]] => 14
[5,2,1,3,3] => [[1,3,3],[2],[5]] => 14
[5,2,3,1,3] => [[1,3,3],[2],[5]] => 14
[5,2,3,3,1] => [[1,3,3],[2],[5]] => 14
[5,3,1,2,3] => [[1,2,3],[3],[5]] => 14
[5,3,1,3,2] => [[1,2],[3,3],[5]] => 14
[5,3,2,1,3] => [[1,3],[2],[3],[5]] => 14
[5,3,2,3,1] => [[1,3],[2],[3],[5]] => 14
[5,3,3,1,2] => [[1,2],[3,3],[5]] => 14
[5,3,3,2,1] => [[1,3],[2],[3],[5]] => 14
[1,2,3,4,4] => [[1,2,3,4,4]] => 14
[1,2,4,3,4] => [[1,2,3,4],[4]] => 14
[1,2,4,4,3] => [[1,2,3,4],[4]] => 14
[1,3,2,4,4] => [[1,2,4,4],[3]] => 14
[1,3,4,2,4] => [[1,2,4,4],[3]] => 14
[1,3,4,4,2] => [[1,2,4,4],[3]] => 14
[1,4,2,3,4] => [[1,2,3,4],[4]] => 14
[1,4,2,4,3] => [[1,2,3],[4,4]] => 14
[1,4,3,2,4] => [[1,2,4],[3],[4]] => 14
[1,4,3,4,2] => [[1,2,4],[3],[4]] => 14
[1,4,4,2,3] => [[1,2,3],[4,4]] => 14
[1,4,4,3,2] => [[1,2,4],[3],[4]] => 14
[2,1,3,4,4] => [[1,3,4,4],[2]] => 14
[2,1,4,3,4] => [[1,3,4],[2,4]] => 14
[2,1,4,4,3] => [[1,3,4],[2,4]] => 14
[2,3,1,4,4] => [[1,3,4,4],[2]] => 14
[2,3,4,1,4] => [[1,3,4,4],[2]] => 14
[2,3,4,4,1] => [[1,3,4,4],[2]] => 14
[2,4,1,3,4] => [[1,3,4],[2,4]] => 14
[2,4,1,4,3] => [[1,3,4],[2,4]] => 14
[2,4,3,1,4] => [[1,3,4],[2],[4]] => 14
[2,4,3,4,1] => [[1,3,4],[2],[4]] => 14
[2,4,4,1,3] => [[1,3,4],[2,4]] => 14
[2,4,4,3,1] => [[1,3,4],[2],[4]] => 14
[3,1,2,4,4] => [[1,2,4,4],[3]] => 14
[3,1,4,2,4] => [[1,2,4],[3,4]] => 14
[3,1,4,4,2] => [[1,2,4],[3,4]] => 14
[3,2,1,4,4] => [[1,4,4],[2],[3]] => 14
[3,2,4,1,4] => [[1,4,4],[2],[3]] => 14
[3,2,4,4,1] => [[1,4,4],[2],[3]] => 14
[3,4,1,2,4] => [[1,2,4],[3,4]] => 14
[3,4,1,4,2] => [[1,2,4],[3,4]] => 14
[3,4,2,1,4] => [[1,4,4],[2],[3]] => 14
[3,4,2,4,1] => [[1,4,4],[2],[3]] => 14
[3,4,4,1,2] => [[1,2,4],[3,4]] => 14
[3,4,4,2,1] => [[1,4,4],[2],[3]] => 14
[4,1,2,3,4] => [[1,2,3,4],[4]] => 14
[4,1,2,4,3] => [[1,2,3],[4,4]] => 14
[4,1,3,2,4] => [[1,2,4],[3],[4]] => 14
[4,1,3,4,2] => [[1,2,4],[3],[4]] => 14
[4,1,4,2,3] => [[1,2,3],[4,4]] => 14
[4,1,4,3,2] => [[1,2],[3,4],[4]] => 14
[4,2,1,3,4] => [[1,3,4],[2],[4]] => 14
[4,2,1,4,3] => [[1,3],[2,4],[4]] => 14
[4,2,3,1,4] => [[1,3,4],[2],[4]] => 14
[4,2,3,4,1] => [[1,3,4],[2],[4]] => 14
[4,2,4,1,3] => [[1,3],[2,4],[4]] => 14
[4,2,4,3,1] => [[1,3],[2,4],[4]] => 14
[4,3,1,2,4] => [[1,2,4],[3],[4]] => 14
[4,3,1,4,2] => [[1,2],[3,4],[4]] => 14
[4,3,2,1,4] => [[1,4],[2],[3],[4]] => 14
[4,3,2,4,1] => [[1,4],[2],[3],[4]] => 14
[4,3,4,1,2] => [[1,2],[3,4],[4]] => 14
[4,3,4,2,1] => [[1,4],[2],[3],[4]] => 14
[4,4,1,2,3] => [[1,2,3],[4,4]] => 14
[4,4,1,3,2] => [[1,2],[3,4],[4]] => 14
[4,4,2,1,3] => [[1,3],[2,4],[4]] => 14
[4,4,2,3,1] => [[1,3],[2,4],[4]] => 14
[4,4,3,1,2] => [[1,2],[3,4],[4]] => 14
[4,4,3,2,1] => [[1,4],[2],[3],[4]] => 14
[1,2,3,4,5] => [[1,2,3,4,5]] => 15
[1,2,3,5,4] => [[1,2,3,4],[5]] => 15
[1,2,4,3,5] => [[1,2,3,5],[4]] => 15
[1,2,4,5,3] => [[1,2,3,5],[4]] => 15
[1,2,5,3,4] => [[1,2,3,4],[5]] => 15
[1,2,5,4,3] => [[1,2,3],[4],[5]] => 15
[1,3,2,4,5] => [[1,2,4,5],[3]] => 15
[1,3,2,5,4] => [[1,2,4],[3,5]] => 15
[1,3,4,2,5] => [[1,2,4,5],[3]] => 15
[1,3,4,5,2] => [[1,2,4,5],[3]] => 15
[1,3,5,2,4] => [[1,2,4],[3,5]] => 15
[1,3,5,4,2] => [[1,2,4],[3],[5]] => 15
[1,4,2,3,5] => [[1,2,3,5],[4]] => 15
[1,4,2,5,3] => [[1,2,3],[4,5]] => 15
[1,4,3,2,5] => [[1,2,5],[3],[4]] => 15
[1,4,3,5,2] => [[1,2,5],[3],[4]] => 15
[1,4,5,2,3] => [[1,2,3],[4,5]] => 15
[1,4,5,3,2] => [[1,2,5],[3],[4]] => 15
[1,5,2,3,4] => [[1,2,3,4],[5]] => 15
[1,5,2,4,3] => [[1,2,3],[4],[5]] => 15
[1,5,3,2,4] => [[1,2,4],[3],[5]] => 15
[1,5,3,4,2] => [[1,2,4],[3],[5]] => 15
[1,5,4,2,3] => [[1,2,3],[4],[5]] => 15
[1,5,4,3,2] => [[1,2],[3],[4],[5]] => 15
[2,1,3,4,5] => [[1,3,4,5],[2]] => 15
[2,1,3,5,4] => [[1,3,4],[2,5]] => 15
[2,1,4,3,5] => [[1,3,5],[2,4]] => 15
[2,1,4,5,3] => [[1,3,5],[2,4]] => 15
[2,1,5,3,4] => [[1,3,4],[2,5]] => 15
[2,1,5,4,3] => [[1,3],[2,4],[5]] => 15
[2,3,1,4,5] => [[1,3,4,5],[2]] => 15
[2,3,1,5,4] => [[1,3,4],[2,5]] => 15
[2,3,4,1,5] => [[1,3,4,5],[2]] => 15
[2,3,4,5,1] => [[1,3,4,5],[2]] => 15
[2,3,5,1,4] => [[1,3,4],[2,5]] => 15
[2,3,5,4,1] => [[1,3,4],[2],[5]] => 15
[2,4,1,3,5] => [[1,3,5],[2,4]] => 15
[2,4,1,5,3] => [[1,3,5],[2,4]] => 15
[2,4,3,1,5] => [[1,3,5],[2],[4]] => 15
[2,4,3,5,1] => [[1,3,5],[2],[4]] => 15
[2,4,5,1,3] => [[1,3,5],[2,4]] => 15
[2,4,5,3,1] => [[1,3,5],[2],[4]] => 15
[2,5,1,3,4] => [[1,3,4],[2,5]] => 15
[2,5,1,4,3] => [[1,3],[2,4],[5]] => 15
[2,5,3,1,4] => [[1,3,4],[2],[5]] => 15
[2,5,3,4,1] => [[1,3,4],[2],[5]] => 15
[2,5,4,1,3] => [[1,3],[2,4],[5]] => 15
[2,5,4,3,1] => [[1,3],[2],[4],[5]] => 15
[3,1,2,4,5] => [[1,2,4,5],[3]] => 15
[3,1,2,5,4] => [[1,2,4],[3,5]] => 15
[3,1,4,2,5] => [[1,2,5],[3,4]] => 15
[3,1,4,5,2] => [[1,2,5],[3,4]] => 15
[3,1,5,2,4] => [[1,2,4],[3,5]] => 15
[3,1,5,4,2] => [[1,2],[3,4],[5]] => 15
[3,2,1,4,5] => [[1,4,5],[2],[3]] => 15
[3,2,1,5,4] => [[1,4],[2,5],[3]] => 15
[3,2,4,1,5] => [[1,4,5],[2],[3]] => 15
[3,2,4,5,1] => [[1,4,5],[2],[3]] => 15
[3,2,5,1,4] => [[1,4],[2,5],[3]] => 15
[3,2,5,4,1] => [[1,4],[2,5],[3]] => 15
[3,4,1,2,5] => [[1,2,5],[3,4]] => 15
[3,4,1,5,2] => [[1,2,5],[3,4]] => 15
[3,4,2,1,5] => [[1,4,5],[2],[3]] => 15
[3,4,2,5,1] => [[1,4,5],[2],[3]] => 15
[3,4,5,1,2] => [[1,2,5],[3,4]] => 15
[3,4,5,2,1] => [[1,4,5],[2],[3]] => 15
[3,5,1,2,4] => [[1,2,4],[3,5]] => 15
[3,5,1,4,2] => [[1,2],[3,4],[5]] => 15
[3,5,2,1,4] => [[1,4],[2,5],[3]] => 15
[3,5,2,4,1] => [[1,4],[2,5],[3]] => 15
[3,5,4,1,2] => [[1,2],[3,4],[5]] => 15
[3,5,4,2,1] => [[1,4],[2],[3],[5]] => 15
[4,1,2,3,5] => [[1,2,3,5],[4]] => 15
[4,1,2,5,3] => [[1,2,3],[4,5]] => 15
[4,1,3,2,5] => [[1,2,5],[3],[4]] => 15
[4,1,3,5,2] => [[1,2,5],[3],[4]] => 15
[4,1,5,2,3] => [[1,2,3],[4,5]] => 15
[4,1,5,3,2] => [[1,2],[3,5],[4]] => 15
[4,2,1,3,5] => [[1,3,5],[2],[4]] => 15
[4,2,1,5,3] => [[1,3],[2,5],[4]] => 15
[4,2,3,1,5] => [[1,3,5],[2],[4]] => 15
[4,2,3,5,1] => [[1,3,5],[2],[4]] => 15
[4,2,5,1,3] => [[1,3],[2,5],[4]] => 15
[4,2,5,3,1] => [[1,3],[2,5],[4]] => 15
[4,3,1,2,5] => [[1,2,5],[3],[4]] => 15
[4,3,1,5,2] => [[1,2],[3,5],[4]] => 15
[4,3,2,1,5] => [[1,5],[2],[3],[4]] => 15
[4,3,2,5,1] => [[1,5],[2],[3],[4]] => 15
[4,3,5,1,2] => [[1,2],[3,5],[4]] => 15
[4,3,5,2,1] => [[1,5],[2],[3],[4]] => 15
[4,5,1,2,3] => [[1,2,3],[4,5]] => 15
[4,5,1,3,2] => [[1,2],[3,5],[4]] => 15
[4,5,2,1,3] => [[1,3],[2,5],[4]] => 15
[4,5,2,3,1] => [[1,3],[2,5],[4]] => 15
[4,5,3,1,2] => [[1,2],[3,5],[4]] => 15
[4,5,3,2,1] => [[1,5],[2],[3],[4]] => 15
[5,1,2,3,4] => [[1,2,3,4],[5]] => 15
[5,1,2,4,3] => [[1,2,3],[4],[5]] => 15
[5,1,3,2,4] => [[1,2,4],[3],[5]] => 15
[5,1,3,4,2] => [[1,2,4],[3],[5]] => 15
[5,1,4,2,3] => [[1,2,3],[4],[5]] => 15
[5,1,4,3,2] => [[1,2],[3],[4],[5]] => 15
[5,2,1,3,4] => [[1,3,4],[2],[5]] => 15
[5,2,1,4,3] => [[1,3],[2,4],[5]] => 15
[5,2,3,1,4] => [[1,3,4],[2],[5]] => 15
[5,2,3,4,1] => [[1,3,4],[2],[5]] => 15
[5,2,4,1,3] => [[1,3],[2,4],[5]] => 15
[5,2,4,3,1] => [[1,3],[2],[4],[5]] => 15
[5,3,1,2,4] => [[1,2,4],[3],[5]] => 15
[5,3,1,4,2] => [[1,2],[3,4],[5]] => 15
[5,3,2,1,4] => [[1,4],[2],[3],[5]] => 15
[5,3,2,4,1] => [[1,4],[2],[3],[5]] => 15
[5,3,4,1,2] => [[1,2],[3,4],[5]] => 15
[5,3,4,2,1] => [[1,4],[2],[3],[5]] => 15
[5,4,1,2,3] => [[1,2,3],[4],[5]] => 15
[5,4,1,3,2] => [[1,2],[3],[4],[5]] => 15
[5,4,2,1,3] => [[1,3],[2],[4],[5]] => 15
[5,4,2,3,1] => [[1,3],[2],[4],[5]] => 15
[5,4,3,1,2] => [[1,2],[3],[4],[5]] => 15
[5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 15
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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 1,5,15,35,70,120,180,240,270,240,120
$F_{1} = q$
$F_{2} = q^{2} + 2\ q^{3}$
$F_{3} = q^{3} + 3\ q^{4} + 6\ q^{5} + 6\ q^{6}$
$F_{4} = q^{4} + 4\ q^{5} + 10\ q^{6} + 20\ q^{7} + 30\ q^{8} + 36\ q^{9} + 24\ q^{10}$
$F_{5} = q^{5} + 5\ q^{6} + 15\ q^{7} + 35\ q^{8} + 70\ q^{9} + 120\ q^{10} + 180\ q^{11} + 240\ q^{12} + 270\ q^{13} + 240\ q^{14} + 120\ q^{15}$
Description
The sum of the entries of a semistandard tableau.
Map
insertion tableau
Description
The insertion tableau obtained by applying RSK to the parking function regarded as a word.
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