Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00308: Integer partitions —Bulgarian solitaire⟶ Integer partitions
St000147: Integer partitions ⟶ ℤ
Values
[1] => [] => [] => 0
[2] => [] => [] => 0
[1,1] => [1] => [1] => 1
[3] => [] => [] => 0
[2,1] => [1] => [1] => 1
[1,1,1] => [1,1] => [2] => 2
[4] => [] => [] => 0
[3,1] => [1] => [1] => 1
[2,2] => [2] => [1,1] => 1
[2,1,1] => [1,1] => [2] => 2
[1,1,1,1] => [1,1,1] => [3] => 3
[5] => [] => [] => 0
[4,1] => [1] => [1] => 1
[3,2] => [2] => [1,1] => 1
[3,1,1] => [1,1] => [2] => 2
[2,2,1] => [2,1] => [2,1] => 2
[2,1,1,1] => [1,1,1] => [3] => 3
[1,1,1,1,1] => [1,1,1,1] => [4] => 4
[6] => [] => [] => 0
[5,1] => [1] => [1] => 1
[4,2] => [2] => [1,1] => 1
[4,1,1] => [1,1] => [2] => 2
[3,3] => [3] => [2,1] => 2
[3,2,1] => [2,1] => [2,1] => 2
[3,1,1,1] => [1,1,1] => [3] => 3
[2,2,2] => [2,2] => [2,1,1] => 2
[2,2,1,1] => [2,1,1] => [3,1] => 3
[2,1,1,1,1] => [1,1,1,1] => [4] => 4
[1,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[7] => [] => [] => 0
[6,1] => [1] => [1] => 1
[5,2] => [2] => [1,1] => 1
[5,1,1] => [1,1] => [2] => 2
[4,3] => [3] => [2,1] => 2
[4,2,1] => [2,1] => [2,1] => 2
[4,1,1,1] => [1,1,1] => [3] => 3
[3,3,1] => [3,1] => [2,2] => 2
[3,2,2] => [2,2] => [2,1,1] => 2
[3,2,1,1] => [2,1,1] => [3,1] => 3
[3,1,1,1,1] => [1,1,1,1] => [4] => 4
[2,2,2,1] => [2,2,1] => [3,1,1] => 3
[2,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[2,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[8] => [] => [] => 0
[7,1] => [1] => [1] => 1
[6,2] => [2] => [1,1] => 1
[6,1,1] => [1,1] => [2] => 2
[5,3] => [3] => [2,1] => 2
[5,2,1] => [2,1] => [2,1] => 2
[5,1,1,1] => [1,1,1] => [3] => 3
[4,4] => [4] => [3,1] => 3
[4,3,1] => [3,1] => [2,2] => 2
[4,2,2] => [2,2] => [2,1,1] => 2
[4,2,1,1] => [2,1,1] => [3,1] => 3
[4,1,1,1,1] => [1,1,1,1] => [4] => 4
[3,3,2] => [3,2] => [2,2,1] => 2
[3,3,1,1] => [3,1,1] => [3,2] => 3
[3,2,2,1] => [2,2,1] => [3,1,1] => 3
[3,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[3,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[2,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[2,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[2,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[9] => [] => [] => 0
[8,1] => [1] => [1] => 1
[7,2] => [2] => [1,1] => 1
[7,1,1] => [1,1] => [2] => 2
[6,3] => [3] => [2,1] => 2
[6,2,1] => [2,1] => [2,1] => 2
[6,1,1,1] => [1,1,1] => [3] => 3
[5,4] => [4] => [3,1] => 3
[5,3,1] => [3,1] => [2,2] => 2
[5,2,2] => [2,2] => [2,1,1] => 2
[5,2,1,1] => [2,1,1] => [3,1] => 3
[5,1,1,1,1] => [1,1,1,1] => [4] => 4
[4,4,1] => [4,1] => [3,2] => 3
[4,3,2] => [3,2] => [2,2,1] => 2
[4,3,1,1] => [3,1,1] => [3,2] => 3
[4,2,2,1] => [2,2,1] => [3,1,1] => 3
[4,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[4,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[3,3,3] => [3,3] => [2,2,2] => 2
[3,3,2,1] => [3,2,1] => [3,2,1] => 3
[3,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[3,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[3,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[3,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[2,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[10] => [] => [] => 0
[9,1] => [1] => [1] => 1
[8,2] => [2] => [1,1] => 1
[8,1,1] => [1,1] => [2] => 2
[7,3] => [3] => [2,1] => 2
>>> Load all 1399 entries. <<<[7,2,1] => [2,1] => [2,1] => 2
[7,1,1,1] => [1,1,1] => [3] => 3
[6,4] => [4] => [3,1] => 3
[6,3,1] => [3,1] => [2,2] => 2
[6,2,2] => [2,2] => [2,1,1] => 2
[6,2,1,1] => [2,1,1] => [3,1] => 3
[6,1,1,1,1] => [1,1,1,1] => [4] => 4
[5,5] => [5] => [4,1] => 4
[5,4,1] => [4,1] => [3,2] => 3
[5,3,2] => [3,2] => [2,2,1] => 2
[5,3,1,1] => [3,1,1] => [3,2] => 3
[5,2,2,1] => [2,2,1] => [3,1,1] => 3
[5,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[5,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[4,4,2] => [4,2] => [3,2,1] => 3
[4,4,1,1] => [4,1,1] => [3,3] => 3
[4,3,3] => [3,3] => [2,2,2] => 2
[4,3,2,1] => [3,2,1] => [3,2,1] => 3
[4,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[4,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[4,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[4,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[3,3,3,1] => [3,3,1] => [3,2,2] => 3
[3,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[3,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[3,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[3,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[3,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[2,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[2,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[11] => [] => [] => 0
[10,1] => [1] => [1] => 1
[9,2] => [2] => [1,1] => 1
[9,1,1] => [1,1] => [2] => 2
[8,3] => [3] => [2,1] => 2
[8,2,1] => [2,1] => [2,1] => 2
[8,1,1,1] => [1,1,1] => [3] => 3
[7,4] => [4] => [3,1] => 3
[7,3,1] => [3,1] => [2,2] => 2
[7,2,2] => [2,2] => [2,1,1] => 2
[7,2,1,1] => [2,1,1] => [3,1] => 3
[7,1,1,1,1] => [1,1,1,1] => [4] => 4
[6,5] => [5] => [4,1] => 4
[6,4,1] => [4,1] => [3,2] => 3
[6,3,2] => [3,2] => [2,2,1] => 2
[6,3,1,1] => [3,1,1] => [3,2] => 3
[6,2,2,1] => [2,2,1] => [3,1,1] => 3
[6,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[6,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[5,5,1] => [5,1] => [4,2] => 4
[5,4,2] => [4,2] => [3,2,1] => 3
[5,4,1,1] => [4,1,1] => [3,3] => 3
[5,3,3] => [3,3] => [2,2,2] => 2
[5,3,2,1] => [3,2,1] => [3,2,1] => 3
[5,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[5,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[5,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[5,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[4,4,3] => [4,3] => [3,2,2] => 3
[4,4,2,1] => [4,2,1] => [3,3,1] => 3
[4,4,1,1,1] => [4,1,1,1] => [4,3] => 4
[4,3,3,1] => [3,3,1] => [3,2,2] => 3
[4,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[4,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[4,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[4,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[4,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[3,3,3,2] => [3,3,2] => [3,2,2,1] => 3
[3,3,3,1,1] => [3,3,1,1] => [4,2,2] => 4
[3,3,2,2,1] => [3,2,2,1] => [4,2,1,1] => 4
[3,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => 5
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,2] => 6
[3,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[3,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[2,2,2,2,2,1] => [2,2,2,2,1] => [5,1,1,1,1] => 5
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,1,1,1] => 6
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,1,1] => 7
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 8
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 10
[12] => [] => [] => 0
[11,1] => [1] => [1] => 1
[10,2] => [2] => [1,1] => 1
[10,1,1] => [1,1] => [2] => 2
[9,3] => [3] => [2,1] => 2
[9,2,1] => [2,1] => [2,1] => 2
[9,1,1,1] => [1,1,1] => [3] => 3
[8,4] => [4] => [3,1] => 3
[8,3,1] => [3,1] => [2,2] => 2
[8,2,2] => [2,2] => [2,1,1] => 2
[8,2,1,1] => [2,1,1] => [3,1] => 3
[8,1,1,1,1] => [1,1,1,1] => [4] => 4
[7,5] => [5] => [4,1] => 4
[7,4,1] => [4,1] => [3,2] => 3
[7,3,2] => [3,2] => [2,2,1] => 2
[7,3,1,1] => [3,1,1] => [3,2] => 3
[7,2,2,1] => [2,2,1] => [3,1,1] => 3
[7,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[7,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[6,6] => [6] => [5,1] => 5
[6,5,1] => [5,1] => [4,2] => 4
[6,4,2] => [4,2] => [3,2,1] => 3
[6,4,1,1] => [4,1,1] => [3,3] => 3
[6,3,3] => [3,3] => [2,2,2] => 2
[6,3,2,1] => [3,2,1] => [3,2,1] => 3
[6,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[6,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[6,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[6,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[5,5,2] => [5,2] => [4,2,1] => 4
[5,5,1,1] => [5,1,1] => [4,3] => 4
[5,4,3] => [4,3] => [3,2,2] => 3
[5,4,2,1] => [4,2,1] => [3,3,1] => 3
[5,4,1,1,1] => [4,1,1,1] => [4,3] => 4
[5,3,3,1] => [3,3,1] => [3,2,2] => 3
[5,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[5,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[5,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[5,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[5,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[4,4,4] => [4,4] => [3,3,2] => 3
[4,4,3,1] => [4,3,1] => [3,3,2] => 3
[4,4,2,2] => [4,2,2] => [3,3,1,1] => 3
[4,4,2,1,1] => [4,2,1,1] => [4,3,1] => 4
[4,4,1,1,1,1] => [4,1,1,1,1] => [5,3] => 5
[4,3,3,2] => [3,3,2] => [3,2,2,1] => 3
[4,3,3,1,1] => [3,3,1,1] => [4,2,2] => 4
[4,3,2,2,1] => [3,2,2,1] => [4,2,1,1] => 4
[4,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => 5
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,2] => 6
[4,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[4,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[3,3,3,3] => [3,3,3] => [3,2,2,2] => 3
[3,3,3,2,1] => [3,3,2,1] => [4,2,2,1] => 4
[3,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => 5
[3,3,2,2,2] => [3,2,2,2] => [4,2,1,1,1] => 4
[3,3,2,2,1,1] => [3,2,2,1,1] => [5,2,1,1] => 5
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => 6
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,2] => 7
[3,2,2,2,2,1] => [2,2,2,2,1] => [5,1,1,1,1] => 5
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,1,1,1] => 6
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,1,1] => 7
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 8
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[2,2,2,2,2,2] => [2,2,2,2,2] => [5,1,1,1,1,1] => 5
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,1,1,1,1] => 6
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 7
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,1,1] => 8
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 10
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 11
[13] => [] => [] => 0
[12,1] => [1] => [1] => 1
[11,2] => [2] => [1,1] => 1
[11,1,1] => [1,1] => [2] => 2
[10,3] => [3] => [2,1] => 2
[10,2,1] => [2,1] => [2,1] => 2
[10,1,1,1] => [1,1,1] => [3] => 3
[9,4] => [4] => [3,1] => 3
[9,3,1] => [3,1] => [2,2] => 2
[9,2,2] => [2,2] => [2,1,1] => 2
[9,2,1,1] => [2,1,1] => [3,1] => 3
[9,1,1,1,1] => [1,1,1,1] => [4] => 4
[8,5] => [5] => [4,1] => 4
[8,4,1] => [4,1] => [3,2] => 3
[8,3,2] => [3,2] => [2,2,1] => 2
[8,3,1,1] => [3,1,1] => [3,2] => 3
[8,2,2,1] => [2,2,1] => [3,1,1] => 3
[8,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[8,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[7,6] => [6] => [5,1] => 5
[7,5,1] => [5,1] => [4,2] => 4
[7,4,2] => [4,2] => [3,2,1] => 3
[7,4,1,1] => [4,1,1] => [3,3] => 3
[7,3,3] => [3,3] => [2,2,2] => 2
[7,3,2,1] => [3,2,1] => [3,2,1] => 3
[7,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[7,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[7,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[7,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[6,6,1] => [6,1] => [5,2] => 5
[6,5,2] => [5,2] => [4,2,1] => 4
[6,5,1,1] => [5,1,1] => [4,3] => 4
[6,4,3] => [4,3] => [3,2,2] => 3
[6,4,2,1] => [4,2,1] => [3,3,1] => 3
[6,4,1,1,1] => [4,1,1,1] => [4,3] => 4
[6,3,3,1] => [3,3,1] => [3,2,2] => 3
[6,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[6,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[6,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[6,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[6,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[5,5,3] => [5,3] => [4,2,2] => 4
[5,5,2,1] => [5,2,1] => [4,3,1] => 4
[5,5,1,1,1] => [5,1,1,1] => [4,4] => 4
[5,4,4] => [4,4] => [3,3,2] => 3
[5,4,3,1] => [4,3,1] => [3,3,2] => 3
[5,4,2,2] => [4,2,2] => [3,3,1,1] => 3
[5,4,2,1,1] => [4,2,1,1] => [4,3,1] => 4
[5,4,1,1,1,1] => [4,1,1,1,1] => [5,3] => 5
[5,3,3,2] => [3,3,2] => [3,2,2,1] => 3
[5,3,3,1,1] => [3,3,1,1] => [4,2,2] => 4
[5,3,2,2,1] => [3,2,2,1] => [4,2,1,1] => 4
[5,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => 5
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,2] => 6
[5,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[5,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[4,4,4,1] => [4,4,1] => [3,3,3] => 3
[4,4,3,2] => [4,3,2] => [3,3,2,1] => 3
[4,4,3,1,1] => [4,3,1,1] => [4,3,2] => 4
[4,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => 4
[4,4,2,1,1,1] => [4,2,1,1,1] => [5,3,1] => 5
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,3] => 6
[4,3,3,3] => [3,3,3] => [3,2,2,2] => 3
[4,3,3,2,1] => [3,3,2,1] => [4,2,2,1] => 4
[4,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => 5
[4,3,2,2,2] => [3,2,2,2] => [4,2,1,1,1] => 4
[4,3,2,2,1,1] => [3,2,2,1,1] => [5,2,1,1] => 5
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => 6
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,2] => 7
[4,2,2,2,2,1] => [2,2,2,2,1] => [5,1,1,1,1] => 5
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,1,1,1] => 6
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,1,1] => 7
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 8
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[3,3,3,3,1] => [3,3,3,1] => [4,2,2,2] => 4
[3,3,3,2,2] => [3,3,2,2] => [4,2,2,1,1] => 4
[3,3,3,2,1,1] => [3,3,2,1,1] => [5,2,2,1] => 5
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => 6
[3,3,2,2,2,1] => [3,2,2,2,1] => [5,2,1,1,1] => 5
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,2,1,1] => 6
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 7
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,2] => 8
[3,2,2,2,2,2] => [2,2,2,2,2] => [5,1,1,1,1,1] => 5
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,1,1,1,1] => 6
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 7
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,1,1] => 8
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 10
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,1,1,1,1,1] => 6
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,1,1,1,1] => 7
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,1,1,1] => 8
[2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,1,1] => 9
[2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 10
[2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 11
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 12
[14] => [] => [] => 0
[13,1] => [1] => [1] => 1
[12,2] => [2] => [1,1] => 1
[12,1,1] => [1,1] => [2] => 2
[11,3] => [3] => [2,1] => 2
[11,2,1] => [2,1] => [2,1] => 2
[11,1,1,1] => [1,1,1] => [3] => 3
[10,4] => [4] => [3,1] => 3
[10,3,1] => [3,1] => [2,2] => 2
[10,2,2] => [2,2] => [2,1,1] => 2
[10,2,1,1] => [2,1,1] => [3,1] => 3
[10,1,1,1,1] => [1,1,1,1] => [4] => 4
[9,5] => [5] => [4,1] => 4
[9,4,1] => [4,1] => [3,2] => 3
[9,3,2] => [3,2] => [2,2,1] => 2
[9,3,1,1] => [3,1,1] => [3,2] => 3
[9,2,2,1] => [2,2,1] => [3,1,1] => 3
[9,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[9,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[8,6] => [6] => [5,1] => 5
[8,5,1] => [5,1] => [4,2] => 4
[8,4,2] => [4,2] => [3,2,1] => 3
[8,4,1,1] => [4,1,1] => [3,3] => 3
[8,3,3] => [3,3] => [2,2,2] => 2
[8,3,2,1] => [3,2,1] => [3,2,1] => 3
[8,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[8,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[8,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[8,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[7,7] => [7] => [6,1] => 6
[7,6,1] => [6,1] => [5,2] => 5
[7,5,2] => [5,2] => [4,2,1] => 4
[7,5,1,1] => [5,1,1] => [4,3] => 4
[7,4,3] => [4,3] => [3,2,2] => 3
[7,4,2,1] => [4,2,1] => [3,3,1] => 3
[7,4,1,1,1] => [4,1,1,1] => [4,3] => 4
[7,3,3,1] => [3,3,1] => [3,2,2] => 3
[7,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[7,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[7,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[7,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[7,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[6,6,2] => [6,2] => [5,2,1] => 5
[6,6,1,1] => [6,1,1] => [5,3] => 5
[6,5,3] => [5,3] => [4,2,2] => 4
[6,5,2,1] => [5,2,1] => [4,3,1] => 4
[6,5,1,1,1] => [5,1,1,1] => [4,4] => 4
[6,4,4] => [4,4] => [3,3,2] => 3
[6,4,3,1] => [4,3,1] => [3,3,2] => 3
[6,4,2,2] => [4,2,2] => [3,3,1,1] => 3
[6,4,2,1,1] => [4,2,1,1] => [4,3,1] => 4
[6,4,1,1,1,1] => [4,1,1,1,1] => [5,3] => 5
[6,3,3,2] => [3,3,2] => [3,2,2,1] => 3
[6,3,3,1,1] => [3,3,1,1] => [4,2,2] => 4
[6,3,2,2,1] => [3,2,2,1] => [4,2,1,1] => 4
[6,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => 5
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,2] => 6
[6,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[6,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[5,5,4] => [5,4] => [4,3,2] => 4
[5,5,3,1] => [5,3,1] => [4,3,2] => 4
[5,5,2,2] => [5,2,2] => [4,3,1,1] => 4
[5,5,2,1,1] => [5,2,1,1] => [4,4,1] => 4
[5,5,1,1,1,1] => [5,1,1,1,1] => [5,4] => 5
[5,4,4,1] => [4,4,1] => [3,3,3] => 3
[5,4,3,2] => [4,3,2] => [3,3,2,1] => 3
[5,4,3,1,1] => [4,3,1,1] => [4,3,2] => 4
[5,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => 4
[5,4,2,1,1,1] => [4,2,1,1,1] => [5,3,1] => 5
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,3] => 6
[5,3,3,3] => [3,3,3] => [3,2,2,2] => 3
[5,3,3,2,1] => [3,3,2,1] => [4,2,2,1] => 4
[5,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => 5
[5,3,2,2,2] => [3,2,2,2] => [4,2,1,1,1] => 4
[5,3,2,2,1,1] => [3,2,2,1,1] => [5,2,1,1] => 5
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => 6
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,2] => 7
[5,2,2,2,2,1] => [2,2,2,2,1] => [5,1,1,1,1] => 5
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,1,1,1] => 6
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,1,1] => 7
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 8
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[4,4,4,2] => [4,4,2] => [3,3,3,1] => 3
[4,4,4,1,1] => [4,4,1,1] => [4,3,3] => 4
[4,4,3,3] => [4,3,3] => [3,3,2,2] => 3
[4,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 4
[4,4,3,1,1,1] => [4,3,1,1,1] => [5,3,2] => 5
[4,4,2,2,2] => [4,2,2,2] => [4,3,1,1,1] => 4
[4,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => 5
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,3,1] => 6
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,3] => 7
[4,3,3,3,1] => [3,3,3,1] => [4,2,2,2] => 4
[4,3,3,2,2] => [3,3,2,2] => [4,2,2,1,1] => 4
[4,3,3,2,1,1] => [3,3,2,1,1] => [5,2,2,1] => 5
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => 6
[4,3,2,2,2,1] => [3,2,2,2,1] => [5,2,1,1,1] => 5
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,2,1,1] => 6
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 7
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,2] => 8
[4,2,2,2,2,2] => [2,2,2,2,2] => [5,1,1,1,1,1] => 5
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,1,1,1,1] => 6
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 7
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,1,1] => 8
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 10
[3,3,3,3,2] => [3,3,3,2] => [4,2,2,2,1] => 4
[3,3,3,3,1,1] => [3,3,3,1,1] => [5,2,2,2] => 5
[3,3,3,2,2,1] => [3,3,2,2,1] => [5,2,2,1,1] => 5
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,2,2,1] => 6
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => 7
[3,3,2,2,2,2] => [3,2,2,2,2] => [5,2,1,1,1,1] => 5
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,2,1,1,1] => 6
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,2,1,1] => 7
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => 8
[3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,2] => 9
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,1,1,1,1,1] => 6
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,1,1,1,1] => 7
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,1,1,1] => 8
[3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,1,1] => 9
[3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 10
[3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 11
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,1,1,1,1,1,1] => 6
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,1,1,1,1,1] => 7
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,1,1,1,1] => 8
[2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,1,1,1] => 9
[2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,1,1] => 10
[2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 11
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 12
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 13
[15] => [] => [] => 0
[14,1] => [1] => [1] => 1
[13,2] => [2] => [1,1] => 1
[13,1,1] => [1,1] => [2] => 2
[12,3] => [3] => [2,1] => 2
[12,2,1] => [2,1] => [2,1] => 2
[12,1,1,1] => [1,1,1] => [3] => 3
[11,4] => [4] => [3,1] => 3
[11,3,1] => [3,1] => [2,2] => 2
[11,2,2] => [2,2] => [2,1,1] => 2
[11,2,1,1] => [2,1,1] => [3,1] => 3
[11,1,1,1,1] => [1,1,1,1] => [4] => 4
[10,5] => [5] => [4,1] => 4
[10,4,1] => [4,1] => [3,2] => 3
[10,3,2] => [3,2] => [2,2,1] => 2
[10,3,1,1] => [3,1,1] => [3,2] => 3
[10,2,2,1] => [2,2,1] => [3,1,1] => 3
[10,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[10,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[9,6] => [6] => [5,1] => 5
[9,5,1] => [5,1] => [4,2] => 4
[9,4,2] => [4,2] => [3,2,1] => 3
[9,4,1,1] => [4,1,1] => [3,3] => 3
[9,3,3] => [3,3] => [2,2,2] => 2
[9,3,2,1] => [3,2,1] => [3,2,1] => 3
[9,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[9,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[9,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[9,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[8,7] => [7] => [6,1] => 6
[8,6,1] => [6,1] => [5,2] => 5
[8,5,2] => [5,2] => [4,2,1] => 4
[8,5,1,1] => [5,1,1] => [4,3] => 4
[8,4,3] => [4,3] => [3,2,2] => 3
[8,4,2,1] => [4,2,1] => [3,3,1] => 3
[8,4,1,1,1] => [4,1,1,1] => [4,3] => 4
[8,3,3,1] => [3,3,1] => [3,2,2] => 3
[8,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[8,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[8,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[8,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[8,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[7,7,1] => [7,1] => [6,2] => 6
[7,6,2] => [6,2] => [5,2,1] => 5
[7,6,1,1] => [6,1,1] => [5,3] => 5
[7,5,3] => [5,3] => [4,2,2] => 4
[7,5,2,1] => [5,2,1] => [4,3,1] => 4
[7,5,1,1,1] => [5,1,1,1] => [4,4] => 4
[7,4,4] => [4,4] => [3,3,2] => 3
[7,4,3,1] => [4,3,1] => [3,3,2] => 3
[7,4,2,2] => [4,2,2] => [3,3,1,1] => 3
[7,4,2,1,1] => [4,2,1,1] => [4,3,1] => 4
[7,4,1,1,1,1] => [4,1,1,1,1] => [5,3] => 5
[7,3,3,2] => [3,3,2] => [3,2,2,1] => 3
[7,3,3,1,1] => [3,3,1,1] => [4,2,2] => 4
[7,3,2,2,1] => [3,2,2,1] => [4,2,1,1] => 4
[7,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => 5
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,2] => 6
[7,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[7,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[6,6,3] => [6,3] => [5,2,2] => 5
[6,6,2,1] => [6,2,1] => [5,3,1] => 5
[6,6,1,1,1] => [6,1,1,1] => [5,4] => 5
[6,5,4] => [5,4] => [4,3,2] => 4
[6,5,3,1] => [5,3,1] => [4,3,2] => 4
[6,5,2,2] => [5,2,2] => [4,3,1,1] => 4
[6,5,2,1,1] => [5,2,1,1] => [4,4,1] => 4
[6,5,1,1,1,1] => [5,1,1,1,1] => [5,4] => 5
[6,4,4,1] => [4,4,1] => [3,3,3] => 3
[6,4,3,2] => [4,3,2] => [3,3,2,1] => 3
[6,4,3,1,1] => [4,3,1,1] => [4,3,2] => 4
[6,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => 4
[6,4,2,1,1,1] => [4,2,1,1,1] => [5,3,1] => 5
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,3] => 6
[6,3,3,3] => [3,3,3] => [3,2,2,2] => 3
[6,3,3,2,1] => [3,3,2,1] => [4,2,2,1] => 4
[6,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => 5
[6,3,2,2,2] => [3,2,2,2] => [4,2,1,1,1] => 4
[6,3,2,2,1,1] => [3,2,2,1,1] => [5,2,1,1] => 5
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => 6
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,2] => 7
[6,2,2,2,2,1] => [2,2,2,2,1] => [5,1,1,1,1] => 5
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,1,1,1] => 6
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,1,1] => 7
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 8
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[5,5,5] => [5,5] => [4,4,2] => 4
[5,5,4,1] => [5,4,1] => [4,3,3] => 4
[5,5,3,2] => [5,3,2] => [4,3,2,1] => 4
[5,5,3,1,1] => [5,3,1,1] => [4,4,2] => 4
[5,5,2,2,1] => [5,2,2,1] => [4,4,1,1] => 4
[5,5,2,1,1,1] => [5,2,1,1,1] => [5,4,1] => 5
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [6,4] => 6
[5,4,4,2] => [4,4,2] => [3,3,3,1] => 3
[5,4,4,1,1] => [4,4,1,1] => [4,3,3] => 4
[5,4,3,3] => [4,3,3] => [3,3,2,2] => 3
[5,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 4
[5,4,3,1,1,1] => [4,3,1,1,1] => [5,3,2] => 5
[5,4,2,2,2] => [4,2,2,2] => [4,3,1,1,1] => 4
[5,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => 5
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,3,1] => 6
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,3] => 7
[5,3,3,3,1] => [3,3,3,1] => [4,2,2,2] => 4
[5,3,3,2,2] => [3,3,2,2] => [4,2,2,1,1] => 4
[5,3,3,2,1,1] => [3,3,2,1,1] => [5,2,2,1] => 5
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => 6
[5,3,2,2,2,1] => [3,2,2,2,1] => [5,2,1,1,1] => 5
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,2,1,1] => 6
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 7
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,2] => 8
[5,2,2,2,2,2] => [2,2,2,2,2] => [5,1,1,1,1,1] => 5
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,1,1,1,1] => 6
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 7
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,1,1] => 8
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 10
[4,4,4,3] => [4,4,3] => [3,3,3,2] => 3
[4,4,4,2,1] => [4,4,2,1] => [4,3,3,1] => 4
[4,4,4,1,1,1] => [4,4,1,1,1] => [5,3,3] => 5
[4,4,3,3,1] => [4,3,3,1] => [4,3,2,2] => 4
[4,4,3,2,2] => [4,3,2,2] => [4,3,2,1,1] => 4
[4,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => 5
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [6,3,2] => 6
[4,4,2,2,2,1] => [4,2,2,2,1] => [5,3,1,1,1] => 5
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => 6
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [7,3,1] => 7
[4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [8,3] => 8
[4,3,3,3,2] => [3,3,3,2] => [4,2,2,2,1] => 4
[4,3,3,3,1,1] => [3,3,3,1,1] => [5,2,2,2] => 5
[4,3,3,2,2,1] => [3,3,2,2,1] => [5,2,2,1,1] => 5
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,2,2,1] => 6
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => 7
[4,3,2,2,2,2] => [3,2,2,2,2] => [5,2,1,1,1,1] => 5
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,2,1,1,1] => 6
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,2,1,1] => 7
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => 8
[4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,2] => 9
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,1,1,1,1,1] => 6
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,1,1,1,1] => 7
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,1,1,1] => 8
[4,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,1,1] => 9
[4,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 10
[4,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 11
[3,3,3,3,3] => [3,3,3,3] => [4,2,2,2,2] => 4
[3,3,3,3,2,1] => [3,3,3,2,1] => [5,2,2,2,1] => 5
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [6,2,2,2] => 6
[3,3,3,2,2,2] => [3,3,2,2,2] => [5,2,2,1,1,1] => 5
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [6,2,2,1,1] => 6
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [7,2,2,1] => 7
[3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [8,2,2] => 8
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [6,2,1,1,1,1] => 6
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [7,2,1,1,1] => 7
[3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [8,2,1,1] => 8
[3,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => 9
[3,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [10,2] => 10
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,1,1,1,1,1,1] => 6
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,1,1,1,1,1] => 7
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,1,1,1,1] => 8
[3,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,1,1] => 10
[3,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 11
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 12
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [7,1,1,1,1,1,1] => 7
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [8,1,1,1,1,1] => 8
[2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [9,1,1,1,1] => 9
[2,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [10,1,1,1] => 10
[2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [11,1,1] => 11
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 12
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 13
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 14
[16] => [] => [] => 0
[15,1] => [1] => [1] => 1
[14,2] => [2] => [1,1] => 1
[14,1,1] => [1,1] => [2] => 2
[13,3] => [3] => [2,1] => 2
[13,2,1] => [2,1] => [2,1] => 2
[13,1,1,1] => [1,1,1] => [3] => 3
[12,4] => [4] => [3,1] => 3
[12,3,1] => [3,1] => [2,2] => 2
[12,2,2] => [2,2] => [2,1,1] => 2
[12,2,1,1] => [2,1,1] => [3,1] => 3
[12,1,1,1,1] => [1,1,1,1] => [4] => 4
[11,5] => [5] => [4,1] => 4
[11,4,1] => [4,1] => [3,2] => 3
[11,3,2] => [3,2] => [2,2,1] => 2
[11,3,1,1] => [3,1,1] => [3,2] => 3
[11,2,2,1] => [2,2,1] => [3,1,1] => 3
[11,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[11,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[10,6] => [6] => [5,1] => 5
[10,5,1] => [5,1] => [4,2] => 4
[10,4,2] => [4,2] => [3,2,1] => 3
[10,4,1,1] => [4,1,1] => [3,3] => 3
[10,3,3] => [3,3] => [2,2,2] => 2
[10,3,2,1] => [3,2,1] => [3,2,1] => 3
[10,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[10,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[10,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[10,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[9,7] => [7] => [6,1] => 6
[9,6,1] => [6,1] => [5,2] => 5
[9,5,2] => [5,2] => [4,2,1] => 4
[9,5,1,1] => [5,1,1] => [4,3] => 4
[9,4,3] => [4,3] => [3,2,2] => 3
[9,4,2,1] => [4,2,1] => [3,3,1] => 3
[9,4,1,1,1] => [4,1,1,1] => [4,3] => 4
[9,3,3,1] => [3,3,1] => [3,2,2] => 3
[9,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[9,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[9,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[9,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[9,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[8,8] => [8] => [7,1] => 7
[8,7,1] => [7,1] => [6,2] => 6
[8,6,2] => [6,2] => [5,2,1] => 5
[8,6,1,1] => [6,1,1] => [5,3] => 5
[8,5,3] => [5,3] => [4,2,2] => 4
[8,5,2,1] => [5,2,1] => [4,3,1] => 4
[8,5,1,1,1] => [5,1,1,1] => [4,4] => 4
[8,4,4] => [4,4] => [3,3,2] => 3
[8,4,3,1] => [4,3,1] => [3,3,2] => 3
[8,4,2,2] => [4,2,2] => [3,3,1,1] => 3
[8,4,2,1,1] => [4,2,1,1] => [4,3,1] => 4
[8,4,1,1,1,1] => [4,1,1,1,1] => [5,3] => 5
[8,3,3,2] => [3,3,2] => [3,2,2,1] => 3
[8,3,3,1,1] => [3,3,1,1] => [4,2,2] => 4
[8,3,2,2,1] => [3,2,2,1] => [4,2,1,1] => 4
[8,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => 5
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,2] => 6
[8,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[8,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[7,7,2] => [7,2] => [6,2,1] => 6
[7,7,1,1] => [7,1,1] => [6,3] => 6
[7,6,3] => [6,3] => [5,2,2] => 5
[7,6,2,1] => [6,2,1] => [5,3,1] => 5
[7,6,1,1,1] => [6,1,1,1] => [5,4] => 5
[7,5,4] => [5,4] => [4,3,2] => 4
[7,5,3,1] => [5,3,1] => [4,3,2] => 4
[7,5,2,2] => [5,2,2] => [4,3,1,1] => 4
[7,5,2,1,1] => [5,2,1,1] => [4,4,1] => 4
[7,5,1,1,1,1] => [5,1,1,1,1] => [5,4] => 5
[7,4,4,1] => [4,4,1] => [3,3,3] => 3
[7,4,3,2] => [4,3,2] => [3,3,2,1] => 3
[7,4,3,1,1] => [4,3,1,1] => [4,3,2] => 4
[7,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => 4
[7,4,2,1,1,1] => [4,2,1,1,1] => [5,3,1] => 5
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,3] => 6
[7,3,3,3] => [3,3,3] => [3,2,2,2] => 3
[7,3,3,2,1] => [3,3,2,1] => [4,2,2,1] => 4
[7,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => 5
[7,3,2,2,2] => [3,2,2,2] => [4,2,1,1,1] => 4
[7,3,2,2,1,1] => [3,2,2,1,1] => [5,2,1,1] => 5
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => 6
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,2] => 7
[7,2,2,2,2,1] => [2,2,2,2,1] => [5,1,1,1,1] => 5
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,1,1,1] => 6
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,1,1] => 7
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 8
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[6,6,4] => [6,4] => [5,3,2] => 5
[6,6,3,1] => [6,3,1] => [5,3,2] => 5
[6,6,2,2] => [6,2,2] => [5,3,1,1] => 5
[6,6,2,1,1] => [6,2,1,1] => [5,4,1] => 5
[6,6,1,1,1,1] => [6,1,1,1,1] => [5,5] => 5
[6,5,5] => [5,5] => [4,4,2] => 4
[6,5,4,1] => [5,4,1] => [4,3,3] => 4
[6,5,3,2] => [5,3,2] => [4,3,2,1] => 4
[6,5,3,1,1] => [5,3,1,1] => [4,4,2] => 4
[6,5,2,2,1] => [5,2,2,1] => [4,4,1,1] => 4
[6,5,2,1,1,1] => [5,2,1,1,1] => [5,4,1] => 5
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [6,4] => 6
[6,4,4,2] => [4,4,2] => [3,3,3,1] => 3
[6,4,4,1,1] => [4,4,1,1] => [4,3,3] => 4
[6,4,3,3] => [4,3,3] => [3,3,2,2] => 3
[6,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 4
[6,4,3,1,1,1] => [4,3,1,1,1] => [5,3,2] => 5
[6,4,2,2,2] => [4,2,2,2] => [4,3,1,1,1] => 4
[6,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => 5
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,3,1] => 6
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,3] => 7
[6,3,3,3,1] => [3,3,3,1] => [4,2,2,2] => 4
[6,3,3,2,2] => [3,3,2,2] => [4,2,2,1,1] => 4
[6,3,3,2,1,1] => [3,3,2,1,1] => [5,2,2,1] => 5
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => 6
[6,3,2,2,2,1] => [3,2,2,2,1] => [5,2,1,1,1] => 5
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,2,1,1] => 6
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 7
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,2] => 8
[6,2,2,2,2,2] => [2,2,2,2,2] => [5,1,1,1,1,1] => 5
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,1,1,1,1] => 6
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 7
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,1,1] => 8
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 10
[5,5,5,1] => [5,5,1] => [4,4,3] => 4
[5,5,4,2] => [5,4,2] => [4,3,3,1] => 4
[5,5,4,1,1] => [5,4,1,1] => [4,4,3] => 4
[5,5,3,3] => [5,3,3] => [4,3,2,2] => 4
[5,5,3,2,1] => [5,3,2,1] => [4,4,2,1] => 4
[5,5,3,1,1,1] => [5,3,1,1,1] => [5,4,2] => 5
[5,5,2,2,2] => [5,2,2,2] => [4,4,1,1,1] => 4
[5,5,2,2,1,1] => [5,2,2,1,1] => [5,4,1,1] => 5
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [6,4,1] => 6
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [7,4] => 7
[5,4,4,3] => [4,4,3] => [3,3,3,2] => 3
[5,4,4,2,1] => [4,4,2,1] => [4,3,3,1] => 4
[5,4,4,1,1,1] => [4,4,1,1,1] => [5,3,3] => 5
[5,4,3,3,1] => [4,3,3,1] => [4,3,2,2] => 4
[5,4,3,2,2] => [4,3,2,2] => [4,3,2,1,1] => 4
[5,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => 5
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [6,3,2] => 6
[5,4,2,2,2,1] => [4,2,2,2,1] => [5,3,1,1,1] => 5
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => 6
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [7,3,1] => 7
[5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [8,3] => 8
[5,3,3,3,2] => [3,3,3,2] => [4,2,2,2,1] => 4
[5,3,3,3,1,1] => [3,3,3,1,1] => [5,2,2,2] => 5
[5,3,3,2,2,1] => [3,3,2,2,1] => [5,2,2,1,1] => 5
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,2,2,1] => 6
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => 7
[5,3,2,2,2,2] => [3,2,2,2,2] => [5,2,1,1,1,1] => 5
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,2,1,1,1] => 6
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,2,1,1] => 7
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => 8
[5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,2] => 9
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,1,1,1,1,1] => 6
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,1,1,1,1] => 7
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,1,1,1] => 8
[5,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,1,1] => 9
[5,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 10
[5,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 11
[4,4,4,4] => [4,4,4] => [3,3,3,3] => 3
[4,4,4,3,1] => [4,4,3,1] => [4,3,3,2] => 4
[4,4,4,2,2] => [4,4,2,2] => [4,3,3,1,1] => 4
[4,4,4,2,1,1] => [4,4,2,1,1] => [5,3,3,1] => 5
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [6,3,3] => 6
[4,4,3,3,2] => [4,3,3,2] => [4,3,2,2,1] => 4
[4,4,3,3,1,1] => [4,3,3,1,1] => [5,3,2,2] => 5
[4,4,3,2,2,1] => [4,3,2,2,1] => [5,3,2,1,1] => 5
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => 6
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [7,3,2] => 7
[4,4,2,2,2,2] => [4,2,2,2,2] => [5,3,1,1,1,1] => 5
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [6,3,1,1,1] => 6
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1] => 7
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [8,3,1] => 8
[4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [9,3] => 9
[4,3,3,3,3] => [3,3,3,3] => [4,2,2,2,2] => 4
[4,3,3,3,2,1] => [3,3,3,2,1] => [5,2,2,2,1] => 5
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [6,2,2,2] => 6
[4,3,3,2,2,2] => [3,3,2,2,2] => [5,2,2,1,1,1] => 5
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [6,2,2,1,1] => 6
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [7,2,2,1] => 7
[4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [8,2,2] => 8
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [6,2,1,1,1,1] => 6
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [7,2,1,1,1] => 7
[4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [8,2,1,1] => 8
[4,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => 9
[4,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [10,2] => 10
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,1,1,1,1,1,1] => 6
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,1,1,1,1,1] => 7
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,1,1,1,1] => 8
[4,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,1,1,1] => 9
[4,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,1,1] => 10
[4,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 11
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 12
[3,3,3,3,3,1] => [3,3,3,3,1] => [5,2,2,2,2] => 5
[3,3,3,3,2,2] => [3,3,3,2,2] => [5,2,2,2,1,1] => 5
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [6,2,2,2,1] => 6
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [7,2,2,2] => 7
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [6,2,2,1,1,1] => 6
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [7,2,2,1,1] => 7
[3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [8,2,2,1] => 8
[3,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => 9
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [6,2,1,1,1,1,1] => 6
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [7,2,1,1,1,1] => 7
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [8,2,1,1,1] => 8
[3,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [9,2,1,1] => 9
[3,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1] => 10
[3,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,2] => 11
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [7,1,1,1,1,1,1] => 7
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [8,1,1,1,1,1] => 8
[3,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [9,1,1,1,1] => 9
[3,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [10,1,1,1] => 10
[3,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [11,1,1] => 11
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 12
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 13
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [7,1,1,1,1,1,1,1] => 7
[2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [8,1,1,1,1,1,1] => 8
[2,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [9,1,1,1,1,1] => 9
[2,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [10,1,1,1,1] => 10
[2,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,1,1,1] => 11
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => 12
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => 13
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 14
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 15
[17] => [] => [] => 0
[16,1] => [1] => [1] => 1
[15,2] => [2] => [1,1] => 1
[15,1,1] => [1,1] => [2] => 2
[14,3] => [3] => [2,1] => 2
[14,2,1] => [2,1] => [2,1] => 2
[14,1,1,1] => [1,1,1] => [3] => 3
[13,4] => [4] => [3,1] => 3
[13,3,1] => [3,1] => [2,2] => 2
[13,2,2] => [2,2] => [2,1,1] => 2
[13,2,1,1] => [2,1,1] => [3,1] => 3
[13,1,1,1,1] => [1,1,1,1] => [4] => 4
[12,5] => [5] => [4,1] => 4
[12,4,1] => [4,1] => [3,2] => 3
[12,3,2] => [3,2] => [2,2,1] => 2
[12,3,1,1] => [3,1,1] => [3,2] => 3
[12,2,2,1] => [2,2,1] => [3,1,1] => 3
[12,2,1,1,1] => [2,1,1,1] => [4,1] => 4
[12,1,1,1,1,1] => [1,1,1,1,1] => [5] => 5
[11,6] => [6] => [5,1] => 5
[11,5,1] => [5,1] => [4,2] => 4
[11,4,2] => [4,2] => [3,2,1] => 3
[11,4,1,1] => [4,1,1] => [3,3] => 3
[11,3,3] => [3,3] => [2,2,2] => 2
[11,3,2,1] => [3,2,1] => [3,2,1] => 3
[11,3,1,1,1] => [3,1,1,1] => [4,2] => 4
[11,2,2,2] => [2,2,2] => [3,1,1,1] => 3
[11,2,2,1,1] => [2,2,1,1] => [4,1,1] => 4
[11,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => 5
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [6] => 6
[10,7] => [7] => [6,1] => 6
[10,6,1] => [6,1] => [5,2] => 5
[10,5,2] => [5,2] => [4,2,1] => 4
[10,5,1,1] => [5,1,1] => [4,3] => 4
[10,4,3] => [4,3] => [3,2,2] => 3
[10,4,2,1] => [4,2,1] => [3,3,1] => 3
[10,4,1,1,1] => [4,1,1,1] => [4,3] => 4
[10,3,3,1] => [3,3,1] => [3,2,2] => 3
[10,3,2,2] => [3,2,2] => [3,2,1,1] => 3
[10,3,2,1,1] => [3,2,1,1] => [4,2,1] => 4
[10,3,1,1,1,1] => [3,1,1,1,1] => [5,2] => 5
[10,2,2,2,1] => [2,2,2,1] => [4,1,1,1] => 4
[10,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 5
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => 6
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [7] => 7
[9,8] => [8] => [7,1] => 7
[9,7,1] => [7,1] => [6,2] => 6
[9,6,2] => [6,2] => [5,2,1] => 5
[9,6,1,1] => [6,1,1] => [5,3] => 5
[9,5,3] => [5,3] => [4,2,2] => 4
[9,5,2,1] => [5,2,1] => [4,3,1] => 4
[9,5,1,1,1] => [5,1,1,1] => [4,4] => 4
[9,4,4] => [4,4] => [3,3,2] => 3
[9,4,3,1] => [4,3,1] => [3,3,2] => 3
[9,4,2,2] => [4,2,2] => [3,3,1,1] => 3
[9,4,2,1,1] => [4,2,1,1] => [4,3,1] => 4
[9,4,1,1,1,1] => [4,1,1,1,1] => [5,3] => 5
[9,3,3,2] => [3,3,2] => [3,2,2,1] => 3
[9,3,3,1,1] => [3,3,1,1] => [4,2,2] => 4
[9,3,2,2,1] => [3,2,2,1] => [4,2,1,1] => 4
[9,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => 5
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,2] => 6
[9,2,2,2,2] => [2,2,2,2] => [4,1,1,1,1] => 4
[9,2,2,2,1,1] => [2,2,2,1,1] => [5,1,1,1] => 5
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,1,1] => 6
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => 7
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [8] => 8
[8,8,1] => [8,1] => [7,2] => 7
[8,7,2] => [7,2] => [6,2,1] => 6
[8,7,1,1] => [7,1,1] => [6,3] => 6
[8,6,3] => [6,3] => [5,2,2] => 5
[8,6,2,1] => [6,2,1] => [5,3,1] => 5
[8,6,1,1,1] => [6,1,1,1] => [5,4] => 5
[8,5,4] => [5,4] => [4,3,2] => 4
[8,5,3,1] => [5,3,1] => [4,3,2] => 4
[8,5,2,2] => [5,2,2] => [4,3,1,1] => 4
[8,5,2,1,1] => [5,2,1,1] => [4,4,1] => 4
[8,5,1,1,1,1] => [5,1,1,1,1] => [5,4] => 5
[8,4,4,1] => [4,4,1] => [3,3,3] => 3
[8,4,3,2] => [4,3,2] => [3,3,2,1] => 3
[8,4,3,1,1] => [4,3,1,1] => [4,3,2] => 4
[8,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => 4
[8,4,2,1,1,1] => [4,2,1,1,1] => [5,3,1] => 5
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,3] => 6
[8,3,3,3] => [3,3,3] => [3,2,2,2] => 3
[8,3,3,2,1] => [3,3,2,1] => [4,2,2,1] => 4
[8,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => 5
[8,3,2,2,2] => [3,2,2,2] => [4,2,1,1,1] => 4
[8,3,2,2,1,1] => [3,2,2,1,1] => [5,2,1,1] => 5
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => 6
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,2] => 7
[8,2,2,2,2,1] => [2,2,2,2,1] => [5,1,1,1,1] => 5
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,1,1,1] => 6
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,1,1] => 7
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 8
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [9] => 9
[7,7,3] => [7,3] => [6,2,2] => 6
[7,7,2,1] => [7,2,1] => [6,3,1] => 6
[7,7,1,1,1] => [7,1,1,1] => [6,4] => 6
[7,6,4] => [6,4] => [5,3,2] => 5
[7,6,3,1] => [6,3,1] => [5,3,2] => 5
[7,6,2,2] => [6,2,2] => [5,3,1,1] => 5
[7,6,2,1,1] => [6,2,1,1] => [5,4,1] => 5
[7,6,1,1,1,1] => [6,1,1,1,1] => [5,5] => 5
[7,5,5] => [5,5] => [4,4,2] => 4
[7,5,4,1] => [5,4,1] => [4,3,3] => 4
[7,5,3,2] => [5,3,2] => [4,3,2,1] => 4
[7,5,3,1,1] => [5,3,1,1] => [4,4,2] => 4
[7,5,2,2,1] => [5,2,2,1] => [4,4,1,1] => 4
[7,5,2,1,1,1] => [5,2,1,1,1] => [5,4,1] => 5
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [6,4] => 6
[7,4,4,2] => [4,4,2] => [3,3,3,1] => 3
[7,4,4,1,1] => [4,4,1,1] => [4,3,3] => 4
[7,4,3,3] => [4,3,3] => [3,3,2,2] => 3
[7,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 4
[7,4,3,1,1,1] => [4,3,1,1,1] => [5,3,2] => 5
[7,4,2,2,2] => [4,2,2,2] => [4,3,1,1,1] => 4
[7,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => 5
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,3,1] => 6
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,3] => 7
[7,3,3,3,1] => [3,3,3,1] => [4,2,2,2] => 4
[7,3,3,2,2] => [3,3,2,2] => [4,2,2,1,1] => 4
[7,3,3,2,1,1] => [3,3,2,1,1] => [5,2,2,1] => 5
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => 6
[7,3,2,2,2,1] => [3,2,2,2,1] => [5,2,1,1,1] => 5
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,2,1,1] => 6
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 7
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,2] => 8
[7,2,2,2,2,2] => [2,2,2,2,2] => [5,1,1,1,1,1] => 5
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,1,1,1,1] => 6
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 7
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,1,1] => 8
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => 9
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 10
[6,6,5] => [6,5] => [5,4,2] => 5
[6,6,4,1] => [6,4,1] => [5,3,3] => 5
[6,6,3,2] => [6,3,2] => [5,3,2,1] => 5
[6,6,3,1,1] => [6,3,1,1] => [5,4,2] => 5
[6,6,2,2,1] => [6,2,2,1] => [5,4,1,1] => 5
[6,6,2,1,1,1] => [6,2,1,1,1] => [5,5,1] => 5
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [6,5] => 6
[6,5,5,1] => [5,5,1] => [4,4,3] => 4
[6,5,4,2] => [5,4,2] => [4,3,3,1] => 4
[6,5,4,1,1] => [5,4,1,1] => [4,4,3] => 4
[6,5,3,3] => [5,3,3] => [4,3,2,2] => 4
[6,5,3,2,1] => [5,3,2,1] => [4,4,2,1] => 4
[6,5,3,1,1,1] => [5,3,1,1,1] => [5,4,2] => 5
[6,5,2,2,2] => [5,2,2,2] => [4,4,1,1,1] => 4
[6,5,2,2,1,1] => [5,2,2,1,1] => [5,4,1,1] => 5
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [6,4,1] => 6
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [7,4] => 7
[6,4,4,3] => [4,4,3] => [3,3,3,2] => 3
[6,4,4,2,1] => [4,4,2,1] => [4,3,3,1] => 4
[6,4,4,1,1,1] => [4,4,1,1,1] => [5,3,3] => 5
[6,4,3,3,1] => [4,3,3,1] => [4,3,2,2] => 4
[6,4,3,2,2] => [4,3,2,2] => [4,3,2,1,1] => 4
[6,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => 5
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [6,3,2] => 6
[6,4,2,2,2,1] => [4,2,2,2,1] => [5,3,1,1,1] => 5
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => 6
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [7,3,1] => 7
[6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [8,3] => 8
[6,3,3,3,2] => [3,3,3,2] => [4,2,2,2,1] => 4
[6,3,3,3,1,1] => [3,3,3,1,1] => [5,2,2,2] => 5
[6,3,3,2,2,1] => [3,3,2,2,1] => [5,2,2,1,1] => 5
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,2,2,1] => 6
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => 7
[6,3,2,2,2,2] => [3,2,2,2,2] => [5,2,1,1,1,1] => 5
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,2,1,1,1] => 6
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,2,1,1] => 7
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => 8
[6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,2] => 9
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,1,1,1,1,1] => 6
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,1,1,1,1] => 7
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,1,1,1] => 8
[6,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,1,1] => 9
[6,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 10
[6,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 11
[5,5,5,2] => [5,5,2] => [4,4,3,1] => 4
[5,5,5,1,1] => [5,5,1,1] => [4,4,4] => 4
[5,5,4,3] => [5,4,3] => [4,3,3,2] => 4
[5,5,4,2,1] => [5,4,2,1] => [4,4,3,1] => 4
[5,5,4,1,1,1] => [5,4,1,1,1] => [5,4,3] => 5
[5,5,3,3,1] => [5,3,3,1] => [4,4,2,2] => 4
[5,5,3,2,2] => [5,3,2,2] => [4,4,2,1,1] => 4
[5,5,3,2,1,1] => [5,3,2,1,1] => [5,4,2,1] => 5
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [6,4,2] => 6
[5,5,2,2,2,1] => [5,2,2,2,1] => [5,4,1,1,1] => 5
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [6,4,1,1] => 6
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [7,4,1] => 7
[5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [8,4] => 8
[5,4,4,4] => [4,4,4] => [3,3,3,3] => 3
[5,4,4,3,1] => [4,4,3,1] => [4,3,3,2] => 4
[5,4,4,2,2] => [4,4,2,2] => [4,3,3,1,1] => 4
[5,4,4,2,1,1] => [4,4,2,1,1] => [5,3,3,1] => 5
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [6,3,3] => 6
[5,4,3,3,2] => [4,3,3,2] => [4,3,2,2,1] => 4
[5,4,3,3,1,1] => [4,3,3,1,1] => [5,3,2,2] => 5
[5,4,3,2,2,1] => [4,3,2,2,1] => [5,3,2,1,1] => 5
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => 6
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [7,3,2] => 7
[5,4,2,2,2,2] => [4,2,2,2,2] => [5,3,1,1,1,1] => 5
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [6,3,1,1,1] => 6
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1] => 7
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [8,3,1] => 8
[5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [9,3] => 9
[5,3,3,3,3] => [3,3,3,3] => [4,2,2,2,2] => 4
[5,3,3,3,2,1] => [3,3,3,2,1] => [5,2,2,2,1] => 5
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [6,2,2,2] => 6
[5,3,3,2,2,2] => [3,3,2,2,2] => [5,2,2,1,1,1] => 5
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [6,2,2,1,1] => 6
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [7,2,2,1] => 7
[5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [8,2,2] => 8
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [6,2,1,1,1,1] => 6
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [7,2,1,1,1] => 7
[5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [8,2,1,1] => 8
[5,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => 9
[5,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [10,2] => 10
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,1,1,1,1,1,1] => 6
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,1,1,1,1,1] => 7
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,1,1,1,1] => 8
[5,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,1,1,1] => 9
[5,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,1,1] => 10
[5,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 11
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 12
[4,4,4,4,1] => [4,4,4,1] => [4,3,3,3] => 4
[4,4,4,3,2] => [4,4,3,2] => [4,3,3,2,1] => 4
[4,4,4,3,1,1] => [4,4,3,1,1] => [5,3,3,2] => 5
[4,4,4,2,2,1] => [4,4,2,2,1] => [5,3,3,1,1] => 5
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [6,3,3,1] => 6
[4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [7,3,3] => 7
[4,4,3,3,3] => [4,3,3,3] => [4,3,2,2,2] => 4
[4,4,3,3,2,1] => [4,3,3,2,1] => [5,3,2,2,1] => 5
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [6,3,2,2] => 6
[4,4,3,2,2,2] => [4,3,2,2,2] => [5,3,2,1,1,1] => 5
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [6,3,2,1,1] => 6
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [7,3,2,1] => 7
[4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [8,3,2] => 8
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [6,3,1,1,1,1] => 6
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [7,3,1,1,1] => 7
[4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [8,3,1,1] => 8
[4,4,2,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [9,3,1] => 9
[4,4,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [10,3] => 10
[4,3,3,3,3,1] => [3,3,3,3,1] => [5,2,2,2,2] => 5
[4,3,3,3,2,2] => [3,3,3,2,2] => [5,2,2,2,1,1] => 5
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [6,2,2,2,1] => 6
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [7,2,2,2] => 7
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [6,2,2,1,1,1] => 6
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [7,2,2,1,1] => 7
[4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [8,2,2,1] => 8
[4,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => 9
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [6,2,1,1,1,1,1] => 6
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [7,2,1,1,1,1] => 7
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [8,2,1,1,1] => 8
[4,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [9,2,1,1] => 9
[4,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1] => 10
[4,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,2] => 11
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [7,1,1,1,1,1,1] => 7
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [8,1,1,1,1,1] => 8
[4,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [9,1,1,1,1] => 9
[4,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [10,1,1,1] => 10
[4,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [11,1,1] => 11
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 12
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 13
[3,3,3,3,3,2] => [3,3,3,3,2] => [5,2,2,2,2,1] => 5
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [6,2,2,2,2] => 6
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [6,2,2,2,1,1] => 6
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [7,2,2,2,1] => 7
[3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [8,2,2,2] => 8
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [6,2,2,1,1,1,1] => 6
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [7,2,2,1,1,1] => 7
[3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [8,2,2,1,1] => 8
[3,3,3,2,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1] => [9,2,2,1] => 9
[3,3,3,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1] => [10,2,2] => 10
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [7,2,1,1,1,1,1] => 7
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [8,2,1,1,1,1] => 8
[3,3,2,2,2,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1] => [9,2,1,1,1] => 9
[3,3,2,2,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1] => [10,2,1,1] => 10
[3,3,2,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => 11
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [12,2] => 12
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [7,1,1,1,1,1,1,1] => 7
[3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [8,1,1,1,1,1,1] => 8
[3,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [9,1,1,1,1,1] => 9
[3,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [10,1,1,1,1] => 10
[3,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,1,1,1] => 11
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => 12
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => 13
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 14
[2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => [8,1,1,1,1,1,1,1] => 8
[2,2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,2,1,1,1] => [9,1,1,1,1,1,1] => 9
[2,2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,2,1,1,1,1,1] => [10,1,1,1,1,1] => 10
[2,2,2,2,2,1,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1,1] => [11,1,1,1,1] => 11
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => 12
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => 13
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => 14
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 16
[6,5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 5
[5,5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 5
[6,4,4,3,2,1] => [4,4,3,2,1] => [5,3,3,2,1] => 5
[5,4,4,3,2,1] => [4,4,3,2,1] => [5,3,3,2,1] => 5
[4,4,4,3,2,1] => [4,4,3,2,1] => [5,3,3,2,1] => 5
[6,5,3,3,2,1] => [5,3,3,2,1] => [5,4,2,2,1] => 5
[5,5,3,3,2,1] => [5,3,3,2,1] => [5,4,2,2,1] => 5
[6,4,3,3,2,1] => [4,3,3,2,1] => [5,3,2,2,1] => 5
[5,4,3,3,2,1] => [4,3,3,2,1] => [5,3,2,2,1] => 5
[6,3,3,3,2,1] => [3,3,3,2,1] => [5,2,2,2,1] => 5
[6,5,4,2,2,1] => [5,4,2,2,1] => [5,4,3,1,1] => 5
[5,5,4,2,2,1] => [5,4,2,2,1] => [5,4,3,1,1] => 5
[6,4,4,2,2,1] => [4,4,2,2,1] => [5,3,3,1,1] => 5
[5,4,4,2,2,1] => [4,4,2,2,1] => [5,3,3,1,1] => 5
[6,5,3,2,2,1] => [5,3,2,2,1] => [5,4,2,1,1] => 5
[5,5,3,2,2,1] => [5,3,2,2,1] => [5,4,2,1,1] => 5
[6,4,3,2,2,1] => [4,3,2,2,1] => [5,3,2,1,1] => 5
[6,5,2,2,2,1] => [5,2,2,2,1] => [5,4,1,1,1] => 5
[6,5,4,3,1,1] => [5,4,3,1,1] => [5,4,3,2] => 5
[5,5,4,3,1,1] => [5,4,3,1,1] => [5,4,3,2] => 5
[6,4,4,3,1,1] => [4,4,3,1,1] => [5,3,3,2] => 5
[5,4,4,3,1,1] => [4,4,3,1,1] => [5,3,3,2] => 5
[6,5,3,3,1,1] => [5,3,3,1,1] => [5,4,2,2] => 5
[5,5,3,3,1,1] => [5,3,3,1,1] => [5,4,2,2] => 5
[6,4,3,3,1,1] => [4,3,3,1,1] => [5,3,2,2] => 5
[6,5,4,2,1,1] => [5,4,2,1,1] => [5,4,3,1] => 5
[5,5,4,2,1,1] => [5,4,2,1,1] => [5,4,3,1] => 5
[6,4,4,2,1,1] => [4,4,2,1,1] => [5,3,3,1] => 5
[6,5,3,2,1,1] => [5,3,2,1,1] => [5,4,2,1] => 5
[6,5,4,1,1,1] => [5,4,1,1,1] => [5,4,3] => 5
[6,5,4,3,2] => [5,4,3,2] => [4,4,3,2,1] => 4
[5,5,4,3,2] => [5,4,3,2] => [4,4,3,2,1] => 4
[6,4,4,3,2] => [4,4,3,2] => [4,3,3,2,1] => 4
[5,4,4,3,2] => [4,4,3,2] => [4,3,3,2,1] => 4
[6,5,3,3,2] => [5,3,3,2] => [4,4,2,2,1] => 4
[5,5,3,3,2] => [5,3,3,2] => [4,4,2,2,1] => 4
[6,4,3,3,2] => [4,3,3,2] => [4,3,2,2,1] => 4
[6,5,4,2,2] => [5,4,2,2] => [4,4,3,1,1] => 4
[5,5,4,2,2] => [5,4,2,2] => [4,4,3,1,1] => 4
[6,4,4,2,2] => [4,4,2,2] => [4,3,3,1,1] => 4
[6,5,3,2,2] => [5,3,2,2] => [4,4,2,1,1] => 4
[6,5,4,3,1] => [5,4,3,1] => [4,4,3,2] => 4
[5,5,4,3,1] => [5,4,3,1] => [4,4,3,2] => 4
[6,4,4,3,1] => [4,4,3,1] => [4,3,3,2] => 4
[6,5,3,3,1] => [5,3,3,1] => [4,4,2,2] => 4
[6,5,4,2,1] => [5,4,2,1] => [4,4,3,1] => 4
[6,5,4,3] => [5,4,3] => [4,3,3,2] => 4
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [6,4,2,2,2,1] => 6
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [6,3,2,2,2,1] => 6
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [6,3,2,2,2,1] => 6
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [6,2,2,2,2,1] => 6
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [6,2,2,2,2,1] => 6
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [6,4,3,2,1,1] => 6
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [6,4,3,2,1,1] => 6
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [6,4,3,1,1,1] => 6
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [6,4,2,1,1,1] => 6
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [6,3,2,1,1,1] => 6
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [6,3,2,1,1,1] => 6
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [6,4,1,1,1,1] => 6
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,1,1,1,1,1] => 6
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [6,3,3,3,1] => 6
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [6,4,3,2,1] => 6
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [6,4,3,2,1] => 6
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [6,3,3,2,1] => 6
[6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [6,4,4,3] => 6
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [6,4,3,2] => 6
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [6,5,4,1] => 6
[5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [6,4,4,1] => 6
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [6,4,3,1] => 6
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [6,4,3,1] => 6
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [6,5,2,1] => 6
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => 6
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => 6
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [6,4,3] => 6
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [6,5,1] => 6
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [6,5] => 6
[5,4,3,3,3,2] => [4,3,3,3,2] => [5,3,2,2,2,1] => 5
[4,3,3,3,3,2] => [3,3,3,3,2] => [5,2,2,2,2,1] => 5
[6,5,4,3,2,2] => [5,4,3,2,2] => [5,4,3,2,1,1] => 5
[4,4,4,3,2,2] => [4,4,3,2,2] => [5,3,3,2,1,1] => 5
[7,6,5,2,2,2] => [6,5,2,2,2] => [5,5,4,1,1,1] => 5
[6,5,4,2,2,2] => [5,4,2,2,2] => [5,4,3,1,1,1] => 5
[5,4,3,2,2,2] => [4,3,2,2,2] => [5,3,2,1,1,1] => 5
[6,6,2,2,2,2] => [6,2,2,2,2] => [5,5,1,1,1,1] => 5
[4,4,4,4,3,1] => [4,4,4,3,1] => [5,3,3,3,2] => 5
[4,4,4,4,2,1] => [4,4,4,2,1] => [5,3,3,3,1] => 5
[7,6,5,3,2,1] => [6,5,3,2,1] => [5,5,4,2,1] => 5
[6,6,5,3,2,1] => [6,5,3,2,1] => [5,5,4,2,1] => 5
[5,5,5,3,2,1] => [5,5,3,2,1] => [5,4,4,2,1] => 5
[7,6,4,3,2,1] => [6,4,3,2,1] => [5,5,3,2,1] => 5
[6,6,4,3,2,1] => [6,4,3,2,1] => [5,5,3,2,1] => 5
[7,5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 5
[7,4,4,3,2,1] => [4,4,3,2,1] => [5,3,3,2,1] => 5
[7,6,3,3,2,1] => [6,3,3,2,1] => [5,5,2,2,1] => 5
[7,4,3,3,2,1] => [4,3,3,2,1] => [5,3,2,2,1] => 5
[7,3,3,3,2,1] => [3,3,3,2,1] => [5,2,2,2,1] => 5
[7,6,5,2,2,1] => [6,5,2,2,1] => [5,5,4,1,1] => 5
[7,6,3,2,2,1] => [6,3,2,2,1] => [5,5,2,1,1] => 5
[7,6,2,2,2,1] => [6,2,2,2,1] => [5,5,1,1,1] => 5
[7,6,5,4,1,1] => [6,5,4,1,1] => [5,5,4,3] => 5
[7,6,5,2,1,1] => [6,5,2,1,1] => [5,5,4,1] => 5
[7,6,3,2,1,1] => [6,3,2,1,1] => [5,5,2,1] => 5
[7,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => 5
[7,6,5,1,1,1] => [6,5,1,1,1] => [5,5,4] => 5
[5,4,4,4,3] => [4,4,4,3] => [4,3,3,3,2] => 4
[5,4,3,3,3] => [4,3,3,3] => [4,3,2,2,2] => 4
[7,3,3,3,3] => [3,3,3,3] => [4,2,2,2,2] => 4
[4,4,4,4,2] => [4,4,4,2] => [4,3,3,3,1] => 4
[7,6,5,3,2] => [6,5,3,2] => [5,4,4,2,1] => 5
[7,6,4,3,2] => [6,4,3,2] => [5,4,3,2,1] => 5
[7,5,4,3,2] => [5,4,3,2] => [4,4,3,2,1] => 4
[7,6,5,4,1] => [6,5,4,1] => [5,4,4,3] => 5
[7,5,4,3,1] => [5,4,3,1] => [4,4,3,2] => 4
[7,6,5,2,1] => [6,5,2,1] => [5,4,4,1] => 5
[6,6,5,2,1] => [6,5,2,1] => [5,4,4,1] => 5
[7,6,4,2,1] => [6,4,2,1] => [5,4,3,1] => 5
[6,6,4,2,1] => [6,4,2,1] => [5,4,3,1] => 5
[7,5,4,2,1] => [5,4,2,1] => [4,4,3,1] => 4
[7,6,3,2,1] => [6,3,2,1] => [5,4,2,1] => 5
[6,6,3,2,1] => [6,3,2,1] => [5,4,2,1] => 5
[7,6,5,4] => [6,5,4] => [5,4,3,3] => 5
[6,5,5,4] => [5,5,4] => [4,4,3,3] => 4
[7,6,5,3] => [6,5,3] => [5,4,3,2] => 5
[7,6,4,3] => [6,4,3] => [5,3,3,2] => 5
[7,5,4,3] => [5,4,3] => [4,3,3,2] => 4
[7,6,5,2] => [6,5,2] => [5,4,3,1] => 5
[7,6,5] => [6,5] => [5,4,2] => 5
[2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => [8,1,1,1,1,1,1,1,1] => 8
[3,3,3,3,3,3] => [3,3,3,3,3] => [5,2,2,2,2,2] => 5
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => [6,2,2,2,2,2] => 6
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [6,2,2,2,2,1,1] => 6
[4,3,3,3,3,3] => [3,3,3,3,3] => [5,2,2,2,2,2] => 5
[4,4,4,4,4] => [4,4,4,4] => [4,3,3,3,3] => 4
[5,5,5,5] => [5,5,5] => [4,4,4,3] => 4
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,1,1,1,1,1,1] => 6
[6,6,6] => [6,6] => [5,5,2] => 5
[7,6,6] => [6,6] => [5,5,2] => 5
[10,4,4] => [4,4] => [3,3,2] => 3
[10,10] => [10] => [9,1] => 9
[11,7,3] => [7,3] => [6,2,2] => 6
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,1,1,1,1,1,1] => 6
[9,6,3] => [6,3] => [5,2,2] => 5
[8,6,4,2] => [6,4,2] => [5,3,3,1] => 5
[8,6,4] => [6,4] => [5,3,2] => 5
[10,6,4] => [6,4] => [5,3,2] => 5
[8,7,6] => [7,6] => [6,5,2] => 6
[9,8,7] => [8,7] => [7,6,2] => 7
[15,15] => [15] => [14,1] => 14
[15,5,5] => [5,5] => [4,4,2] => 4
[7,7,7] => [7,7] => [6,6,2] => 6
[11,7,5,1] => [7,5,1] => [6,4,3] => 6
[9,7,5,3,1] => [7,5,3,1] => [6,4,4,2] => 6
[9,6,4] => [6,4] => [5,3,2] => 5
[10,7,3] => [7,3] => [6,2,2] => 6
[8,5,4,2] => [5,4,2] => [4,3,3,1] => 4
[9,6,5,3] => [6,5,3] => [5,4,3,2] => 5
[10,7,5,3] => [7,5,3] => [6,4,3,2] => 6
[9,6,4,3] => [6,4,3] => [5,3,3,2] => 5
[9,7,4] => [7,4] => [6,3,2] => 6
[9,7,5,4,1] => [7,5,4,1] => [6,4,4,3] => 6
[8,6,5,3,1] => [6,5,3,1] => [5,4,4,2] => 5
[8,5,5,1] => [5,5,1] => [4,4,3] => 4
[9,5,5,1] => [5,5,1] => [4,4,3] => 4
[9,7,5,3] => [7,5,3] => [6,4,3,2] => 6
[3,3,3,3,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1] => [9,2,2,2] => 9
[9,9] => [9] => [8,1] => 8
[8,8,8] => [8,8] => [7,7,2] => 7
[16,16] => [16] => [15,1] => 15
[7,7,1,1,1,1] => [7,1,1,1,1] => [6,5] => 6
[8,5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 5
[8,7,4,3,2,1] => [7,4,3,2,1] => [6,5,3,2,1] => 6
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [7,6] => 7
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [7,3,2,1] => 7
[6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [7,4,3,2,1] => 7
[5,4,3,2,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [8,3,2,1] => 8
[6,5,4,3,1,1,1,1] => [5,4,3,1,1,1,1] => [7,4,3,2] => 7
[7,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [7,4,3,2,1] => 7
[5,4,3,3,3,3,1] => [4,3,3,3,3,1] => [6,3,2,2,2,2] => 6
[5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [6,3,2,1,1,1,1] => 6
[6,5,5,5] => [5,5,5] => [4,4,4,3] => 4
[5,4,4,4,4] => [4,4,4,4] => [4,3,3,3,3] => 4
[8,7,5] => [7,5] => [6,4,2] => 6
[8,7,6,4] => [7,6,4] => [6,5,3,3] => 6
[5,5,5,5,1] => [5,5,5,1] => [4,4,4,4] => 4
[6,6,6,1] => [6,6,1] => [5,5,3] => 5
[6,6,6,1,1] => [6,6,1,1] => [5,5,4] => 5
[7,7,4,3,2,1] => [7,4,3,2,1] => [6,5,3,2,1] => 6
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [6,4,3,2,1] => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,1 1,2,1,1 1,2,2,1,1 1,2,4,2,1,1 1,2,5,3,2,1,1 1,2,6,6,3,2,1,1 1,2,7,8,5,3,2,1,1 1,2,7,12,8,5,3,2,1,1 1,2,7,15,12,7,5,3,2,1,1 1,2,7,19,17,12,7,5,3,2,1,1 1,2,7,21,24,16,11,7,5,3,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + q + q^{2}$
$F_{4} = 1 + 2\ q + q^{2} + q^{3}$
$F_{5} = 1 + 2\ q + 2\ q^{2} + q^{3} + q^{4}$
$F_{6} = 1 + 2\ q + 4\ q^{2} + 2\ q^{3} + q^{4} + q^{5}$
$F_{7} = 1 + 2\ q + 5\ q^{2} + 3\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{8} = 1 + 2\ q + 6\ q^{2} + 6\ q^{3} + 3\ q^{4} + 2\ q^{5} + q^{6} + q^{7}$
$F_{9} = 1 + 2\ q + 7\ q^{2} + 8\ q^{3} + 5\ q^{4} + 3\ q^{5} + 2\ q^{6} + q^{7} + q^{8}$
$F_{10} = 1 + 2\ q + 7\ q^{2} + 12\ q^{3} + 8\ q^{4} + 5\ q^{5} + 3\ q^{6} + 2\ q^{7} + q^{8} + q^{9}$
$F_{11} = 1 + 2\ q + 7\ q^{2} + 15\ q^{3} + 12\ q^{4} + 7\ q^{5} + 5\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{12} = 1 + 2\ q + 7\ q^{2} + 19\ q^{3} + 17\ q^{4} + 12\ q^{5} + 7\ q^{6} + 5\ q^{7} + 3\ q^{8} + 2\ q^{9} + q^{10} + q^{11}$
$F_{13} = 1 + 2\ q + 7\ q^{2} + 21\ q^{3} + 24\ q^{4} + 16\ q^{5} + 11\ q^{6} + 7\ q^{7} + 5\ q^{8} + 3\ q^{9} + 2\ q^{10} + q^{11} + q^{12}$
$F_{14} = 1 + 2\ q + 7\ q^{2} + 23\ q^{3} + 32\ q^{4} + 24\ q^{5} + 16\ q^{6} + 11\ q^{7} + 7\ q^{8} + 5\ q^{9} + 3\ q^{10} + 2\ q^{11} + q^{12} + q^{13}$
$F_{15} = 1 + 2\ q + 7\ q^{2} + 24\ q^{3} + 41\ q^{4} + 33\ q^{5} + 23\ q^{6} + 15\ q^{7} + 11\ q^{8} + 7\ q^{9} + 5\ q^{10} + 3\ q^{11} + 2\ q^{12} + q^{13} + q^{14}$
$F_{16} = 1 + 2\ q + 7\ q^{2} + 25\ q^{3} + 50\ q^{4} + 46\ q^{5} + 32\ q^{6} + 23\ q^{7} + 15\ q^{8} + 11\ q^{9} + 7\ q^{10} + 5\ q^{11} + 3\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
$F_{17} = 1 + 2\ q + 7\ q^{2} + 25\ q^{3} + 59\ q^{4} + 60\ q^{5} + 45\ q^{6} + 31\ q^{7} + 22\ q^{8} + 15\ q^{9} + 11\ q^{10} + 7\ q^{11} + 5\ q^{12} + 3\ q^{13} + 2\ q^{14} + q^{15} + q^{16}$
Description
The largest part of an integer partition.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
Bulgarian solitaire
Description
A move in Bulgarian solitaire.
Remove the first column of the Ferrers diagram and insert it as a new row.
If the partition is empty, return the empty partition.
Remove the first column of the Ferrers diagram and insert it as a new row.
If the partition is empty, return the empty partition.
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