Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
St000531: Integer partitions ⟶ ℤ
Values
[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] => 2
[3,1,1] => [1,1] => [1] => [1] => 1
[2,2,1] => [2,1] => [1] => [1] => 1
[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] => 3
[4,1,1] => [1,1] => [1] => [1] => 1
[3,2,1] => [2,1] => [1] => [1] => 1
[3,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[2,2,2] => [2,2] => [2] => [2] => 2
[2,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[2,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[5,1,1] => [1,1] => [1] => [1] => 1
[4,2,1] => [2,1] => [1] => [1] => 1
[4,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[3,3,1] => [3,1] => [1] => [1] => 1
[3,2,2] => [2,2] => [2] => [2] => 2
[3,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[3,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[2,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[2,2,1,1,1] => [2,1,1,1] => [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] => 4
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[6,1,1] => [1,1] => [1] => [1] => 1
[5,2,1] => [2,1] => [1] => [1] => 1
[5,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[4,3,1] => [3,1] => [1] => [1] => 1
[4,2,2] => [2,2] => [2] => [2] => 2
[4,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[4,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[3,3,2] => [3,2] => [2] => [2] => 2
[3,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[3,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[3,2,1,1,1] => [2,1,1,1] => [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] => 4
[2,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[2,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [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] => 6
[7,1,1] => [1,1] => [1] => [1] => 1
[6,2,1] => [2,1] => [1] => [1] => 1
[6,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[5,3,1] => [3,1] => [1] => [1] => 1
[5,2,2] => [2,2] => [2] => [2] => 2
[5,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[5,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[4,4,1] => [4,1] => [1] => [1] => 1
[4,3,2] => [3,2] => [2] => [2] => 2
[4,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[4,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[4,2,1,1,1] => [2,1,1,1] => [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] => 4
[3,3,3] => [3,3] => [3] => [2,1] => 1
[3,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[3,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[3,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[3,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[2,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [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] => 7
[8,1,1] => [1,1] => [1] => [1] => 1
[7,2,1] => [2,1] => [1] => [1] => 1
[7,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[6,3,1] => [3,1] => [1] => [1] => 1
[6,2,2] => [2,2] => [2] => [2] => 2
[6,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[6,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[5,4,1] => [4,1] => [1] => [1] => 1
[5,3,2] => [3,2] => [2] => [2] => 2
[5,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[5,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[5,2,1,1,1] => [2,1,1,1] => [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] => 4
[4,4,2] => [4,2] => [2] => [2] => 2
[4,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[4,3,3] => [3,3] => [3] => [2,1] => 1
[4,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[4,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[4,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[4,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[3,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[3,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[3,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[3,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[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] => 6
[2,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
>>> Load all 1302 entries. <<<[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] => 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] => 8
[9,1,1] => [1,1] => [1] => [1] => 1
[8,2,1] => [2,1] => [1] => [1] => 1
[8,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[7,3,1] => [3,1] => [1] => [1] => 1
[7,2,2] => [2,2] => [2] => [2] => 2
[7,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[7,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[6,4,1] => [4,1] => [1] => [1] => 1
[6,3,2] => [3,2] => [2] => [2] => 2
[6,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[6,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[6,2,1,1,1] => [2,1,1,1] => [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] => 4
[5,5,1] => [5,1] => [1] => [1] => 1
[5,4,2] => [4,2] => [2] => [2] => 2
[5,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[5,3,3] => [3,3] => [3] => [2,1] => 1
[5,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[5,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[5,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[5,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[4,4,3] => [4,3] => [3] => [2,1] => 1
[4,4,2,1] => [4,2,1] => [2,1] => [3] => 3
[4,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,1] => 3
[4,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[4,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[4,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[4,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[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] => 6
[3,3,3,2] => [3,3,2] => [3,2] => [4,1] => 3
[3,3,3,1,1] => [3,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[3,3,2,2,1] => [3,2,2,1] => [2,2,1] => [5] => 5
[3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[3,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[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] => 7
[2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [7] => 7
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[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] => 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] => [1,1,1,1,1,1,1,1,1] => 9
[10,1,1] => [1,1] => [1] => [1] => 1
[9,2,1] => [2,1] => [1] => [1] => 1
[9,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[8,3,1] => [3,1] => [1] => [1] => 1
[8,2,2] => [2,2] => [2] => [2] => 2
[8,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[8,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[7,4,1] => [4,1] => [1] => [1] => 1
[7,3,2] => [3,2] => [2] => [2] => 2
[7,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[7,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[7,2,1,1,1] => [2,1,1,1] => [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] => 4
[6,5,1] => [5,1] => [1] => [1] => 1
[6,4,2] => [4,2] => [2] => [2] => 2
[6,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[6,3,3] => [3,3] => [3] => [2,1] => 1
[6,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[6,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[6,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[6,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[5,5,2] => [5,2] => [2] => [2] => 2
[5,5,1,1] => [5,1,1] => [1,1] => [1,1] => 2
[5,4,3] => [4,3] => [3] => [2,1] => 1
[5,4,2,1] => [4,2,1] => [2,1] => [3] => 3
[5,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,1] => 3
[5,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[5,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[5,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[5,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[4,4,4] => [4,4] => [4] => [2,2] => 2
[4,4,3,1] => [4,3,1] => [3,1] => [2,1,1] => 2
[4,4,2,2] => [4,2,2] => [2,2] => [4] => 4
[4,4,2,1,1] => [4,2,1,1] => [2,1,1] => [3,1] => 2
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[4,3,3,2] => [3,3,2] => [3,2] => [4,1] => 3
[4,3,3,1,1] => [3,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[4,3,2,2,1] => [3,2,2,1] => [2,2,1] => [5] => 5
[4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[4,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[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] => 7
[3,3,3,3] => [3,3,3] => [3,3] => [3,2,1] => 1
[3,3,3,2,1] => [3,3,2,1] => [3,2,1] => [3,3] => 6
[3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[3,3,2,2,2] => [3,2,2,2] => [2,2,2] => [6] => 6
[3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [7] => 7
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[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] => 8
[2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [8] => 8
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[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] => 9
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 10
[11,1,1] => [1,1] => [1] => [1] => 1
[10,2,1] => [2,1] => [1] => [1] => 1
[10,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[9,3,1] => [3,1] => [1] => [1] => 1
[9,2,2] => [2,2] => [2] => [2] => 2
[9,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[9,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[8,4,1] => [4,1] => [1] => [1] => 1
[8,3,2] => [3,2] => [2] => [2] => 2
[8,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[8,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[8,2,1,1,1] => [2,1,1,1] => [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] => 4
[7,5,1] => [5,1] => [1] => [1] => 1
[7,4,2] => [4,2] => [2] => [2] => 2
[7,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[7,3,3] => [3,3] => [3] => [2,1] => 1
[7,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[7,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[7,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[7,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[6,6,1] => [6,1] => [1] => [1] => 1
[6,5,2] => [5,2] => [2] => [2] => 2
[6,5,1,1] => [5,1,1] => [1,1] => [1,1] => 2
[6,4,3] => [4,3] => [3] => [2,1] => 1
[6,4,2,1] => [4,2,1] => [2,1] => [3] => 3
[6,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,1] => 3
[6,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[6,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[6,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[6,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[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] => 6
[5,5,3] => [5,3] => [3] => [2,1] => 1
[5,5,2,1] => [5,2,1] => [2,1] => [3] => 3
[5,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1,1] => 3
[5,4,4] => [4,4] => [4] => [2,2] => 2
[5,4,3,1] => [4,3,1] => [3,1] => [2,1,1] => 2
[5,4,2,2] => [4,2,2] => [2,2] => [4] => 4
[5,4,2,1,1] => [4,2,1,1] => [2,1,1] => [3,1] => 2
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[5,3,3,2] => [3,3,2] => [3,2] => [4,1] => 3
[5,3,3,1,1] => [3,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[5,3,2,2,1] => [3,2,2,1] => [2,2,1] => [5] => 5
[5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[5,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[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] => 7
[4,4,4,1] => [4,4,1] => [4,1] => [3,2] => 4
[4,4,3,2] => [4,3,2] => [3,2] => [4,1] => 3
[4,4,3,1,1] => [4,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[4,4,2,2,1] => [4,2,2,1] => [2,2,1] => [5] => 5
[4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[4,3,3,3] => [3,3,3] => [3,3] => [3,2,1] => 1
[4,3,3,2,1] => [3,3,2,1] => [3,2,1] => [3,3] => 6
[4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[4,3,2,2,2] => [3,2,2,2] => [2,2,2] => [6] => 6
[4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [7] => 7
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[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] => 8
[3,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[3,3,3,2,2] => [3,3,2,2] => [3,2,2] => [6,1] => 5
[3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [7] => 7
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [8] => 8
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[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] => 9
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[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] => 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] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[12,1,1] => [1,1] => [1] => [1] => 1
[11,2,1] => [2,1] => [1] => [1] => 1
[11,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[10,3,1] => [3,1] => [1] => [1] => 1
[10,2,2] => [2,2] => [2] => [2] => 2
[10,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[10,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[9,4,1] => [4,1] => [1] => [1] => 1
[9,3,2] => [3,2] => [2] => [2] => 2
[9,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[9,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[9,2,1,1,1] => [2,1,1,1] => [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] => 4
[8,5,1] => [5,1] => [1] => [1] => 1
[8,4,2] => [4,2] => [2] => [2] => 2
[8,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[8,3,3] => [3,3] => [3] => [2,1] => 1
[8,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[8,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[8,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[8,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[7,6,1] => [6,1] => [1] => [1] => 1
[7,5,2] => [5,2] => [2] => [2] => 2
[7,5,1,1] => [5,1,1] => [1,1] => [1,1] => 2
[7,4,3] => [4,3] => [3] => [2,1] => 1
[7,4,2,1] => [4,2,1] => [2,1] => [3] => 3
[7,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,1] => 3
[7,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[7,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[7,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[7,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[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] => 6
[6,6,2] => [6,2] => [2] => [2] => 2
[6,6,1,1] => [6,1,1] => [1,1] => [1,1] => 2
[6,5,3] => [5,3] => [3] => [2,1] => 1
[6,5,2,1] => [5,2,1] => [2,1] => [3] => 3
[6,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1,1] => 3
[6,4,4] => [4,4] => [4] => [2,2] => 2
[6,4,3,1] => [4,3,1] => [3,1] => [2,1,1] => 2
[6,4,2,2] => [4,2,2] => [2,2] => [4] => 4
[6,4,2,1,1] => [4,2,1,1] => [2,1,1] => [3,1] => 2
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[6,3,3,2] => [3,3,2] => [3,2] => [4,1] => 3
[6,3,3,1,1] => [3,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[6,3,2,2,1] => [3,2,2,1] => [2,2,1] => [5] => 5
[6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[6,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[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] => 7
[5,5,4] => [5,4] => [4] => [2,2] => 2
[5,5,3,1] => [5,3,1] => [3,1] => [2,1,1] => 2
[5,5,2,2] => [5,2,2] => [2,2] => [4] => 4
[5,5,2,1,1] => [5,2,1,1] => [2,1,1] => [3,1] => 2
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[5,4,4,1] => [4,4,1] => [4,1] => [3,2] => 4
[5,4,3,2] => [4,3,2] => [3,2] => [4,1] => 3
[5,4,3,1,1] => [4,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[5,4,2,2,1] => [4,2,2,1] => [2,2,1] => [5] => 5
[5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[5,3,3,3] => [3,3,3] => [3,3] => [3,2,1] => 1
[5,3,3,2,1] => [3,3,2,1] => [3,2,1] => [3,3] => 6
[5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[5,3,2,2,2] => [3,2,2,2] => [2,2,2] => [6] => 6
[5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [7] => 7
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[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] => 8
[4,4,4,2] => [4,4,2] => [4,2] => [4,2] => 6
[4,4,4,1,1] => [4,4,1,1] => [4,1,1] => [4,1,1] => 0
[4,4,3,3] => [4,3,3] => [3,3] => [3,2,1] => 1
[4,4,3,2,1] => [4,3,2,1] => [3,2,1] => [3,3] => 6
[4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[4,4,2,2,2] => [4,2,2,2] => [2,2,2] => [6] => 6
[4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[4,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[4,3,3,2,2] => [3,3,2,2] => [3,2,2] => [6,1] => 5
[4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [7] => 7
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [8] => 8
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[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] => 9
[3,3,3,3,2] => [3,3,3,2] => [3,3,2] => [5,2,1] => 3
[3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [8] => 8
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[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] => 10
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [9,1] => 8
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 0
[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] => [5,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1] => 10
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [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
[13,1,1] => [1,1] => [1] => [1] => 1
[12,2,1] => [2,1] => [1] => [1] => 1
[12,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[11,3,1] => [3,1] => [1] => [1] => 1
[11,2,2] => [2,2] => [2] => [2] => 2
[11,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[11,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[10,4,1] => [4,1] => [1] => [1] => 1
[10,3,2] => [3,2] => [2] => [2] => 2
[10,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[10,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[10,2,1,1,1] => [2,1,1,1] => [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] => 4
[9,5,1] => [5,1] => [1] => [1] => 1
[9,4,2] => [4,2] => [2] => [2] => 2
[9,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[9,3,3] => [3,3] => [3] => [2,1] => 1
[9,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[9,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[9,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[9,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[8,6,1] => [6,1] => [1] => [1] => 1
[8,5,2] => [5,2] => [2] => [2] => 2
[8,5,1,1] => [5,1,1] => [1,1] => [1,1] => 2
[8,4,3] => [4,3] => [3] => [2,1] => 1
[8,4,2,1] => [4,2,1] => [2,1] => [3] => 3
[8,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,1] => 3
[8,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[8,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[8,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[8,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[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] => 6
[7,7,1] => [7,1] => [1] => [1] => 1
[7,6,2] => [6,2] => [2] => [2] => 2
[7,6,1,1] => [6,1,1] => [1,1] => [1,1] => 2
[7,5,3] => [5,3] => [3] => [2,1] => 1
[7,5,2,1] => [5,2,1] => [2,1] => [3] => 3
[7,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1,1] => 3
[7,4,4] => [4,4] => [4] => [2,2] => 2
[7,4,3,1] => [4,3,1] => [3,1] => [2,1,1] => 2
[7,4,2,2] => [4,2,2] => [2,2] => [4] => 4
[7,4,2,1,1] => [4,2,1,1] => [2,1,1] => [3,1] => 2
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[7,3,3,2] => [3,3,2] => [3,2] => [4,1] => 3
[7,3,3,1,1] => [3,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[7,3,2,2,1] => [3,2,2,1] => [2,2,1] => [5] => 5
[7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[7,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[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] => 7
[6,6,3] => [6,3] => [3] => [2,1] => 1
[6,6,2,1] => [6,2,1] => [2,1] => [3] => 3
[6,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1,1] => 3
[6,5,4] => [5,4] => [4] => [2,2] => 2
[6,5,3,1] => [5,3,1] => [3,1] => [2,1,1] => 2
[6,5,2,2] => [5,2,2] => [2,2] => [4] => 4
[6,5,2,1,1] => [5,2,1,1] => [2,1,1] => [3,1] => 2
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[6,4,4,1] => [4,4,1] => [4,1] => [3,2] => 4
[6,4,3,2] => [4,3,2] => [3,2] => [4,1] => 3
[6,4,3,1,1] => [4,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[6,4,2,2,1] => [4,2,2,1] => [2,2,1] => [5] => 5
[6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[6,3,3,3] => [3,3,3] => [3,3] => [3,2,1] => 1
[6,3,3,2,1] => [3,3,2,1] => [3,2,1] => [3,3] => 6
[6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[6,3,2,2,2] => [3,2,2,2] => [2,2,2] => [6] => 6
[6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [7] => 7
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[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] => 8
[5,5,5] => [5,5] => [5] => [2,2,1] => 4
[5,5,4,1] => [5,4,1] => [4,1] => [3,2] => 4
[5,5,3,2] => [5,3,2] => [3,2] => [4,1] => 3
[5,5,3,1,1] => [5,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[5,5,2,2,1] => [5,2,2,1] => [2,2,1] => [5] => 5
[5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[5,4,4,2] => [4,4,2] => [4,2] => [4,2] => 6
[5,4,4,1,1] => [4,4,1,1] => [4,1,1] => [4,1,1] => 0
[5,4,3,3] => [4,3,3] => [3,3] => [3,2,1] => 1
[5,4,3,2,1] => [4,3,2,1] => [3,2,1] => [3,3] => 6
[5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[5,4,2,2,2] => [4,2,2,2] => [2,2,2] => [6] => 6
[5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[5,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[5,3,3,2,2] => [3,3,2,2] => [3,2,2] => [6,1] => 5
[5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [7] => 7
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [8] => 8
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[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] => 9
[4,4,4,3] => [4,4,3] => [4,3] => [4,3] => 9
[4,4,4,2,1] => [4,4,2,1] => [4,2,1] => [5,2] => 8
[4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => 0
[4,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[4,4,3,2,2] => [4,3,2,2] => [3,2,2] => [6,1] => 5
[4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [7] => 7
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[4,3,3,3,2] => [3,3,3,2] => [3,3,2] => [5,2,1] => 3
[4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [8] => 8
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[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] => 10
[3,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3,2,1] => 8
[3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,2,1,1,1,1] => 4
[3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [8,1] => 7
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => 6
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [3,3,1,1,1] => 6
[3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [9,1] => 8
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 0
[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] => [5,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1] => 10
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [11] => 11
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [9,1,1] => 0
[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] => [7,1,1,1,1] => 0
[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] => [5,1,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [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
[14,1,1] => [1,1] => [1] => [1] => 1
[13,2,1] => [2,1] => [1] => [1] => 1
[13,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[12,3,1] => [3,1] => [1] => [1] => 1
[12,2,2] => [2,2] => [2] => [2] => 2
[12,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[12,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[11,4,1] => [4,1] => [1] => [1] => 1
[11,3,2] => [3,2] => [2] => [2] => 2
[11,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[11,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[11,2,1,1,1] => [2,1,1,1] => [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] => 4
[10,5,1] => [5,1] => [1] => [1] => 1
[10,4,2] => [4,2] => [2] => [2] => 2
[10,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[10,3,3] => [3,3] => [3] => [2,1] => 1
[10,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[10,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[10,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[10,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[9,6,1] => [6,1] => [1] => [1] => 1
[9,5,2] => [5,2] => [2] => [2] => 2
[9,5,1,1] => [5,1,1] => [1,1] => [1,1] => 2
[9,4,3] => [4,3] => [3] => [2,1] => 1
[9,4,2,1] => [4,2,1] => [2,1] => [3] => 3
[9,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,1] => 3
[9,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[9,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[9,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[9,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[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] => 6
[8,7,1] => [7,1] => [1] => [1] => 1
[8,6,2] => [6,2] => [2] => [2] => 2
[8,6,1,1] => [6,1,1] => [1,1] => [1,1] => 2
[8,5,3] => [5,3] => [3] => [2,1] => 1
[8,5,2,1] => [5,2,1] => [2,1] => [3] => 3
[8,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1,1] => 3
[8,4,4] => [4,4] => [4] => [2,2] => 2
[8,4,3,1] => [4,3,1] => [3,1] => [2,1,1] => 2
[8,4,2,2] => [4,2,2] => [2,2] => [4] => 4
[8,4,2,1,1] => [4,2,1,1] => [2,1,1] => [3,1] => 2
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[8,3,3,2] => [3,3,2] => [3,2] => [4,1] => 3
[8,3,3,1,1] => [3,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[8,3,2,2,1] => [3,2,2,1] => [2,2,1] => [5] => 5
[8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[8,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[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] => 7
[7,7,2] => [7,2] => [2] => [2] => 2
[7,7,1,1] => [7,1,1] => [1,1] => [1,1] => 2
[7,6,3] => [6,3] => [3] => [2,1] => 1
[7,6,2,1] => [6,2,1] => [2,1] => [3] => 3
[7,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1,1] => 3
[7,5,4] => [5,4] => [4] => [2,2] => 2
[7,5,3,1] => [5,3,1] => [3,1] => [2,1,1] => 2
[7,5,2,2] => [5,2,2] => [2,2] => [4] => 4
[7,5,2,1,1] => [5,2,1,1] => [2,1,1] => [3,1] => 2
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[7,4,4,1] => [4,4,1] => [4,1] => [3,2] => 4
[7,4,3,2] => [4,3,2] => [3,2] => [4,1] => 3
[7,4,3,1,1] => [4,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[7,4,2,2,1] => [4,2,2,1] => [2,2,1] => [5] => 5
[7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[7,3,3,3] => [3,3,3] => [3,3] => [3,2,1] => 1
[7,3,3,2,1] => [3,3,2,1] => [3,2,1] => [3,3] => 6
[7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[7,3,2,2,2] => [3,2,2,2] => [2,2,2] => [6] => 6
[7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [7] => 7
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[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] => 8
[6,6,4] => [6,4] => [4] => [2,2] => 2
[6,6,3,1] => [6,3,1] => [3,1] => [2,1,1] => 2
[6,6,2,2] => [6,2,2] => [2,2] => [4] => 4
[6,6,2,1,1] => [6,2,1,1] => [2,1,1] => [3,1] => 2
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[6,5,5] => [5,5] => [5] => [2,2,1] => 4
[6,5,4,1] => [5,4,1] => [4,1] => [3,2] => 4
[6,5,3,2] => [5,3,2] => [3,2] => [4,1] => 3
[6,5,3,1,1] => [5,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[6,5,2,2,1] => [5,2,2,1] => [2,2,1] => [5] => 5
[6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[6,4,4,2] => [4,4,2] => [4,2] => [4,2] => 6
[6,4,4,1,1] => [4,4,1,1] => [4,1,1] => [4,1,1] => 0
[6,4,3,3] => [4,3,3] => [3,3] => [3,2,1] => 1
[6,4,3,2,1] => [4,3,2,1] => [3,2,1] => [3,3] => 6
[6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[6,4,2,2,2] => [4,2,2,2] => [2,2,2] => [6] => 6
[6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[6,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[6,3,3,2,2] => [3,3,2,2] => [3,2,2] => [6,1] => 5
[6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [7] => 7
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [8] => 8
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[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] => 9
[5,5,5,1] => [5,5,1] => [5,1] => [2,2,1,1] => 6
[5,5,4,2] => [5,4,2] => [4,2] => [4,2] => 6
[5,5,4,1,1] => [5,4,1,1] => [4,1,1] => [4,1,1] => 0
[5,5,3,3] => [5,3,3] => [3,3] => [3,2,1] => 1
[5,5,3,2,1] => [5,3,2,1] => [3,2,1] => [3,3] => 6
[5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[5,5,2,2,2] => [5,2,2,2] => [2,2,2] => [6] => 6
[5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[5,4,4,3] => [4,4,3] => [4,3] => [4,3] => 9
[5,4,4,2,1] => [4,4,2,1] => [4,2,1] => [5,2] => 8
[5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => 0
[5,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[5,4,3,2,2] => [4,3,2,2] => [3,2,2] => [6,1] => 5
[5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [7] => 7
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[5,3,3,3,2] => [3,3,3,2] => [3,3,2] => [5,2,1] => 3
[5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [8] => 8
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[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] => 10
[4,4,4,4] => [4,4,4] => [4,4] => [4,4] => 12
[4,4,4,3,1] => [4,4,3,1] => [4,3,1] => [4,3,1] => 4
[4,4,4,2,2] => [4,4,2,2] => [4,2,2] => [6,2] => 10
[4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [6,1,1] => 0
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [4,1,1,1,1] => 0
[4,4,3,3,2] => [4,3,3,2] => [3,3,2] => [5,2,1] => 3
[4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [8] => 8
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[4,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3,2,1] => 8
[4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,2,1,1,1,1] => 4
[4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [8,1] => 7
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => 6
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [3,3,1,1,1] => 6
[4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [9,1] => 8
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 0
[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] => [5,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1] => 10
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,2,1,1] => 12
[3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => [7,2,1] => 5
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,3,3,1] => 12
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,2,1,1,1,1,1] => 5
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => [7,3] => 18
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [5,3,1,1] => 0
[3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [3,3,1,1,1,1] => 8
[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] => [2,1,1,1,1,1,1,1,1] => 8
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [9,1] => 8
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 0
[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] => [5,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1] => 10
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [11] => 11
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [9,1,1] => 0
[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] => [7,1,1,1,1] => 0
[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] => [5,1,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 12
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [12] => 12
[2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [11,1] => 10
[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] => [9,1,1,1] => 0
[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] => [7,1,1,1,1,1] => 0
[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] => [5,1,1,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1,1,1] => 12
[15,1,1] => [1,1] => [1] => [1] => 1
[14,2,1] => [2,1] => [1] => [1] => 1
[14,1,1,1] => [1,1,1] => [1,1] => [1,1] => 2
[13,3,1] => [3,1] => [1] => [1] => 1
[13,2,2] => [2,2] => [2] => [2] => 2
[13,2,1,1] => [2,1,1] => [1,1] => [1,1] => 2
[13,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1,1] => 3
[12,4,1] => [4,1] => [1] => [1] => 1
[12,3,2] => [3,2] => [2] => [2] => 2
[12,3,1,1] => [3,1,1] => [1,1] => [1,1] => 2
[12,2,2,1] => [2,2,1] => [2,1] => [3] => 3
[12,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1,1] => 3
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[11,5,1] => [5,1] => [1] => [1] => 1
[11,4,2] => [4,2] => [2] => [2] => 2
[11,4,1,1] => [4,1,1] => [1,1] => [1,1] => 2
[11,3,3] => [3,3] => [3] => [2,1] => 1
[11,3,2,1] => [3,2,1] => [2,1] => [3] => 3
[11,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1,1] => 3
[11,2,2,2] => [2,2,2] => [2,2] => [4] => 4
[11,2,2,1,1] => [2,2,1,1] => [2,1,1] => [3,1] => 2
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[10,6,1] => [6,1] => [1] => [1] => 1
[10,5,2] => [5,2] => [2] => [2] => 2
[10,5,1,1] => [5,1,1] => [1,1] => [1,1] => 2
[10,4,3] => [4,3] => [3] => [2,1] => 1
[10,4,2,1] => [4,2,1] => [2,1] => [3] => 3
[10,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,1] => 3
[10,3,3,1] => [3,3,1] => [3,1] => [2,1,1] => 2
[10,3,2,2] => [3,2,2] => [2,2] => [4] => 4
[10,3,2,1,1] => [3,2,1,1] => [2,1,1] => [3,1] => 2
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[10,2,2,2,1] => [2,2,2,1] => [2,2,1] => [5] => 5
[10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[9,7,1] => [7,1] => [1] => [1] => 1
[9,6,2] => [6,2] => [2] => [2] => 2
[9,6,1,1] => [6,1,1] => [1,1] => [1,1] => 2
[9,5,3] => [5,3] => [3] => [2,1] => 1
[9,5,2,1] => [5,2,1] => [2,1] => [3] => 3
[9,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1,1] => 3
[9,4,4] => [4,4] => [4] => [2,2] => 2
[9,4,3,1] => [4,3,1] => [3,1] => [2,1,1] => 2
[9,4,2,2] => [4,2,2] => [2,2] => [4] => 4
[9,4,2,1,1] => [4,2,1,1] => [2,1,1] => [3,1] => 2
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[9,3,3,2] => [3,3,2] => [3,2] => [4,1] => 3
[9,3,3,1,1] => [3,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[9,3,2,2,1] => [3,2,2,1] => [2,2,1] => [5] => 5
[9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[9,2,2,2,2] => [2,2,2,2] => [2,2,2] => [6] => 6
[9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[8,8,1] => [8,1] => [1] => [1] => 1
[8,7,2] => [7,2] => [2] => [2] => 2
[8,7,1,1] => [7,1,1] => [1,1] => [1,1] => 2
[8,6,3] => [6,3] => [3] => [2,1] => 1
[8,6,2,1] => [6,2,1] => [2,1] => [3] => 3
[8,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1,1] => 3
[8,5,4] => [5,4] => [4] => [2,2] => 2
[8,5,3,1] => [5,3,1] => [3,1] => [2,1,1] => 2
[8,5,2,2] => [5,2,2] => [2,2] => [4] => 4
[8,5,2,1,1] => [5,2,1,1] => [2,1,1] => [3,1] => 2
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[8,4,4,1] => [4,4,1] => [4,1] => [3,2] => 4
[8,4,3,2] => [4,3,2] => [3,2] => [4,1] => 3
[8,4,3,1,1] => [4,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[8,4,2,2,1] => [4,2,2,1] => [2,2,1] => [5] => 5
[8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[8,3,3,3] => [3,3,3] => [3,3] => [3,2,1] => 1
[8,3,3,2,1] => [3,3,2,1] => [3,2,1] => [3,3] => 6
[8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[8,3,2,2,2] => [3,2,2,2] => [2,2,2] => [6] => 6
[8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [7] => 7
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[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] => [1,1,1,1,1,1,1,1] => 8
[7,7,3] => [7,3] => [3] => [2,1] => 1
[7,7,2,1] => [7,2,1] => [2,1] => [3] => 3
[7,7,1,1,1] => [7,1,1,1] => [1,1,1] => [1,1,1] => 3
[7,6,4] => [6,4] => [4] => [2,2] => 2
[7,6,3,1] => [6,3,1] => [3,1] => [2,1,1] => 2
[7,6,2,2] => [6,2,2] => [2,2] => [4] => 4
[7,6,2,1,1] => [6,2,1,1] => [2,1,1] => [3,1] => 2
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[7,5,5] => [5,5] => [5] => [2,2,1] => 4
[7,5,4,1] => [5,4,1] => [4,1] => [3,2] => 4
[7,5,3,2] => [5,3,2] => [3,2] => [4,1] => 3
[7,5,3,1,1] => [5,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[7,5,2,2,1] => [5,2,2,1] => [2,2,1] => [5] => 5
[7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[7,4,4,2] => [4,4,2] => [4,2] => [4,2] => 6
[7,4,4,1,1] => [4,4,1,1] => [4,1,1] => [4,1,1] => 0
[7,4,3,3] => [4,3,3] => [3,3] => [3,2,1] => 1
[7,4,3,2,1] => [4,3,2,1] => [3,2,1] => [3,3] => 6
[7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[7,4,2,2,2] => [4,2,2,2] => [2,2,2] => [6] => 6
[7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[7,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[7,3,3,2,2] => [3,3,2,2] => [3,2,2] => [6,1] => 5
[7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [7] => 7
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [8] => 8
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[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] => [1,1,1,1,1,1,1,1,1] => 9
[6,6,5] => [6,5] => [5] => [2,2,1] => 4
[6,6,4,1] => [6,4,1] => [4,1] => [3,2] => 4
[6,6,3,2] => [6,3,2] => [3,2] => [4,1] => 3
[6,6,3,1,1] => [6,3,1,1] => [3,1,1] => [2,1,1,1] => 3
[6,6,2,2,1] => [6,2,2,1] => [2,2,1] => [5] => 5
[6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => [3,1,1] => 0
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[6,5,5,1] => [5,5,1] => [5,1] => [2,2,1,1] => 6
[6,5,4,2] => [5,4,2] => [4,2] => [4,2] => 6
[6,5,4,1,1] => [5,4,1,1] => [4,1,1] => [4,1,1] => 0
[6,5,3,3] => [5,3,3] => [3,3] => [3,2,1] => 1
[6,5,3,2,1] => [5,3,2,1] => [3,2,1] => [3,3] => 6
[6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [2,1,1,1,1] => 4
[6,5,2,2,2] => [5,2,2,2] => [2,2,2] => [6] => 6
[6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [5,1] => 4
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[6,4,4,3] => [4,4,3] => [4,3] => [4,3] => 9
[6,4,4,2,1] => [4,4,2,1] => [4,2,1] => [5,2] => 8
[6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => 0
[6,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[6,4,3,2,2] => [4,3,2,2] => [3,2,2] => [6,1] => 5
[6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [7] => 7
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[6,3,3,3,2] => [3,3,3,2] => [3,3,2] => [5,2,1] => 3
[6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [8] => 8
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[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] => [1,1,1,1,1,1,1,1,1,1] => 10
[5,5,5,2] => [5,5,2] => [5,2] => [4,2,1] => 2
[5,5,5,1,1] => [5,5,1,1] => [5,1,1] => [2,2,1,1,1] => 8
[5,5,4,3] => [5,4,3] => [4,3] => [4,3] => 9
[5,5,4,2,1] => [5,4,2,1] => [4,2,1] => [5,2] => 8
[5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => 0
[5,5,3,3,1] => [5,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[5,5,3,2,2] => [5,3,2,2] => [3,2,2] => [6,1] => 5
[5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [2,1,1,1,1,1] => 5
[5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [7] => 7
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [5,1,1] => 0
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [3,1,1,1,1] => 0
[5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[5,4,4,4] => [4,4,4] => [4,4] => [4,4] => 12
[5,4,4,3,1] => [4,4,3,1] => [4,3,1] => [4,3,1] => 4
[5,4,4,2,2] => [4,4,2,2] => [4,2,2] => [6,2] => 10
[5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [6,1,1] => 0
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [4,1,1,1,1] => 0
[5,4,3,3,2] => [4,3,3,2] => [3,3,2] => [5,2,1] => 3
[5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [8] => 8
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [7,1] => 6
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [5,1,1,1] => 0
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1] => 8
[5,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3,2,1] => 8
[5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,2,1,1,1,1] => 4
[5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [8,1] => 7
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => 6
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [3,3,1,1,1] => 6
[5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [9,1] => 8
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 0
[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] => [5,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1] => 10
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[4,4,4,4,1] => [4,4,4,1] => [4,4,1] => [5,4] => 16
[4,4,4,3,2] => [4,4,3,2] => [4,3,2] => [6,3] => 15
[4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [5,2,1,1] => 0
[4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [7,2] => 12
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => [6,1,1,1] => 0
[4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[4,4,3,3,3] => [4,3,3,3] => [3,3,3] => [3,3,2,1] => 8
[4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,2,1,1,1,1] => 4
[4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => [8,1] => 7
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => 6
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [3,3,1,1,1] => 6
[4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [7,1,1] => 0
[4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1] => 9
[4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,2,1,1] => 12
[4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => [7,2,1] => 5
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,3,3,1] => 12
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,2,1,1,1,1,1] => 5
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => [7,3] => 18
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [5,3,1,1] => 0
[4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [3,3,1,1,1,1] => 8
[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] => [2,1,1,1,1,1,1,1,1] => 8
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [9,1] => 8
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,1,1,1] => 0
[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] => [5,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1] => 10
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [11] => 11
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [9,1,1] => 0
[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] => [7,1,1,1,1] => 0
[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] => [5,1,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [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
[3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => [5,3,2,1] => 2
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,2,1,1,1] => 16
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => [5,3,3] => 18
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,3,3,1,1] => 18
[3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 6
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => [10,1] => 9
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [7,3,1] => 10
[3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [5,3,1,1,1] => 0
[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] => [3,3,1,1,1,1,1] => 10
[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] => [2,1,1,1,1,1,1,1,1,1] => 9
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [11] => 11
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [9,1,1] => 0
[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] => [7,1,1,1,1] => 0
[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] => [5,1,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [12] => 12
[3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [11,1] => 10
[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] => [9,1,1,1] => 0
[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] => [7,1,1,1,1,1] => 0
[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] => [5,1,1,1,1,1,1,1] => 0
[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] => [3,1,1,1,1,1,1,1,1,1] => 0
[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] => [1,1,1,1,1,1,1,1,1,1,1,1] => 12
[6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[5,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[6,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[6,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [7,2] => 12
[5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [7,2] => 12
[6,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [7,2] => 12
[5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [7,2] => 12
[6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [7] => 7
[6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => [5,2,1,1] => 0
[5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => [5,2,1,1] => 0
[6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [5,2,1,1] => 0
[5,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [5,2,1,1] => 0
[6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,2,1,1,1] => 3
[6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [6,1,1] => 0
[5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [6,1,1] => 0
[6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [6,1,1] => 0
[6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => 0
[6,5,4,3,2] => [5,4,3,2] => [4,3,2] => [6,3] => 15
[5,5,4,3,2] => [5,4,3,2] => [4,3,2] => [6,3] => 15
[6,4,4,3,2] => [4,4,3,2] => [4,3,2] => [6,3] => 15
[5,4,4,3,2] => [4,4,3,2] => [4,3,2] => [6,3] => 15
[6,5,3,3,2] => [5,3,3,2] => [3,3,2] => [5,2,1] => 3
[5,5,3,3,2] => [5,3,3,2] => [3,3,2] => [5,2,1] => 3
[6,4,3,3,2] => [4,3,3,2] => [3,3,2] => [5,2,1] => 3
[6,5,4,2,2] => [5,4,2,2] => [4,2,2] => [6,2] => 10
[5,5,4,2,2] => [5,4,2,2] => [4,2,2] => [6,2] => 10
[6,4,4,2,2] => [4,4,2,2] => [4,2,2] => [6,2] => 10
[6,5,3,2,2] => [5,3,2,2] => [3,2,2] => [6,1] => 5
[6,5,4,3,1] => [5,4,3,1] => [4,3,1] => [4,3,1] => 4
[5,5,4,3,1] => [5,4,3,1] => [4,3,1] => [4,3,1] => 4
[6,4,4,3,1] => [4,4,3,1] => [4,3,1] => [4,3,1] => 4
[6,5,3,3,1] => [5,3,3,1] => [3,3,1] => [3,2,1,1] => 2
[6,5,4,2,1] => [5,4,2,1] => [4,2,1] => [5,2] => 8
[6,5,4,3] => [5,4,3] => [4,3] => [4,3] => 9
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,3,3] => 24
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,3,3] => 24
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,3,3] => 24
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,3,3] => 24
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,3,3] => 24
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [7,5] => 30
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [7,5] => 30
[7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [5,2,2,2,1] => [7,3,2] => 20
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => [9,2] => 16
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => [7,3] => 18
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [7,3] => 18
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [7,3] => 18
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [9] => 9
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => [8,3,1] => 12
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [5,5,1] => 12
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [5,5,1] => 12
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => [5,5,1] => 12
[7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [5,4,1,1,1] => [5,4,1,1,1] => 0
[6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => [5,4,1,1,1] => 0
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [5,2,1,1,1] => 0
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => [4,3,1,1,1] => 0
[5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => [4,3,1,1,1] => 0
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [6,1,1,1] => 0
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [6,1,1,1] => 0
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [3,3,1,1] => 4
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [4,1,1,1,1] => 0
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [3,1,1,1] => 0
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[6,5,4,3,3,2] => [5,4,3,3,2] => [4,3,3,2] => [7,4,1] => 15
[5,4,3,3,3,2] => [4,3,3,3,2] => [3,3,3,2] => [5,3,2,1] => 2
[4,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => [5,3,2,1] => 2
[6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => [8,3] => 21
[4,4,4,3,2,2] => [4,4,3,2,2] => [4,3,2,2] => [8,3] => 21
[7,6,5,2,2,2] => [6,5,2,2,2] => [5,2,2,2] => [8,2,1] => 6
[6,5,4,2,2,2] => [5,4,2,2,2] => [4,2,2,2] => [8,2] => 14
[5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => [8,1] => 7
[6,6,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => [8] => 8
[4,4,4,4,3,1] => [4,4,4,3,1] => [4,4,3,1] => [6,5,1] => 16
[7,6,5,4,2,1] => [6,5,4,2,1] => [5,4,2,1] => [6,3,3] => 24
[5,5,5,4,2,1] => [5,5,4,2,1] => [5,4,2,1] => [6,3,3] => 24
[4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => [7,4] => 24
[7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => [3,3,3,2] => 18
[6,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => [3,3,3,2] => 18
[5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => [3,3,3,2] => 18
[7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[7,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[7,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,3,3] => 6
[7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => [5,3,2] => 12
[7,6,3,2,2,1] => [6,3,2,2,1] => [3,2,2,1] => [5,3] => 12
[7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => [7] => 7
[7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => [4,3,3,1] => 2
[7,6,5,2,1,1] => [6,5,2,1,1] => [5,2,1,1] => [4,3,1,1] => 0
[7,6,3,2,1,1] => [6,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[7,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [3,3,1] => 2
[7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => [2,2,1,1,1,1] => 10
[7,6,5,4,3] => [6,5,4,3] => [5,4,3] => [5,4,3] => 27
[6,6,5,4,3] => [6,5,4,3] => [5,4,3] => [5,4,3] => 27
[6,5,5,4,3] => [5,5,4,3] => [5,4,3] => [5,4,3] => 27
[5,4,4,4,3] => [4,4,4,3] => [4,4,3] => [6,5] => 25
[5,4,3,3,3] => [4,3,3,3] => [3,3,3] => [3,3,2,1] => 8
[7,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3,2,1] => 8
[7,6,5,4,2] => [6,5,4,2] => [5,4,2] => [6,4,1] => 12
[4,4,4,4,2] => [4,4,4,2] => [4,4,2] => [6,4] => 20
[7,6,5,3,2] => [6,5,3,2] => [5,3,2] => [5,2,2,1] => 0
[7,6,4,3,2] => [6,4,3,2] => [4,3,2] => [6,3] => 15
[7,5,4,3,2] => [5,4,3,2] => [4,3,2] => [6,3] => 15
[7,6,5,4,1] => [6,5,4,1] => [5,4,1] => [4,3,3] => 12
[7,5,4,3,1] => [5,4,3,1] => [4,3,1] => [4,3,1] => 4
[7,6,5,2,1] => [6,5,2,1] => [5,2,1] => [3,3,2] => 4
[6,6,5,2,1] => [6,5,2,1] => [5,2,1] => [3,3,2] => 4
[7,6,4,2,1] => [6,4,2,1] => [4,2,1] => [5,2] => 8
[6,6,4,2,1] => [6,4,2,1] => [4,2,1] => [5,2] => 8
[7,5,4,2,1] => [5,4,2,1] => [4,2,1] => [5,2] => 8
[7,6,3,2,1] => [6,3,2,1] => [3,2,1] => [3,3] => 6
[6,6,3,2,1] => [6,3,2,1] => [3,2,1] => [3,3] => 6
[7,6,5,4] => [6,5,4] => [5,4] => [4,4,1] => 6
[6,5,5,4] => [5,5,4] => [5,4] => [4,4,1] => 6
[7,6,5,3] => [6,5,3] => [5,3] => [3,2,2,1] => 4
[7,6,4,3] => [6,4,3] => [4,3] => [4,3] => 9
[7,5,4,3] => [5,4,3] => [4,3] => [4,3] => 9
[7,6,5,2] => [6,5,2] => [5,2] => [4,2,1] => 2
[7,6,5] => [6,5] => [5] => [2,2,1] => 4
[3,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3,2,1] => 27
[4,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3,2,1] => 27
[4,4,4,4,4] => [4,4,4,4] => [4,4,4] => [6,6] => 30
[5,5,5,5] => [5,5,5] => [5,5] => [4,3,2,1] => 1
[6,6,6,6] => [6,6,6] => [6,6] => [4,4,4] => 24
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[6,6,6] => [6,6] => [6] => [2,2,2] => 6
[7,6,6] => [6,6] => [6] => [2,2,2] => 6
[10,4,4] => [4,4] => [4] => [2,2] => 2
[11,7,3] => [7,3] => [3] => [2,1] => 1
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [10] => 10
[9,6,3] => [6,3] => [3] => [2,1] => 1
[8,6,4,2] => [6,4,2] => [4,2] => [4,2] => 6
[8,6,4] => [6,4] => [4] => [2,2] => 2
[10,6,4] => [6,4] => [4] => [2,2] => 2
[8,7,6] => [7,6] => [6] => [2,2,2] => 6
[9,8,7] => [8,7] => [7] => [2,2,2,1] => 9
[15,5,5] => [5,5] => [5] => [2,2,1] => 4
[7,7,7] => [7,7] => [7] => [2,2,2,1] => 9
[11,7,5,1] => [7,5,1] => [5,1] => [2,2,1,1] => 6
[9,7,5,3,1] => [7,5,3,1] => [5,3,1] => [3,2,2,1,1] => 6
[9,6,4] => [6,4] => [4] => [2,2] => 2
[10,7,3] => [7,3] => [3] => [2,1] => 1
[8,5,4,2] => [5,4,2] => [4,2] => [4,2] => 6
[9,6,5,3] => [6,5,3] => [5,3] => [3,2,2,1] => 4
[10,7,5,3] => [7,5,3] => [5,3] => [3,2,2,1] => 4
[9,6,4,3] => [6,4,3] => [4,3] => [4,3] => 9
[9,7,4] => [7,4] => [4] => [2,2] => 2
[9,7,5,4,1] => [7,5,4,1] => [5,4,1] => [4,3,3] => 12
[8,6,5,3,1] => [6,5,3,1] => [5,3,1] => [3,2,2,1,1] => 6
[10,8,6,4,2] => [8,6,4,2] => [6,4,2] => [6,4,2] => 24
[8,5,5,1] => [5,5,1] => [5,1] => [2,2,1,1] => 6
[9,5,5,1] => [5,5,1] => [5,1] => [2,2,1,1] => 6
[9,7,5,3] => [7,5,3] => [5,3] => [3,2,2,1] => 4
[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] => [3,2,1,1,1,1,1,1,1] => 7
[8,8,8] => [8,8] => [8] => [2,2,2,2] => 12
[7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4
[8,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[8,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [3,3,1,1,1] => 6
[6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [5,5,1,1] => 0
[5,4,3,2,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [3,3,1,1,1,1] => 8
[6,5,4,3,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [5,2,1,1,1,1] => 0
[7,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [5,5,1,1] => 0
[5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [3,2,2,2,2] => [10,1] => 9
[6,5,5,5] => [5,5,5] => [5,5] => [4,3,2,1] => 1
[5,4,4,4,4] => [4,4,4,4] => [4,4,4] => [6,6] => 30
[8,7,6,3,2,1] => [7,6,3,2,1] => [6,3,2,1] => [5,5,2] => 24
[8,7,6,5] => [7,6,5] => [6,5] => [4,4,3] => 18
[8,7,5] => [7,5] => [5] => [2,2,1] => 4
[8,7,6,4] => [7,6,4] => [6,4] => [4,4,2] => 12
[5,5,5,5,1] => [5,5,5,1] => [5,5,1] => [4,3,2,1,1] => 2
[6,6,6,1] => [6,6,1] => [6,1] => [3,2,2] => 2
[6,6,6,1,1] => [6,6,1,1] => [6,1,1] => [4,2,1,1] => 0
[7,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => [5,5] => 20
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [5,5,1] => 12
search for individual values
searching the database for the individual values of this statistic
Description
The leading coefficient of the rook polynomial of an integer partition.
Let $m$ be the minimum of the number of parts and the size of the first part of an integer partition $\lambda$. Then this statistic yields the number of ways to place $m$ non-attacking rooks on the Ferrers board of $\lambda$.
Let $m$ be the minimum of the number of parts and the size of the first part of an integer partition $\lambda$. Then this statistic yields the number of ways to place $m$ non-attacking rooks on the Ferrers board of $\lambda$.
Map
2-conjugate
Description
Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
Map
first row removal
Description
Removes the first entry of an integer partition
searching the database
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