Identifier
-
Mp00321:
Integer partitions
—2-conjugate⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000284: 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] => 4
[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] => 4
[7,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 9
[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] => 4
[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] => 25
[8,1] => [3,2,2,2] => [2,2,2] => [2,2] => 4
[7,2] => [4,2,2,1] => [2,2,1] => [2,1] => 4
[7,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 16
[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] => 9
[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] => 4
[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] => 25
[9,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[8,2] => [4,2,2,2] => [2,2,2] => [2,2] => 4
[8,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 9
[7,3] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[7,2,1] => [3,3,2,2] => [3,2,2] => [2,2] => 4
[7,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 25
[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] => 4
[5,4,1] => [4,3,3] => [3,3] => [3] => 1
[5,3,2] => [5,2,2,1] => [2,2,1] => [2,1] => 4
[5,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 16
[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] => 9
[3,3,2,1,1] => [3,3,3,1] => [3,3,1] => [3,1] => 9
[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] => 196
[10,1] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 25
[9,2] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[9,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 196
[8,3] => [4,3,2,2] => [3,2,2] => [2,2] => 4
[8,2,1] => [5,2,2,2] => [2,2,2] => [2,2] => 4
[8,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 16
[7,4] => [4,4,2,1] => [4,2,1] => [2,1] => 4
[7,3,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[7,2,2] => [6,2,2,1] => [2,2,1] => [2,1] => 4
[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] => 36
[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] => 9
[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] => 9
[5,4,1,1] => [4,3,3,1] => [3,3,1] => [3,1] => 9
[5,3,3] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 25
[5,3,2,1] => [3,3,3,2] => [3,3,2] => [3,2] => 25
[5,3,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 25
[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] => 4
[3,3,3,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 16
[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] => 36
[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] => 196
[11,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 784
[10,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 25
[10,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[9,3] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 196
[9,2,1] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 25
[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] => 400
[8,4] => [4,4,2,2] => [4,2,2] => [2,2] => 4
[8,3,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 9
[8,2,2] => [6,2,2,2] => [2,2,2] => [2,2] => 4
[8,2,1,1] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 9
[8,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 25
[7,5] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 25
[7,4,1] => [4,3,3,2] => [3,3,2] => [3,2] => 25
[7,3,2] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[7,3,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 196
[7,2,2,1] => [5,3,2,2] => [3,2,2] => [2,2] => 4
[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] => 49
[6,6] => [4,4,4] => [4,4] => [4] => 1
[6,5,1] => [4,4,3,1] => [4,3,1] => [3,1] => 9
[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] => 4
[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] => 16
[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] => 4
[5,5,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 16
[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] => 81
[5,3,2,2] => [7,2,2,1] => [2,2,1] => [2,1] => 4
[5,3,2,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 36
[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] => 36
[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] => 9
[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] => 256
[3,3,3,2,1] => [3,3,3,3] => [3,3,3] => [3,3] => 25
[3,3,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 25
[3,3,2,2,1,1] => [5,3,3,1] => [3,3,1] => [3,1] => 9
[3,3,2,1,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 100
[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] => 1764
[12,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 196
[11,2] => [4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 196
[11,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 2304
[10,3] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 25
[10,2,1] => [5,2,2,2,2] => [2,2,2,2] => [2,2,2] => 25
[10,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 196
[9,4] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 25
[9,3,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 784
[9,2,2] => [6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[9,2,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 16
[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] => 729
[8,5] => [4,4,3,2] => [4,3,2] => [3,2] => 25
[8,4,1] => [5,4,2,2] => [4,2,2] => [2,2] => 4
[8,3,2] => [6,3,2,2] => [3,2,2] => [2,2] => 4
[8,3,1,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[8,2,2,1] => [7,2,2,2] => [2,2,2] => [2,2] => 4
[8,2,1,1,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 16
[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] => 36
[7,6] => [4,4,4,1] => [4,4,1] => [4,1] => 16
[7,5,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 81
[7,4,2] => [6,4,2,1] => [4,2,1] => [2,1] => 4
[7,4,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 36
[7,3,3] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 196
[7,3,2,1] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 441
[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] => 400
[7,2,2,2] => [8,2,2,1] => [2,2,1] => [2,1] => 4
[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] => 64
[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] => 9
[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] => 9
[6,3,3,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 9
[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] => 25
[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] => 256
[5,5,2,1] => [4,3,3,3] => [3,3,3] => [3,3] => 25
[5,5,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 25
[5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 9
[5,4,2,1,1] => [6,3,3,1] => [3,3,1] => [3,1] => 9
[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] => 25
[5,3,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 196
[5,3,2,2,1] => [5,3,3,2] => [3,3,2] => [3,2] => 25
[5,3,2,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 100
[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] => 49
[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] => 4
[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] => 16
[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] => 1225
[3,3,3,2,2] => [7,3,2,1] => [3,2,1] => [2,1] => 4
[3,3,3,2,1,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 441
[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] => 36
[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] => 36
[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] => 225
[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] => 1764
[13,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 8100
[12,2] => [4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 196
[12,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 784
[11,3] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1764
[11,2,1] => [3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 196
[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] => 5625
[10,4] => [4,4,2,2,2] => [4,2,2,2] => [2,2,2] => 25
[10,3,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 81
[10,2,2] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 25
[10,2,1,1] => [6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[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] => 400
[9,5] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 196
[9,4,1] => [4,3,3,2,2] => [3,3,2,2] => [3,2,2] => 441
[9,3,2] => [5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 196
[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] => 2304
[9,2,2,1] => [5,3,2,2,2] => [3,2,2,2] => [2,2,2] => 25
[9,2,1,1,1] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 25
[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] => 1225
[8,6] => [4,4,4,2] => [4,4,2] => [4,2] => 81
[8,5,1] => [4,4,4,1,1] => [4,4,1,1] => [4,1,1] => 100
[8,4,2] => [6,4,2,2] => [4,2,2] => [2,2] => 4
[8,4,1,1] => [6,4,2,1,1] => [4,2,1,1] => [2,1,1] => 9
[8,3,3] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 25
[8,3,2,1] => [5,5,2,2] => [5,2,2] => [2,2] => 4
[8,3,1,1,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 196
[8,2,2,2] => [8,2,2,2] => [2,2,2] => [2,2] => 4
[8,2,2,1,1] => [8,2,2,1,1] => [2,2,1,1] => [2,1,1] => 9
[8,2,1,1,1,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 25
[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] => 49
[7,7] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 256
[7,6,1] => [4,4,3,3] => [4,3,3] => [3,3] => 25
[7,5,2] => [6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 25
[7,5,1,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 196
[7,4,3] => [5,4,3,2] => [4,3,2] => [3,2] => 25
[7,4,2,1] => [6,3,3,2] => [3,3,2] => [3,2] => 25
[7,4,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 16
[7,3,3,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 784
[7,3,2,2] => [7,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[7,3,2,1,1] => [4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 100
[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] => 729
[7,2,2,2,1] => [7,3,2,2] => [3,2,2] => [2,2] => 4
[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] => 81
[6,6,2] => [6,4,4] => [4,4] => [4] => 1
[6,6,1,1] => [6,4,3,1] => [4,3,1] => [3,1] => 9
[6,5,3] => [5,4,4,1] => [4,4,1] => [4,1] => 16
[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] => 16
[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] => 16
[6,3,3,2] => [7,4,2,1] => [4,2,1] => [2,1] => 4
[6,3,3,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 81
[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] => 36
[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] => 4
[5,5,3,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1225
[5,5,2,2] => [8,3,2,1] => [3,2,1] => [2,1] => 4
[5,5,2,1,1] => [4,3,3,3,1] => [3,3,3,1] => [3,3,1] => 441
[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] => 36
[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] => 36
[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] => 4900
[5,3,3,2,1] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 1764
[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] => 400
[5,3,2,2,2] => [9,2,2,1] => [2,2,1] => [2,1] => 4
[5,3,2,2,1,1] => [6,3,3,1,1] => [3,3,1,1] => [3,1,1] => 36
[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] => 225
[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] => 64
[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] => 9
[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] => 9
[4,3,3,2,1,1] => [5,5,3,1] => [5,3,1] => [3,1] => 9
[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] => 25
[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] => 256
[3,3,3,3,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 4096
[3,3,3,2,2,1] => [5,3,3,3] => [3,3,3] => [3,3] => 25
[3,3,3,2,1,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3136
[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] => 49
[3,3,2,2,2,1,1] => [7,3,3,1] => [3,3,1] => [3,1] => 9
[3,3,2,2,1,1,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 100
[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] => 441
[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] => 17424
[14,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1764
[13,2] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1764
[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] => 27225
[12,3] => [4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 196
[12,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 196
[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] => 2304
[11,4] => [4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 196
[11,3,1] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 8100
[11,2,2] => [6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 196
[11,2,1,1] => [4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 196
[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] => 12100
[10,5] => [4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 441
[10,4,1] => [5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 25
[10,3,2] => [6,3,2,2,2] => [3,2,2,2] => [2,2,2] => 25
[10,3,1,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 784
[10,2,2,1] => [7,2,2,2,2] => [2,2,2,2] => [2,2,2] => 25
[10,2,1,1,1] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 196
[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] => 729
[9,6] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 1225
[9,5,1] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 784
[9,4,2] => [6,4,2,2,1] => [4,2,2,1] => [2,2,1] => 25
[9,4,1,1] => [4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 400
[9,3,3] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1764
[9,3,2,1] => [3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 7056
[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] => 5625
[9,2,2,2] => [8,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[9,2,2,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 16
[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] => 36
[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] => 1936
[8,7] => [4,4,4,3] => [4,4,3] => [4,3] => 196
[8,6,1] => [5,4,4,2] => [4,4,2] => [4,2] => 81
[8,5,2] => [6,4,3,2] => [4,3,2] => [3,2] => 25
[8,5,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 81
[8,4,3] => [6,5,2,2] => [5,2,2] => [2,2] => 4
[8,4,2,1] => [7,4,2,2] => [4,2,2] => [2,2] => 4
[8,4,1,1,1] => [7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[8,3,3,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 81
[8,3,2,2] => [8,3,2,2] => [3,2,2] => [2,2] => 4
[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] => 400
[8,2,2,2,1] => [9,2,2,2] => [2,2,2] => [2,2] => 4
[8,2,2,1,1,1] => [8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 16
[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] => 36
[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] => 64
[7,7,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 1225
[7,6,2] => [6,4,4,1] => [4,4,1] => [4,1] => 16
[7,6,1,1] => [4,4,3,3,1] => [4,3,3,1] => [3,3,1] => 441
[7,5,3] => [4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4900
[7,5,2,1] => [4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 1764
[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] => 400
[7,4,4] => [6,6,2,1] => [6,2,1] => [2,1] => 4
[7,4,3,1] => [5,4,4,1,1] => [4,4,1,1] => [4,1,1] => 100
[7,4,2,2] => [8,4,2,1] => [4,2,1] => [2,1] => 4
[7,4,2,1,1] => [6,4,3,1,1] => [4,3,1,1] => [3,1,1] => 36
[7,4,1,1,1,1] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 25
[7,3,3,2] => [5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 196
[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] => 2304
[7,3,2,2,1] => [5,3,3,2,2] => [3,3,2,2] => [3,2,2] => 441
[7,3,2,1,1,1] => [4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 225
[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] => 1225
[7,2,2,2,2] => [10,2,2,1] => [2,2,1] => [2,1] => 4
[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] => 100
[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] => 9
[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] => 9
[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] => 9
[6,5,1,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 25
[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] => 9
[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] => 9
[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] => 25
[6,3,3,3] => [5,5,2,2,1] => [5,2,2,1] => [2,2,1] => 25
[6,3,3,2,1] => [5,5,3,2] => [5,3,2] => [3,2] => 25
[6,3,3,1,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 196
[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] => 49
[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] => 256
[5,5,4,1] => [5,4,3,3] => [4,3,3] => [3,3] => 25
[5,5,3,2] => [6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 256
[5,5,3,1,1] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 4096
[5,5,2,2,1] => [6,3,3,3] => [3,3,3] => [3,3] => 25
[5,5,2,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 100
[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] => 49
[5,4,4,1,1] => [7,4,3,1] => [4,3,1] => [3,1] => 9
[5,4,3,3] => [5,5,4,1] => [5,4,1] => [4,1] => 16
[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] => 16
[5,4,2,2,1,1] => [8,3,3,1] => [3,3,1] => [3,1] => 9
[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] => 26244
[5,3,3,2,2] => [7,3,2,2,1] => [3,2,2,1] => [2,2,1] => 25
[5,3,3,2,1,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3136
[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] => 729
[5,3,2,2,2,1] => [7,3,3,2] => [3,3,2] => [3,2] => 25
[5,3,2,2,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 100
[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] => 441
[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] => 81
[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] => 16
[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] => 4
[4,3,3,3,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1225
[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] => 36
[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] => 36
[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] => 28224
[3,3,3,3,2,1] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 1764
[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] => 11025
[3,3,3,2,2,2] => [9,3,2,1] => [3,2,1] => [2,1] => 4
[3,3,3,2,2,1,1] => [5,3,3,3,1] => [3,3,3,1] => [3,3,1] => 441
[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] => 14400
[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] => 64
[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] => 36
[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] => 225
[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] => 784
[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] => 17424
[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] => 88209
[14,2] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1764
[14,1,1] => [4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 8100
[13,3] => [3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 17424
[13,2,1] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1764
[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] => 75625
[12,4] => [4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 196
[12,3,1] => [4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 784
[12,2,2] => [6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 196
[12,2,1,1] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 784
[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] => 5625
[11,5] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1764
[11,4,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 7056
[11,3,2] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1764
[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] => 27225
[11,2,2,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 196
[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] => 400
[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] => 23716
[10,6] => [4,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3136
[10,5,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 8100
[10,4,2] => [6,4,2,2,2] => [4,2,2,2] => [2,2,2] => 25
[10,4,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 81
[10,3,3] => [5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 196
[10,3,2,1] => [5,5,2,2,2] => [5,2,2,2] => [2,2,2] => 25
[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] => 2304
[10,2,2,2] => [8,2,2,2,2] => [2,2,2,2] => [2,2,2] => 25
[10,2,2,1,1] => [8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[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] => 400
[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] => 1225
[9,7] => [4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4900
[9,6,1] => [4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 1764
[9,5,2] => [6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 196
[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] => 2304
[9,4,3] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 441
[9,4,2,1] => [6,3,3,2,2] => [3,3,2,2] => [3,2,2] => 441
[9,4,1,1,1] => [5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 196
[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] => 8100
[9,3,2,2] => [7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 196
[9,3,2,1,1] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 1225
[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] => 12100
[9,2,2,2,1] => [7,3,2,2,2] => [3,2,2,2] => [2,2,2] => 25
[9,2,2,1,1,1] => [6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 25
[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] => 49
[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] => 2916
[8,8] => [4,4,4,4] => [4,4,4] => [4,4] => 196
[8,7,1] => [4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 4900
[8,6,2] => [6,4,4,2] => [4,4,2] => [4,2] => 81
[8,6,1,1] => [6,4,4,1,1] => [4,4,1,1] => [4,1,1] => 100
[8,5,3] => [5,4,4,2,1] => [4,4,2,1] => [4,2,1] => 1225
[8,5,2,1] => [5,5,4,2] => [5,4,2] => [4,2] => 81
[8,5,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 196
[8,4,4] => [6,6,2,2] => [6,2,2] => [2,2] => 4
[8,4,3,1] => [6,6,2,1,1] => [6,2,1,1] => [2,1,1] => 9
[8,4,2,2] => [8,4,2,2] => [4,2,2] => [2,2] => 4
[8,4,2,1,1] => [8,4,2,1,1] => [4,2,1,1] => [2,1,1] => 9
[8,4,1,1,1,1] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 196
[8,3,3,2] => [7,4,2,2,1] => [4,2,2,1] => [2,2,1] => 25
[8,3,3,1,1] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 784
[8,3,2,2,1] => [7,5,2,2] => [5,2,2] => [2,2] => 4
[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] => 729
[8,2,2,2,2] => [10,2,2,2] => [2,2,2] => [2,2] => 4
[8,2,2,2,1,1] => [10,2,2,1,1] => [2,2,1,1] => [2,1,1] => 9
[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] => 25
[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] => 49
[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] => 81
[7,7,2] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 256
[7,7,1,1] => [4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 4096
[7,6,3] => [5,4,4,3] => [4,4,3] => [4,3] => 196
[7,6,2,1] => [6,4,3,3] => [4,3,3] => [3,3] => 25
[7,6,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 16
[7,5,4] => [6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 25
[7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 26244
[7,5,2,2] => [8,3,2,2,1] => [3,2,2,1] => [2,2,1] => 25
[7,5,2,1,1] => [4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3136
[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] => 729
[7,4,4,1] => [6,5,3,2] => [5,3,2] => [3,2] => 25
[7,4,3,2] => [7,4,3,2] => [4,3,2] => [3,2] => 25
[7,4,3,1,1] => [5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 400
[7,4,2,2,1] => [8,3,3,2] => [3,3,2] => [3,2] => 25
[7,4,2,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 16
[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] => 36
[7,3,3,3] => [3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 82944
[7,3,3,2,1] => [3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 63504
[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] => 5625
[7,3,2,2,2] => [9,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[7,3,2,2,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 100
[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] => 441
[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] => 1936
[7,2,2,2,2,1] => [9,3,2,2] => [3,2,2] => [2,2] => 4
[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] => 121
[6,6,4] => [6,6,4] => [6,4] => [4] => 1
[6,6,3,1] => [6,6,3,1] => [6,3,1] => [3,1] => 9
[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] => 9
[6,6,1,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 16
[6,5,5] => [6,5,4,1] => [5,4,1] => [4,1] => 16
[6,5,4,1] => [6,5,5] => [5,5] => [5] => 1
[6,5,3,2] => [7,4,4,1] => [4,4,1] => [4,1] => 16
[6,5,3,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1225
[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] => 36
[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] => 4
[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] => 81
[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] => 16
[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] => 36
[6,3,3,3,1] => [5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 81
[6,3,3,2,2] => [9,4,2,1] => [4,2,1] => [2,1] => 4
[6,3,3,2,1,1] => [6,5,3,1,1] => [5,3,1,1] => [3,1,1] => 36
[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] => 400
[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] => 64
[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] => 1225
[5,5,4,2] => [8,5,2,1] => [5,2,1] => [2,1] => 4
[5,5,4,1,1] => [5,4,3,3,1] => [4,3,3,1] => [3,3,1] => 441
[5,5,3,3] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 28224
[5,5,3,2,1] => [4,3,3,3,3] => [3,3,3,3] => [3,3,3] => 1764
[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] => 11025
[5,5,2,2,2] => [10,3,2,1] => [3,2,1] => [2,1] => 4
[5,5,2,2,1,1] => [6,3,3,3,1] => [3,3,3,1] => [3,3,1] => 441
[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] => 225
[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] => 64
[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] => 36
[5,4,3,3,1] => [5,5,4,1,1] => [5,4,1,1] => [4,1,1] => 100
[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] => 25
[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] => 25
[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] => 4900
[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] => 99225
[5,3,3,2,2,1] => [5,3,3,3,2] => [3,3,3,2] => [3,3,2] => 1764
[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] => 14400
[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] => 1225
[5,3,2,2,2,2] => [11,2,2,1] => [2,2,1] => [2,1] => 4
[5,3,2,2,2,1,1] => [8,3,3,1,1] => [3,3,1,1] => [3,1,1] => 36
[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] => 225
[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] => 784
[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] => 100
[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] => 9
[4,4,3,3,1,1] => [7,5,2,1,1] => [5,2,1,1] => [2,1,1] => 9
[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] => 25
[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] => 256
[4,3,3,3,2,1] => [5,5,3,3] => [5,3,3] => [3,3] => 25
[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] => 4096
[4,3,3,2,2,1,1] => [7,5,3,1] => [5,3,1] => [3,1] => 9
[4,3,3,2,1,1,1,1] => [5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 100
[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] => 49
[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] => 202500
[3,3,3,3,2,2] => [7,3,3,2,1] => [3,3,2,1] => [3,2,1] => 256
[3,3,3,3,2,1,1] => [3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 44100
[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] => 25600
[3,3,3,2,2,2,1] => [7,3,3,3] => [3,3,3] => [3,3] => 25
[3,3,3,2,2,1,1,1] => [5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3136
[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] => 50625
[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] => 81
[3,3,2,2,2,2,1,1] => [9,3,3,1] => [3,3,1] => [3,1] => 9
[3,3,2,2,2,1,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 100
[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] => 441
[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] => 1296
[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] => 17424
[15,2] => [4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 17424
[14,3] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1764
[14,2,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1764
[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] => 27225
[13,4] => [4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 1764
[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] => 88209
[13,2,2] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1764
[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] => 2304
[12,5] => [4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 7056
[12,4,1] => [5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 196
[12,3,2] => [6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 196
[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] => 8100
[12,2,2,1] => [7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 196
[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] => 2304
[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] => 12100
[11,6] => [4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 46656
[11,5,1] => [4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 8100
[11,4,2] => [6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 196
[11,4,1,1] => [4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 35721
[11,3,3] => [3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 17424
[11,3,2,1] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 108900
[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] => 75625
[11,2,2,2] => [8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 196
[11,2,2,1,1] => [6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 196
[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] => 729
[10,7] => [4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 28224
[10,6,1] => [5,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3136
[10,5,2] => [6,4,3,2,2] => [4,3,2,2] => [3,2,2] => 441
[10,5,1,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 784
[10,4,3] => [6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 25
[10,4,2,1] => [7,4,2,2,2] => [4,2,2,2] => [2,2,2] => 25
[10,4,1,1,1] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 784
[10,3,3,1] => [5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 784
[10,3,2,2] => [8,3,2,2,2] => [3,2,2,2] => [2,2,2] => 25
[10,3,2,1,1] => [6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 16
[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] => 5625
[10,2,2,2,1] => [9,2,2,2,2] => [2,2,2,2] => [2,2,2] => 25
[10,2,2,1,1,1] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 196
[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] => 729
[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] => 1936
[9,8] => [4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 7056
[9,7,1] => [4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 26244
[9,6,2] => [6,4,4,2,1] => [4,4,2,1] => [4,2,1] => 1225
[9,6,1,1] => [4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 46656
[9,5,3] => [4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 82944
[9,5,2,1] => [4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 63504
[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] => 5625
[9,4,4] => [6,6,2,2,1] => [6,2,2,1] => [2,2,1] => 25
[9,4,3,1] => [5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 8100
[9,4,2,2] => [8,4,2,2,1] => [4,2,2,1] => [2,2,1] => 25
[9,4,2,1,1] => [6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 400
[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] => 400
[9,3,3,2] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1764
[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] => 27225
[9,3,2,2,1] => [5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 7056
[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] => 3136
[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] => 23716
[9,2,2,2,2] => [10,2,2,2,1] => [2,2,2,1] => [2,2,1] => 25
[9,2,2,2,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 16
[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] => 36
[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] => 64
[8,8,1] => [5,4,4,4] => [4,4,4] => [4,4] => 196
[8,7,2] => [6,4,4,3] => [4,4,3] => [4,3] => 196
[8,7,1,1] => [6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 1225
[8,6,3] => [6,5,4,2] => [5,4,2] => [4,2] => 81
[8,6,2,1] => [7,4,4,2] => [4,4,2] => [4,2] => 81
[8,6,1,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 81
[8,5,4] => [6,6,3,2] => [6,3,2] => [3,2] => 25
[8,5,3,1] => [6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 81
[8,5,2,2] => [8,4,3,2] => [4,3,2] => [3,2] => 25
[8,5,2,1,1] => [6,6,3,1,1] => [6,3,1,1] => [3,1,1] => 36
[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] => 400
[8,4,4,1] => [7,6,2,2] => [6,2,2] => [2,2] => 4
[8,4,3,2] => [8,5,2,2] => [5,2,2] => [2,2] => 4
[8,4,3,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 81
[8,4,2,2,1] => [9,4,2,2] => [4,2,2] => [2,2] => 4
[8,4,2,1,1,1] => [9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 81
[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] => 400
[8,3,3,3] => [5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 196
[8,3,3,2,1] => [5,5,3,2,2] => [5,3,2,2] => [3,2,2] => 441
[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] => 2304
[8,3,2,2,2] => [10,3,2,2] => [3,2,2] => [2,2] => 4
[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] => 1225
[8,2,2,2,2,1] => [11,2,2,2] => [2,2,2] => [2,2] => 4
[8,2,2,2,1,1,1] => [10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 16
[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] => 36
[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] => 64
[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] => 100
[7,7,3] => [4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 28224
[7,7,2,1] => [4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 1764
[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] => 11025
[7,6,4] => [6,6,4,1] => [6,4,1] => [4,1] => 16
[7,6,3,1] => [5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 4900
[7,6,2,2] => [8,4,4,1] => [4,4,1] => [4,1] => 16
[7,6,2,1,1] => [6,4,3,3,1] => [4,3,3,1] => [3,3,1] => 441
[7,6,1,1,1,1] => [6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 25
[7,5,5] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4900
[7,5,4,1] => [5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 1764
[7,5,3,2] => [6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4900
[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] => 99225
[7,5,2,2,1] => [6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 1764
[7,5,2,1,1,1] => [5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 1225
[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] => 1225
[7,4,4,2] => [8,6,2,1] => [6,2,1] => [2,1] => 4
[7,4,4,1,1] => [7,4,4,1,1] => [4,4,1,1] => [4,1,1] => 100
[7,4,3,3] => [5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 1225
[7,4,3,2,1] => [5,5,5,2] => [5,5,2] => [5,2] => 196
[7,4,3,1,1,1] => [5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 196
[7,4,2,2,2] => [10,4,2,1] => [4,2,1] => [2,1] => 4
[7,4,2,2,1,1] => [8,4,3,1,1] => [4,3,1,1] => [3,1,1] => 36
[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] => 25
[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] => 49
[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] => 480249
[7,3,3,2,2] => [7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 196
[7,3,3,2,1,1] => [4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 14400
[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] => 12100
[7,3,2,2,2,1] => [7,3,3,2,2] => [3,3,2,2] => [3,2,2] => 441
[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] => 225
[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] => 784
[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] => 2916
[7,2,2,2,2,2] => [12,2,2,1] => [2,2,1] => [2,1] => 4
[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] => 9
[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] => 9
[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] => 25
[6,5,5,1] => [6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 100
[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] => 25
[6,5,3,3] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 256
[6,5,3,2,1] => [6,5,3,3] => [5,3,3] => [3,3] => 25
[6,5,3,1,1,1] => [6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 4096
[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] => 9
[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] => 49
[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] => 9
[6,4,3,3,1] => [7,6,2,1,1] => [6,2,1,1] => [2,1,1] => 9
[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] => 196
[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] => 9
[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] => 25
[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] => 49
[6,3,3,3,2] => [7,5,2,2,1] => [5,2,2,1] => [2,2,1] => 25
[6,3,3,3,1,1] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 26244
[6,3,3,2,2,1] => [7,5,3,2] => [5,3,2] => [3,2] => 25
[6,3,3,2,1,1,1] => [6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 100
[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] => 729
[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] => 81
[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] => 256
[5,5,5,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 4096
[5,5,4,3] => [5,5,4,3] => [5,4,3] => [4,3] => 196
[5,5,4,2,1] => [7,4,3,3] => [4,3,3] => [3,3] => 25
[5,5,4,1,1,1] => [5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3136
[5,5,3,3,1] => [4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 202500
[5,5,3,2,2] => [8,3,3,2,1] => [3,3,2,1] => [3,2,1] => 256
[5,5,3,2,1,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 44100
[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] => 25600
[5,5,2,2,2,1] => [8,3,3,3] => [3,3,3] => [3,3] => 25
[5,5,2,2,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 100
[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] => 441
[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] => 81
[5,4,4,3,1] => [7,6,3,1] => [6,3,1] => [3,1] => 9
[5,4,4,2,1,1] => [9,4,3,1] => [4,3,1] => [3,1] => 9
[5,4,4,1,1,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 16
[5,4,3,3,2] => [7,5,4,1] => [5,4,1] => [4,1] => 16
[5,4,3,3,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 400
[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] => 225
[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] => 36
[5,4,2,2,2,1,1] => [10,3,3,1] => [3,3,1] => [3,1] => 9
[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] => 980100
[5,3,3,3,2,1] => [3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 213444
[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] => 302500
[5,3,3,2,2,2] => [9,3,2,2,1] => [3,2,2,1] => [2,2,1] => 25
[5,3,3,2,2,1,1] => [6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3136
[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] => 50625
[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] => 1936
[5,3,2,2,2,2,1] => [9,3,3,2] => [3,3,2] => [3,2] => 25
[5,3,2,2,2,1,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 100
[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] => 441
[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] => 1296
[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] => 121
[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] => 16
[4,4,3,3,3] => [7,7,2,1] => [7,2,1] => [2,1] => 4
[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] => 1225
[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] => 36
[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] => 1225
[4,3,3,3,2,2] => [9,5,2,1] => [5,2,1] => [2,1] => 4
[4,3,3,3,2,1,1] => [5,5,3,3,1] => [5,3,3,1] => [3,3,1] => 441
[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] => 11025
[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] => 36
[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] => 225
[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] => 64
[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] => 28224
[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] => 980100
[3,3,3,3,2,2,1] => [5,3,3,3,3] => [3,3,3,3] => [3,3,3] => 1764
[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] => 435600
[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] => 53361
[3,3,3,2,2,2,2] => [11,3,2,1] => [3,2,1] => [2,1] => 4
[3,3,3,2,2,2,1,1] => [7,3,3,3,1] => [3,3,3,1] => [3,3,1] => 441
[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] => 14400
[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] => 148225
[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] => 100
[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] => 36
[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] => 225
[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] => 784
[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] => 2025
[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 Plancherel distribution on integer partitions.
This is defined as the distribution induced by the RSK shape of the uniform distribution on permutations. In other words, this is the size of the preimage of the map 'Robinson-Schensted tableau shape' from permutations to integer partitions.
Equivalently, this is given by the square of the number of standard Young tableaux of the given shape.
This is defined as the distribution induced by the RSK shape of the uniform distribution on permutations. In other words, this is the size of the preimage of the map 'Robinson-Schensted tableau shape' from permutations to integer partitions.
Equivalently, this is given by the square of the number of standard Young tableaux of the given shape.
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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