Identifier
Values
[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
[3,1,1,1] => [1,1,1] => [1,1] => 1
[2,2,2] => [2,2] => [2] => 1
[2,2,1,1] => [2,1,1] => [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
[4,1,1,1] => [1,1,1] => [1,1] => 1
[3,2,2] => [2,2] => [2] => 1
[3,2,1,1] => [2,1,1] => [1,1] => 1
[3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,2,2,1] => [2,2,1] => [2,1] => 2
[2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,1,1,1] => [1,1,1] => [1,1] => 1
[4,2,2] => [2,2] => [2] => 1
[4,2,1,1] => [2,1,1] => [1,1] => 1
[4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[3,3,2] => [3,2] => [2] => 1
[3,3,1,1] => [3,1,1] => [1,1] => 1
[3,2,2,1] => [2,2,1] => [2,1] => 2
[3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,2] => [2,2,2] => [2,2] => 1
[2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[2,2,1,1,1,1] => [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] => 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[6,1,1,1] => [1,1,1] => [1,1] => 1
[5,2,2] => [2,2] => [2] => 1
[5,2,1,1] => [2,1,1] => [1,1] => 1
[5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,3,2] => [3,2] => [2] => 1
[4,3,1,1] => [3,1,1] => [1,1] => 1
[4,2,2,1] => [2,2,1] => [2,1] => 2
[4,2,1,1,1] => [2,1,1,1] => [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] => [3] => 1
[3,3,2,1] => [3,2,1] => [2,1] => 2
[3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,2,2,2] => [2,2,2] => [2,2] => 1
[3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[3,2,1,1,1,1] => [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
[2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[2,2,1,1,1,1,1] => [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] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[7,1,1,1] => [1,1,1] => [1,1] => 1
[6,2,2] => [2,2] => [2] => 1
[6,2,1,1] => [2,1,1] => [1,1] => 1
[6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[5,3,2] => [3,2] => [2] => 1
[5,3,1,1] => [3,1,1] => [1,1] => 1
[5,2,2,1] => [2,2,1] => [2,1] => 2
[5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[4,4,2] => [4,2] => [2] => 1
[4,4,1,1] => [4,1,1] => [1,1] => 1
[4,3,3] => [3,3] => [3] => 1
[4,3,2,1] => [3,2,1] => [2,1] => 2
[4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[4,2,2,2] => [2,2,2] => [2,2] => 1
[4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[4,2,1,1,1,1] => [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] => 1
[3,3,3,1] => [3,3,1] => [3,1] => 3
[3,3,2,2] => [3,2,2] => [2,2] => 1
[3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[3,2,1,1,1,1,1] => [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
[2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[8,1,1,1] => [1,1,1] => [1,1] => 1
[7,2,2] => [2,2] => [2] => 1
[7,2,1,1] => [2,1,1] => [1,1] => 1
[7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,3,2] => [3,2] => [2] => 1
[6,3,1,1] => [3,1,1] => [1,1] => 1
[6,2,2,1] => [2,2,1] => [2,1] => 2
[6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[5,4,2] => [4,2] => [2] => 1
[5,4,1,1] => [4,1,1] => [1,1] => 1
[5,3,3] => [3,3] => [3] => 1
[5,3,2,1] => [3,2,1] => [2,1] => 2
[5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[5,2,2,2] => [2,2,2] => [2,2] => 1
[5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[5,2,1,1,1,1] => [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] => 1
>>> Load all 1238 entries. <<<
[4,4,3] => [4,3] => [3] => 1
[4,4,2,1] => [4,2,1] => [2,1] => 2
[4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[4,3,3,1] => [3,3,1] => [3,1] => 3
[4,3,2,2] => [3,2,2] => [2,2] => 1
[4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [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
[3,3,3,2] => [3,3,2] => [3,2] => 2
[3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 6
[3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[3,2,1,1,1,1,1,1] => [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
[2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 4
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[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] => [1,1,1,1,1,1,1,1,1] => 1
[9,1,1,1] => [1,1,1] => [1,1] => 1
[8,2,2] => [2,2] => [2] => 1
[8,2,1,1] => [2,1,1] => [1,1] => 1
[8,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[7,3,2] => [3,2] => [2] => 1
[7,3,1,1] => [3,1,1] => [1,1] => 1
[7,2,2,1] => [2,2,1] => [2,1] => 2
[7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[6,4,2] => [4,2] => [2] => 1
[6,4,1,1] => [4,1,1] => [1,1] => 1
[6,3,3] => [3,3] => [3] => 1
[6,3,2,1] => [3,2,1] => [2,1] => 2
[6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[6,2,2,2] => [2,2,2] => [2,2] => 1
[6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[6,2,1,1,1,1] => [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] => 1
[5,5,2] => [5,2] => [2] => 1
[5,5,1,1] => [5,1,1] => [1,1] => 1
[5,4,3] => [4,3] => [3] => 1
[5,4,2,1] => [4,2,1] => [2,1] => 2
[5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[5,3,3,1] => [3,3,1] => [3,1] => 3
[5,3,2,2] => [3,2,2] => [2,2] => 1
[5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[5,2,1,1,1,1,1] => [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
[4,4,4] => [4,4] => [4] => 1
[4,4,3,1] => [4,3,1] => [3,1] => 3
[4,4,2,2] => [4,2,2] => [2,2] => 1
[4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 3
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[4,3,3,2] => [3,3,2] => [3,2] => 2
[4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 6
[4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [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
[3,3,3,3] => [3,3,3] => [3,3] => 1
[3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 8
[3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 10
[3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 5
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 4
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[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] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[10,1,1,1] => [1,1,1] => [1,1] => 1
[9,2,2] => [2,2] => [2] => 1
[9,2,1,1] => [2,1,1] => [1,1] => 1
[9,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[8,3,2] => [3,2] => [2] => 1
[8,3,1,1] => [3,1,1] => [1,1] => 1
[8,2,2,1] => [2,2,1] => [2,1] => 2
[8,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[7,4,2] => [4,2] => [2] => 1
[7,4,1,1] => [4,1,1] => [1,1] => 1
[7,3,3] => [3,3] => [3] => 1
[7,3,2,1] => [3,2,1] => [2,1] => 2
[7,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[7,2,2,2] => [2,2,2] => [2,2] => 1
[7,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[7,2,1,1,1,1] => [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] => 1
[6,5,2] => [5,2] => [2] => 1
[6,5,1,1] => [5,1,1] => [1,1] => 1
[6,4,3] => [4,3] => [3] => 1
[6,4,2,1] => [4,2,1] => [2,1] => 2
[6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[6,3,3,1] => [3,3,1] => [3,1] => 3
[6,3,2,2] => [3,2,2] => [2,2] => 1
[6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[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] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,5,3] => [5,3] => [3] => 1
[5,5,2,1] => [5,2,1] => [2,1] => 2
[5,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[5,4,4] => [4,4] => [4] => 1
[5,4,3,1] => [4,3,1] => [3,1] => 3
[5,4,2,2] => [4,2,2] => [2,2] => 1
[5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 3
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[5,3,3,2] => [3,3,2] => [3,2] => 2
[5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 6
[5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[5,2,1,1,1,1,1,1] => [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
[4,4,4,1] => [4,4,1] => [4,1] => 4
[4,4,3,2] => [4,3,2] => [3,2] => 2
[4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 6
[4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 4
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,3,3] => [3,3,3] => [3,3] => 1
[4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 8
[4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 10
[4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 5
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 4
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[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] => [3,3,3,1] => [3,3,1] => 6
[3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 3
[3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 20
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 15
[3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 4
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 5
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[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] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[11,1,1,1] => [1,1,1] => [1,1] => 1
[10,2,2] => [2,2] => [2] => 1
[10,2,1,1] => [2,1,1] => [1,1] => 1
[10,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[9,3,2] => [3,2] => [2] => 1
[9,3,1,1] => [3,1,1] => [1,1] => 1
[9,2,2,1] => [2,2,1] => [2,1] => 2
[9,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[8,4,2] => [4,2] => [2] => 1
[8,4,1,1] => [4,1,1] => [1,1] => 1
[8,3,3] => [3,3] => [3] => 1
[8,3,2,1] => [3,2,1] => [2,1] => 2
[8,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[8,2,2,2] => [2,2,2] => [2,2] => 1
[8,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[8,2,1,1,1,1] => [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] => 1
[7,5,2] => [5,2] => [2] => 1
[7,5,1,1] => [5,1,1] => [1,1] => 1
[7,4,3] => [4,3] => [3] => 1
[7,4,2,1] => [4,2,1] => [2,1] => 2
[7,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[7,3,3,1] => [3,3,1] => [3,1] => 3
[7,3,2,2] => [3,2,2] => [2,2] => 1
[7,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[7,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[7,2,1,1,1,1,1] => [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
[6,6,2] => [6,2] => [2] => 1
[6,6,1,1] => [6,1,1] => [1,1] => 1
[6,5,3] => [5,3] => [3] => 1
[6,5,2,1] => [5,2,1] => [2,1] => 2
[6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[6,4,4] => [4,4] => [4] => 1
[6,4,3,1] => [4,3,1] => [3,1] => 3
[6,4,2,2] => [4,2,2] => [2,2] => 1
[6,4,2,1,1] => [4,2,1,1] => [2,1,1] => 3
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[6,3,3,2] => [3,3,2] => [3,2] => 2
[6,3,3,1,1] => [3,3,1,1] => [3,1,1] => 6
[6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[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] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[5,5,4] => [5,4] => [4] => 1
[5,5,3,1] => [5,3,1] => [3,1] => 3
[5,5,2,2] => [5,2,2] => [2,2] => 1
[5,5,2,1,1] => [5,2,1,1] => [2,1,1] => 3
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[5,4,4,1] => [4,4,1] => [4,1] => 4
[5,4,3,2] => [4,3,2] => [3,2] => 2
[5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 6
[5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 4
[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] => [3,3] => 1
[5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 8
[5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 10
[5,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 5
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 4
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[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
[4,4,4,2] => [4,4,2] => [4,2] => 3
[4,4,4,1,1] => [4,4,1,1] => [4,1,1] => 10
[4,4,3,3] => [4,3,3] => [3,3] => 1
[4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 8
[4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 10
[4,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 5
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,3,3,3,1] => [3,3,3,1] => [3,3,1] => 6
[4,3,3,2,2] => [3,3,2,2] => [3,2,2] => 3
[4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 20
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 15
[4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 4
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[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] => [3,3,3,2] => [3,3,2] => 3
[3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 20
[3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 15
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 40
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 21
[3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 10
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 5
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 15
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 35
[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] => 28
[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] => 9
[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
[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
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[12,1,1,1] => [1,1,1] => [1,1] => 1
[11,2,2] => [2,2] => [2] => 1
[11,2,1,1] => [2,1,1] => [1,1] => 1
[11,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[10,3,2] => [3,2] => [2] => 1
[10,3,1,1] => [3,1,1] => [1,1] => 1
[10,2,2,1] => [2,2,1] => [2,1] => 2
[10,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[9,4,2] => [4,2] => [2] => 1
[9,4,1,1] => [4,1,1] => [1,1] => 1
[9,3,3] => [3,3] => [3] => 1
[9,3,2,1] => [3,2,1] => [2,1] => 2
[9,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[9,2,2,2] => [2,2,2] => [2,2] => 1
[9,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[9,2,1,1,1,1] => [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] => 1
[8,5,2] => [5,2] => [2] => 1
[8,5,1,1] => [5,1,1] => [1,1] => 1
[8,4,3] => [4,3] => [3] => 1
[8,4,2,1] => [4,2,1] => [2,1] => 2
[8,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[8,3,3,1] => [3,3,1] => [3,1] => 3
[8,3,2,2] => [3,2,2] => [2,2] => 1
[8,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[8,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [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
[7,6,2] => [6,2] => [2] => 1
[7,6,1,1] => [6,1,1] => [1,1] => 1
[7,5,3] => [5,3] => [3] => 1
[7,5,2,1] => [5,2,1] => [2,1] => 2
[7,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[7,4,4] => [4,4] => [4] => 1
[7,4,3,1] => [4,3,1] => [3,1] => 3
[7,4,2,2] => [4,2,2] => [2,2] => 1
[7,4,2,1,1] => [4,2,1,1] => [2,1,1] => 3
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[7,3,3,2] => [3,3,2] => [3,2] => 2
[7,3,3,1,1] => [3,3,1,1] => [3,1,1] => 6
[7,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [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
[6,6,3] => [6,3] => [3] => 1
[6,6,2,1] => [6,2,1] => [2,1] => 2
[6,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[6,5,4] => [5,4] => [4] => 1
[6,5,3,1] => [5,3,1] => [3,1] => 3
[6,5,2,2] => [5,2,2] => [2,2] => 1
[6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 3
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[6,4,4,1] => [4,4,1] => [4,1] => 4
[6,4,3,2] => [4,3,2] => [3,2] => 2
[6,4,3,1,1] => [4,3,1,1] => [3,1,1] => 6
[6,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 4
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,3,3,3] => [3,3,3] => [3,3] => 1
[6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 8
[6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 10
[6,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 5
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 4
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[5,5,5] => [5,5] => [5] => 1
[5,5,4,1] => [5,4,1] => [4,1] => 4
[5,5,3,2] => [5,3,2] => [3,2] => 2
[5,5,3,1,1] => [5,3,1,1] => [3,1,1] => 6
[5,5,2,2,1] => [5,2,2,1] => [2,2,1] => 3
[5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 4
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,4,4,2] => [4,4,2] => [4,2] => 3
[5,4,4,1,1] => [4,4,1,1] => [4,1,1] => 10
[5,4,3,3] => [4,3,3] => [3,3] => 1
[5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 8
[5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 10
[5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 5
[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] => [3,3,3,1] => [3,3,1] => 6
[5,3,3,2,2] => [3,3,2,2] => [3,2,2] => 3
[5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 20
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 15
[5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 4
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[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
[4,4,4,3] => [4,4,3] => [4,3] => 2
[4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 15
[4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 20
[4,4,3,3,1] => [4,3,3,1] => [3,3,1] => 6
[4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 3
[4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 20
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 15
[4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 4
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 10
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 20
[4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 15
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 40
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 21
[4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 10
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 5
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[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] => [3,3,3] => 1
[3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 20
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 50
[3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 4
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 45
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 70
[3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 28
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 5
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 15
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 35
[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] => 28
[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] => 9
[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
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 6
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 35
[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] => 56
[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] => 36
[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] => 10
[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
[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
[13,1,1,1] => [1,1,1] => [1,1] => 1
[12,2,2] => [2,2] => [2] => 1
[12,2,1,1] => [2,1,1] => [1,1] => 1
[12,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[11,3,2] => [3,2] => [2] => 1
[11,3,1,1] => [3,1,1] => [1,1] => 1
[11,2,2,1] => [2,2,1] => [2,1] => 2
[11,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[10,4,2] => [4,2] => [2] => 1
[10,4,1,1] => [4,1,1] => [1,1] => 1
[10,3,3] => [3,3] => [3] => 1
[10,3,2,1] => [3,2,1] => [2,1] => 2
[10,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[10,2,2,2] => [2,2,2] => [2,2] => 1
[10,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[10,2,1,1,1,1] => [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] => 1
[9,5,2] => [5,2] => [2] => 1
[9,5,1,1] => [5,1,1] => [1,1] => 1
[9,4,3] => [4,3] => [3] => 1
[9,4,2,1] => [4,2,1] => [2,1] => 2
[9,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[9,3,3,1] => [3,3,1] => [3,1] => 3
[9,3,2,2] => [3,2,2] => [2,2] => 1
[9,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[9,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [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
[8,6,2] => [6,2] => [2] => 1
[8,6,1,1] => [6,1,1] => [1,1] => 1
[8,5,3] => [5,3] => [3] => 1
[8,5,2,1] => [5,2,1] => [2,1] => 2
[8,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[8,4,4] => [4,4] => [4] => 1
[8,4,3,1] => [4,3,1] => [3,1] => 3
[8,4,2,2] => [4,2,2] => [2,2] => 1
[8,4,2,1,1] => [4,2,1,1] => [2,1,1] => 3
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[8,3,3,2] => [3,3,2] => [3,2] => 2
[8,3,3,1,1] => [3,3,1,1] => [3,1,1] => 6
[8,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [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
[7,7,2] => [7,2] => [2] => 1
[7,7,1,1] => [7,1,1] => [1,1] => 1
[7,6,3] => [6,3] => [3] => 1
[7,6,2,1] => [6,2,1] => [2,1] => 2
[7,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[7,5,4] => [5,4] => [4] => 1
[7,5,3,1] => [5,3,1] => [3,1] => 3
[7,5,2,2] => [5,2,2] => [2,2] => 1
[7,5,2,1,1] => [5,2,1,1] => [2,1,1] => 3
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[7,4,4,1] => [4,4,1] => [4,1] => 4
[7,4,3,2] => [4,3,2] => [3,2] => 2
[7,4,3,1,1] => [4,3,1,1] => [3,1,1] => 6
[7,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 4
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,3,3,3] => [3,3,3] => [3,3] => 1
[7,3,3,2,1] => [3,3,2,1] => [3,2,1] => 8
[7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 10
[7,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 5
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 4
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[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
[6,6,4] => [6,4] => [4] => 1
[6,6,3,1] => [6,3,1] => [3,1] => 3
[6,6,2,2] => [6,2,2] => [2,2] => 1
[6,6,2,1,1] => [6,2,1,1] => [2,1,1] => 3
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[6,5,5] => [5,5] => [5] => 1
[6,5,4,1] => [5,4,1] => [4,1] => 4
[6,5,3,2] => [5,3,2] => [3,2] => 2
[6,5,3,1,1] => [5,3,1,1] => [3,1,1] => 6
[6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 3
[6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 4
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,4,4,2] => [4,4,2] => [4,2] => 3
[6,4,4,1,1] => [4,4,1,1] => [4,1,1] => 10
[6,4,3,3] => [4,3,3] => [3,3] => 1
[6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 8
[6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 10
[6,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 5
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[6,3,3,3,1] => [3,3,3,1] => [3,3,1] => 6
[6,3,3,2,2] => [3,3,2,2] => [3,2,2] => 3
[6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 20
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 15
[6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 4
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[5,5,5,1] => [5,5,1] => [5,1] => 5
[5,5,4,2] => [5,4,2] => [4,2] => 3
[5,5,4,1,1] => [5,4,1,1] => [4,1,1] => 10
[5,5,3,3] => [5,3,3] => [3,3] => 1
[5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 8
[5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 10
[5,5,2,2,2] => [5,2,2,2] => [2,2,2] => 1
[5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 6
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 5
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,4,4,3] => [4,4,3] => [4,3] => 2
[5,4,4,2,1] => [4,4,2,1] => [4,2,1] => 15
[5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 20
[5,4,3,3,1] => [4,3,3,1] => [3,3,1] => 6
[5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 3
[5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 20
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 15
[5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 4
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 10
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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] => [3,3,3,2] => [3,3,2] => 3
[5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 20
[5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 15
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 40
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 21
[5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 10
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 5
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[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
[4,4,4,4] => [4,4,4] => [4,4] => 1
[4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 15
[4,4,4,2,2] => [4,4,2,2] => [4,2,2] => 6
[4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 45
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 35
[4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 20
[4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 15
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 40
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 21
[4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 1
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 10
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[4,3,3,3,3] => [3,3,3,3] => [3,3,3] => 1
[4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 20
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 50
[4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 4
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 45
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 70
[4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 28
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 5
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 15
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 35
[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] => 28
[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] => 9
[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
[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] => [3,3,3,3,1] => [3,3,3,1] => 10
[3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 6
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 75
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 105
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 24
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 105
[3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 112
[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] => 36
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 15
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 35
[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] => 28
[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] => 9
[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
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 6
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 35
[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] => 56
[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] => 36
[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] => 10
[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
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 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] => 21
[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] => 70
[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] => 84
[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] => 45
[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] => 11
[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
[14,1,1,1] => [1,1,1] => [1,1] => 1
[13,2,2] => [2,2] => [2] => 1
[13,2,1,1] => [2,1,1] => [1,1] => 1
[13,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[12,3,2] => [3,2] => [2] => 1
[12,3,1,1] => [3,1,1] => [1,1] => 1
[12,2,2,1] => [2,2,1] => [2,1] => 2
[12,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[11,4,2] => [4,2] => [2] => 1
[11,4,1,1] => [4,1,1] => [1,1] => 1
[11,3,3] => [3,3] => [3] => 1
[11,3,2,1] => [3,2,1] => [2,1] => 2
[11,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[11,2,2,2] => [2,2,2] => [2,2] => 1
[11,2,2,1,1] => [2,2,1,1] => [2,1,1] => 3
[11,2,1,1,1,1] => [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] => 1
[10,5,2] => [5,2] => [2] => 1
[10,5,1,1] => [5,1,1] => [1,1] => 1
[10,4,3] => [4,3] => [3] => 1
[10,4,2,1] => [4,2,1] => [2,1] => 2
[10,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[10,3,3,1] => [3,3,1] => [3,1] => 3
[10,3,2,2] => [3,2,2] => [2,2] => 1
[10,3,2,1,1] => [3,2,1,1] => [2,1,1] => 3
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[10,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[9,6,2] => [6,2] => [2] => 1
[9,6,1,1] => [6,1,1] => [1,1] => 1
[9,5,3] => [5,3] => [3] => 1
[9,5,2,1] => [5,2,1] => [2,1] => 2
[9,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[9,4,4] => [4,4] => [4] => 1
[9,4,3,1] => [4,3,1] => [3,1] => 3
[9,4,2,2] => [4,2,2] => [2,2] => 1
[9,4,2,1,1] => [4,2,1,1] => [2,1,1] => 3
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[9,3,3,2] => [3,3,2] => [3,2] => 2
[9,3,3,1,1] => [3,3,1,1] => [3,1,1] => 6
[9,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[9,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 5
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [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
[8,7,2] => [7,2] => [2] => 1
[8,7,1,1] => [7,1,1] => [1,1] => 1
[8,6,3] => [6,3] => [3] => 1
[8,6,2,1] => [6,2,1] => [2,1] => 2
[8,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[8,5,4] => [5,4] => [4] => 1
[8,5,3,1] => [5,3,1] => [3,1] => 3
[8,5,2,2] => [5,2,2] => [2,2] => 1
[8,5,2,1,1] => [5,2,1,1] => [2,1,1] => 3
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[8,4,4,1] => [4,4,1] => [4,1] => 4
[8,4,3,2] => [4,3,2] => [3,2] => 2
[8,4,3,1,1] => [4,3,1,1] => [3,1,1] => 6
[8,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 4
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,3,3,3] => [3,3,3] => [3,3] => 1
[8,3,3,2,1] => [3,3,2,1] => [3,2,1] => 8
[8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 10
[8,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 5
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 4
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[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
[7,7,3] => [7,3] => [3] => 1
[7,7,2,1] => [7,2,1] => [2,1] => 2
[7,7,1,1,1] => [7,1,1,1] => [1,1,1] => 1
[7,6,4] => [6,4] => [4] => 1
[7,6,3,1] => [6,3,1] => [3,1] => 3
[7,6,2,2] => [6,2,2] => [2,2] => 1
[7,6,2,1,1] => [6,2,1,1] => [2,1,1] => 3
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[7,5,5] => [5,5] => [5] => 1
[7,5,4,1] => [5,4,1] => [4,1] => 4
[7,5,3,2] => [5,3,2] => [3,2] => 2
[7,5,3,1,1] => [5,3,1,1] => [3,1,1] => 6
[7,5,2,2,1] => [5,2,2,1] => [2,2,1] => 3
[7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 4
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,4,4,2] => [4,4,2] => [4,2] => 3
[7,4,4,1,1] => [4,4,1,1] => [4,1,1] => 10
[7,4,3,3] => [4,3,3] => [3,3] => 1
[7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 8
[7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 10
[7,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 5
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,3,3,3,1] => [3,3,3,1] => [3,3,1] => 6
[7,3,3,2,2] => [3,3,2,2] => [3,2,2] => 3
[7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 20
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 15
[7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 4
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[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
[6,6,5] => [6,5] => [5] => 1
[6,6,4,1] => [6,4,1] => [4,1] => 4
[6,6,3,2] => [6,3,2] => [3,2] => 2
[6,6,3,1,1] => [6,3,1,1] => [3,1,1] => 6
[6,6,2,2,1] => [6,2,2,1] => [2,2,1] => 3
[6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 4
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,5,5,1] => [5,5,1] => [5,1] => 5
[6,5,4,2] => [5,4,2] => [4,2] => 3
[6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 10
[6,5,3,3] => [5,3,3] => [3,3] => 1
[6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 8
[6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 10
[6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 1
[6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 6
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 5
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[6,4,4,3] => [4,4,3] => [4,3] => 2
[6,4,4,2,1] => [4,4,2,1] => [4,2,1] => 15
[6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 20
[6,4,3,3,1] => [4,3,3,1] => [3,3,1] => 6
[6,4,3,2,2] => [4,3,2,2] => [3,2,2] => 3
[6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 20
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 15
[6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 4
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 10
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 20
[6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 15
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 40
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 21
[6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 10
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 5
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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] => [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] => [5,5,2] => [5,2] => 4
[5,5,5,1,1] => [5,5,1,1] => [5,1,1] => 15
[5,5,4,3] => [5,4,3] => [4,3] => 2
[5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 15
[5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 20
[5,5,3,3,1] => [5,3,3,1] => [3,3,1] => 6
[5,5,3,2,2] => [5,3,2,2] => [3,2,2] => 3
[5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 20
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 15
[5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 4
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 10
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[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
[5,4,4,4] => [4,4,4] => [4,4] => 1
[5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 15
[5,4,4,2,2] => [4,4,2,2] => [4,2,2] => 6
[5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 45
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 35
[5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 20
[5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 15
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 40
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 21
[5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 1
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 10
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[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] => [3,3,3] => 1
[5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 20
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 50
[5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 4
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 45
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 70
[5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 28
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 5
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 15
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 35
[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] => 28
[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] => 9
[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
[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
[4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 10
[4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 8
[4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 60
[4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 36
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 105
[4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 56
[4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 1
[4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 20
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 50
[4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 4
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 45
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 70
[4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 28
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 5
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 20
[4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[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] => 8
[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
[4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 10
[4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 6
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 75
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 105
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 24
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 105
[4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 112
[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] => 36
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 15
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 35
[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] => 28
[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] => 9
[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
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 6
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 35
[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] => 56
[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] => 36
[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] => 10
[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
[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] => [3,3,3,3,2] => [3,3,3,2] => 4
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => 50
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => 45
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 210
[3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 196
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 5
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 84
[3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 210
[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] => 168
[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] => 45
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 6
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 35
[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] => 56
[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] => 36
[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] => 10
[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
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 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] => 21
[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] => 70
[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] => 84
[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] => 45
[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] => 11
[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
[6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 64
[5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 64
[6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 64
[5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 64
[4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 64
[6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 20
[5,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 20
[6,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 20
[5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 20
[6,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 20
[6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 36
[5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 36
[6,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 36
[5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 36
[6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 15
[5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 15
[6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 15
[6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 4
[6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 60
[5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 60
[6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 60
[5,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 60
[6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 20
[5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 20
[6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 20
[6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 45
[5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 45
[6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 45
[6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 20
[6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 20
[6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 8
[5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 8
[6,4,4,3,2] => [4,4,3,2] => [4,3,2] => 8
[5,4,4,3,2] => [4,4,3,2] => [4,3,2] => 8
[6,5,3,3,2] => [5,3,3,2] => [3,3,2] => 3
[5,5,3,3,2] => [5,3,3,2] => [3,3,2] => 3
[6,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[6,5,4,2,2] => [5,4,2,2] => [4,2,2] => 6
[5,5,4,2,2] => [5,4,2,2] => [4,2,2] => 6
[6,4,4,2,2] => [4,4,2,2] => [4,2,2] => 6
[6,5,3,2,2] => [5,3,2,2] => [3,2,2] => 3
[6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 15
[5,5,4,3,1] => [5,4,3,1] => [4,3,1] => 15
[6,4,4,3,1] => [4,4,3,1] => [4,3,1] => 15
[6,5,3,3,1] => [5,3,3,1] => [3,3,1] => 6
[6,5,4,2,1] => [5,4,2,1] => [4,2,1] => 15
[6,5,4,3] => [5,4,3] => [4,3] => 2
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => 40
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 40
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 40
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 40
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 40
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 175
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 175
[7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [5,2,2,2,1] => 160
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => 70
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => 24
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 24
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 24
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 5
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 5
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => 315
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 280
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 280
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => 280
[7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [5,4,1,1,1] => 560
[6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => 560
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 175
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => 224
[5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => 224
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 105
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 105
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 40
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 40
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 40
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 35
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 5
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,5,4,3,3,2] => [5,4,3,3,2] => [4,3,3,2] => 15
[5,4,3,3,3,2] => [4,3,3,3,2] => [3,3,3,2] => 4
[4,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 4
[6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => 20
[4,4,4,3,2,2] => [4,4,3,2,2] => [4,3,2,2] => 20
[7,6,5,2,2,2] => [6,5,2,2,2] => [5,2,2,2] => 20
[6,5,4,2,2,2] => [5,4,2,2,2] => [4,2,2,2] => 10
[5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 4
[6,6,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => 1
[4,4,4,4,3,1] => [4,4,4,3,1] => [4,4,3,1] => 45
[7,6,5,4,2,1] => [6,5,4,2,1] => [5,4,2,1] => 175
[5,5,5,4,2,1] => [5,5,4,2,1] => [5,4,2,1] => 175
[4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => 60
[7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 140
[6,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 140
[5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => 140
[7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 64
[6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 64
[7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 64
[7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 64
[7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => 20
[7,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 20
[7,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 20
[7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => 70
[7,6,3,2,2,1] => [6,3,2,2,1] => [3,2,2,1] => 15
[7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 4
[7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => 140
[7,6,5,2,1,1] => [6,5,2,1,1] => [5,2,1,1] => 84
[7,6,3,2,1,1] => [6,3,2,1,1] => [3,2,1,1] => 20
[7,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 20
[7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => 35
[7,6,5,4,3] => [6,5,4,3] => [5,4,3] => 8
[6,6,5,4,3] => [6,5,4,3] => [5,4,3] => 8
[6,5,5,4,3] => [5,5,4,3] => [5,4,3] => 8
[5,4,4,4,3] => [4,4,4,3] => [4,4,3] => 3
[5,4,3,3,3] => [4,3,3,3] => [3,3,3] => 1
[7,3,3,3,3] => [3,3,3,3] => [3,3,3] => 1
[7,6,5,4,2] => [6,5,4,2] => [5,4,2] => 15
[4,4,4,4,2] => [4,4,4,2] => [4,4,2] => 6
[7,6,5,3,2] => [6,5,3,2] => [5,3,2] => 15
[7,6,4,3,2] => [6,4,3,2] => [4,3,2] => 8
[7,5,4,3,2] => [5,4,3,2] => [4,3,2] => 8
[7,6,5,4,1] => [6,5,4,1] => [5,4,1] => 24
[7,5,4,3,1] => [5,4,3,1] => [4,3,1] => 15
[7,6,5,2,1] => [6,5,2,1] => [5,2,1] => 24
[6,6,5,2,1] => [6,5,2,1] => [5,2,1] => 24
[7,6,4,2,1] => [6,4,2,1] => [4,2,1] => 15
[6,6,4,2,1] => [6,4,2,1] => [4,2,1] => 15
[7,5,4,2,1] => [5,4,2,1] => [4,2,1] => 15
[7,6,3,2,1] => [6,3,2,1] => [3,2,1] => 8
[6,6,3,2,1] => [6,3,2,1] => [3,2,1] => 8
[7,6,5,4] => [6,5,4] => [5,4] => 2
[6,5,5,4] => [5,5,4] => [5,4] => 2
[7,6,5,3] => [6,5,3] => [5,3] => 3
[7,6,4,3] => [6,4,3] => [4,3] => 2
[7,5,4,3] => [5,4,3] => [4,3] => 2
[7,6,5,2] => [6,5,2] => [5,2] => 4
[7,6,5] => [6,5] => [5] => 1
[3,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 1
[4,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 1
[4,4,4,4,4] => [4,4,4,4] => [4,4,4] => 1
[5,5,5,5] => [5,5,5] => [5,5] => 1
[6,6,6,6] => [6,6,6] => [6,6] => 1
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[6,6,6] => [6,6] => [6] => 1
[7,6,6] => [6,6] => [6] => 1
[10,4,4] => [4,4] => [4] => 1
[11,7,3] => [7,3] => [3] => 1
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[9,6,3] => [6,3] => [3] => 1
[8,6,4,2] => [6,4,2] => [4,2] => 3
[8,6,4] => [6,4] => [4] => 1
[10,6,4] => [6,4] => [4] => 1
[8,7,6] => [7,6] => [6] => 1
[9,8,7] => [8,7] => [7] => 1
[15,5,5] => [5,5] => [5] => 1
[7,7,7] => [7,7] => [7] => 1
[11,7,5,1] => [7,5,1] => [5,1] => 5
[9,7,5,3,1] => [7,5,3,1] => [5,3,1] => 27
[9,6,4] => [6,4] => [4] => 1
[10,7,3] => [7,3] => [3] => 1
[8,5,4,2] => [5,4,2] => [4,2] => 3
[9,6,5,3] => [6,5,3] => [5,3] => 3
[10,7,5,3] => [7,5,3] => [5,3] => 3
[9,6,4,3] => [6,4,3] => [4,3] => 2
[9,7,4] => [7,4] => [4] => 1
[9,7,5,4,1] => [7,5,4,1] => [5,4,1] => 24
[8,6,5,3,1] => [6,5,3,1] => [5,3,1] => 27
[10,8,6,4,2] => [8,6,4,2] => [6,4,2] => 27
[8,5,5,1] => [5,5,1] => [5,1] => 5
[9,5,5,1] => [5,5,1] => [5,1] => 5
[9,7,5,3] => [7,5,3] => [5,3] => 3
[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] => 336
[8,8,8] => [8,8] => [8] => 1
[7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 1
[8,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 64
[8,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => 64
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 70
[6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => 896
[5,4,3,2,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 112
[6,5,4,3,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => 420
[7,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => 896
[5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [3,2,2,2,2] => 5
[6,5,5,5] => [5,5,5] => [5,5] => 1
[5,4,4,4,4] => [4,4,4,4] => [4,4,4] => 1
[8,7,6,3,2,1] => [7,6,3,2,1] => [6,3,2,1] => 256
[8,7,6,5] => [7,6,5] => [6,5] => 2
[8,7,5] => [7,5] => [5] => 1
[8,7,6,4] => [7,6,4] => [6,4] => 3
[5,5,5,5,1] => [5,5,5,1] => [5,5,1] => 15
[6,6,6,1] => [6,6,1] => [6,1] => 6
[6,6,6,1,1] => [6,6,1,1] => [6,1,1] => 21
[7,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => 64
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 280
search for individual values
searching the database for the individual values of this statistic
Description
The number of semistandard tableaux on a given integer partition with minimal maximal entry.
This is, for an integer partition $\lambda = (\lambda_1 > \cdots > \lambda_k > 0)$, the number of semistandard tableaux of shape $\lambda$ with maximal entry $k$.
Equivalently, this is the evaluation $s_\lambda(1,\ldots,1)$ of the Schur function $s_\lambda$ in $k$ variables, or, explicitly,
$$ \prod_{(i,j) \in L} \frac{k + j - i}{ \operatorname{hook}(i,j) }$$
where the product is over all cells $(i,j) \in L$ and $\operatorname{hook}(i,j)$ is the hook length of a cell.
See [Theorem 6.3, 1] for details.
Map
first row removal
Description
Removes the first entry of an integer partition