Identifier
-
Mp00321:
Integer partitions
—2-conjugate⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000901: Integer partitions ⟶ ℤ
Values
[1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[3,1,1] => [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
[6] => [2,2,2] => [2,2] => [2] => 1
[5,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[3,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,1,1,1,1] => [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] => [1,1,1,1] => 1
[7] => [2,2,2,1] => [2,2,1] => [2,1] => 8
[6,1] => [3,2,2] => [2,2] => [2] => 1
[5,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[3,3,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[3,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,1,1] => [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] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[8] => [2,2,2,2] => [2,2,2] => [2,2] => 8
[7,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[6,2] => [4,2,2] => [2,2] => [2] => 1
[6,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[5,3] => [3,2,2,1] => [2,2,1] => [2,1] => 8
[5,2,1] => [3,3,2] => [3,2] => [2] => 1
[5,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[3,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,2,1,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,1,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[2,1,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[9] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[8,1] => [3,2,2,2] => [2,2,2] => [2,2] => 8
[7,2] => [4,2,2,1] => [2,2,1] => [2,1] => 8
[7,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[6,3] => [4,3,2] => [3,2] => [2] => 1
[6,2,1] => [5,2,2] => [2,2] => [2] => 1
[6,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[5,2,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[5,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[4,2,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[3,3,3] => [3,3,2,1] => [3,2,1] => [2,1] => 8
[3,3,2,1] => [3,3,3] => [3,3] => [3] => 1
[3,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,2,1,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[10] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[9,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[8,2] => [4,2,2,2] => [2,2,2] => [2,2] => 8
[8,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[7,3] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[7,2,1] => [3,3,2,2] => [3,2,2] => [2,2] => 8
[7,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[6,4] => [4,4,2] => [4,2] => [2] => 1
[6,3,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[6,2,2] => [6,2,2] => [2,2] => [2] => 1
[6,2,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[6,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[5,5] => [4,3,2,1] => [3,2,1] => [2,1] => 8
[5,4,1] => [4,3,3] => [3,3] => [3] => 1
[5,3,2] => [5,2,2,1] => [2,2,1] => [2,1] => 8
[5,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[5,2,2,1] => [5,3,2] => [3,2] => [2] => 1
[5,2,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[5,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,3,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,2,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[3,3,2,1,1] => [3,3,3,1] => [3,3,1] => [3,1] => 27
[3,3,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,2,1,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[3,2,1,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,1,1,1,1,1] => [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
[2,2,2,1,1,1,1] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[2,2,1,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => [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
[11] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 2744
[10,1] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[9,2] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[9,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2744
[8,3] => [4,3,2,2] => [3,2,2] => [2,2] => 8
[8,2,1] => [5,2,2,2] => [2,2,2] => [2,2] => 8
[8,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[7,4] => [4,4,2,1] => [4,2,1] => [2,1] => 8
[7,3,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[7,2,2] => [6,2,2,1] => [2,2,1] => [2,1] => 8
[7,2,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[7,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[6,5] => [4,4,3] => [4,3] => [3] => 1
[6,4,1] => [5,4,2] => [4,2] => [2] => 1
[6,3,2] => [6,3,2] => [3,2] => [2] => 1
[6,3,1,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[6,2,2,1] => [7,2,2] => [2,2] => [2] => 1
[6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
>>> Load all 1045 entries. <<<[6,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,5,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[5,4,1,1] => [4,3,3,1] => [3,3,1] => [3,1] => 27
[5,3,3] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 125
[5,3,2,1] => [3,3,3,2] => [3,3,2] => [3,2] => 125
[5,3,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[5,2,2,1,1] => [6,3,1,1] => [3,1,1] => [1,1] => 1
[5,2,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[5,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[4,4,1,1,1] => [7,2,1,1] => [2,1,1] => [1,1] => 1
[4,3,3,1] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[4,3,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,1,1,1] => [8,1,1,1] => [1,1,1] => [1,1] => 1
[4,2,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,3,3,2] => [5,3,2,1] => [3,2,1] => [2,1] => 8
[3,3,3,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 64
[3,3,2,2,1] => [5,3,3] => [3,3] => [3] => 1
[3,3,2,1,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 216
[3,3,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,2,2,1,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,2,1,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1] => [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
[2,2,2,1,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,2,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1] => [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
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[12] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 2744
[11,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 21952
[10,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[10,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[9,3] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 2744
[9,2,1] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 125
[9,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[8,4] => [4,4,2,2] => [4,2,2] => [2,2] => 8
[8,3,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 27
[8,2,2] => [6,2,2,2] => [2,2,2] => [2,2] => 8
[8,2,1,1] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[8,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[7,5] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 125
[7,4,1] => [4,3,3,2] => [3,3,2] => [3,2] => 125
[7,3,2] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[7,3,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2744
[7,2,2,1] => [5,3,2,2] => [3,2,2] => [2,2] => 8
[7,2,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[7,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[6,6] => [4,4,4] => [4,4] => [4] => 1
[6,5,1] => [4,4,3,1] => [4,3,1] => [3,1] => 27
[6,4,2] => [6,4,2] => [4,2] => [2] => 1
[6,4,1,1] => [6,4,1,1] => [4,1,1] => [1,1] => 1
[6,3,3] => [5,4,2,1] => [4,2,1] => [2,1] => 8
[6,3,2,1] => [5,5,2] => [5,2] => [2] => 1
[6,3,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[6,2,2,2] => [8,2,2] => [2,2] => [2] => 1
[6,2,2,1,1] => [8,2,1,1] => [2,1,1] => [1,1] => 1
[6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[6,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,5,2] => [6,3,2,1] => [3,2,1] => [2,1] => 8
[5,5,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 64
[5,4,3] => [5,4,3] => [4,3] => [3] => 1
[5,4,2,1] => [6,3,3] => [3,3] => [3] => 1
[5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[5,3,3,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 729
[5,3,2,2] => [7,2,2,1] => [2,2,1] => [2,1] => 8
[5,3,2,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 216
[5,3,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[5,2,2,2,1] => [7,3,2] => [3,2] => [2] => 1
[5,2,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[5,2,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[4,4,1,1,1,1] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,3,3,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[4,3,2,1,1,1] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[4,3,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,2,2,1,1,1,1] => [8,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,2,1,1,1,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1,1] => [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
[3,3,3,3] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 4096
[3,3,3,2,1] => [3,3,3,3] => [3,3,3] => [3,3] => 125
[3,3,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 125
[3,3,2,2,1,1] => [5,3,3,1] => [3,3,1] => [3,1] => 27
[3,3,2,1,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1000
[3,3,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[3,2,2,2,1,1,1] => [7,3,1,1] => [3,1,1] => [1,1] => 1
[3,2,2,1,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,2,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1,1] => [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
[2,2,2,2,1,1,1,1] => [9,1,1,1] => [1,1,1] => [1,1] => 1
[2,2,2,1,1,1,1,1,1] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1] => [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
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[13] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 74088
[12,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 2744
[11,2] => [4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 2744
[11,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[10,3] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 125
[10,2,1] => [5,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[10,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2744
[9,4] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 125
[9,3,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 21952
[9,2,2] => [6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[9,2,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 64
[9,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[8,5] => [4,4,3,2] => [4,3,2] => [3,2] => 125
[8,4,1] => [5,4,2,2] => [4,2,2] => [2,2] => 8
[8,3,2] => [6,3,2,2] => [3,2,2] => [2,2] => 8
[8,3,1,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[8,2,2,1] => [7,2,2,2] => [2,2,2] => [2,2] => 8
[8,2,1,1,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[8,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[7,6] => [4,4,4,1] => [4,4,1] => [4,1] => 64
[7,5,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 729
[7,4,2] => [6,4,2,1] => [4,2,1] => [2,1] => 8
[7,4,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 216
[7,3,3] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 2744
[7,3,2,1] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 9261
[7,3,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[7,2,2,2] => [8,2,2,1] => [2,2,1] => [2,1] => 8
[7,2,2,1,1] => [6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[7,2,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[6,6,1] => [5,4,4] => [4,4] => [4] => 1
[6,5,2] => [6,4,3] => [4,3] => [3] => 1
[6,5,1,1] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[6,4,3] => [6,5,2] => [5,2] => [2] => 1
[6,4,2,1] => [7,4,2] => [4,2] => [2] => 1
[6,4,1,1,1] => [7,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[6,3,3,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 27
[6,3,2,2] => [8,3,2] => [3,2] => [2] => 1
[6,3,2,1,1] => [6,5,1,1] => [5,1,1] => [1,1] => 1
[6,3,1,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[6,2,2,2,1] => [9,2,2] => [2,2] => [2] => 1
[6,2,2,1,1,1] => [8,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,2,1,1,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[5,5,3] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 4096
[5,5,2,1] => [4,3,3,3] => [3,3,3] => [3,3] => 125
[5,5,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 125
[5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 27
[5,4,2,1,1] => [6,3,3,1] => [3,3,1] => [3,1] => 27
[5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[5,3,3,2] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 125
[5,3,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2744
[5,3,2,2,1] => [5,3,3,2] => [3,3,2] => [3,2] => 125
[5,3,2,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1000
[5,3,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[5,2,2,2,1,1] => [8,3,1,1] => [3,1,1] => [1,1] => 1
[5,2,2,1,1,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[5,2,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[4,4,3,1,1] => [7,4,1,1] => [4,1,1] => [1,1] => 1
[4,4,2,1,1,1] => [9,2,1,1] => [2,1,1] => [1,1] => 1
[4,4,1,1,1,1,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,3,3,3] => [5,5,2,1] => [5,2,1] => [2,1] => 8
[4,3,3,2,1] => [5,5,3] => [5,3] => [3] => 1
[4,3,3,1,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 64
[4,3,2,1,1,1,1] => [5,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[4,3,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,2,2,2,1,1,1] => [10,1,1,1] => [1,1,1] => [1,1] => 1
[4,2,2,1,1,1,1,1] => [8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[4,2,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1,1,1] => [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] => 1
[3,3,3,3,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 42875
[3,3,3,2,2] => [7,3,2,1] => [3,2,1] => [2,1] => 8
[3,3,3,2,1,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 9261
[3,3,3,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[3,3,2,2,2,1] => [7,3,3] => [3,3] => [3] => 1
[3,3,2,2,1,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 216
[3,3,2,1,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 3375
[3,3,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[3,2,2,2,1,1,1,1] => [7,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,2,2,1,1,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1] => [9,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1] => [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
[2,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 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] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[14] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 74088
[13,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 729000
[12,2] => [4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 2744
[12,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 21952
[11,3] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 74088
[11,2,1] => [3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 2744
[11,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 421875
[10,4] => [4,4,2,2,2] => [4,2,2,2] => [2,2,2] => 125
[10,3,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 729
[10,2,2] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[10,2,1,1] => [6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[10,1,1,1,1] => [4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[9,5] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 2744
[9,4,1] => [4,3,3,2,2] => [3,3,2,2] => [3,2,2] => 9261
[9,3,2] => [5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 2744
[9,3,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[9,2,2,1] => [5,3,2,2,2] => [3,2,2,2] => [2,2,2] => 125
[9,2,1,1,1] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 125
[9,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 42875
[8,6] => [4,4,4,2] => [4,4,2] => [4,2] => 729
[8,5,1] => [4,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000
[8,4,2] => [6,4,2,2] => [4,2,2] => [2,2] => 8
[8,4,1,1] => [6,4,2,1,1] => [4,2,1,1] => [2,1,1] => 27
[8,3,3] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 125
[8,3,2,1] => [5,5,2,2] => [5,2,2] => [2,2] => 8
[8,3,1,1,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2744
[8,2,2,2] => [8,2,2,2] => [2,2,2] => [2,2] => 8
[8,2,2,1,1] => [8,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[8,2,1,1,1,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[8,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[7,7] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 4096
[7,6,1] => [4,4,3,3] => [4,3,3] => [3,3] => 125
[7,5,2] => [6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 125
[7,5,1,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2744
[7,4,3] => [5,4,3,2] => [4,3,2] => [3,2] => 125
[7,4,2,1] => [6,3,3,2] => [3,3,2] => [3,2] => 125
[7,4,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 64
[7,3,3,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 21952
[7,3,2,2] => [7,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[7,3,2,1,1] => [4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1000
[7,3,1,1,1,1] => [3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[7,2,2,2,1] => [7,3,2,2] => [3,2,2] => [2,2] => 8
[7,2,2,1,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[7,2,1,1,1,1,1] => [4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 729
[6,6,2] => [6,4,4] => [4,4] => [4] => 1
[6,6,1,1] => [6,4,3,1] => [4,3,1] => [3,1] => 27
[6,5,3] => [5,4,4,1] => [4,4,1] => [4,1] => 64
[6,5,2,1] => [5,5,4] => [5,4] => [4] => 1
[6,5,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 64
[6,4,4] => [6,6,2] => [6,2] => [2] => 1
[6,4,3,1] => [6,6,1,1] => [6,1,1] => [1,1] => 1
[6,4,2,2] => [8,4,2] => [4,2] => [2] => 1
[6,4,2,1,1] => [8,4,1,1] => [4,1,1] => [1,1] => 1
[6,4,1,1,1,1] => [7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[6,3,3,2] => [7,4,2,1] => [4,2,1] => [2,1] => 8
[6,3,3,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 729
[6,3,2,2,1] => [7,5,2] => [5,2] => [2] => 1
[6,3,2,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[6,3,1,1,1,1,1] => [5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[6,2,2,2,2] => [10,2,2] => [2,2] => [2] => 1
[6,2,2,2,1,1] => [10,2,1,1] => [2,1,1] => [1,1] => 1
[6,2,2,1,1,1,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[6,2,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[6,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[5,5,4] => [6,5,2,1] => [5,2,1] => [2,1] => 8
[5,5,3,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 42875
[5,5,2,2] => [8,3,2,1] => [3,2,1] => [2,1] => 8
[5,5,2,1,1] => [4,3,3,3,1] => [3,3,3,1] => [3,3,1] => 9261
[5,5,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[5,4,4,1] => [6,5,3] => [5,3] => [3] => 1
[5,4,3,2] => [7,4,3] => [4,3] => [3] => 1
[5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 216
[5,4,2,2,1] => [8,3,3] => [3,3] => [3] => 1
[5,4,2,1,1,1] => [7,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[5,4,1,1,1,1,1] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,3,3,3] => [3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 343000
[5,3,3,2,1] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 74088
[5,3,3,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[5,3,2,2,2] => [9,2,2,1] => [2,2,1] => [2,1] => 8
[5,3,2,2,1,1] => [6,3,3,1,1] => [3,3,1,1] => [3,1,1] => 216
[5,3,2,1,1,1,1] => [4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 3375
[5,3,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[5,2,2,2,2,1] => [9,3,2] => [3,2] => [2] => 1
[5,2,2,2,1,1,1] => [8,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[5,2,2,1,1,1,1,1] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,2,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[5,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[4,4,3,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[4,4,2,1,1,1,1] => [9,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,4,1,1,1,1,1,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,3,3,1] => [5,5,2,1,1] => [5,2,1,1] => [2,1,1] => 27
[4,3,3,2,1,1] => [5,5,3,1] => [5,3,1] => [3,1] => 27
[4,3,3,1,1,1,1] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 125
[4,3,2,2,1,1,1] => [7,5,1,1] => [5,1,1] => [1,1] => 1
[4,3,2,1,1,1,1,1] => [5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[4,3,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[4,2,2,2,1,1,1,1] => [10,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,2,2,1,1,1,1,1,1] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,2,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[3,3,3,3,2] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 4096
[3,3,3,3,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 262144
[3,3,3,2,2,1] => [5,3,3,3] => [3,3,3] => [3,3] => 125
[3,3,3,2,1,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 175616
[3,3,3,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[3,3,2,2,2,1,1] => [7,3,3,1] => [3,3,1] => [3,1] => 27
[3,3,2,2,1,1,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1000
[3,3,2,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 9261
[3,3,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[3,2,2,2,2,1,1,1] => [9,3,1,1] => [3,1,1] => [1,1] => 1
[3,2,2,2,1,1,1,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,2,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,1,1,1,1] => [11,1,1,1] => [1,1,1] => [1,1] => 1
[2,2,2,2,1,1,1,1,1,1] => [9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 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] => [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] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 2299968
[14,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 74088
[13,2] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 74088
[13,1,1] => [2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 4492125
[12,3] => [4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 2744
[12,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 2744
[12,1,1,1] => [4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[11,4] => [4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 2744
[11,3,1] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 729000
[11,2,2] => [6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 2744
[11,2,1,1] => [4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 2744
[11,1,1,1,1] => [2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1331000
[10,5] => [4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 9261
[10,4,1] => [5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 125
[10,3,2] => [6,3,2,2,2] => [3,2,2,2] => [2,2,2] => 125
[10,3,1,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 21952
[10,2,2,1] => [7,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[10,2,1,1,1] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2744
[10,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[9,6] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 42875
[9,5,1] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 21952
[9,4,2] => [6,4,2,2,1] => [4,2,2,1] => [2,2,1] => 125
[9,4,1,1] => [4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 8000
[9,3,3] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 74088
[9,3,2,1] => [3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 592704
[9,3,1,1,1] => [3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 421875
[9,2,2,2] => [8,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[9,2,2,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 64
[9,2,1,1,1,1] => [4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[9,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 85184
[8,7] => [4,4,4,3] => [4,4,3] => [4,3] => 2744
[8,6,1] => [5,4,4,2] => [4,4,2] => [4,2] => 729
[8,5,2] => [6,4,3,2] => [4,3,2] => [3,2] => 125
[8,5,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 729
[8,4,3] => [6,5,2,2] => [5,2,2] => [2,2] => 8
[8,4,2,1] => [7,4,2,2] => [4,2,2] => [2,2] => 8
[8,4,1,1,1] => [7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[8,3,3,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 729
[8,3,2,2] => [8,3,2,2] => [3,2,2] => [2,2] => 8
[8,3,2,1,1] => [6,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[8,3,1,1,1,1] => [5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[8,2,2,2,1] => [9,2,2,2] => [2,2,2] => [2,2] => 8
[8,2,2,1,1,1] => [8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[8,2,1,1,1,1,1] => [6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[8,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[7,7,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 42875
[7,6,2] => [6,4,4,1] => [4,4,1] => [4,1] => 64
[7,6,1,1] => [4,4,3,3,1] => [4,3,3,1] => [3,3,1] => 9261
[7,5,3] => [4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 343000
[7,5,2,1] => [4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 74088
[7,5,1,1,1] => [4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[7,4,4] => [6,6,2,1] => [6,2,1] => [2,1] => 8
[7,4,3,1] => [5,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000
[7,4,2,2] => [8,4,2,1] => [4,2,1] => [2,1] => 8
[7,4,2,1,1] => [6,4,3,1,1] => [4,3,1,1] => [3,1,1] => 216
[7,4,1,1,1,1] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 125
[7,3,3,2] => [5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 2744
[7,3,3,1,1] => [3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[7,3,2,2,1] => [5,3,3,2,2] => [3,3,2,2] => [3,2,2] => 9261
[7,3,2,1,1,1] => [4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 3375
[7,3,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 42875
[7,2,2,2,2] => [10,2,2,1] => [2,2,1] => [2,1] => 8
[7,2,2,2,1,1] => [8,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[7,2,2,1,1,1,1] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[7,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1000
[6,6,3] => [6,5,4] => [5,4] => [4] => 1
[6,6,2,1] => [7,4,4] => [4,4] => [4] => 1
[6,6,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[6,5,4] => [6,6,3] => [6,3] => [3] => 1
[6,5,3,1] => [6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 27
[6,5,2,2] => [8,4,3] => [4,3] => [3] => 1
[6,5,2,1,1] => [6,5,3,1] => [5,3,1] => [3,1] => 27
[6,5,1,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 125
[6,4,4,1] => [7,6,2] => [6,2] => [2] => 1
[6,4,3,2] => [8,5,2] => [5,2] => [2] => 1
[6,4,3,1,1] => [7,4,2,1,1] => [4,2,1,1] => [2,1,1] => 27
[6,4,2,2,1] => [9,4,2] => [4,2] => [2] => 1
[6,4,2,1,1,1] => [9,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[6,4,1,1,1,1,1] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[6,3,3,3] => [5,5,2,2,1] => [5,2,2,1] => [2,2,1] => 125
[6,3,3,2,1] => [5,5,3,2] => [5,3,2] => [3,2] => 125
[6,3,3,1,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2744
[6,3,2,2,2] => [10,3,2] => [3,2] => [2] => 1
[6,3,2,2,1,1] => [8,5,1,1] => [5,1,1] => [1,1] => 1
[6,3,2,1,1,1,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[6,3,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[6,2,2,2,2,1] => [11,2,2] => [2,2] => [2] => 1
[6,2,2,2,1,1,1] => [10,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,2,2,1,1,1,1,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,2,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[6,1,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[5,5,5] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 4096
[5,5,4,1] => [5,4,3,3] => [4,3,3] => [3,3] => 125
[5,5,3,2] => [6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 4096
[5,5,3,1,1] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 262144
[5,5,2,2,1] => [6,3,3,3] => [3,3,3] => [3,3] => 125
[5,5,2,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1000
[5,5,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[5,4,4,1,1] => [7,4,3,1] => [4,3,1] => [3,1] => 27
[5,4,3,3] => [5,5,4,1] => [5,4,1] => [4,1] => 64
[5,4,3,2,1] => [5,5,5] => [5,5] => [5] => 1
[5,4,3,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 64
[5,4,2,2,1,1] => [8,3,3,1] => [3,3,1] => [3,1] => 27
[5,4,2,1,1,1,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[5,4,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,3,3,3,1] => [3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 4251528
[5,3,3,2,2] => [7,3,2,2,1] => [3,2,2,1] => [2,2,1] => 125
[5,3,3,2,1,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 175616
[5,3,3,1,1,1,1] => [3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[5,3,2,2,2,1] => [7,3,3,2] => [3,3,2] => [3,2] => 125
[5,3,2,2,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1000
[5,3,2,1,1,1,1,1] => [4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 9261
[5,3,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 729
[5,2,2,2,2,1,1] => [10,3,1,1] => [3,1,1] => [1,1] => 1
[5,2,2,2,1,1,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[5,2,2,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,2,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[5,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[4,4,4,1,1,1] => [9,4,1,1] => [4,1,1] => [1,1] => 1
[4,4,3,3,1] => [7,6,1,1] => [6,1,1] => [1,1] => 1
[4,4,3,1,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 64
[4,4,2,2,1,1,1] => [11,2,1,1] => [2,1,1] => [1,1] => 1
[4,4,2,1,1,1,1,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,4,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,3,3,3,2] => [7,5,2,1] => [5,2,1] => [2,1] => 8
[4,3,3,3,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 42875
[4,3,3,2,2,1] => [7,5,3] => [5,3] => [3] => 1
[4,3,3,2,1,1,1] => [5,5,3,1,1] => [5,3,1,1] => [3,1,1] => 216
[4,3,3,1,1,1,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[4,3,2,2,1,1,1,1] => [7,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[4,3,2,1,1,1,1,1,1] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[4,2,2,2,2,1,1,1] => [12,1,1,1] => [1,1,1] => [1,1] => 1
[4,2,2,2,1,1,1,1,1] => [10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,2,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[3,3,3,3,3] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 4741632
[3,3,3,3,2,1] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 74088
[3,3,3,3,1,1,1] => [3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1157625
[3,3,3,2,2,2] => [9,3,2,1] => [3,2,1] => [2,1] => 8
[3,3,3,2,2,1,1] => [5,3,3,3,1] => [3,3,3,1] => [3,3,1] => 9261
[3,3,3,2,1,1,1,1] => [3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 1728000
[3,3,3,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[3,3,2,2,2,2,1] => [9,3,3] => [3,3] => [3] => 1
[3,3,2,2,2,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => [3,1,1] => 216
[3,3,2,2,1,1,1,1,1] => [5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 3375
[3,3,2,1,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 21952
[3,3,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[3,2,2,2,2,1,1,1,1] => [9,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,2,2,2,1,1,1,1,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[3,2,1,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [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
[2,2,2,2,2,1,1,1,1,1] => [11,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[16] => [2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 2299968
[15,1] => [2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 26198073
[14,2] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 74088
[14,1,1] => [4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 729000
[13,3] => [3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 2299968
[13,2,1] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 74088
[13,1,1,1] => [2,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 20796875
[12,4] => [4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 2744
[12,3,1] => [4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 21952
[12,2,2] => [6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 2744
[12,2,1,1] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 21952
[12,1,1,1,1] => [4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 421875
[11,5] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 74088
[11,4,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 592704
[11,3,2] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 74088
[11,3,1,1] => [3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 4492125
[11,2,2,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 2744
[11,2,1,1,1] => [4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[11,1,1,1,1,1] => [2,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 3652264
[10,6] => [4,4,4,2,2] => [4,4,2,2] => [4,2,2] => 175616
[10,5,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 729000
[10,4,2] => [6,4,2,2,2] => [4,2,2,2] => [2,2,2] => 125
[10,4,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 729
[10,3,3] => [5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 2744
[10,3,2,1] => [5,5,2,2,2] => [5,2,2,2] => [2,2,2] => 125
[10,3,1,1,1] => [5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[10,2,2,2] => [8,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[10,2,2,1,1] => [8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[10,2,1,1,1,1] => [6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[10,1,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 42875
[9,7] => [4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 343000
[9,6,1] => [4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 74088
[9,5,2] => [6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 2744
[9,5,1,1] => [4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[9,4,3] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 9261
[9,4,2,1] => [6,3,3,2,2] => [3,3,2,2] => [3,2,2] => 9261
[9,4,1,1,1] => [5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 2744
[9,3,3,1] => [3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 729000
[9,3,2,2] => [7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 2744
[9,3,2,1,1] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 42875
[9,3,1,1,1,1] => [3,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1331000
[9,2,2,2,1] => [7,3,2,2,2] => [3,2,2,2] => [2,2,2] => 125
[9,2,2,1,1,1] => [6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 125
[9,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[9,1,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 157464
[8,8] => [4,4,4,4] => [4,4,4] => [4,4] => 2744
[8,7,1] => [4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 343000
[8,6,2] => [6,4,4,2] => [4,4,2] => [4,2] => 729
[8,6,1,1] => [6,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000
[8,5,3] => [5,4,4,2,1] => [4,4,2,1] => [4,2,1] => 42875
[8,5,2,1] => [5,5,4,2] => [5,4,2] => [4,2] => 729
[8,5,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2744
[8,4,4] => [6,6,2,2] => [6,2,2] => [2,2] => 8
[8,4,3,1] => [6,6,2,1,1] => [6,2,1,1] => [2,1,1] => 27
[8,4,2,2] => [8,4,2,2] => [4,2,2] => [2,2] => 8
[8,4,2,1,1] => [8,4,2,1,1] => [4,2,1,1] => [2,1,1] => 27
[8,4,1,1,1,1] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2744
[8,3,3,2] => [7,4,2,2,1] => [4,2,2,1] => [2,2,1] => 125
[8,3,3,1,1] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 21952
[8,3,2,2,1] => [7,5,2,2] => [5,2,2] => [2,2] => 8
[8,3,2,1,1,1] => [6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[8,3,1,1,1,1,1] => [5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[8,2,2,2,2] => [10,2,2,2] => [2,2,2] => [2,2] => 8
[8,2,2,2,1,1] => [10,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[8,2,2,1,1,1,1] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[8,2,1,1,1,1,1,1] => [6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[8,1,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 729
[7,7,2] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 4096
[7,7,1,1] => [4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 262144
[7,6,3] => [5,4,4,3] => [4,4,3] => [4,3] => 2744
[7,6,2,1] => [6,4,3,3] => [4,3,3] => [3,3] => 125
[7,6,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 64
[7,5,4] => [6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 125
[7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 4251528
[7,5,2,2] => [8,3,2,2,1] => [3,2,2,1] => [2,2,1] => 125
[7,5,2,1,1] => [4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 175616
[7,5,1,1,1,1] => [4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[7,4,4,1] => [6,5,3,2] => [5,3,2] => [3,2] => 125
[7,4,3,2] => [7,4,3,2] => [4,3,2] => [3,2] => 125
[7,4,3,1,1] => [5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 8000
[7,4,2,2,1] => [8,3,3,2] => [3,3,2] => [3,2] => 125
[7,4,2,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 64
[7,4,1,1,1,1,1] => [5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[7,3,3,3] => [3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 23887872
[7,3,3,2,1] => [3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 16003008
[7,3,3,1,1,1] => [3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 421875
[7,3,2,2,2] => [9,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[7,3,2,2,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1000
[7,3,2,1,1,1,1] => [4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 9261
[7,3,1,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 85184
[7,2,2,2,2,1] => [9,3,2,2] => [3,2,2] => [2,2] => 8
[7,2,2,2,1,1,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[7,2,2,1,1,1,1,1] => [6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,2,1,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[7,1,1,1,1,1,1,1,1,1] => [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] => [2,1,1,1,1,1,1,1,1,1,1] => 1331
[6,6,4] => [6,6,4] => [6,4] => [4] => 1
[6,6,3,1] => [6,6,3,1] => [6,3,1] => [3,1] => 27
[6,6,2,2] => [8,4,4] => [4,4] => [4] => 1
[6,6,2,1,1] => [8,4,3,1] => [4,3,1] => [3,1] => 27
[6,6,1,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 64
[6,5,5] => [6,5,4,1] => [5,4,1] => [4,1] => 64
[6,5,4,1] => [6,5,5] => [5,5] => [5] => 1
[6,5,3,2] => [7,4,4,1] => [4,4,1] => [4,1] => 64
[6,5,3,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 42875
[6,5,2,2,1] => [7,5,4] => [5,4] => [4] => 1
[6,5,2,1,1,1] => [7,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[6,5,1,1,1,1,1] => [6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[6,4,4,2] => [8,6,2] => [6,2] => [2] => 1
[6,4,4,1,1] => [8,6,1,1] => [6,1,1] => [1,1] => 1
[6,4,3,3] => [7,6,2,1] => [6,2,1] => [2,1] => 8
[6,4,3,2,1] => [7,7,2] => [7,2] => [2] => 1
[6,4,3,1,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 729
[6,4,2,2,2] => [10,4,2] => [4,2] => [2] => 1
[6,4,2,2,1,1] => [10,4,1,1] => [4,1,1] => [1,1] => 1
[6,4,2,1,1,1,1] => [9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[6,4,1,1,1,1,1,1] => [7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[6,3,3,3,1] => [5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 729
[6,3,3,2,2] => [9,4,2,1] => [4,2,1] => [2,1] => 8
[6,3,3,2,1,1] => [6,5,3,1,1] => [5,3,1,1] => [3,1,1] => 216
[6,3,3,1,1,1,1] => [5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[6,3,2,2,2,1] => [9,5,2] => [5,2] => [2] => 1
[6,3,2,2,1,1,1] => [8,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[6,3,2,1,1,1,1,1] => [6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,3,1,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[6,2,2,2,2,2] => [12,2,2] => [2,2] => [2] => 1
[6,2,2,2,2,1,1] => [12,2,1,1] => [2,1,1] => [1,1] => 1
[6,2,2,2,1,1,1,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[6,2,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[6,2,1,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[6,1,1,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[5,5,5,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 42875
[5,5,4,2] => [8,5,2,1] => [5,2,1] => [2,1] => 8
[5,5,4,1,1] => [5,4,3,3,1] => [4,3,3,1] => [3,3,1] => 9261
[5,5,3,3] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 4741632
[5,5,3,2,1] => [4,3,3,3,3] => [3,3,3,3] => [3,3,3] => 74088
[5,5,3,1,1,1] => [4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1157625
[5,5,2,2,2] => [10,3,2,1] => [3,2,1] => [2,1] => 8
[5,5,2,2,1,1] => [6,3,3,3,1] => [3,3,3,1] => [3,3,1] => 9261
[5,5,2,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 3375
[5,5,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[5,4,4,3] => [7,6,3] => [6,3] => [3] => 1
[5,4,4,2,1] => [8,5,3] => [5,3] => [3] => 1
[5,4,4,1,1,1] => [7,4,3,1,1] => [4,3,1,1] => [3,1,1] => 216
[5,4,3,3,1] => [5,5,4,1,1] => [5,4,1,1] => [4,1,1] => 1000
[5,4,3,2,2] => [9,4,3] => [4,3] => [3] => 1
[5,4,3,2,1,1] => [5,5,5,1] => [5,5,1] => [5,1] => 125
[5,4,3,1,1,1,1] => [5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 125
[5,4,2,2,2,1] => [10,3,3] => [3,3] => [3] => 1
[5,4,2,2,1,1,1] => [9,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[5,4,2,1,1,1,1,1] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,4,1,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[5,3,3,3,2] => [5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 343000
[5,3,3,3,1,1] => [3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 31255875
[5,3,3,2,2,1] => [5,3,3,3,2] => [3,3,3,2] => [3,3,2] => 74088
[5,3,3,2,1,1,1] => [4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 1728000
[5,3,3,1,1,1,1,1] => [3,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 42875
[5,3,2,2,2,2] => [11,2,2,1] => [2,2,1] => [2,1] => 8
[5,3,2,2,2,1,1] => [8,3,3,1,1] => [3,3,1,1] => [3,1,1] => 216
[5,3,2,2,1,1,1,1] => [6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 3375
[5,3,2,1,1,1,1,1,1] => [4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 21952
[5,3,1,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1000
[5,2,2,2,2,2,1] => [11,3,2] => [3,2] => [2] => 1
[5,2,2,2,2,1,1,1] => [10,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[5,2,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,2,2,1,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[5,2,1,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[5,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[4,4,4,1,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[4,4,3,3,1,1] => [7,5,2,1,1] => [5,2,1,1] => [2,1,1] => 27
[4,4,3,2,1,1,1] => [7,7,1,1] => [7,1,1] => [1,1] => 1
[4,4,3,1,1,1,1,1] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 125
[4,4,2,2,1,1,1,1] => [11,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,4,2,1,1,1,1,1,1] => [9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,4,1,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[4,3,3,3,3] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 4096
[4,3,3,3,2,1] => [5,5,3,3] => [5,3,3] => [3,3] => 125
[4,3,3,3,1,1,1] => [5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 262144
[4,3,3,2,2,1,1] => [7,5,3,1] => [5,3,1] => [3,1] => 27
[4,3,3,2,1,1,1,1] => [5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1000
[4,3,3,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[4,3,2,2,2,1,1,1] => [9,5,1,1] => [5,1,1] => [1,1] => 1
[4,3,2,2,1,1,1,1,1] => [7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[4,3,2,1,1,1,1,1,1,1] => [5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,3,1,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[4,2,2,2,2,1,1,1,1] => [12,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,2,2,2,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[4,2,1,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[3,3,3,3,3,1] => [3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 91125000
[3,3,3,3,2,2] => [7,3,3,2,1] => [3,3,2,1] => [3,2,1] => 4096
[3,3,3,3,2,1,1] => [3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 9261000
[3,3,3,3,1,1,1,1] => [3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 4096000
[3,3,3,2,2,2,1] => [7,3,3,3] => [3,3,3] => [3,3] => 125
[3,3,3,2,2,1,1,1] => [5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 175616
[3,3,3,2,1,1,1,1,1] => [3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 11390625
[3,3,3,1,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 729
[3,3,2,2,2,2,1,1] => [9,3,3,1] => [3,3,1] => [3,1] => 27
[3,3,2,2,2,1,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1000
[3,3,2,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 9261
[3,3,2,1,1,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 46656
[3,3,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[3,2,2,2,2,2,1,1,1] => [11,3,1,1] => [3,1,1] => [1,1] => 1
[3,2,2,2,2,1,1,1,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,2,2,2,1,1,1,1,1,1,1] => [7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,1,1,1,1] => [13,1,1,1] => [1,1,1] => [1,1] => 1
[2,2,2,2,2,1,1,1,1,1,1] => [11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[16,1] => [3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 2299968
[15,2] => [4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 2299968
[14,3] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 74088
[14,2,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 74088
[14,1,1,1] => [4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 4492125
[13,4] => [4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 74088
[13,3,1] => [3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 26198073
[13,2,2] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 74088
[13,2,1,1] => [4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[12,5] => [4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 592704
[12,4,1] => [5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 2744
[12,3,2] => [6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 2744
[12,3,1,1] => [5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 729000
[12,2,2,1] => [7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 2744
[12,2,1,1,1] => [6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[12,1,1,1,1,1] => [4,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1331000
[11,6] => [4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 10077696
[11,5,1] => [4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 729000
[11,4,2] => [6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 2744
[11,4,1,1] => [4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 6751269
[11,3,3] => [3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 2299968
[11,3,2,1] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 35937000
[11,3,1,1,1] => [3,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 20796875
[11,2,2,2] => [8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 2744
[11,2,2,1,1] => [6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 2744
[11,2,1,1,1,1] => [4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[10,7] => [4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 4741632
[10,6,1] => [5,4,4,2,2] => [4,4,2,2] => [4,2,2] => 175616
[10,5,2] => [6,4,3,2,2] => [4,3,2,2] => [3,2,2] => 9261
[10,5,1,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 21952
[10,4,3] => [6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 125
[10,4,2,1] => [7,4,2,2,2] => [4,2,2,2] => [2,2,2] => 125
[10,4,1,1,1] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 21952
[10,3,3,1] => [5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 21952
[10,3,2,2] => [8,3,2,2,2] => [3,2,2,2] => [2,2,2] => 125
[10,3,2,1,1] => [6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 64
[10,3,1,1,1,1] => [5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 421875
[10,2,2,2,1] => [9,2,2,2,2] => [2,2,2,2] => [2,2,2] => 125
[10,2,2,1,1,1] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2744
[10,2,1,1,1,1,1] => [6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[10,1,1,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 85184
[9,8] => [4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 592704
[9,7,1] => [4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 4251528
[9,6,2] => [6,4,4,2,1] => [4,4,2,1] => [4,2,1] => 42875
[9,6,1,1] => [4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10077696
[9,5,3] => [4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 23887872
[9,5,2,1] => [4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 16003008
[9,5,1,1,1] => [4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 421875
[9,4,4] => [6,6,2,2,1] => [6,2,2,1] => [2,2,1] => 125
[9,4,3,1] => [5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 729000
[9,4,2,2] => [8,4,2,2,1] => [4,2,2,1] => [2,2,1] => 125
[9,4,2,1,1] => [6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 8000
[9,4,1,1,1,1] => [5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[9,3,3,2] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 74088
[9,3,3,1,1] => [3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 4492125
[9,3,2,2,1] => [5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 592704
[9,3,2,1,1,1] => [4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 175616
[9,3,1,1,1,1,1] => [3,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 3652264
[9,2,2,2,2] => [10,2,2,2,1] => [2,2,2,1] => [2,2,1] => 125
[9,2,2,2,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 64
[9,2,2,1,1,1,1] => [6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[9,2,1,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[8,8,1] => [5,4,4,4] => [4,4,4] => [4,4] => 2744
[8,7,2] => [6,4,4,3] => [4,4,3] => [4,3] => 2744
[8,7,1,1] => [6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 42875
[8,6,3] => [6,5,4,2] => [5,4,2] => [4,2] => 729
[8,6,2,1] => [7,4,4,2] => [4,4,2] => [4,2] => 729
[8,6,1,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 729
[8,5,4] => [6,6,3,2] => [6,3,2] => [3,2] => 125
[8,5,3,1] => [6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 729
[8,5,2,2] => [8,4,3,2] => [4,3,2] => [3,2] => 125
[8,5,2,1,1] => [6,6,3,1,1] => [6,3,1,1] => [3,1,1] => 216
[8,5,1,1,1,1] => [6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[8,4,4,1] => [7,6,2,2] => [6,2,2] => [2,2] => 8
[8,4,3,2] => [8,5,2,2] => [5,2,2] => [2,2] => 8
[8,4,3,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 729
[8,4,2,2,1] => [9,4,2,2] => [4,2,2] => [2,2] => 8
[8,4,2,1,1,1] => [9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 729
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 8000
[8,3,3,3] => [5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 2744
[8,3,3,2,1] => [5,5,3,2,2] => [5,3,2,2] => [3,2,2] => 9261
[8,3,3,1,1,1] => [5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 110592
[8,3,2,2,2] => [10,3,2,2] => [3,2,2] => [2,2] => 8
[8,3,2,2,1,1] => [8,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[8,3,2,1,1,1,1] => [6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,3,1,1,1,1,1,1] => [5,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 42875
[8,2,2,2,2,1] => [11,2,2,2] => [2,2,2] => [2,2] => 8
[8,2,2,2,1,1,1] => [10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 64
[8,2,2,1,1,1,1,1] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[8,2,1,1,1,1,1,1,1] => [6,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[8,1,1,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1000
[7,7,3] => [4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 4741632
[7,7,2,1] => [4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 74088
[7,7,1,1,1] => [4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1157625
[7,6,4] => [6,6,4,1] => [6,4,1] => [4,1] => 64
[7,6,3,1] => [5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 343000
[7,6,2,2] => [8,4,4,1] => [4,4,1] => [4,1] => 64
[7,6,2,1,1] => [6,4,3,3,1] => [4,3,3,1] => [3,3,1] => 9261
[7,6,1,1,1,1] => [6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 125
[7,5,5] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 343000
[7,5,4,1] => [5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 74088
[7,5,3,2] => [6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 343000
[7,5,3,1,1] => [4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 31255875
[7,5,2,2,1] => [6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 74088
[7,5,2,1,1,1] => [5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 42875
[7,5,1,1,1,1,1] => [4,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 42875
[7,4,4,2] => [8,6,2,1] => [6,2,1] => [2,1] => 8
[7,4,4,1,1] => [7,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000
[7,4,3,3] => [5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 42875
[7,4,3,2,1] => [5,5,5,2] => [5,5,2] => [5,2] => 2744
[7,4,3,1,1,1] => [5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 2744
[7,4,2,2,2] => [10,4,2,1] => [4,2,1] => [2,1] => 8
[7,4,2,2,1,1] => [8,4,3,1,1] => [4,3,1,1] => [3,1,1] => 216
[7,4,2,1,1,1,1] => [7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 125
[7,4,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[7,3,3,3,1] => [3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 332812557
[7,3,3,2,2] => [7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 2744
[7,3,3,2,1,1] => [4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 1728000
[7,3,3,1,1,1,1] => [3,3,2,2,2,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1331000
[7,3,2,2,2,1] => [7,3,3,2,2] => [3,3,2,2] => [3,2,2] => 9261
[7,3,2,2,1,1,1] => [6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 3375
[7,3,2,1,1,1,1,1] => [4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 21952
[7,3,1,1,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 157464
[7,2,2,2,2,2] => [12,2,2,1] => [2,2,1] => [2,1] => 8
[7,2,2,2,2,1,1] => [10,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,2,1,1,1,1,1,1] => [6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[7,2,1,1,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[6,6,5] => [6,6,5] => [6,5] => [5] => 1
[6,6,4,1] => [7,6,4] => [6,4] => [4] => 1
[6,6,3,2] => [8,5,4] => [5,4] => [4] => 1
[6,6,3,1,1] => [8,5,2,1,1] => [5,2,1,1] => [2,1,1] => 27
[6,6,2,2,1] => [9,4,4] => [4,4] => [4] => 1
[6,6,2,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => [2,1,1] => 27
[6,6,1,1,1,1,1] => [8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 125
[6,5,5,1] => [6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 1000
[6,5,4,2] => [8,6,3] => [6,3] => [3] => 1
[6,5,4,1,1] => [6,5,5,1] => [5,5,1] => [5,1] => 125
[6,5,3,3] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 4096
[6,5,3,2,1] => [6,5,3,3] => [5,3,3] => [3,3] => 125
[6,5,3,1,1,1] => [6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 262144
[6,5,2,2,2] => [10,4,3] => [4,3] => [3] => 1
[6,5,2,2,1,1] => [8,5,3,1] => [5,3,1] => [3,1] => 27
[6,5,2,1,1,1,1] => [7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[6,5,1,1,1,1,1,1] => [6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[6,4,4,3] => [8,7,2] => [7,2] => [2] => 1
[6,4,4,2,1] => [9,6,2] => [6,2] => [2] => 1
[6,4,4,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => [2,1,1] => 27
[6,4,3,3,1] => [7,6,2,1,1] => [6,2,1,1] => [2,1,1] => 27
[6,4,3,2,2] => [10,5,2] => [5,2] => [2] => 1
[6,4,3,2,1,1] => [8,7,1,1] => [7,1,1] => [1,1] => 1
[6,4,3,1,1,1,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2744
[6,4,2,2,2,1] => [11,4,2] => [4,2] => [2] => 1
[6,4,2,2,1,1,1] => [11,2,2,1,1] => [2,2,1,1] => [2,1,1] => 27
[6,4,2,1,1,1,1,1] => [9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 125
[6,4,1,1,1,1,1,1,1] => [7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 343
[6,3,3,3,2] => [7,5,2,2,1] => [5,2,2,1] => [2,2,1] => 125
[6,3,3,3,1,1] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 4251528
[6,3,3,2,2,1] => [7,5,3,2] => [5,3,2] => [3,2] => 125
[6,3,3,2,1,1,1] => [6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1000
[6,3,3,1,1,1,1,1] => [5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 19683
[6,3,2,2,2,2] => [12,3,2] => [3,2] => [2] => 1
[6,3,2,2,2,1,1] => [10,5,1,1] => [5,1,1] => [1,1] => 1
[6,3,2,2,1,1,1,1] => [8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[6,3,2,1,1,1,1,1,1] => [6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[6,3,1,1,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 729
[6,2,2,2,2,2,1] => [13,2,2] => [2,2] => [2] => 1
[6,2,2,2,2,1,1,1] => [12,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,2,2,2,1,1,1,1,1] => [10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,2,2,1,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[6,2,1,1,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[6,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[5,5,5,2] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 4096
[5,5,5,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 262144
[5,5,4,3] => [5,5,4,3] => [5,4,3] => [4,3] => 2744
[5,5,4,2,1] => [7,4,3,3] => [4,3,3] => [3,3] => 125
[5,5,4,1,1,1] => [5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 175616
[5,5,3,3,1] => [4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 91125000
[5,5,3,2,2] => [8,3,3,2,1] => [3,3,2,1] => [3,2,1] => 4096
[5,5,3,2,1,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 9261000
[5,5,3,1,1,1,1] => [4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 4096000
[5,5,2,2,2,1] => [8,3,3,3] => [3,3,3] => [3,3] => 125
[5,5,2,2,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1000
[5,5,2,1,1,1,1,1] => [5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 9261
[5,5,1,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 729
[5,4,4,3,1] => [7,6,3,1] => [6,3,1] => [3,1] => 27
[5,4,4,2,1,1] => [9,4,3,1] => [4,3,1] => [3,1] => 27
[5,4,4,1,1,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 64
[5,4,3,3,2] => [7,5,4,1] => [5,4,1] => [4,1] => 64
[5,4,3,3,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 8000
[5,4,3,2,2,1] => [7,5,5] => [5,5] => [5] => 1
[5,4,3,2,1,1,1] => [5,5,5,1,1] => [5,5,1,1] => [5,1,1] => 3375
[5,4,3,1,1,1,1,1] => [5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[5,4,2,2,2,1,1] => [10,3,3,1] => [3,3,1] => [3,1] => 27
[5,4,2,2,1,1,1,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[5,4,2,1,1,1,1,1,1] => [7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,4,1,1,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[5,3,3,3,3] => [3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => 970299000
[5,3,3,3,2,1] => [3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 98611128
[5,3,3,3,1,1,1] => [3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 166375000
[5,3,3,2,2,2] => [9,3,2,2,1] => [3,2,2,1] => [2,2,1] => 125
[5,3,3,2,2,1,1] => [6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 175616
[5,3,3,2,1,1,1,1] => [4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 11390625
[5,3,3,1,1,1,1,1,1] => [3,3,2,2,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 85184
[5,3,2,2,2,2,1] => [9,3,3,2] => [3,3,2] => [3,2] => 125
[5,3,2,2,2,1,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1000
[5,3,2,2,1,1,1,1,1] => [6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 9261
[5,3,2,1,1,1,1,1,1,1] => [4,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 46656
[5,3,1,1,1,1,1,1,1,1,1] => [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] => [2,1,1,1,1,1,1,1,1,1,1] => 1331
[5,2,2,2,2,2,1,1] => [12,3,1,1] => [3,1,1] => [1,1] => 1
[5,2,2,2,2,1,1,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[5,2,2,2,1,1,1,1,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,2,2,1,1,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[5,2,1,1,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[4,4,4,3,1,1] => [9,6,1,1] => [6,1,1] => [1,1] => 1
[4,4,4,2,1,1,1] => [11,4,1,1] => [4,1,1] => [1,1] => 1
[4,4,4,1,1,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 64
[4,4,3,3,3] => [7,7,2,1] => [7,2,1] => [2,1] => 8
[4,4,3,3,2,1] => [7,7,3] => [7,3] => [3] => 1
[4,4,3,3,1,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 42875
[4,4,3,2,1,1,1,1] => [7,7,1,1,1] => [7,1,1,1] => [1,1,1] => 1
[4,4,3,1,1,1,1,1,1] => [7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 216
[4,4,2,2,2,1,1,1] => [13,2,1,1] => [2,1,1] => [1,1] => 1
[4,4,2,2,1,1,1,1,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,4,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,4,1,1,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[4,3,3,3,3,1] => [5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 42875
[4,3,3,3,2,2] => [9,5,2,1] => [5,2,1] => [2,1] => 8
[4,3,3,3,2,1,1] => [5,5,3,3,1] => [5,3,3,1] => [3,3,1] => 9261
[4,3,3,3,1,1,1,1] => [5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1157625
[4,3,3,2,2,2,1] => [9,5,3] => [5,3] => [3] => 1
[4,3,3,2,2,1,1,1] => [7,5,3,1,1] => [5,3,1,1] => [3,1,1] => 216
[4,3,3,2,1,1,1,1,1] => [5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 3375
[4,3,3,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 512
[4,3,2,2,2,1,1,1,1] => [9,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[4,3,2,2,1,1,1,1,1,1] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,2,1,1,1,1,1,1,1,1] => [5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[4,3,1,1,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[4,2,2,2,2,2,1,1,1] => [14,1,1,1] => [1,1,1] => [1,1] => 1
[4,2,2,2,2,1,1,1,1,1] => [12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,2,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[3,3,3,3,3,2] => [5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 4741632
[3,3,3,3,3,1,1] => [3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 970299000
[3,3,3,3,2,2,1] => [5,3,3,3,3] => [3,3,3,3] => [3,3,3] => 74088
[3,3,3,3,2,1,1,1] => [3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => 287496000
[3,3,3,3,1,1,1,1,1] => [3,3,3,2,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 12326391
[3,3,3,2,2,2,2] => [11,3,2,1] => [3,2,1] => [2,1] => 8
[3,3,3,2,2,2,1,1] => [7,3,3,3,1] => [3,3,3,1] => [3,3,1] => 9261
[3,3,3,2,2,1,1,1,1] => [5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 1728000
[3,3,3,2,1,1,1,1,1,1] => [3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 57066625
[3,3,3,1,1,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1000
[3,3,2,2,2,2,2,1] => [11,3,3] => [3,3] => [3] => 1
[3,3,2,2,2,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => [3,1,1] => 216
[3,3,2,2,2,1,1,1,1,1] => [7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 3375
[3,3,2,2,1,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 21952
[3,3,2,1,1,1,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 91125
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[3,2,2,2,2,2,1,1,1,1] => [11,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,2,2,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,2,2,1,1,1,1,1,1,1,1] => [7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,1,1,1,1,1] => [13,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1,1,1,1] => 1
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Description
The cube of the number of standard Young tableaux with shape given by the partition.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
2-conjugate
Description
Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
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