Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000206: Integer partitions ⟶ ℤ
Values
[2,2] => [2] => [1,1] => [1] => 0
[3,2] => [2] => [1,1] => [1] => 0
[2,2,1] => [2,1] => [2,1] => [1] => 0
[4,2] => [2] => [1,1] => [1] => 0
[3,3] => [3] => [1,1,1] => [1,1] => 0
[3,2,1] => [2,1] => [2,1] => [1] => 0
[2,2,2] => [2,2] => [2,2] => [2] => 0
[2,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[5,2] => [2] => [1,1] => [1] => 0
[4,3] => [3] => [1,1,1] => [1,1] => 0
[4,2,1] => [2,1] => [2,1] => [1] => 0
[3,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[3,2,2] => [2,2] => [2,2] => [2] => 0
[3,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[2,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[2,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[6,2] => [2] => [1,1] => [1] => 0
[5,3] => [3] => [1,1,1] => [1,1] => 0
[5,2,1] => [2,1] => [2,1] => [1] => 0
[4,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[4,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[4,2,2] => [2,2] => [2,2] => [2] => 0
[4,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[3,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[3,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[3,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[3,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[2,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[2,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[7,2] => [2] => [1,1] => [1] => 0
[6,3] => [3] => [1,1,1] => [1,1] => 0
[6,2,1] => [2,1] => [2,1] => [1] => 0
[5,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[5,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[5,2,2] => [2,2] => [2,2] => [2] => 0
[5,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[4,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[4,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[4,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[4,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[4,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[3,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[3,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[3,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[3,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[3,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[2,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[8,2] => [2] => [1,1] => [1] => 0
[7,3] => [3] => [1,1,1] => [1,1] => 0
[7,2,1] => [2,1] => [2,1] => [1] => 0
[6,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[6,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[6,2,2] => [2,2] => [2,2] => [2] => 0
[6,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[5,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[5,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[5,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[5,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[5,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[4,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[4,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[4,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[4,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[4,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[4,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[4,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[3,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[3,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[3,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[3,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[2,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[2,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[9,2] => [2] => [1,1] => [1] => 0
[8,3] => [3] => [1,1,1] => [1,1] => 0
[8,2,1] => [2,1] => [2,1] => [1] => 0
[7,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[7,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[7,2,2] => [2,2] => [2,2] => [2] => 0
[7,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[6,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[6,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[6,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[6,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[6,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[6,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[5,5,1] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[5,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[5,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
>>> Load all 1116 entries. <<<[5,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[5,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[5,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[4,4,3] => [4,3] => [2,2,2,1] => [2,2,1] => 1
[4,4,2,1] => [4,2,1] => [3,2,1,1] => [2,1,1] => 0
[4,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[4,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[4,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[4,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[4,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[3,3,3,2] => [3,3,2] => [3,3,2] => [3,2] => 1
[3,3,3,1,1] => [3,3,1,1] => [4,2,2] => [2,2] => 0
[3,3,2,2,1] => [3,2,2,1] => [4,3,1] => [3,1] => 0
[3,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => [2,1] => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,1,1] => [1,1] => 0
[3,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[3,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [5,4] => [4] => 0
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,3] => [3] => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,2] => [2] => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => [1] => 0
[10,2] => [2] => [1,1] => [1] => 0
[9,3] => [3] => [1,1,1] => [1,1] => 0
[9,2,1] => [2,1] => [2,1] => [1] => 0
[8,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[8,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[8,2,2] => [2,2] => [2,2] => [2] => 0
[8,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[7,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[7,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[7,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[7,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[7,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[7,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[6,6] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,5,1] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[6,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[6,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[6,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[6,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[5,5,2] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 0
[5,5,1,1] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[5,4,3] => [4,3] => [2,2,2,1] => [2,2,1] => 1
[5,4,2,1] => [4,2,1] => [3,2,1,1] => [2,1,1] => 0
[5,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[5,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[5,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[5,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[5,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[4,4,4] => [4,4] => [2,2,2,2] => [2,2,2] => 1
[4,4,3,1] => [4,3,1] => [3,2,2,1] => [2,2,1] => 1
[4,4,2,2] => [4,2,2] => [3,3,1,1] => [3,1,1] => 0
[4,4,2,1,1] => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => [5,1,1,1] => [1,1,1] => 0
[4,3,3,2] => [3,3,2] => [3,3,2] => [3,2] => 1
[4,3,3,1,1] => [3,3,1,1] => [4,2,2] => [2,2] => 0
[4,3,2,2,1] => [3,2,2,1] => [4,3,1] => [3,1] => 0
[4,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => [2,1] => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,1,1] => [1,1] => 0
[4,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[4,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[3,3,3,3] => [3,3,3] => [3,3,3] => [3,3] => 1
[3,3,3,2,1] => [3,3,2,1] => [4,3,2] => [3,2] => 1
[3,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => [2,2] => 0
[3,3,2,2,2] => [3,2,2,2] => [4,4,1] => [4,1] => 0
[3,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => [3,1] => 0
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => [2,1] => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,1,1] => [1,1] => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => [5,4] => [4] => 0
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,3] => [3] => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,2] => [2] => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => [1] => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [5,5] => [5] => 0
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,4] => [4] => 0
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,3] => [3] => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => [2] => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => [1] => 0
[11,2] => [2] => [1,1] => [1] => 0
[10,3] => [3] => [1,1,1] => [1,1] => 0
[10,2,1] => [2,1] => [2,1] => [1] => 0
[9,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[9,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[9,2,2] => [2,2] => [2,2] => [2] => 0
[9,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[8,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[8,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[8,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[8,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[8,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[8,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[7,6] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,5,1] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[7,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[7,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[7,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[7,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[7,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[7,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[7,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[6,6,1] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,5,2] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 0
[6,5,1,1] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[6,4,3] => [4,3] => [2,2,2,1] => [2,2,1] => 1
[6,4,2,1] => [4,2,1] => [3,2,1,1] => [2,1,1] => 0
[6,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[6,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[6,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[6,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[6,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[5,5,3] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 1
[5,5,2,1] => [5,2,1] => [3,2,1,1,1] => [2,1,1,1] => 0
[5,5,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[5,4,4] => [4,4] => [2,2,2,2] => [2,2,2] => 1
[5,4,3,1] => [4,3,1] => [3,2,2,1] => [2,2,1] => 1
[5,4,2,2] => [4,2,2] => [3,3,1,1] => [3,1,1] => 0
[5,4,2,1,1] => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => [5,1,1,1] => [1,1,1] => 0
[5,3,3,2] => [3,3,2] => [3,3,2] => [3,2] => 1
[5,3,3,1,1] => [3,3,1,1] => [4,2,2] => [2,2] => 0
[5,3,2,2,1] => [3,2,2,1] => [4,3,1] => [3,1] => 0
[5,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => [2,1] => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,1,1] => [1,1] => 0
[5,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[5,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[4,4,4,1] => [4,4,1] => [3,2,2,2] => [2,2,2] => 1
[4,4,3,2] => [4,3,2] => [3,3,2,1] => [3,2,1] => 6
[4,4,3,1,1] => [4,3,1,1] => [4,2,2,1] => [2,2,1] => 1
[4,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => [3,1,1] => 0
[4,4,2,1,1,1] => [4,2,1,1,1] => [5,2,1,1] => [2,1,1] => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => 0
[4,3,3,3] => [3,3,3] => [3,3,3] => [3,3] => 1
[4,3,3,2,1] => [3,3,2,1] => [4,3,2] => [3,2] => 1
[4,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => [2,2] => 0
[4,3,2,2,2] => [3,2,2,2] => [4,4,1] => [4,1] => 0
[4,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => [3,1] => 0
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => [2,1] => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,1,1] => [1,1] => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => [5,4] => [4] => 0
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,3] => [3] => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,2] => [2] => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => [1] => 0
[3,3,3,3,1] => [3,3,3,1] => [4,3,3] => [3,3] => 1
[3,3,3,2,2] => [3,3,2,2] => [4,4,2] => [4,2] => 3
[3,3,3,2,1,1] => [3,3,2,1,1] => [5,3,2] => [3,2] => 1
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => [2,2] => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => [5,4,1] => [4,1] => 0
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,3,1] => [3,1] => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => [2,1] => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => [5,5] => [5] => 0
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,4] => [4] => 0
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,3] => [3] => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => [2] => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => [1] => 0
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,5] => [5] => 0
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,4] => [4] => 0
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => [3] => 0
[2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,2] => [2] => 0
[2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => 0
[12,2] => [2] => [1,1] => [1] => 0
[11,3] => [3] => [1,1,1] => [1,1] => 0
[11,2,1] => [2,1] => [2,1] => [1] => 0
[10,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[10,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[10,2,2] => [2,2] => [2,2] => [2] => 0
[10,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[9,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[9,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[9,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[9,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[9,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[9,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[8,6] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,5,1] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[8,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[8,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[8,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[8,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[8,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[8,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[8,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[7,7] => [7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,6,1] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,5,2] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 0
[7,5,1,1] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[7,4,3] => [4,3] => [2,2,2,1] => [2,2,1] => 1
[7,4,2,1] => [4,2,1] => [3,2,1,1] => [2,1,1] => 0
[7,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[7,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[7,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[7,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[7,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[6,6,2] => [6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[6,6,1,1] => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,5,3] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 1
[6,5,2,1] => [5,2,1] => [3,2,1,1,1] => [2,1,1,1] => 0
[6,5,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[6,4,4] => [4,4] => [2,2,2,2] => [2,2,2] => 1
[6,4,3,1] => [4,3,1] => [3,2,2,1] => [2,2,1] => 1
[6,4,2,2] => [4,2,2] => [3,3,1,1] => [3,1,1] => 0
[6,4,2,1,1] => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => [5,1,1,1] => [1,1,1] => 0
[6,3,3,2] => [3,3,2] => [3,3,2] => [3,2] => 1
[6,3,3,1,1] => [3,3,1,1] => [4,2,2] => [2,2] => 0
[6,3,2,2,1] => [3,2,2,1] => [4,3,1] => [3,1] => 0
[6,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => [2,1] => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,1,1] => [1,1] => 0
[6,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[6,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[5,5,4] => [5,4] => [2,2,2,2,1] => [2,2,2,1] => 7
[5,5,3,1] => [5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[5,5,2,2] => [5,2,2] => [3,3,1,1,1] => [3,1,1,1] => 0
[5,5,2,1,1] => [5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
[5,4,4,1] => [4,4,1] => [3,2,2,2] => [2,2,2] => 1
[5,4,3,2] => [4,3,2] => [3,3,2,1] => [3,2,1] => 6
[5,4,3,1,1] => [4,3,1,1] => [4,2,2,1] => [2,2,1] => 1
[5,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => [3,1,1] => 0
[5,4,2,1,1,1] => [4,2,1,1,1] => [5,2,1,1] => [2,1,1] => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => 0
[5,3,3,3] => [3,3,3] => [3,3,3] => [3,3] => 1
[5,3,3,2,1] => [3,3,2,1] => [4,3,2] => [3,2] => 1
[5,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => [2,2] => 0
[5,3,2,2,2] => [3,2,2,2] => [4,4,1] => [4,1] => 0
[5,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => [3,1] => 0
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => [2,1] => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,1,1] => [1,1] => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => [5,4] => [4] => 0
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,3] => [3] => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,2] => [2] => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => [1] => 0
[4,4,4,2] => [4,4,2] => [3,3,2,2] => [3,2,2] => 8
[4,4,4,1,1] => [4,4,1,1] => [4,2,2,2] => [2,2,2] => 1
[4,4,3,3] => [4,3,3] => [3,3,3,1] => [3,3,1] => 17
[4,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [3,2,1] => 6
[4,4,3,1,1,1] => [4,3,1,1,1] => [5,2,2,1] => [2,2,1] => 1
[4,4,2,2,2] => [4,2,2,2] => [4,4,1,1] => [4,1,1] => 0
[4,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => [3,1,1] => 0
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => 0
[4,3,3,3,1] => [3,3,3,1] => [4,3,3] => [3,3] => 1
[4,3,3,2,2] => [3,3,2,2] => [4,4,2] => [4,2] => 3
[4,3,3,2,1,1] => [3,3,2,1,1] => [5,3,2] => [3,2] => 1
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => [2,2] => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => [5,4,1] => [4,1] => 0
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,3,1] => [3,1] => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => [2,1] => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => [5,5] => [5] => 0
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,4] => [4] => 0
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,3] => [3] => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => [2] => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => [1] => 0
[3,3,3,3,2] => [3,3,3,2] => [4,4,3] => [4,3] => 11
[3,3,3,3,1,1] => [3,3,3,1,1] => [5,3,3] => [3,3] => 1
[3,3,3,2,2,1] => [3,3,2,2,1] => [5,4,2] => [4,2] => 3
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => [3,2] => 1
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => [2,2] => 0
[3,3,2,2,2,2] => [3,2,2,2,2] => [5,5,1] => [5,1] => 0
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,4,1] => [4,1] => 0
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,3,1] => [3,1] => 0
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => 0
[3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => 0
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,5] => [5] => 0
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,4] => [4] => 0
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => [3] => 0
[3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,2] => [2] => 0
[3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => 0
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,6] => [6] => 0
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,5] => [5] => 0
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => [4] => 0
[2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,3] => [3] => 0
[2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => 0
[2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [1] => 0
[13,2] => [2] => [1,1] => [1] => 0
[12,3] => [3] => [1,1,1] => [1,1] => 0
[12,2,1] => [2,1] => [2,1] => [1] => 0
[11,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[11,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[11,2,2] => [2,2] => [2,2] => [2] => 0
[11,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[10,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[10,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[10,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[10,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[10,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[10,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[9,6] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[9,5,1] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[9,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[9,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[9,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[9,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[9,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[9,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[9,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[8,7] => [7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,6,1] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,5,2] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 0
[8,5,1,1] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[8,4,3] => [4,3] => [2,2,2,1] => [2,2,1] => 1
[8,4,2,1] => [4,2,1] => [3,2,1,1] => [2,1,1] => 0
[8,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[8,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[8,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[8,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[8,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[7,7,1] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,6,2] => [6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[7,6,1,1] => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,5,3] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 1
[7,5,2,1] => [5,2,1] => [3,2,1,1,1] => [2,1,1,1] => 0
[7,5,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[7,4,4] => [4,4] => [2,2,2,2] => [2,2,2] => 1
[7,4,3,1] => [4,3,1] => [3,2,2,1] => [2,2,1] => 1
[7,4,2,2] => [4,2,2] => [3,3,1,1] => [3,1,1] => 0
[7,4,2,1,1] => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => [5,1,1,1] => [1,1,1] => 0
[7,3,3,2] => [3,3,2] => [3,3,2] => [3,2] => 1
[7,3,3,1,1] => [3,3,1,1] => [4,2,2] => [2,2] => 0
[7,3,2,2,1] => [3,2,2,1] => [4,3,1] => [3,1] => 0
[7,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => [2,1] => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,1,1] => [1,1] => 0
[7,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[7,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[6,6,3] => [6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[6,6,2,1] => [6,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[6,6,1,1,1] => [6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,5,4] => [5,4] => [2,2,2,2,1] => [2,2,2,1] => 7
[6,5,3,1] => [5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[6,5,2,2] => [5,2,2] => [3,3,1,1,1] => [3,1,1,1] => 0
[6,5,2,1,1] => [5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
[6,4,4,1] => [4,4,1] => [3,2,2,2] => [2,2,2] => 1
[6,4,3,2] => [4,3,2] => [3,3,2,1] => [3,2,1] => 6
[6,4,3,1,1] => [4,3,1,1] => [4,2,2,1] => [2,2,1] => 1
[6,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => [3,1,1] => 0
[6,4,2,1,1,1] => [4,2,1,1,1] => [5,2,1,1] => [2,1,1] => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => 0
[6,3,3,3] => [3,3,3] => [3,3,3] => [3,3] => 1
[6,3,3,2,1] => [3,3,2,1] => [4,3,2] => [3,2] => 1
[6,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => [2,2] => 0
[6,3,2,2,2] => [3,2,2,2] => [4,4,1] => [4,1] => 0
[6,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => [3,1] => 0
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => [2,1] => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,1,1] => [1,1] => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => [5,4] => [4] => 0
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,3] => [3] => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,2] => [2] => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => [1] => 0
[5,5,5] => [5,5] => [2,2,2,2,2] => [2,2,2,2] => 8
[5,5,4,1] => [5,4,1] => [3,2,2,2,1] => [2,2,2,1] => 7
[5,5,3,2] => [5,3,2] => [3,3,2,1,1] => [3,2,1,1] => 8
[5,5,3,1,1] => [5,3,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[5,5,2,2,1] => [5,2,2,1] => [4,3,1,1,1] => [3,1,1,1] => 0
[5,5,2,1,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
[5,4,4,2] => [4,4,2] => [3,3,2,2] => [3,2,2] => 8
[5,4,4,1,1] => [4,4,1,1] => [4,2,2,2] => [2,2,2] => 1
[5,4,3,3] => [4,3,3] => [3,3,3,1] => [3,3,1] => 17
[5,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [3,2,1] => 6
[5,4,3,1,1,1] => [4,3,1,1,1] => [5,2,2,1] => [2,2,1] => 1
[5,4,2,2,2] => [4,2,2,2] => [4,4,1,1] => [4,1,1] => 0
[5,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => [3,1,1] => 0
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => 0
[5,3,3,3,1] => [3,3,3,1] => [4,3,3] => [3,3] => 1
[5,3,3,2,2] => [3,3,2,2] => [4,4,2] => [4,2] => 3
[5,3,3,2,1,1] => [3,3,2,1,1] => [5,3,2] => [3,2] => 1
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => [2,2] => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => [5,4,1] => [4,1] => 0
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,3,1] => [3,1] => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => [2,1] => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => [5,5] => [5] => 0
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,4] => [4] => 0
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,3] => [3] => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => [2] => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => [1] => 0
[4,4,4,3] => [4,4,3] => [3,3,3,2] => [3,3,2] => 39
[4,4,4,2,1] => [4,4,2,1] => [4,3,2,2] => [3,2,2] => 8
[4,4,4,1,1,1] => [4,4,1,1,1] => [5,2,2,2] => [2,2,2] => 1
[4,4,3,3,1] => [4,3,3,1] => [4,3,3,1] => [3,3,1] => 17
[4,4,3,2,2] => [4,3,2,2] => [4,4,2,1] => [4,2,1] => 16
[4,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => [3,2,1] => 6
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [6,2,2,1] => [2,2,1] => 1
[4,4,2,2,2,1] => [4,2,2,2,1] => [5,4,1,1] => [4,1,1] => 0
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => [3,1,1] => 0
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [7,2,1,1] => [2,1,1] => 0
[4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [8,1,1,1] => [1,1,1] => 0
[4,3,3,3,2] => [3,3,3,2] => [4,4,3] => [4,3] => 11
[4,3,3,3,1,1] => [3,3,3,1,1] => [5,3,3] => [3,3] => 1
[4,3,3,2,2,1] => [3,3,2,2,1] => [5,4,2] => [4,2] => 3
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => [3,2] => 1
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => [2,2] => 0
[4,3,2,2,2,2] => [3,2,2,2,2] => [5,5,1] => [5,1] => 0
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,4,1] => [4,1] => 0
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,3,1] => [3,1] => 0
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => 0
[4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => 0
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,5] => [5] => 0
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,4] => [4] => 0
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => [3] => 0
[4,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,2] => [2] => 0
[4,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => 0
[3,3,3,3,3] => [3,3,3,3] => [4,4,4] => [4,4] => 14
[3,3,3,3,2,1] => [3,3,3,2,1] => [5,4,3] => [4,3] => 11
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [6,3,3] => [3,3] => 1
[3,3,3,2,2,2] => [3,3,2,2,2] => [5,5,2] => [5,2] => 7
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [6,4,2] => [4,2] => 3
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [7,3,2] => [3,2] => 1
[3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [8,2,2] => [2,2] => 0
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [6,5,1] => [5,1] => 0
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [7,4,1] => [4,1] => 0
[3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [8,3,1] => [3,1] => 0
[3,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => [2,1] => 0
[3,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [1,1] => 0
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,6] => [6] => 0
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,5] => [5] => 0
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => [4] => 0
[3,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,3] => [3] => 0
[3,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => 0
[3,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [1] => 0
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [7,6] => [6] => 0
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [8,5] => [5] => 0
[2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [9,4] => [4] => 0
[2,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [10,3] => [3] => 0
[2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2] => 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] => [12,1] => [1] => 0
[14,2] => [2] => [1,1] => [1] => 0
[13,3] => [3] => [1,1,1] => [1,1] => 0
[13,2,1] => [2,1] => [2,1] => [1] => 0
[12,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[12,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[12,2,2] => [2,2] => [2,2] => [2] => 0
[12,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[11,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[11,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[11,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[11,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[11,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[11,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[10,6] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[10,5,1] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[10,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[10,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[10,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[10,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[10,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[10,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[10,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[9,7] => [7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[9,6,1] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[9,5,2] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 0
[9,5,1,1] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[9,4,3] => [4,3] => [2,2,2,1] => [2,2,1] => 1
[9,4,2,1] => [4,2,1] => [3,2,1,1] => [2,1,1] => 0
[9,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[9,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[9,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[9,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[9,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[8,8] => [8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[8,7,1] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,6,2] => [6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[8,6,1,1] => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,5,3] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 1
[8,5,2,1] => [5,2,1] => [3,2,1,1,1] => [2,1,1,1] => 0
[8,5,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[8,4,4] => [4,4] => [2,2,2,2] => [2,2,2] => 1
[8,4,3,1] => [4,3,1] => [3,2,2,1] => [2,2,1] => 1
[8,4,2,2] => [4,2,2] => [3,3,1,1] => [3,1,1] => 0
[8,4,2,1,1] => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => [5,1,1,1] => [1,1,1] => 0
[8,3,3,2] => [3,3,2] => [3,3,2] => [3,2] => 1
[8,3,3,1,1] => [3,3,1,1] => [4,2,2] => [2,2] => 0
[8,3,2,2,1] => [3,2,2,1] => [4,3,1] => [3,1] => 0
[8,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => [2,1] => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,1,1] => [1,1] => 0
[8,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[8,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[7,7,2] => [7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[7,7,1,1] => [7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,6,3] => [6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[7,6,2,1] => [6,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[7,6,1,1,1] => [6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,5,4] => [5,4] => [2,2,2,2,1] => [2,2,2,1] => 7
[7,5,3,1] => [5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[7,5,2,2] => [5,2,2] => [3,3,1,1,1] => [3,1,1,1] => 0
[7,5,2,1,1] => [5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
[7,4,4,1] => [4,4,1] => [3,2,2,2] => [2,2,2] => 1
[7,4,3,2] => [4,3,2] => [3,3,2,1] => [3,2,1] => 6
[7,4,3,1,1] => [4,3,1,1] => [4,2,2,1] => [2,2,1] => 1
[7,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => [3,1,1] => 0
[7,4,2,1,1,1] => [4,2,1,1,1] => [5,2,1,1] => [2,1,1] => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => 0
[7,3,3,3] => [3,3,3] => [3,3,3] => [3,3] => 1
[7,3,3,2,1] => [3,3,2,1] => [4,3,2] => [3,2] => 1
[7,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => [2,2] => 0
[7,3,2,2,2] => [3,2,2,2] => [4,4,1] => [4,1] => 0
[7,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => [3,1] => 0
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => [2,1] => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,1,1] => [1,1] => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => [5,4] => [4] => 0
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,3] => [3] => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,2] => [2] => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => [1] => 0
[6,6,4] => [6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 8
[6,6,3,1] => [6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[6,6,2,2] => [6,2,2] => [3,3,1,1,1,1] => [3,1,1,1,1] => 0
[6,6,2,1,1] => [6,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,5,5] => [5,5] => [2,2,2,2,2] => [2,2,2,2] => 8
[6,5,4,1] => [5,4,1] => [3,2,2,2,1] => [2,2,2,1] => 7
[6,5,3,2] => [5,3,2] => [3,3,2,1,1] => [3,2,1,1] => 8
[6,5,3,1,1] => [5,3,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[6,5,2,2,1] => [5,2,2,1] => [4,3,1,1,1] => [3,1,1,1] => 0
[6,5,2,1,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
[6,4,4,2] => [4,4,2] => [3,3,2,2] => [3,2,2] => 8
[6,4,4,1,1] => [4,4,1,1] => [4,2,2,2] => [2,2,2] => 1
[6,4,3,3] => [4,3,3] => [3,3,3,1] => [3,3,1] => 17
[6,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [3,2,1] => 6
[6,4,3,1,1,1] => [4,3,1,1,1] => [5,2,2,1] => [2,2,1] => 1
[6,4,2,2,2] => [4,2,2,2] => [4,4,1,1] => [4,1,1] => 0
[6,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => [3,1,1] => 0
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => 0
[6,3,3,3,1] => [3,3,3,1] => [4,3,3] => [3,3] => 1
[6,3,3,2,2] => [3,3,2,2] => [4,4,2] => [4,2] => 3
[6,3,3,2,1,1] => [3,3,2,1,1] => [5,3,2] => [3,2] => 1
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => [2,2] => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => [5,4,1] => [4,1] => 0
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,3,1] => [3,1] => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => [2,1] => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => [5,5] => [5] => 0
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,4] => [4] => 0
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,3] => [3] => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => [2] => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => [1] => 0
[5,5,5,1] => [5,5,1] => [3,2,2,2,2] => [2,2,2,2] => 8
[5,5,4,2] => [5,4,2] => [3,3,2,2,1] => [3,2,2,1] => 30
[5,5,4,1,1] => [5,4,1,1] => [4,2,2,2,1] => [2,2,2,1] => 7
[5,5,3,3] => [5,3,3] => [3,3,3,1,1] => [3,3,1,1] => 24
[5,5,3,2,1] => [5,3,2,1] => [4,3,2,1,1] => [3,2,1,1] => 8
[5,5,3,1,1,1] => [5,3,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => 1
[5,5,2,2,2] => [5,2,2,2] => [4,4,1,1,1] => [4,1,1,1] => 0
[5,5,2,2,1,1] => [5,2,2,1,1] => [5,3,1,1,1] => [3,1,1,1] => 0
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 0
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 0
[5,4,4,3] => [4,4,3] => [3,3,3,2] => [3,3,2] => 39
[5,4,4,2,1] => [4,4,2,1] => [4,3,2,2] => [3,2,2] => 8
[5,4,4,1,1,1] => [4,4,1,1,1] => [5,2,2,2] => [2,2,2] => 1
[5,4,3,3,1] => [4,3,3,1] => [4,3,3,1] => [3,3,1] => 17
[5,4,3,2,2] => [4,3,2,2] => [4,4,2,1] => [4,2,1] => 16
[5,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => [3,2,1] => 6
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [6,2,2,1] => [2,2,1] => 1
[5,4,2,2,2,1] => [4,2,2,2,1] => [5,4,1,1] => [4,1,1] => 0
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => [3,1,1] => 0
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [7,2,1,1] => [2,1,1] => 0
[5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [8,1,1,1] => [1,1,1] => 0
[5,3,3,3,2] => [3,3,3,2] => [4,4,3] => [4,3] => 11
[5,3,3,3,1,1] => [3,3,3,1,1] => [5,3,3] => [3,3] => 1
[5,3,3,2,2,1] => [3,3,2,2,1] => [5,4,2] => [4,2] => 3
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => [3,2] => 1
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => [2,2] => 0
[5,3,2,2,2,2] => [3,2,2,2,2] => [5,5,1] => [5,1] => 0
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,4,1] => [4,1] => 0
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,3,1] => [3,1] => 0
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => 0
[5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => 0
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,5] => [5] => 0
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,4] => [4] => 0
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => [3] => 0
[5,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,2] => [2] => 0
[5,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => 0
[4,4,4,3,1] => [4,4,3,1] => [4,3,3,2] => [3,3,2] => 39
[4,4,4,2,2] => [4,4,2,2] => [4,4,2,2] => [4,2,2] => 28
[4,4,4,2,1,1] => [4,4,2,1,1] => [5,3,2,2] => [3,2,2] => 8
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [6,2,2,2] => [2,2,2] => 1
[4,4,3,3,2] => [4,3,3,2] => [4,4,3,1] => [4,3,1] => 53
[4,4,3,3,1,1] => [4,3,3,1,1] => [5,3,3,1] => [3,3,1] => 17
[4,4,3,2,2,1] => [4,3,2,2,1] => [5,4,2,1] => [4,2,1] => 16
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => 6
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [7,2,2,1] => [2,2,1] => 1
[4,4,2,2,2,2] => [4,2,2,2,2] => [5,5,1,1] => [5,1,1] => 0
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [6,4,1,1] => [4,1,1] => 0
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1] => [3,1,1] => 0
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [8,2,1,1] => [2,1,1] => 0
[4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [1,1,1] => 0
[4,3,3,3,3] => [3,3,3,3] => [4,4,4] => [4,4] => 14
[4,3,3,3,2,1] => [3,3,3,2,1] => [5,4,3] => [4,3] => 11
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [6,3,3] => [3,3] => 1
[4,3,3,2,2,2] => [3,3,2,2,2] => [5,5,2] => [5,2] => 7
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [6,4,2] => [4,2] => 3
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [7,3,2] => [3,2] => 1
[4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [8,2,2] => [2,2] => 0
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [6,5,1] => [5,1] => 0
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [7,4,1] => [4,1] => 0
[4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [8,3,1] => [3,1] => 0
[4,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => [2,1] => 0
[4,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [1,1] => 0
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,6] => [6] => 0
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,5] => [5] => 0
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => [4] => 0
[4,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,3] => [3] => 0
[4,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => 0
[4,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [1] => 0
[3,3,3,3,3,1] => [3,3,3,3,1] => [5,4,4] => [4,4] => 14
[3,3,3,3,2,2] => [3,3,3,2,2] => [5,5,3] => [5,3] => 31
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [6,4,3] => [4,3] => 11
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [7,3,3] => [3,3] => 1
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [6,5,2] => [5,2] => 7
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [7,4,2] => [4,2] => 3
[3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [8,3,2] => [3,2] => 1
[3,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => [2,2] => 0
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [6,6,1] => [6,1] => 0
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [7,5,1] => [5,1] => 0
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [8,4,1] => [4,1] => 0
[3,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [9,3,1] => [3,1] => 0
[3,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [2,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [1,1] => 0
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [7,6] => [6] => 0
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [8,5] => [5] => 0
[3,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [9,4] => [4] => 0
[3,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [10,3] => [3] => 0
[3,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2] => 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] => [12,1] => [1] => 0
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [7,7] => [7] => 0
[2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [8,6] => [6] => 0
[2,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [9,5] => [5] => 0
[2,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [10,4] => [4] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [3] => 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] => [12,2] => [2] => 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] => [13,1] => [1] => 0
[15,2] => [2] => [1,1] => [1] => 0
[14,3] => [3] => [1,1,1] => [1,1] => 0
[14,2,1] => [2,1] => [2,1] => [1] => 0
[13,4] => [4] => [1,1,1,1] => [1,1,1] => 0
[13,3,1] => [3,1] => [2,1,1] => [1,1] => 0
[13,2,2] => [2,2] => [2,2] => [2] => 0
[13,2,1,1] => [2,1,1] => [3,1] => [1] => 0
[12,5] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[12,4,1] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[12,3,2] => [3,2] => [2,2,1] => [2,1] => 0
[12,3,1,1] => [3,1,1] => [3,1,1] => [1,1] => 0
[12,2,2,1] => [2,2,1] => [3,2] => [2] => 0
[12,2,1,1,1] => [2,1,1,1] => [4,1] => [1] => 0
[11,6] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[11,5,1] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[11,4,2] => [4,2] => [2,2,1,1] => [2,1,1] => 0
[11,4,1,1] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[11,3,3] => [3,3] => [2,2,2] => [2,2] => 0
[11,3,2,1] => [3,2,1] => [3,2,1] => [2,1] => 0
[11,3,1,1,1] => [3,1,1,1] => [4,1,1] => [1,1] => 0
[11,2,2,2] => [2,2,2] => [3,3] => [3] => 0
[11,2,2,1,1] => [2,2,1,1] => [4,2] => [2] => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => [5,1] => [1] => 0
[10,7] => [7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[10,6,1] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[10,5,2] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 0
[10,5,1,1] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[10,4,3] => [4,3] => [2,2,2,1] => [2,2,1] => 1
[10,4,2,1] => [4,2,1] => [3,2,1,1] => [2,1,1] => 0
[10,4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[10,3,3,1] => [3,3,1] => [3,2,2] => [2,2] => 0
[10,3,2,2] => [3,2,2] => [3,3,1] => [3,1] => 0
[10,3,2,1,1] => [3,2,1,1] => [4,2,1] => [2,1] => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => [5,1,1] => [1,1] => 0
[10,2,2,2,1] => [2,2,2,1] => [4,3] => [3] => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => [5,2] => [2] => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [6,1] => [1] => 0
[9,8] => [8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[9,7,1] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[9,6,2] => [6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[9,6,1,1] => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[9,5,3] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 1
[9,5,2,1] => [5,2,1] => [3,2,1,1,1] => [2,1,1,1] => 0
[9,5,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[9,4,4] => [4,4] => [2,2,2,2] => [2,2,2] => 1
[9,4,3,1] => [4,3,1] => [3,2,2,1] => [2,2,1] => 1
[9,4,2,2] => [4,2,2] => [3,3,1,1] => [3,1,1] => 0
[9,4,2,1,1] => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => [5,1,1,1] => [1,1,1] => 0
[9,3,3,2] => [3,3,2] => [3,3,2] => [3,2] => 1
[9,3,3,1,1] => [3,3,1,1] => [4,2,2] => [2,2] => 0
[9,3,2,2,1] => [3,2,2,1] => [4,3,1] => [3,1] => 0
[9,3,2,1,1,1] => [3,2,1,1,1] => [5,2,1] => [2,1] => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [6,1,1] => [1,1] => 0
[9,2,2,2,2] => [2,2,2,2] => [4,4] => [4] => 0
[9,2,2,2,1,1] => [2,2,2,1,1] => [5,3] => [3] => 0
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [6,2] => [2] => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [7,1] => [1] => 0
[8,8,1] => [8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[8,7,2] => [7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[8,7,1,1] => [7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,6,3] => [6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[8,6,2,1] => [6,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[8,6,1,1,1] => [6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,5,4] => [5,4] => [2,2,2,2,1] => [2,2,2,1] => 7
[8,5,3,1] => [5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[8,5,2,2] => [5,2,2] => [3,3,1,1,1] => [3,1,1,1] => 0
[8,5,2,1,1] => [5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
[8,4,4,1] => [4,4,1] => [3,2,2,2] => [2,2,2] => 1
[8,4,3,2] => [4,3,2] => [3,3,2,1] => [3,2,1] => 6
[8,4,3,1,1] => [4,3,1,1] => [4,2,2,1] => [2,2,1] => 1
[8,4,2,2,1] => [4,2,2,1] => [4,3,1,1] => [3,1,1] => 0
[8,4,2,1,1,1] => [4,2,1,1,1] => [5,2,1,1] => [2,1,1] => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => 0
[8,3,3,3] => [3,3,3] => [3,3,3] => [3,3] => 1
[8,3,3,2,1] => [3,3,2,1] => [4,3,2] => [3,2] => 1
[8,3,3,1,1,1] => [3,3,1,1,1] => [5,2,2] => [2,2] => 0
[8,3,2,2,2] => [3,2,2,2] => [4,4,1] => [4,1] => 0
[8,3,2,2,1,1] => [3,2,2,1,1] => [5,3,1] => [3,1] => 0
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [6,2,1] => [2,1] => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [7,1,1] => [1,1] => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => [5,4] => [4] => 0
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [6,3] => [3] => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [7,2] => [2] => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => [1] => 0
[7,7,3] => [7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[7,7,2,1] => [7,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[7,7,1,1,1] => [7,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,6,4] => [6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 8
[7,6,3,1] => [6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[7,6,2,2] => [6,2,2] => [3,3,1,1,1,1] => [3,1,1,1,1] => 0
[7,6,2,1,1] => [6,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,5,5] => [5,5] => [2,2,2,2,2] => [2,2,2,2] => 8
[7,5,4,1] => [5,4,1] => [3,2,2,2,1] => [2,2,2,1] => 7
[7,5,3,2] => [5,3,2] => [3,3,2,1,1] => [3,2,1,1] => 8
[7,5,3,1,1] => [5,3,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[7,5,2,2,1] => [5,2,2,1] => [4,3,1,1,1] => [3,1,1,1] => 0
[7,5,2,1,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
[7,4,4,2] => [4,4,2] => [3,3,2,2] => [3,2,2] => 8
[7,4,4,1,1] => [4,4,1,1] => [4,2,2,2] => [2,2,2] => 1
[7,4,3,3] => [4,3,3] => [3,3,3,1] => [3,3,1] => 17
[7,4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [3,2,1] => 6
[7,4,3,1,1,1] => [4,3,1,1,1] => [5,2,2,1] => [2,2,1] => 1
[7,4,2,2,2] => [4,2,2,2] => [4,4,1,1] => [4,1,1] => 0
[7,4,2,2,1,1] => [4,2,2,1,1] => [5,3,1,1] => [3,1,1] => 0
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => 0
[7,3,3,3,1] => [3,3,3,1] => [4,3,3] => [3,3] => 1
[7,3,3,2,2] => [3,3,2,2] => [4,4,2] => [4,2] => 3
[7,3,3,2,1,1] => [3,3,2,1,1] => [5,3,2] => [3,2] => 1
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [6,2,2] => [2,2] => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => [5,4,1] => [4,1] => 0
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [6,3,1] => [3,1] => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => [2,1] => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => [5,5] => [5] => 0
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [6,4] => [4] => 0
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [7,3] => [3] => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => [2] => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [9,1] => [1] => 0
[6,6,4,1] => [6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 8
[6,6,3,2] => [6,3,2] => [3,3,2,1,1,1] => [3,2,1,1,1] => 11
[6,6,3,1,1] => [6,3,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 1
[6,6,2,2,1] => [6,2,2,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 0
[6,6,2,1,1,1] => [6,2,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 0
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,5,5,1] => [5,5,1] => [3,2,2,2,2] => [2,2,2,2] => 8
[6,5,4,2] => [5,4,2] => [3,3,2,2,1] => [3,2,2,1] => 30
[6,5,4,1,1] => [5,4,1,1] => [4,2,2,2,1] => [2,2,2,1] => 7
[6,5,3,3] => [5,3,3] => [3,3,3,1,1] => [3,3,1,1] => 24
[6,5,3,2,1] => [5,3,2,1] => [4,3,2,1,1] => [3,2,1,1] => 8
[6,5,3,1,1,1] => [5,3,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => 1
[6,5,2,2,2] => [5,2,2,2] => [4,4,1,1,1] => [4,1,1,1] => 0
[6,5,2,2,1,1] => [5,2,2,1,1] => [5,3,1,1,1] => [3,1,1,1] => 0
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 0
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 0
[6,4,4,3] => [4,4,3] => [3,3,3,2] => [3,3,2] => 39
[6,4,4,2,1] => [4,4,2,1] => [4,3,2,2] => [3,2,2] => 8
[6,4,4,1,1,1] => [4,4,1,1,1] => [5,2,2,2] => [2,2,2] => 1
[6,4,3,3,1] => [4,3,3,1] => [4,3,3,1] => [3,3,1] => 17
[6,4,3,2,2] => [4,3,2,2] => [4,4,2,1] => [4,2,1] => 16
[6,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => [3,2,1] => 6
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [6,2,2,1] => [2,2,1] => 1
[6,4,2,2,2,1] => [4,2,2,2,1] => [5,4,1,1] => [4,1,1] => 0
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => [3,1,1] => 0
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [7,2,1,1] => [2,1,1] => 0
[6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [8,1,1,1] => [1,1,1] => 0
[6,3,3,3,2] => [3,3,3,2] => [4,4,3] => [4,3] => 11
[6,3,3,3,1,1] => [3,3,3,1,1] => [5,3,3] => [3,3] => 1
[6,3,3,2,2,1] => [3,3,2,2,1] => [5,4,2] => [4,2] => 3
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => [3,2] => 1
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [7,2,2] => [2,2] => 0
[6,3,2,2,2,2] => [3,2,2,2,2] => [5,5,1] => [5,1] => 0
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [6,4,1] => [4,1] => 0
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [7,3,1] => [3,1] => 0
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => 0
[6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => 0
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,5] => [5] => 0
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [7,4] => [4] => 0
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => [3] => 0
[6,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [9,2] => [2] => 0
[6,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => 0
[5,5,5,1,1] => [5,5,1,1] => [4,2,2,2,2] => [2,2,2,2] => 8
[5,5,4,2,1] => [5,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => 30
[5,5,4,1,1,1] => [5,4,1,1,1] => [5,2,2,2,1] => [2,2,2,1] => 7
[5,5,3,3,1] => [5,3,3,1] => [4,3,3,1,1] => [3,3,1,1] => 24
[5,5,3,2,2] => [5,3,2,2] => [4,4,2,1,1] => [4,2,1,1] => 31
[5,5,3,2,1,1] => [5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 8
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [6,2,2,1,1] => [2,2,1,1] => 1
[5,5,2,2,2,1] => [5,2,2,2,1] => [5,4,1,1,1] => [4,1,1,1] => 0
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 0
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [7,2,1,1,1] => [2,1,1,1] => 0
[5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [8,1,1,1,1] => [1,1,1,1] => 0
[5,4,4,3,1] => [4,4,3,1] => [4,3,3,2] => [3,3,2] => 39
[5,4,4,2,2] => [4,4,2,2] => [4,4,2,2] => [4,2,2] => 28
[5,4,4,2,1,1] => [4,4,2,1,1] => [5,3,2,2] => [3,2,2] => 8
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [6,2,2,2] => [2,2,2] => 1
[5,4,3,3,2] => [4,3,3,2] => [4,4,3,1] => [4,3,1] => 53
[5,4,3,3,1,1] => [4,3,3,1,1] => [5,3,3,1] => [3,3,1] => 17
[5,4,3,2,2,1] => [4,3,2,2,1] => [5,4,2,1] => [4,2,1] => 16
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => 6
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [7,2,2,1] => [2,2,1] => 1
[5,4,2,2,2,2] => [4,2,2,2,2] => [5,5,1,1] => [5,1,1] => 0
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [6,4,1,1] => [4,1,1] => 0
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1] => [3,1,1] => 0
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [8,2,1,1] => [2,1,1] => 0
[5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [1,1,1] => 0
[5,3,3,3,3] => [3,3,3,3] => [4,4,4] => [4,4] => 14
[5,3,3,3,2,1] => [3,3,3,2,1] => [5,4,3] => [4,3] => 11
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [6,3,3] => [3,3] => 1
[5,3,3,2,2,2] => [3,3,2,2,2] => [5,5,2] => [5,2] => 7
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [6,4,2] => [4,2] => 3
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [7,3,2] => [3,2] => 1
[5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [8,2,2] => [2,2] => 0
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [6,5,1] => [5,1] => 0
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [7,4,1] => [4,1] => 0
[5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [8,3,1] => [3,1] => 0
[5,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => [2,1] => 0
[5,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [1,1] => 0
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,6] => [6] => 0
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [7,5] => [5] => 0
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => [4] => 0
[5,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [9,3] => [3] => 0
[5,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => 0
[5,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [1] => 0
[4,4,4,3,1,1] => [4,4,3,1,1] => [5,3,3,2] => [3,3,2] => 39
[4,4,4,2,2,1] => [4,4,2,2,1] => [5,4,2,2] => [4,2,2] => 28
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [6,3,2,2] => [3,2,2] => 8
[4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [7,2,2,2] => [2,2,2] => 1
[4,4,3,3,2,1] => [4,3,3,2,1] => [5,4,3,1] => [4,3,1] => 53
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [6,3,3,1] => [3,3,1] => 17
[4,4,3,2,2,2] => [4,3,2,2,2] => [5,5,2,1] => [5,2,1] => 43
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [6,4,2,1] => [4,2,1] => 16
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [7,3,2,1] => [3,2,1] => 6
[4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [8,2,2,1] => [2,2,1] => 1
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [6,5,1,1] => [5,1,1] => 0
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [7,4,1,1] => [4,1,1] => 0
[4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [8,3,1,1] => [3,1,1] => 0
[4,4,2,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [9,2,1,1] => [2,1,1] => 0
[4,4,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => [1,1,1] => 0
[4,3,3,3,3,1] => [3,3,3,3,1] => [5,4,4] => [4,4] => 14
[4,3,3,3,2,2] => [3,3,3,2,2] => [5,5,3] => [5,3] => 31
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [6,4,3] => [4,3] => 11
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [7,3,3] => [3,3] => 1
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [6,5,2] => [5,2] => 7
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [7,4,2] => [4,2] => 3
[4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [8,3,2] => [3,2] => 1
[4,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => [2,2] => 0
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [6,6,1] => [6,1] => 0
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [7,5,1] => [5,1] => 0
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [8,4,1] => [4,1] => 0
[4,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [9,3,1] => [3,1] => 0
[4,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [2,1] => 0
[4,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [1,1] => 0
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [7,6] => [6] => 0
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [8,5] => [5] => 0
[4,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [9,4] => [4] => 0
[4,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [10,3] => [3] => 0
[4,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2] => 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] => [12,1] => [1] => 0
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [6,4,4] => [4,4] => 14
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [6,5,3] => [5,3] => 31
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [7,4,3] => [4,3] => 11
[3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [8,3,3] => [3,3] => 1
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [6,6,2] => [6,2] => 15
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [7,5,2] => [5,2] => 7
[3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [8,4,2] => [4,2] => 3
[3,3,3,2,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1] => [9,3,2] => [3,2] => 1
[3,3,3,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1] => [10,2,2] => [2,2] => 0
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [7,6,1] => [6,1] => 0
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [8,5,1] => [5,1] => 0
[3,3,2,2,2,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1] => [9,4,1] => [4,1] => 0
[3,3,2,2,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1] => [10,3,1] => [3,1] => 0
[3,3,2,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => [2,1] => 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] => [12,1,1] => [1,1] => 0
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [7,7] => [7] => 0
[3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [8,6] => [6] => 0
[3,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [9,5] => [5] => 0
[3,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [10,4] => [4] => 0
[3,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [3] => 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] => [12,2] => [2] => 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] => [13,1] => [1] => 0
[2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => [8,7] => [7] => 0
[2,2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,2,1,1,1] => [9,6] => [6] => 0
[2,2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,2,1,1,1,1,1] => [10,5] => [5] => 0
[2,2,2,2,2,1,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1,1] => [11,4] => [4] => 0
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => [3] => 0
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => [2] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => [1] => 0
[6,4,3,3,2,1] => [4,3,3,2,1] => [5,4,3,1] => [4,3,1] => 53
[5,4,3,3,2,1] => [4,3,3,2,1] => [5,4,3,1] => [4,3,1] => 53
[6,3,3,3,2,1] => [3,3,3,2,1] => [5,4,3] => [4,3] => 11
[6,4,4,2,2,1] => [4,4,2,2,1] => [5,4,2,2] => [4,2,2] => 28
[5,4,4,2,2,1] => [4,4,2,2,1] => [5,4,2,2] => [4,2,2] => 28
[6,5,3,2,2,1] => [5,3,2,2,1] => [5,4,2,1,1] => [4,2,1,1] => 31
[5,5,3,2,2,1] => [5,3,2,2,1] => [5,4,2,1,1] => [4,2,1,1] => 31
[6,4,3,2,2,1] => [4,3,2,2,1] => [5,4,2,1] => [4,2,1] => 16
[6,5,2,2,2,1] => [5,2,2,2,1] => [5,4,1,1,1] => [4,1,1,1] => 0
[6,4,4,3,1,1] => [4,4,3,1,1] => [5,3,3,2] => [3,3,2] => 39
[5,4,4,3,1,1] => [4,4,3,1,1] => [5,3,3,2] => [3,3,2] => 39
[6,5,3,3,1,1] => [5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 24
[5,5,3,3,1,1] => [5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 24
[6,4,3,3,1,1] => [4,3,3,1,1] => [5,3,3,1] => [3,3,1] => 17
[6,5,4,2,1,1] => [5,4,2,1,1] => [5,3,2,2,1] => [3,2,2,1] => 30
[5,5,4,2,1,1] => [5,4,2,1,1] => [5,3,2,2,1] => [3,2,2,1] => 30
[6,4,4,2,1,1] => [4,4,2,1,1] => [5,3,2,2] => [3,2,2] => 8
[6,5,3,2,1,1] => [5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 8
[6,5,4,1,1,1] => [5,4,1,1,1] => [5,2,2,2,1] => [2,2,2,1] => 7
[6,4,3,3,2] => [4,3,3,2] => [4,4,3,1] => [4,3,1] => 53
[6,4,4,2,2] => [4,4,2,2] => [4,4,2,2] => [4,2,2] => 28
[6,5,3,2,2] => [5,3,2,2] => [4,4,2,1,1] => [4,2,1,1] => 31
[6,4,4,3,1] => [4,4,3,1] => [4,3,3,2] => [3,3,2] => 39
[6,5,3,3,1] => [5,3,3,1] => [4,3,3,1,1] => [3,3,1,1] => 24
[6,5,4,2,1] => [5,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => 30
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [6,5,2,1] => [5,2,1] => 43
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [6,5,2,1] => [5,2,1] => 43
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [6,5,1,1,1] => [5,1,1,1] => 0
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [6,5] => [5] => 0
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [6,3,2,2,1] => [3,2,2,1] => 30
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [6,3,2,2,1] => [3,2,2,1] => 30
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 11
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => 6
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => 6
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [6,2,2,2,1] => [2,2,2,1] => 7
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 0
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,4,3,2,2,2] => [4,3,2,2,2] => [5,5,2,1] => [5,2,1] => 43
[7,4,3,3,2,1] => [4,3,3,2,1] => [5,4,3,1] => [4,3,1] => 53
[7,3,3,3,2,1] => [3,3,3,2,1] => [5,4,3] => [4,3] => 11
[7,6,2,2,2,1] => [6,2,2,2,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 0
[7,6,3,2,1,1] => [6,3,2,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => 11
[7,4,3,2,1,1] => [4,3,2,1,1] => [5,3,2,1] => [3,2,1] => 6
[7,3,3,3,3] => [3,3,3,3] => [4,4,4] => [4,4] => 14
[7,5,4,2,1] => [5,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => 30
[7,6,3,2,1] => [6,3,2,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 11
[6,6,3,2,1] => [6,3,2,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 11
[2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => [8,8] => [8] => 0
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,6] => [6] => 0
[10,4,4] => [4,4] => [2,2,2,2] => [2,2,2] => 1
[11,7,3] => [7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [6,6] => [6] => 0
[9,6,3] => [6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[8,6,4] => [6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 8
[10,6,4] => [6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 8
[15,5,5] => [5,5] => [2,2,2,2,2] => [2,2,2,2] => 8
[9,6,4] => [6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 8
[10,7,3] => [7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[8,5,4,2] => [5,4,2] => [3,3,2,2,1] => [3,2,2,1] => 30
[8,5,5,1] => [5,5,1] => [3,2,2,2,2] => [2,2,2,2] => 8
[9,5,5,1] => [5,5,1] => [3,2,2,2,2] => [2,2,2,2] => 8
[3,3,3,3,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1] => [9,3,3] => [3,3] => 1
[9,9] => [9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[7,7,1,1,1,1] => [7,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [7,3,2,1] => [3,2,1] => 6
[5,4,3,2,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => 6
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Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight.
Given λ count how many integer compositions w (weight) there are, such that
Pλ,w is non-integral, i.e., w such that the Gelfand-Tsetlin polytope Pλ,w has at least one non-integral vertex.
See also St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Each value in this statistic is greater than or equal to corresponding value in St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Given λ count how many integer compositions w (weight) there are, such that
Pλ,w is non-integral, i.e., w such that the Gelfand-Tsetlin polytope Pλ,w has at least one non-integral vertex.
See also St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Each value in this statistic is greater than or equal to corresponding value in St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
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first row removal
Description
Removes the first entry of an integer partition
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition λ of n is the partition λ∗ whose Ferrers diagram is obtained from the diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition λ of n is the partition λ∗ whose Ferrers diagram is obtained from the diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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