Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001099: Integer partitions ⟶ ℤ
Values
[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
[1,1,1,1,1,1] => [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] => [1,1] => 1
[2,2,1,1,1] => [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] => 3
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[4,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[3,2,1,1,1] => [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] => 3
[2,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[2,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[4,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[3,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[3,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[3,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[2,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[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] => 105
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[6,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[5,2,1,1,1] => [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] => 3
[4,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[4,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[4,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[3,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[3,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[3,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[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] => 105
[2,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[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] => 945
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 10395
[7,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[6,2,1,1,1] => [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] => 3
[5,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[5,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[5,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[4,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[4,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[4,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[4,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[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] => 105
[3,3,3,2] => [3,3,2] => [3,2] => [2] => 0
[3,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[3,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 2
[3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[3,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[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] => 945
[2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => 10395
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 135135
[8,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[7,2,1,1,1] => [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] => 3
[6,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[6,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[6,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[5,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[5,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[5,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[5,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[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] => 105
[4,4,2,2] => [4,2,2] => [2,2] => [2] => 0
[4,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[4,3,3,2] => [3,3,2] => [3,2] => [2] => 0
>>> Load all 1090 entries. <<<[4,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[4,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 2
[4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[4,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[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] => 945
[3,3,3,3] => [3,3,3] => [3,3] => [3] => 0
[3,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 2
[3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[3,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 10
[3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => 10395
[2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[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] => 135135
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 2027025
[9,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[8,2,1,1,1] => [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] => 3
[7,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[7,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[7,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[6,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[6,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[6,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[6,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[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] => 105
[5,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[5,4,2,2] => [4,2,2] => [2,2] => [2] => 0
[5,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[5,3,3,2] => [3,3,2] => [3,2] => [2] => 0
[5,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[5,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 2
[5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[5,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[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] => 945
[4,4,3,2] => [4,3,2] => [3,2] => [2] => 0
[4,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[4,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 2
[4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[4,3,3,3] => [3,3,3] => [3,3] => [3] => 0
[4,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 2
[4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[4,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 10
[4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => 10395
[3,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 6
[3,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 10
[3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[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] => 135135
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[10,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[9,2,1,1,1] => [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] => 3
[8,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[8,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[8,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[7,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[7,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[7,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[7,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[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] => 105
[6,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[6,4,2,2] => [4,2,2] => [2,2] => [2] => 0
[6,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[6,3,3,2] => [3,3,2] => [3,2] => [2] => 0
[6,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[6,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 2
[6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[6,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[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] => 945
[5,5,2,2] => [5,2,2] => [2,2] => [2] => 0
[5,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[5,4,3,2] => [4,3,2] => [3,2] => [2] => 0
[5,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[5,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 2
[5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[5,3,3,3] => [3,3,3] => [3,3] => [3] => 0
[5,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 2
[5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[5,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 10
[5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => 10395
[4,4,4,2] => [4,4,2] => [4,2] => [2] => 0
[4,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[4,4,3,3] => [4,3,3] => [3,3] => [3] => 0
[4,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[4,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 10
[4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 6
[4,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 10
[4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[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] => 135135
[3,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 54
[3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 105
[3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => 2027025
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 106680
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 115290
[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] => [2,1,1,1,1,1,1] => 124740
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 654729075
[11,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[10,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[9,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[9,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[9,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[8,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[8,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[8,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[8,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[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] => 105
[7,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[7,4,2,2] => [4,2,2] => [2,2] => [2] => 0
[7,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[7,3,3,2] => [3,3,2] => [3,2] => [2] => 0
[7,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[7,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 2
[7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[7,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[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] => 945
[6,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[6,5,2,2] => [5,2,2] => [2,2] => [2] => 0
[6,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[6,4,3,2] => [4,3,2] => [3,2] => [2] => 0
[6,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[6,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 2
[6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[6,3,3,3] => [3,3,3] => [3,3] => [3] => 0
[6,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 2
[6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[6,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 10
[6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => 10395
[5,5,3,2] => [5,3,2] => [3,2] => [2] => 0
[5,5,3,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[5,5,2,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 2
[5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[5,4,4,2] => [4,4,2] => [4,2] => [2] => 0
[5,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[5,4,3,3] => [4,3,3] => [3,3] => [3] => 0
[5,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[5,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 10
[5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 6
[5,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 10
[5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[4,4,4,3] => [4,4,3] => [4,3] => [3] => 0
[4,4,4,2,1] => [4,4,2,1] => [4,2,1] => [2,1] => 2
[4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 3
[4,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,1] => 6
[4,4,3,2,2] => [4,3,2,2] => [3,2,2] => [2,2] => 10
[4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[4,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 54
[4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[3,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 450
[3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 630
[3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 672
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 750
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 840
[3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 106680
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 115290
[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] => [2,1,1,1,1,1,1] => 124740
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => 34459425
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1545180
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1651860
[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] => [2,2,1,1,1,1,1] => 1767150
[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] => [2,1,1,1,1,1,1,1] => 1891890
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 654729075
[12,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[11,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[10,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[10,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[10,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[9,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[9,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[9,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[9,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[8,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[8,4,2,2] => [4,2,2] => [2,2] => [2] => 0
[8,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[8,3,3,2] => [3,3,2] => [3,2] => [2] => 0
[8,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[8,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 2
[8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[8,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[7,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[7,5,2,2] => [5,2,2] => [2,2] => [2] => 0
[7,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[7,4,3,2] => [4,3,2] => [3,2] => [2] => 0
[7,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[7,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 2
[7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[7,3,3,3] => [3,3,3] => [3,3] => [3] => 0
[7,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 2
[7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[7,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 10
[7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[6,6,2,2] => [6,2,2] => [2,2] => [2] => 0
[6,6,2,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[6,5,3,2] => [5,3,2] => [3,2] => [2] => 0
[6,5,3,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[6,5,2,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 2
[6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[6,4,4,2] => [4,4,2] => [4,2] => [2] => 0
[6,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[6,4,3,3] => [4,3,3] => [3,3] => [3] => 0
[6,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[6,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 10
[6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[6,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 6
[6,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 10
[6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[5,5,4,2] => [5,4,2] => [4,2] => [2] => 0
[5,5,4,1,1] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[5,5,3,3] => [5,3,3] => [3,3] => [3] => 0
[5,5,3,2,1] => [5,3,2,1] => [3,2,1] => [2,1] => 2
[5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[5,5,2,2,2] => [5,2,2,2] => [2,2,2] => [2,2] => 10
[5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,4,4,3] => [4,4,3] => [4,3] => [3] => 0
[5,4,4,2,1] => [4,4,2,1] => [4,2,1] => [2,1] => 2
[5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 3
[5,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,1] => 6
[5,4,3,2,2] => [4,3,2,2] => [3,2,2] => [2,2] => 10
[5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[5,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 54
[5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[4,4,4,4] => [4,4,4] => [4,4] => [4] => 0
[4,4,4,3,1] => [4,4,3,1] => [4,3,1] => [3,1] => 6
[4,4,4,2,2] => [4,4,2,2] => [4,2,2] => [2,2] => 10
[4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 12
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 15
[4,4,3,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 54
[4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[4,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 450
[4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 630
[4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 672
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 750
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 840
[4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 106680
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 115290
[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] => [2,1,1,1,1,1,1] => 124740
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 5670
[3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 6360
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 6930
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 7560
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 7860
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 8610
[3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 106680
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 115290
[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] => [2,1,1,1,1,1,1] => 124740
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1545180
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1651860
[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] => [2,2,1,1,1,1,1] => 1767150
[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] => [2,1,1,1,1,1,1,1] => 1891890
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[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] => 654729075
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 25576320
[2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 27121500
[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] => [2,2,2,1,1,1,1] => 28773360
[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] => [2,2,1,1,1,1,1,1] => 30540510
[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] => [2,1,1,1,1,1,1,1,1] => 32432400
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 654729075
[13,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[12,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[11,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[11,2,2,2] => [2,2,2] => [2,2] => [2] => 0
[11,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[10,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[10,3,2,2] => [3,2,2] => [2,2] => [2] => 0
[10,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[10,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 2
[10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[9,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[9,4,2,2] => [4,2,2] => [2,2] => [2] => 0
[9,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[9,3,3,2] => [3,3,2] => [3,2] => [2] => 0
[9,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[9,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 2
[9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[9,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 10
[9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[8,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[8,5,2,2] => [5,2,2] => [2,2] => [2] => 0
[8,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[8,4,3,2] => [4,3,2] => [3,2] => [2] => 0
[8,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[8,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 2
[8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[8,3,3,3] => [3,3,3] => [3,3] => [3] => 0
[8,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 2
[8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[8,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 10
[8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[7,7,1,1,1] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[7,6,2,2] => [6,2,2] => [2,2] => [2] => 0
[7,6,2,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[7,5,3,2] => [5,3,2] => [3,2] => [2] => 0
[7,5,3,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[7,5,2,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 2
[7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[7,4,4,2] => [4,4,2] => [4,2] => [2] => 0
[7,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[7,4,3,3] => [4,3,3] => [3,3] => [3] => 0
[7,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[7,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 10
[7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[7,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 6
[7,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 10
[7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[6,6,3,2] => [6,3,2] => [3,2] => [2] => 0
[6,6,3,1,1] => [6,3,1,1] => [3,1,1] => [1,1] => 1
[6,6,2,2,1] => [6,2,2,1] => [2,2,1] => [2,1] => 2
[6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 3
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[6,5,4,2] => [5,4,2] => [4,2] => [2] => 0
[6,5,4,1,1] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[6,5,3,3] => [5,3,3] => [3,3] => [3] => 0
[6,5,3,2,1] => [5,3,2,1] => [3,2,1] => [2,1] => 2
[6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 3
[6,5,2,2,2] => [5,2,2,2] => [2,2,2] => [2,2] => 10
[6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 12
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[6,4,4,3] => [4,4,3] => [4,3] => [3] => 0
[6,4,4,2,1] => [4,4,2,1] => [4,2,1] => [2,1] => 2
[6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 3
[6,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,1] => 6
[6,4,3,2,2] => [4,3,2,2] => [3,2,2] => [2,2] => 10
[6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[6,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 54
[6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 105
[6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[5,5,5,2] => [5,5,2] => [5,2] => [2] => 0
[5,5,5,1,1] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[5,5,4,3] => [5,4,3] => [4,3] => [3] => 0
[5,5,4,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 2
[5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 3
[5,5,3,3,1] => [5,3,3,1] => [3,3,1] => [3,1] => 6
[5,5,3,2,2] => [5,3,2,2] => [3,2,2] => [2,2] => 10
[5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 15
[5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 90
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[5,4,4,4] => [4,4,4] => [4,4] => [4] => 0
[5,4,4,3,1] => [4,4,3,1] => [4,3,1] => [3,1] => 6
[5,4,4,2,2] => [4,4,2,2] => [4,2,2] => [2,2] => 10
[5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 12
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 15
[5,4,3,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 54
[5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 750
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 840
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[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] => [1,1,1,1,1,1,1] => 10395
[5,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 450
[5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 630
[5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 672
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 750
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 840
[5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 106680
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 115290
[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] => [2,1,1,1,1,1,1] => 124740
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[4,4,4,4,1] => [4,4,4,1] => [4,4,1] => [4,1] => 24
[4,4,4,3,2] => [4,4,3,2] => [4,3,2] => [3,2] => 54
[4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 60
[4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 78
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 90
[4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 105
[4,4,3,3,3] => [4,3,3,3] => [3,3,3] => [3,3] => 450
[4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 630
[4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 672
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 750
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 840
[4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 945
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 8610
[4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[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] => [1,1,1,1,1,1,1,1] => 135135
[4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 5670
[4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 6360
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 6930
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 7560
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 7860
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 8610
[4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[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] => [1,1,1,1,1,1,1] => 10395
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 106680
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 115290
[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] => [2,1,1,1,1,1,1] => 124740
[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] => [1,1,1,1,1,1,1,1] => 135135
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1545180
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1651860
[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] => [2,2,1,1,1,1,1] => 1767150
[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] => [2,1,1,1,1,1,1,1] => 1891890
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 654729075
[3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 75600
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 81270
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 89460
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 96390
[3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 103950
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 98820
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 106680
[3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 115290
[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] => [2,1,1,1,1,1,1] => 124740
[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] => [1,1,1,1,1,1,1,1] => 135135
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1545180
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1651860
[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] => [2,2,1,1,1,1,1] => 1767150
[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] => [2,1,1,1,1,1,1,1] => 1891890
[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] => [1,1,1,1,1,1,1,1,1] => 2027025
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 25576320
[3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 27121500
[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] => [2,2,2,1,1,1,1] => 28773360
[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] => [2,2,1,1,1,1,1,1] => 30540510
[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] => [2,1,1,1,1,1,1,1,1] => 32432400
[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] => [1,1,1,1,1,1,1,1,1,1] => 34459425
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 654729075
[2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 501401880
[2,2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 528523380
[2,2,2,2,2,2,1,1,1,1,1] => [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] => 557296740
[2,2,2,2,2,1,1,1,1,1,1,1] => [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] => 587837250
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 620269650
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 654729075
[6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[5,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[6,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[6,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 78
[5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 78
[6,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 78
[5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 78
[6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 60
[5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 60
[6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 60
[5,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 60
[6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 60
[6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 12
[5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 12
[6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 12
[6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 3
[6,5,4,3,2] => [5,4,3,2] => [4,3,2] => [3,2] => 54
[5,5,4,3,2] => [5,4,3,2] => [4,3,2] => [3,2] => 54
[6,4,4,3,2] => [4,4,3,2] => [4,3,2] => [3,2] => 54
[5,4,4,3,2] => [4,4,3,2] => [4,3,2] => [3,2] => 54
[6,5,3,3,2] => [5,3,3,2] => [3,3,2] => [3,2] => 54
[5,5,3,3,2] => [5,3,3,2] => [3,3,2] => [3,2] => 54
[6,4,3,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 54
[6,5,4,2,2] => [5,4,2,2] => [4,2,2] => [2,2] => 10
[5,5,4,2,2] => [5,4,2,2] => [4,2,2] => [2,2] => 10
[6,4,4,2,2] => [4,4,2,2] => [4,2,2] => [2,2] => 10
[6,5,3,2,2] => [5,3,2,2] => [3,2,2] => [2,2] => 10
[6,5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 6
[5,5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 6
[6,4,4,3,1] => [4,4,3,1] => [4,3,1] => [3,1] => 6
[6,5,3,3,1] => [5,3,3,1] => [3,3,1] => [3,1] => 6
[6,5,4,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 2
[6,5,4,3] => [5,4,3] => [4,3] => [3] => 0
[7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[7,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[7,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[6,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[5,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[7,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[6,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[4,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[6,6,5,3,3,2,1] => [6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 1228500
[6,5,4,3,3,2,1] => [5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 1228500
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1228500
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1228500
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1228500
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1228500
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1228500
[6,6,5,4,2,2,1] => [6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 1101240
[6,5,5,4,2,2,1] => [5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 1101240
[6,5,4,4,2,2,1] => [5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 1101240
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 89460
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 89460
[7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 7860
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 7860
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 7860
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 7860
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 7860
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 7860
[7,6,5,4,3,1,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 1020600
[6,6,5,4,3,1,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 1020600
[6,5,5,4,3,1,1] => [5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 1020600
[6,6,5,4,2,1,1] => [6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 70560
[6,5,5,4,2,1,1] => [5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 70560
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 70560
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 6930
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 6930
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 6930
[7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 5040
[6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 5040
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 630
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 90
[5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 90
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 90
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 90
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 90
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 15
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 15
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 15
[7,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 960120
[6,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 960120
[7,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 960120
[6,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 960120
[5,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 960120
[7,6,4,4,3,2] => [6,4,4,3,2] => [4,4,3,2] => [4,3,2] => 960120
[6,5,4,4,3,2] => [5,4,4,3,2] => [4,4,3,2] => [4,3,2] => 960120
[6,5,4,3,3,2] => [5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 75600
[5,4,3,3,3,2] => [4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 75600
[4,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 75600
[6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 6360
[4,4,4,3,2,2] => [4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 6360
[7,6,5,2,2,2] => [6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 672
[6,5,4,2,2,2] => [5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 672
[5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 672
[6,6,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 672
[7,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 60480
[6,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 60480
[6,5,5,4,3,1] => [5,5,4,3,1] => [5,4,3,1] => [4,3,1] => 60480
[4,4,4,4,3,1] => [4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 60480
[7,6,5,4,2,1] => [6,5,4,2,1] => [5,4,2,1] => [4,2,1] => 4680
[5,5,5,4,2,1] => [5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 4680
[4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 4680
[7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 570
[6,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 570
[5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 570
[7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[7,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[7,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 570
[7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 78
[7,6,3,2,2,1] => [6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 78
[7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 78
[7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 360
[7,6,5,2,1,1] => [6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 12
[7,6,3,2,1,1] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[7,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 12
[7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 3
[7,6,5,4,3] => [6,5,4,3] => [5,4,3] => [4,3] => 3960
[6,6,5,4,3] => [6,5,4,3] => [5,4,3] => [4,3] => 3960
[6,5,5,4,3] => [5,5,4,3] => [5,4,3] => [4,3] => 3960
[5,4,4,4,3] => [4,4,4,3] => [4,4,3] => [4,3] => 3960
[5,4,3,3,3] => [4,3,3,3] => [3,3,3] => [3,3] => 450
[7,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 450
[7,6,5,4,2] => [6,5,4,2] => [5,4,2] => [4,2] => 336
[4,4,4,4,2] => [4,4,4,2] => [4,4,2] => [4,2] => 336
[7,6,5,3,2] => [6,5,3,2] => [5,3,2] => [3,2] => 54
[7,6,4,3,2] => [6,4,3,2] => [4,3,2] => [3,2] => 54
[7,5,4,3,2] => [5,4,3,2] => [4,3,2] => [3,2] => 54
[7,6,5,4,1] => [6,5,4,1] => [5,4,1] => [4,1] => 24
[7,5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 6
[7,6,5,2,1] => [6,5,2,1] => [5,2,1] => [2,1] => 2
[6,6,5,2,1] => [6,5,2,1] => [5,2,1] => [2,1] => 2
[7,6,4,2,1] => [6,4,2,1] => [4,2,1] => [2,1] => 2
[6,6,4,2,1] => [6,4,2,1] => [4,2,1] => [2,1] => 2
[7,5,4,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 2
[7,6,3,2,1] => [6,3,2,1] => [3,2,1] => [2,1] => 2
[6,6,3,2,1] => [6,3,2,1] => [3,2,1] => [2,1] => 2
[7,6,5,4] => [6,5,4] => [5,4] => [4] => 0
[6,5,5,4] => [5,5,4] => [5,4] => [4] => 0
[7,6,5,3] => [6,5,3] => [5,3] => [3] => 0
[7,6,4,3] => [6,4,3] => [4,3] => [3] => 0
[7,5,4,3] => [5,4,3] => [4,3] => [3] => 0
[7,6,5,2] => [6,5,2] => [5,2] => [2] => 0
[3,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 1065960
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 19584180
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 20975220
[4,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 1065960
[4,4,4,4,4] => [4,4,4,4] => [4,4,4] => [4,4] => 46440
[4,4,4,3,3,3] => [4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 1065960
[5,5,5,5] => [5,5,5] => [5,5] => [5] => 0
[6,6,6,6] => [6,6,6] => [6,6] => [6] => 0
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 98820
[8,6,4,2] => [6,4,2] => [4,2] => [2] => 0
[7,7,7,7] => [7,7,7] => [7,7] => [7] => 0
[9,7,5,3,1] => [7,5,3,1] => [5,3,1] => [3,1] => 6
[11,9,7,5,3,1] => [9,7,5,3,1] => [7,5,3,1] => [5,3,1] => 695520
[7,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 366985080
[7,6,5,4,2,2,2,1] => [6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => 389612160
[7,6,5,4,3,1,1,1] => [6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 18960480
[8,7,6,5,3,2,1] => [7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 278170200
[8,7,6,4,3,2,1] => [7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 17939880
[8,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[8,7,6,5,4,1,1] => [7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => 245737800
[8,7,6,5,2,2,1] => [7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => 14598360
[8,7,6,3,3,2,1] => [7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => 1228500
[8,7,4,4,3,2,1] => [7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 17939880
[8,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[8,5,4,2] => [5,4,2] => [4,2] => [2] => 0
[9,6,5,3] => [6,5,3] => [5,3] => [3] => 0
[10,7,5,3] => [7,5,3] => [5,3] => [3] => 0
[9,6,4,3] => [6,4,3] => [4,3] => [3] => 0
[9,7,5,4,1] => [7,5,4,1] => [5,4,1] => [4,1] => 24
[8,6,5,3,1] => [6,5,3,1] => [5,3,1] => [3,1] => 6
[10,8,6,4,2] => [8,6,4,2] => [6,4,2] => [4,2] => 336
[9,7,5,3] => [7,5,3] => [5,3] => [3] => 0
[3,3,3,3,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1621620
[5,5,5,5,5] => [5,5,5,5] => [5,5,5] => [5,5] => 8580600
[7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 3
[8,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[8,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 105
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 840
[6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 96390
[5,4,3,2,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 9450
[6,5,4,3,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 7560
[6,5,4,3,2,1,1,1,1] => [5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1517670
[8,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 960120
[7,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 96390
[7,6,4,3,2,2,2,1] => [6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 23817780
[6,6,6,4,3,2,1] => [6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 17939880
[5,5,5,5,3,2,1] => [5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => 278170200
[5,4,4,4,4,2,1] => [4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => 306134640
[5,4,3,3,3,3,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 19584180
[5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 98820
[6,5,4,3,2,2,2,1] => [5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 23817780
[6,5,5,5] => [5,5,5] => [5,5] => [5] => 0
[5,4,4,4,4] => [4,4,4,4] => [4,4,4] => [4,4] => 46440
[8,7,6,3,2,1] => [7,6,3,2,1] => [6,3,2,1] => [3,2,1] => 570
[8,7,6,5,2,1] => [7,6,5,2,1] => [6,5,2,1] => [5,2,1] => 42840
[8,7,6,5,4,1] => [7,6,5,4,1] => [6,5,4,1] => [5,4,1] => 11362680
[7,7,6,5,3,2,1] => [7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 278170200
[8,7,6,5] => [7,6,5] => [6,5] => [5] => 0
[8,7,6,5,4] => [7,6,5,4] => [6,5,4] => [5,4] => 567000
[9,8,7,6] => [8,7,6] => [7,6] => [6] => 0
[8,7,6,4] => [7,6,4] => [6,4] => [4] => 0
[9,8,7,6,5] => [8,7,6,5] => [7,6,5] => [6,5] => 134038800
[8,7,6,5,3] => [7,6,5,3] => [6,5,3] => [5,3] => 37800
[8,7,6,5,4,2] => [7,6,5,4,2] => [6,5,4,2] => [5,4,2] => 234375120
[4,4,4,4,4,1] => [4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 808920
[5,5,5,5,1] => [5,5,5,1] => [5,5,1] => [5,1] => 120
[7,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 17939880
[6,6,6,1,1] => [6,6,1,1] => [6,1,1] => [1,1] => 1
[7,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 570
[6,5,4,3,2,2,2] => [5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 1331820
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 6930
[6,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 366985080
[7,6,5,4,3,2,2] => [6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => 349045200
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Description
The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees.
For a generating function $f$ the associated formal group law is the symmetric function $f(f^{(-1)}(x_1) + f^{(-1)}(x_2), \dots)$, see [1].
This statistic records the coefficient of the monomial symmetric function $m_\lambda$ times the product of the factorials of the parts of $\lambda$ in the formal group law for leaf labelled binary trees, with generating function $f(x) = 1-\sqrt{1-2x}$, see [1, sec. 3.2]
Fix a set of distinguishable vertices and a coloring of the vertices so that $\lambda_i$ are colored $i$. This statistic gives the number of rooted binary trees with leaves labeled with this set of vertices and internal vertices unlabeled so that no pair of 'twin' leaves have the same color.
For a generating function $f$ the associated formal group law is the symmetric function $f(f^{(-1)}(x_1) + f^{(-1)}(x_2), \dots)$, see [1].
This statistic records the coefficient of the monomial symmetric function $m_\lambda$ times the product of the factorials of the parts of $\lambda$ in the formal group law for leaf labelled binary trees, with generating function $f(x) = 1-\sqrt{1-2x}$, see [1, sec. 3.2]
Fix a set of distinguishable vertices and a coloring of the vertices so that $\lambda_i$ are colored $i$. This statistic gives the number of rooted binary trees with leaves labeled with this set of vertices and internal vertices unlabeled so that no pair of 'twin' leaves have the same color.
Map
first row removal
Description
Removes the first entry of an integer partition
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