Identifier
Mp00044:
Integer partitions
—conjugate⟶
Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Images
[1] => [1] => [1]
[2] => [1,1] => [2]
[1,1] => [2] => [1,1]
[3] => [1,1,1] => [3]
[2,1] => [2,1] => [2,1]
[1,1,1] => [3] => [1,1,1]
[4] => [1,1,1,1] => [4]
[3,1] => [2,1,1] => [3,1]
[2,2] => [2,2] => [2,2]
[2,1,1] => [3,1] => [2,1,1]
[1,1,1,1] => [4] => [1,1,1,1]
[5] => [1,1,1,1,1] => [5]
[4,1] => [2,1,1,1] => [4,1]
[3,2] => [2,2,1] => [3,2]
[3,1,1] => [3,1,1] => [3,1,1]
[2,2,1] => [3,2] => [2,2,1]
[2,1,1,1] => [4,1] => [2,1,1,1]
[1,1,1,1,1] => [5] => [1,1,1,1,1]
[6] => [1,1,1,1,1,1] => [6]
[5,1] => [2,1,1,1,1] => [5,1]
[4,2] => [2,2,1,1] => [4,2]
[4,1,1] => [3,1,1,1] => [4,1,1]
[3,3] => [2,2,2] => [3,3]
[3,2,1] => [3,2,1] => [3,2,1]
[3,1,1,1] => [4,1,1] => [3,1,1,1]
[2,2,2] => [3,3] => [2,2,2]
[2,2,1,1] => [4,2] => [2,2,1,1]
[2,1,1,1,1] => [5,1] => [2,1,1,1,1]
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1]
[7] => [1,1,1,1,1,1,1] => [7]
[6,1] => [2,1,1,1,1,1] => [6,1]
[5,2] => [2,2,1,1,1] => [5,2]
[5,1,1] => [3,1,1,1,1] => [5,1,1]
[4,3] => [2,2,2,1] => [4,3]
[4,2,1] => [3,2,1,1] => [4,2,1]
[4,1,1,1] => [4,1,1,1] => [4,1,1,1]
[3,3,1] => [3,2,2] => [3,3,1]
[3,2,2] => [3,3,1] => [3,2,2]
[3,2,1,1] => [4,2,1] => [3,2,1,1]
[3,1,1,1,1] => [5,1,1] => [3,1,1,1,1]
[2,2,2,1] => [4,3] => [2,2,2,1]
[2,2,1,1,1] => [5,2] => [2,2,1,1,1]
[2,1,1,1,1,1] => [6,1] => [2,1,1,1,1,1]
[1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1]
[8] => [1,1,1,1,1,1,1,1] => [8]
[7,1] => [2,1,1,1,1,1,1] => [7,1]
[6,2] => [2,2,1,1,1,1] => [6,2]
[6,1,1] => [3,1,1,1,1,1] => [6,1,1]
[5,3] => [2,2,2,1,1] => [5,3]
[5,2,1] => [3,2,1,1,1] => [5,2,1]
[5,1,1,1] => [4,1,1,1,1] => [5,1,1,1]
[4,4] => [2,2,2,2] => [4,4]
[4,3,1] => [3,2,2,1] => [4,3,1]
[4,2,2] => [3,3,1,1] => [4,2,2]
[4,2,1,1] => [4,2,1,1] => [4,2,1,1]
[4,1,1,1,1] => [5,1,1,1] => [4,1,1,1,1]
[3,3,2] => [3,3,2] => [3,3,2]
[3,3,1,1] => [4,2,2] => [3,3,1,1]
[3,2,2,1] => [4,3,1] => [3,2,2,1]
[3,2,1,1,1] => [5,2,1] => [3,2,1,1,1]
[3,1,1,1,1,1] => [6,1,1] => [3,1,1,1,1,1]
[2,2,2,2] => [4,4] => [2,2,2,2]
[2,2,2,1,1] => [5,3] => [2,2,2,1,1]
[2,2,1,1,1,1] => [6,2] => [2,2,1,1,1,1]
[2,1,1,1,1,1,1] => [7,1] => [2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1] => [8] => [1,1,1,1,1,1,1,1]
[9] => [1,1,1,1,1,1,1,1,1] => [9]
[8,1] => [2,1,1,1,1,1,1,1] => [8,1]
[7,2] => [2,2,1,1,1,1,1] => [7,2]
[7,1,1] => [3,1,1,1,1,1,1] => [7,1,1]
[6,3] => [2,2,2,1,1,1] => [6,3]
[6,2,1] => [3,2,1,1,1,1] => [6,2,1]
[6,1,1,1] => [4,1,1,1,1,1] => [6,1,1,1]
[5,4] => [2,2,2,2,1] => [5,4]
[5,3,1] => [3,2,2,1,1] => [5,3,1]
[5,2,2] => [3,3,1,1,1] => [5,2,2]
[5,2,1,1] => [4,2,1,1,1] => [5,2,1,1]
[5,1,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1]
[4,4,1] => [3,2,2,2] => [4,4,1]
[4,3,2] => [3,3,2,1] => [4,3,2]
[4,3,1,1] => [4,2,2,1] => [4,3,1,1]
[4,2,2,1] => [4,3,1,1] => [4,2,2,1]
[4,2,1,1,1] => [5,2,1,1] => [4,2,1,1,1]
[4,1,1,1,1,1] => [6,1,1,1] => [4,1,1,1,1,1]
[3,3,3] => [3,3,3] => [3,3,3]
[3,3,2,1] => [4,3,2] => [3,3,2,1]
[3,3,1,1,1] => [5,2,2] => [3,3,1,1,1]
[3,2,2,2] => [4,4,1] => [3,2,2,2]
[3,2,2,1,1] => [5,3,1] => [3,2,2,1,1]
[3,2,1,1,1,1] => [6,2,1] => [3,2,1,1,1,1]
[3,1,1,1,1,1,1] => [7,1,1] => [3,1,1,1,1,1,1]
[2,2,2,2,1] => [5,4] => [2,2,2,2,1]
[2,2,2,1,1,1] => [6,3] => [2,2,2,1,1,1]
[2,2,1,1,1,1,1] => [7,2] => [2,2,1,1,1,1,1]
[2,1,1,1,1,1,1,1] => [8,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1] => [9] => [1,1,1,1,1,1,1,1,1]
[10] => [1,1,1,1,1,1,1,1,1,1] => [10]
[9,1] => [2,1,1,1,1,1,1,1,1] => [9,1]
[8,2] => [2,2,1,1,1,1,1,1] => [8,2]
[8,1,1] => [3,1,1,1,1,1,1,1] => [8,1,1]
[7,3] => [2,2,2,1,1,1,1] => [7,3]
>>> Load all 1480 entries. <<<
[7,2,1] => [3,2,1,1,1,1,1] => [7,2,1]
[7,1,1,1] => [4,1,1,1,1,1,1] => [7,1,1,1]
[6,4] => [2,2,2,2,1,1] => [6,4]
[6,3,1] => [3,2,2,1,1,1] => [6,3,1]
[6,2,2] => [3,3,1,1,1,1] => [6,2,2]
[6,2,1,1] => [4,2,1,1,1,1] => [6,2,1,1]
[6,1,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1]
[5,5] => [2,2,2,2,2] => [5,5]
[5,4,1] => [3,2,2,2,1] => [5,4,1]
[5,3,2] => [3,3,2,1,1] => [5,3,2]
[5,3,1,1] => [4,2,2,1,1] => [5,3,1,1]
[5,2,2,1] => [4,3,1,1,1] => [5,2,2,1]
[5,2,1,1,1] => [5,2,1,1,1] => [5,2,1,1,1]
[5,1,1,1,1,1] => [6,1,1,1,1] => [5,1,1,1,1,1]
[4,4,2] => [3,3,2,2] => [4,4,2]
[4,4,1,1] => [4,2,2,2] => [4,4,1,1]
[4,3,3] => [3,3,3,1] => [4,3,3]
[4,3,2,1] => [4,3,2,1] => [4,3,2,1]
[4,3,1,1,1] => [5,2,2,1] => [4,3,1,1,1]
[4,2,2,2] => [4,4,1,1] => [4,2,2,2]
[4,2,2,1,1] => [5,3,1,1] => [4,2,2,1,1]
[4,2,1,1,1,1] => [6,2,1,1] => [4,2,1,1,1,1]
[4,1,1,1,1,1,1] => [7,1,1,1] => [4,1,1,1,1,1,1]
[3,3,3,1] => [4,3,3] => [3,3,3,1]
[3,3,2,2] => [4,4,2] => [3,3,2,2]
[3,3,2,1,1] => [5,3,2] => [3,3,2,1,1]
[3,3,1,1,1,1] => [6,2,2] => [3,3,1,1,1,1]
[3,2,2,2,1] => [5,4,1] => [3,2,2,2,1]
[3,2,2,1,1,1] => [6,3,1] => [3,2,2,1,1,1]
[3,2,1,1,1,1,1] => [7,2,1] => [3,2,1,1,1,1,1]
[3,1,1,1,1,1,1,1] => [8,1,1] => [3,1,1,1,1,1,1,1]
[2,2,2,2,2] => [5,5] => [2,2,2,2,2]
[2,2,2,2,1,1] => [6,4] => [2,2,2,2,1,1]
[2,2,2,1,1,1,1] => [7,3] => [2,2,2,1,1,1,1]
[2,2,1,1,1,1,1,1] => [8,2] => [2,2,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1] => [9,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1] => [10] => [1,1,1,1,1,1,1,1,1,1]
[11] => [1,1,1,1,1,1,1,1,1,1,1] => [11]
[10,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1]
[9,2] => [2,2,1,1,1,1,1,1,1] => [9,2]
[9,1,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1]
[8,3] => [2,2,2,1,1,1,1,1] => [8,3]
[8,2,1] => [3,2,1,1,1,1,1,1] => [8,2,1]
[8,1,1,1] => [4,1,1,1,1,1,1,1] => [8,1,1,1]
[7,4] => [2,2,2,2,1,1,1] => [7,4]
[7,3,1] => [3,2,2,1,1,1,1] => [7,3,1]
[7,2,2] => [3,3,1,1,1,1,1] => [7,2,2]
[7,2,1,1] => [4,2,1,1,1,1,1] => [7,2,1,1]
[7,1,1,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1]
[6,5] => [2,2,2,2,2,1] => [6,5]
[6,4,1] => [3,2,2,2,1,1] => [6,4,1]
[6,3,2] => [3,3,2,1,1,1] => [6,3,2]
[6,3,1,1] => [4,2,2,1,1,1] => [6,3,1,1]
[6,2,2,1] => [4,3,1,1,1,1] => [6,2,2,1]
[6,2,1,1,1] => [5,2,1,1,1,1] => [6,2,1,1,1]
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1]
[5,5,1] => [3,2,2,2,2] => [5,5,1]
[5,4,2] => [3,3,2,2,1] => [5,4,2]
[5,4,1,1] => [4,2,2,2,1] => [5,4,1,1]
[5,3,3] => [3,3,3,1,1] => [5,3,3]
[5,3,2,1] => [4,3,2,1,1] => [5,3,2,1]
[5,3,1,1,1] => [5,2,2,1,1] => [5,3,1,1,1]
[5,2,2,2] => [4,4,1,1,1] => [5,2,2,2]
[5,2,2,1,1] => [5,3,1,1,1] => [5,2,2,1,1]
[5,2,1,1,1,1] => [6,2,1,1,1] => [5,2,1,1,1,1]
[5,1,1,1,1,1,1] => [7,1,1,1,1] => [5,1,1,1,1,1,1]
[4,4,3] => [3,3,3,2] => [4,4,3]
[4,4,2,1] => [4,3,2,2] => [4,4,2,1]
[4,4,1,1,1] => [5,2,2,2] => [4,4,1,1,1]
[4,3,3,1] => [4,3,3,1] => [4,3,3,1]
[4,3,2,2] => [4,4,2,1] => [4,3,2,2]
[4,3,2,1,1] => [5,3,2,1] => [4,3,2,1,1]
[4,3,1,1,1,1] => [6,2,2,1] => [4,3,1,1,1,1]
[4,2,2,2,1] => [5,4,1,1] => [4,2,2,2,1]
[4,2,2,1,1,1] => [6,3,1,1] => [4,2,2,1,1,1]
[4,2,1,1,1,1,1] => [7,2,1,1] => [4,2,1,1,1,1,1]
[4,1,1,1,1,1,1,1] => [8,1,1,1] => [4,1,1,1,1,1,1,1]
[3,3,3,2] => [4,4,3] => [3,3,3,2]
[3,3,3,1,1] => [5,3,3] => [3,3,3,1,1]
[3,3,2,2,1] => [5,4,2] => [3,3,2,2,1]
[3,3,2,1,1,1] => [6,3,2] => [3,3,2,1,1,1]
[3,3,1,1,1,1,1] => [7,2,2] => [3,3,1,1,1,1,1]
[3,2,2,2,2] => [5,5,1] => [3,2,2,2,2]
[3,2,2,2,1,1] => [6,4,1] => [3,2,2,2,1,1]
[3,2,2,1,1,1,1] => [7,3,1] => [3,2,2,1,1,1,1]
[3,2,1,1,1,1,1,1] => [8,2,1] => [3,2,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1] => [9,1,1] => [3,1,1,1,1,1,1,1,1]
[2,2,2,2,2,1] => [6,5] => [2,2,2,2,2,1]
[2,2,2,2,1,1,1] => [7,4] => [2,2,2,2,1,1,1]
[2,2,2,1,1,1,1,1] => [8,3] => [2,2,2,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1] => [9,2] => [2,2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1] => [10,1] => [2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1] => [11] => [1,1,1,1,1,1,1,1,1,1,1]
[12] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12]
[11,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1]
[10,2] => [2,2,1,1,1,1,1,1,1,1] => [10,2]
[10,1,1] => [3,1,1,1,1,1,1,1,1,1] => [10,1,1]
[9,3] => [2,2,2,1,1,1,1,1,1] => [9,3]
[9,2,1] => [3,2,1,1,1,1,1,1,1] => [9,2,1]
[9,1,1,1] => [4,1,1,1,1,1,1,1,1] => [9,1,1,1]
[8,4] => [2,2,2,2,1,1,1,1] => [8,4]
[8,3,1] => [3,2,2,1,1,1,1,1] => [8,3,1]
[8,2,2] => [3,3,1,1,1,1,1,1] => [8,2,2]
[8,2,1,1] => [4,2,1,1,1,1,1,1] => [8,2,1,1]
[8,1,1,1,1] => [5,1,1,1,1,1,1,1] => [8,1,1,1,1]
[7,5] => [2,2,2,2,2,1,1] => [7,5]
[7,4,1] => [3,2,2,2,1,1,1] => [7,4,1]
[7,3,2] => [3,3,2,1,1,1,1] => [7,3,2]
[7,3,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1]
[7,2,2,1] => [4,3,1,1,1,1,1] => [7,2,2,1]
[7,2,1,1,1] => [5,2,1,1,1,1,1] => [7,2,1,1,1]
[7,1,1,1,1,1] => [6,1,1,1,1,1,1] => [7,1,1,1,1,1]
[6,6] => [2,2,2,2,2,2] => [6,6]
[6,5,1] => [3,2,2,2,2,1] => [6,5,1]
[6,4,2] => [3,3,2,2,1,1] => [6,4,2]
[6,4,1,1] => [4,2,2,2,1,1] => [6,4,1,1]
[6,3,3] => [3,3,3,1,1,1] => [6,3,3]
[6,3,2,1] => [4,3,2,1,1,1] => [6,3,2,1]
[6,3,1,1,1] => [5,2,2,1,1,1] => [6,3,1,1,1]
[6,2,2,2] => [4,4,1,1,1,1] => [6,2,2,2]
[6,2,2,1,1] => [5,3,1,1,1,1] => [6,2,2,1,1]
[6,2,1,1,1,1] => [6,2,1,1,1,1] => [6,2,1,1,1,1]
[6,1,1,1,1,1,1] => [7,1,1,1,1,1] => [6,1,1,1,1,1,1]
[5,5,2] => [3,3,2,2,2] => [5,5,2]
[5,5,1,1] => [4,2,2,2,2] => [5,5,1,1]
[5,4,3] => [3,3,3,2,1] => [5,4,3]
[5,4,2,1] => [4,3,2,2,1] => [5,4,2,1]
[5,4,1,1,1] => [5,2,2,2,1] => [5,4,1,1,1]
[5,3,3,1] => [4,3,3,1,1] => [5,3,3,1]
[5,3,2,2] => [4,4,2,1,1] => [5,3,2,2]
[5,3,2,1,1] => [5,3,2,1,1] => [5,3,2,1,1]
[5,3,1,1,1,1] => [6,2,2,1,1] => [5,3,1,1,1,1]
[5,2,2,2,1] => [5,4,1,1,1] => [5,2,2,2,1]
[5,2,2,1,1,1] => [6,3,1,1,1] => [5,2,2,1,1,1]
[5,2,1,1,1,1,1] => [7,2,1,1,1] => [5,2,1,1,1,1,1]
[5,1,1,1,1,1,1,1] => [8,1,1,1,1] => [5,1,1,1,1,1,1,1]
[4,4,4] => [3,3,3,3] => [4,4,4]
[4,4,3,1] => [4,3,3,2] => [4,4,3,1]
[4,4,2,2] => [4,4,2,2] => [4,4,2,2]
[4,4,2,1,1] => [5,3,2,2] => [4,4,2,1,1]
[4,4,1,1,1,1] => [6,2,2,2] => [4,4,1,1,1,1]
[4,3,3,2] => [4,4,3,1] => [4,3,3,2]
[4,3,3,1,1] => [5,3,3,1] => [4,3,3,1,1]
[4,3,2,2,1] => [5,4,2,1] => [4,3,2,2,1]
[4,3,2,1,1,1] => [6,3,2,1] => [4,3,2,1,1,1]
[4,3,1,1,1,1,1] => [7,2,2,1] => [4,3,1,1,1,1,1]
[4,2,2,2,2] => [5,5,1,1] => [4,2,2,2,2]
[4,2,2,2,1,1] => [6,4,1,1] => [4,2,2,2,1,1]
[4,2,2,1,1,1,1] => [7,3,1,1] => [4,2,2,1,1,1,1]
[4,2,1,1,1,1,1,1] => [8,2,1,1] => [4,2,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [4,1,1,1,1,1,1,1,1]
[3,3,3,3] => [4,4,4] => [3,3,3,3]
[3,3,3,2,1] => [5,4,3] => [3,3,3,2,1]
[3,3,3,1,1,1] => [6,3,3] => [3,3,3,1,1,1]
[3,3,2,2,2] => [5,5,2] => [3,3,2,2,2]
[3,3,2,2,1,1] => [6,4,2] => [3,3,2,2,1,1]
[3,3,2,1,1,1,1] => [7,3,2] => [3,3,2,1,1,1,1]
[3,3,1,1,1,1,1,1] => [8,2,2] => [3,3,1,1,1,1,1,1]
[3,2,2,2,2,1] => [6,5,1] => [3,2,2,2,2,1]
[3,2,2,2,1,1,1] => [7,4,1] => [3,2,2,2,1,1,1]
[3,2,2,1,1,1,1,1] => [8,3,1] => [3,2,2,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1] => [9,2,1] => [3,2,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [3,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2] => [6,6] => [2,2,2,2,2,2]
[2,2,2,2,2,1,1] => [7,5] => [2,2,2,2,2,1,1]
[2,2,2,2,1,1,1,1] => [8,4] => [2,2,2,2,1,1,1,1]
[2,2,2,1,1,1,1,1,1] => [9,3] => [2,2,2,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1] => [10,2] => [2,2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1] => [12] => [1,1,1,1,1,1,1,1,1,1,1,1]
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13]
[12,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [12,1]
[11,2] => [2,2,1,1,1,1,1,1,1,1,1] => [11,2]
[11,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,1,1]
[10,3] => [2,2,2,1,1,1,1,1,1,1] => [10,3]
[10,2,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1]
[10,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [10,1,1,1]
[9,4] => [2,2,2,2,1,1,1,1,1] => [9,4]
[9,3,1] => [3,2,2,1,1,1,1,1,1] => [9,3,1]
[9,2,2] => [3,3,1,1,1,1,1,1,1] => [9,2,2]
[9,2,1,1] => [4,2,1,1,1,1,1,1,1] => [9,2,1,1]
[9,1,1,1,1] => [5,1,1,1,1,1,1,1,1] => [9,1,1,1,1]
[8,5] => [2,2,2,2,2,1,1,1] => [8,5]
[8,4,1] => [3,2,2,2,1,1,1,1] => [8,4,1]
[8,3,2] => [3,3,2,1,1,1,1,1] => [8,3,2]
[8,3,1,1] => [4,2,2,1,1,1,1,1] => [8,3,1,1]
[8,2,2,1] => [4,3,1,1,1,1,1,1] => [8,2,2,1]
[8,2,1,1,1] => [5,2,1,1,1,1,1,1] => [8,2,1,1,1]
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => [8,1,1,1,1,1]
[7,6] => [2,2,2,2,2,2,1] => [7,6]
[7,5,1] => [3,2,2,2,2,1,1] => [7,5,1]
[7,4,2] => [3,3,2,2,1,1,1] => [7,4,2]
[7,4,1,1] => [4,2,2,2,1,1,1] => [7,4,1,1]
[7,3,3] => [3,3,3,1,1,1,1] => [7,3,3]
[7,3,2,1] => [4,3,2,1,1,1,1] => [7,3,2,1]
[7,3,1,1,1] => [5,2,2,1,1,1,1] => [7,3,1,1,1]
[7,2,2,2] => [4,4,1,1,1,1,1] => [7,2,2,2]
[7,2,2,1,1] => [5,3,1,1,1,1,1] => [7,2,2,1,1]
[7,2,1,1,1,1] => [6,2,1,1,1,1,1] => [7,2,1,1,1,1]
[7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [7,1,1,1,1,1,1]
[6,6,1] => [3,2,2,2,2,2] => [6,6,1]
[6,5,2] => [3,3,2,2,2,1] => [6,5,2]
[6,5,1,1] => [4,2,2,2,2,1] => [6,5,1,1]
[6,4,3] => [3,3,3,2,1,1] => [6,4,3]
[6,4,2,1] => [4,3,2,2,1,1] => [6,4,2,1]
[6,4,1,1,1] => [5,2,2,2,1,1] => [6,4,1,1,1]
[6,3,3,1] => [4,3,3,1,1,1] => [6,3,3,1]
[6,3,2,2] => [4,4,2,1,1,1] => [6,3,2,2]
[6,3,2,1,1] => [5,3,2,1,1,1] => [6,3,2,1,1]
[6,3,1,1,1,1] => [6,2,2,1,1,1] => [6,3,1,1,1,1]
[6,2,2,2,1] => [5,4,1,1,1,1] => [6,2,2,2,1]
[6,2,2,1,1,1] => [6,3,1,1,1,1] => [6,2,2,1,1,1]
[6,2,1,1,1,1,1] => [7,2,1,1,1,1] => [6,2,1,1,1,1,1]
[6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => [6,1,1,1,1,1,1,1]
[5,5,3] => [3,3,3,2,2] => [5,5,3]
[5,5,2,1] => [4,3,2,2,2] => [5,5,2,1]
[5,5,1,1,1] => [5,2,2,2,2] => [5,5,1,1,1]
[5,4,4] => [3,3,3,3,1] => [5,4,4]
[5,4,3,1] => [4,3,3,2,1] => [5,4,3,1]
[5,4,2,2] => [4,4,2,2,1] => [5,4,2,2]
[5,4,2,1,1] => [5,3,2,2,1] => [5,4,2,1,1]
[5,4,1,1,1,1] => [6,2,2,2,1] => [5,4,1,1,1,1]
[5,3,3,2] => [4,4,3,1,1] => [5,3,3,2]
[5,3,3,1,1] => [5,3,3,1,1] => [5,3,3,1,1]
[5,3,2,2,1] => [5,4,2,1,1] => [5,3,2,2,1]
[5,3,2,1,1,1] => [6,3,2,1,1] => [5,3,2,1,1,1]
[5,3,1,1,1,1,1] => [7,2,2,1,1] => [5,3,1,1,1,1,1]
[5,2,2,2,2] => [5,5,1,1,1] => [5,2,2,2,2]
[5,2,2,2,1,1] => [6,4,1,1,1] => [5,2,2,2,1,1]
[5,2,2,1,1,1,1] => [7,3,1,1,1] => [5,2,2,1,1,1,1]
[5,2,1,1,1,1,1,1] => [8,2,1,1,1] => [5,2,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1] => [9,1,1,1,1] => [5,1,1,1,1,1,1,1,1]
[4,4,4,1] => [4,3,3,3] => [4,4,4,1]
[4,4,3,2] => [4,4,3,2] => [4,4,3,2]
[4,4,3,1,1] => [5,3,3,2] => [4,4,3,1,1]
[4,4,2,2,1] => [5,4,2,2] => [4,4,2,2,1]
[4,4,2,1,1,1] => [6,3,2,2] => [4,4,2,1,1,1]
[4,4,1,1,1,1,1] => [7,2,2,2] => [4,4,1,1,1,1,1]
[4,3,3,3] => [4,4,4,1] => [4,3,3,3]
[4,3,3,2,1] => [5,4,3,1] => [4,3,3,2,1]
[4,3,3,1,1,1] => [6,3,3,1] => [4,3,3,1,1,1]
[4,3,2,2,2] => [5,5,2,1] => [4,3,2,2,2]
[4,3,2,2,1,1] => [6,4,2,1] => [4,3,2,2,1,1]
[4,3,2,1,1,1,1] => [7,3,2,1] => [4,3,2,1,1,1,1]
[4,3,1,1,1,1,1,1] => [8,2,2,1] => [4,3,1,1,1,1,1,1]
[4,2,2,2,2,1] => [6,5,1,1] => [4,2,2,2,2,1]
[4,2,2,2,1,1,1] => [7,4,1,1] => [4,2,2,2,1,1,1]
[4,2,2,1,1,1,1,1] => [8,3,1,1] => [4,2,2,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1] => [9,2,1,1] => [4,2,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => [4,1,1,1,1,1,1,1,1,1]
[3,3,3,3,1] => [5,4,4] => [3,3,3,3,1]
[3,3,3,2,2] => [5,5,3] => [3,3,3,2,2]
[3,3,3,2,1,1] => [6,4,3] => [3,3,3,2,1,1]
[3,3,3,1,1,1,1] => [7,3,3] => [3,3,3,1,1,1,1]
[3,3,2,2,2,1] => [6,5,2] => [3,3,2,2,2,1]
[3,3,2,2,1,1,1] => [7,4,2] => [3,3,2,2,1,1,1]
[3,3,2,1,1,1,1,1] => [8,3,2] => [3,3,2,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1] => [9,2,2] => [3,3,1,1,1,1,1,1,1]
[3,2,2,2,2,2] => [6,6,1] => [3,2,2,2,2,2]
[3,2,2,2,2,1,1] => [7,5,1] => [3,2,2,2,2,1,1]
[3,2,2,2,1,1,1,1] => [8,4,1] => [3,2,2,2,1,1,1,1]
[3,2,2,1,1,1,1,1,1] => [9,3,1] => [3,2,2,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [3,2,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [3,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,1] => [7,6] => [2,2,2,2,2,2,1]
[2,2,2,2,2,1,1,1] => [8,5] => [2,2,2,2,2,1,1,1]
[2,2,2,2,1,1,1,1,1] => [9,4] => [2,2,2,2,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1] => [10,3] => [2,2,2,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2,2,1,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => [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] => [13] => [1,1,1,1,1,1,1,1,1,1,1,1,1]
[14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14]
[13,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1]
[12,2] => [2,2,1,1,1,1,1,1,1,1,1,1] => [12,2]
[12,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1]
[11,3] => [2,2,2,1,1,1,1,1,1,1,1] => [11,3]
[11,2,1] => [3,2,1,1,1,1,1,1,1,1,1] => [11,2,1]
[11,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1]
[10,4] => [2,2,2,2,1,1,1,1,1,1] => [10,4]
[10,3,1] => [3,2,2,1,1,1,1,1,1,1] => [10,3,1]
[10,2,2] => [3,3,1,1,1,1,1,1,1,1] => [10,2,2]
[10,2,1,1] => [4,2,1,1,1,1,1,1,1,1] => [10,2,1,1]
[10,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1]
[9,5] => [2,2,2,2,2,1,1,1,1] => [9,5]
[9,4,1] => [3,2,2,2,1,1,1,1,1] => [9,4,1]
[9,3,2] => [3,3,2,1,1,1,1,1,1] => [9,3,2]
[9,3,1,1] => [4,2,2,1,1,1,1,1,1] => [9,3,1,1]
[9,2,2,1] => [4,3,1,1,1,1,1,1,1] => [9,2,2,1]
[9,2,1,1,1] => [5,2,1,1,1,1,1,1,1] => [9,2,1,1,1]
[9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1]
[8,6] => [2,2,2,2,2,2,1,1] => [8,6]
[8,5,1] => [3,2,2,2,2,1,1,1] => [8,5,1]
[8,4,2] => [3,3,2,2,1,1,1,1] => [8,4,2]
[8,4,1,1] => [4,2,2,2,1,1,1,1] => [8,4,1,1]
[8,3,3] => [3,3,3,1,1,1,1,1] => [8,3,3]
[8,3,2,1] => [4,3,2,1,1,1,1,1] => [8,3,2,1]
[8,3,1,1,1] => [5,2,2,1,1,1,1,1] => [8,3,1,1,1]
[8,2,2,2] => [4,4,1,1,1,1,1,1] => [8,2,2,2]
[8,2,2,1,1] => [5,3,1,1,1,1,1,1] => [8,2,2,1,1]
[8,2,1,1,1,1] => [6,2,1,1,1,1,1,1] => [8,2,1,1,1,1]
[8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1]
[7,7] => [2,2,2,2,2,2,2] => [7,7]
[7,6,1] => [3,2,2,2,2,2,1] => [7,6,1]
[7,5,2] => [3,3,2,2,2,1,1] => [7,5,2]
[7,5,1,1] => [4,2,2,2,2,1,1] => [7,5,1,1]
[7,4,3] => [3,3,3,2,1,1,1] => [7,4,3]
[7,4,2,1] => [4,3,2,2,1,1,1] => [7,4,2,1]
[7,4,1,1,1] => [5,2,2,2,1,1,1] => [7,4,1,1,1]
[7,3,3,1] => [4,3,3,1,1,1,1] => [7,3,3,1]
[7,3,2,2] => [4,4,2,1,1,1,1] => [7,3,2,2]
[7,3,2,1,1] => [5,3,2,1,1,1,1] => [7,3,2,1,1]
[7,3,1,1,1,1] => [6,2,2,1,1,1,1] => [7,3,1,1,1,1]
[7,2,2,2,1] => [5,4,1,1,1,1,1] => [7,2,2,2,1]
[7,2,2,1,1,1] => [6,3,1,1,1,1,1] => [7,2,2,1,1,1]
[7,2,1,1,1,1,1] => [7,2,1,1,1,1,1] => [7,2,1,1,1,1,1]
[7,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1]
[6,6,2] => [3,3,2,2,2,2] => [6,6,2]
[6,6,1,1] => [4,2,2,2,2,2] => [6,6,1,1]
[6,5,3] => [3,3,3,2,2,1] => [6,5,3]
[6,5,2,1] => [4,3,2,2,2,1] => [6,5,2,1]
[6,5,1,1,1] => [5,2,2,2,2,1] => [6,5,1,1,1]
[6,4,4] => [3,3,3,3,1,1] => [6,4,4]
[6,4,3,1] => [4,3,3,2,1,1] => [6,4,3,1]
[6,4,2,2] => [4,4,2,2,1,1] => [6,4,2,2]
[6,4,2,1,1] => [5,3,2,2,1,1] => [6,4,2,1,1]
[6,4,1,1,1,1] => [6,2,2,2,1,1] => [6,4,1,1,1,1]
[6,3,3,2] => [4,4,3,1,1,1] => [6,3,3,2]
[6,3,3,1,1] => [5,3,3,1,1,1] => [6,3,3,1,1]
[6,3,2,2,1] => [5,4,2,1,1,1] => [6,3,2,2,1]
[6,3,2,1,1,1] => [6,3,2,1,1,1] => [6,3,2,1,1,1]
[6,3,1,1,1,1,1] => [7,2,2,1,1,1] => [6,3,1,1,1,1,1]
[6,2,2,2,2] => [5,5,1,1,1,1] => [6,2,2,2,2]
[6,2,2,2,1,1] => [6,4,1,1,1,1] => [6,2,2,2,1,1]
[6,2,2,1,1,1,1] => [7,3,1,1,1,1] => [6,2,2,1,1,1,1]
[6,2,1,1,1,1,1,1] => [8,2,1,1,1,1] => [6,2,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1]
[5,5,4] => [3,3,3,3,2] => [5,5,4]
[5,5,3,1] => [4,3,3,2,2] => [5,5,3,1]
[5,5,2,2] => [4,4,2,2,2] => [5,5,2,2]
[5,5,2,1,1] => [5,3,2,2,2] => [5,5,2,1,1]
[5,5,1,1,1,1] => [6,2,2,2,2] => [5,5,1,1,1,1]
[5,4,4,1] => [4,3,3,3,1] => [5,4,4,1]
[5,4,3,2] => [4,4,3,2,1] => [5,4,3,2]
[5,4,3,1,1] => [5,3,3,2,1] => [5,4,3,1,1]
[5,4,2,2,1] => [5,4,2,2,1] => [5,4,2,2,1]
[5,4,2,1,1,1] => [6,3,2,2,1] => [5,4,2,1,1,1]
[5,4,1,1,1,1,1] => [7,2,2,2,1] => [5,4,1,1,1,1,1]
[5,3,3,3] => [4,4,4,1,1] => [5,3,3,3]
[5,3,3,2,1] => [5,4,3,1,1] => [5,3,3,2,1]
[5,3,3,1,1,1] => [6,3,3,1,1] => [5,3,3,1,1,1]
[5,3,2,2,2] => [5,5,2,1,1] => [5,3,2,2,2]
[5,3,2,2,1,1] => [6,4,2,1,1] => [5,3,2,2,1,1]
[5,3,2,1,1,1,1] => [7,3,2,1,1] => [5,3,2,1,1,1,1]
[5,3,1,1,1,1,1,1] => [8,2,2,1,1] => [5,3,1,1,1,1,1,1]
[5,2,2,2,2,1] => [6,5,1,1,1] => [5,2,2,2,2,1]
[5,2,2,2,1,1,1] => [7,4,1,1,1] => [5,2,2,2,1,1,1]
[5,2,2,1,1,1,1,1] => [8,3,1,1,1] => [5,2,2,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1] => [9,2,1,1,1] => [5,2,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1]
[4,4,4,2] => [4,4,3,3] => [4,4,4,2]
[4,4,4,1,1] => [5,3,3,3] => [4,4,4,1,1]
[4,4,3,3] => [4,4,4,2] => [4,4,3,3]
[4,4,3,2,1] => [5,4,3,2] => [4,4,3,2,1]
[4,4,3,1,1,1] => [6,3,3,2] => [4,4,3,1,1,1]
[4,4,2,2,2] => [5,5,2,2] => [4,4,2,2,2]
[4,4,2,2,1,1] => [6,4,2,2] => [4,4,2,2,1,1]
[4,4,2,1,1,1,1] => [7,3,2,2] => [4,4,2,1,1,1,1]
[4,4,1,1,1,1,1,1] => [8,2,2,2] => [4,4,1,1,1,1,1,1]
[4,3,3,3,1] => [5,4,4,1] => [4,3,3,3,1]
[4,3,3,2,2] => [5,5,3,1] => [4,3,3,2,2]
[4,3,3,2,1,1] => [6,4,3,1] => [4,3,3,2,1,1]
[4,3,3,1,1,1,1] => [7,3,3,1] => [4,3,3,1,1,1,1]
[4,3,2,2,2,1] => [6,5,2,1] => [4,3,2,2,2,1]
[4,3,2,2,1,1,1] => [7,4,2,1] => [4,3,2,2,1,1,1]
[4,3,2,1,1,1,1,1] => [8,3,2,1] => [4,3,2,1,1,1,1,1]
[4,3,1,1,1,1,1,1,1] => [9,2,2,1] => [4,3,1,1,1,1,1,1,1]
[4,2,2,2,2,2] => [6,6,1,1] => [4,2,2,2,2,2]
[4,2,2,2,2,1,1] => [7,5,1,1] => [4,2,2,2,2,1,1]
[4,2,2,2,1,1,1,1] => [8,4,1,1] => [4,2,2,2,1,1,1,1]
[4,2,2,1,1,1,1,1,1] => [9,3,1,1] => [4,2,2,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1] => [10,2,1,1] => [4,2,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,2] => [5,5,4] => [3,3,3,3,2]
[3,3,3,3,1,1] => [6,4,4] => [3,3,3,3,1,1]
[3,3,3,2,2,1] => [6,5,3] => [3,3,3,2,2,1]
[3,3,3,2,1,1,1] => [7,4,3] => [3,3,3,2,1,1,1]
[3,3,3,1,1,1,1,1] => [8,3,3] => [3,3,3,1,1,1,1,1]
[3,3,2,2,2,2] => [6,6,2] => [3,3,2,2,2,2]
[3,3,2,2,2,1,1] => [7,5,2] => [3,3,2,2,2,1,1]
[3,3,2,2,1,1,1,1] => [8,4,2] => [3,3,2,2,1,1,1,1]
[3,3,2,1,1,1,1,1,1] => [9,3,2] => [3,3,2,1,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1] => [10,2,2] => [3,3,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,1] => [7,6,1] => [3,2,2,2,2,2,1]
[3,2,2,2,2,1,1,1] => [8,5,1] => [3,2,2,2,2,1,1,1]
[3,2,2,2,1,1,1,1,1] => [9,4,1] => [3,2,2,2,1,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1] => [10,3,1] => [3,2,2,1,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => [3,2,1,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2] => [7,7] => [2,2,2,2,2,2,2]
[2,2,2,2,2,2,1,1] => [8,6] => [2,2,2,2,2,2,1,1]
[2,2,2,2,2,1,1,1,1] => [9,5] => [2,2,2,2,2,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1] => [10,4] => [2,2,2,2,1,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [2,2,2,1,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => [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] => [13,1] => [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] => [14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15]
[14,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1]
[13,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2]
[13,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1]
[12,3] => [2,2,2,1,1,1,1,1,1,1,1,1] => [12,3]
[12,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1]
[12,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1]
[11,4] => [2,2,2,2,1,1,1,1,1,1,1] => [11,4]
[11,3,1] => [3,2,2,1,1,1,1,1,1,1,1] => [11,3,1]
[11,2,2] => [3,3,1,1,1,1,1,1,1,1,1] => [11,2,2]
[11,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1]
[11,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1]
[10,5] => [2,2,2,2,2,1,1,1,1,1] => [10,5]
[10,4,1] => [3,2,2,2,1,1,1,1,1,1] => [10,4,1]
[10,3,2] => [3,3,2,1,1,1,1,1,1,1] => [10,3,2]
[10,3,1,1] => [4,2,2,1,1,1,1,1,1,1] => [10,3,1,1]
[10,2,2,1] => [4,3,1,1,1,1,1,1,1,1] => [10,2,2,1]
[10,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1]
[10,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1]
[9,6] => [2,2,2,2,2,2,1,1,1] => [9,6]
[9,5,1] => [3,2,2,2,2,1,1,1,1] => [9,5,1]
[9,4,2] => [3,3,2,2,1,1,1,1,1] => [9,4,2]
[9,4,1,1] => [4,2,2,2,1,1,1,1,1] => [9,4,1,1]
[9,3,3] => [3,3,3,1,1,1,1,1,1] => [9,3,3]
[9,3,2,1] => [4,3,2,1,1,1,1,1,1] => [9,3,2,1]
[9,3,1,1,1] => [5,2,2,1,1,1,1,1,1] => [9,3,1,1,1]
[9,2,2,2] => [4,4,1,1,1,1,1,1,1] => [9,2,2,2]
[9,2,2,1,1] => [5,3,1,1,1,1,1,1,1] => [9,2,2,1,1]
[9,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1]
[9,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1]
[8,7] => [2,2,2,2,2,2,2,1] => [8,7]
[8,6,1] => [3,2,2,2,2,2,1,1] => [8,6,1]
[8,5,2] => [3,3,2,2,2,1,1,1] => [8,5,2]
[8,5,1,1] => [4,2,2,2,2,1,1,1] => [8,5,1,1]
[8,4,3] => [3,3,3,2,1,1,1,1] => [8,4,3]
[8,4,2,1] => [4,3,2,2,1,1,1,1] => [8,4,2,1]
[8,4,1,1,1] => [5,2,2,2,1,1,1,1] => [8,4,1,1,1]
[8,3,3,1] => [4,3,3,1,1,1,1,1] => [8,3,3,1]
[8,3,2,2] => [4,4,2,1,1,1,1,1] => [8,3,2,2]
[8,3,2,1,1] => [5,3,2,1,1,1,1,1] => [8,3,2,1,1]
[8,3,1,1,1,1] => [6,2,2,1,1,1,1,1] => [8,3,1,1,1,1]
[8,2,2,2,1] => [5,4,1,1,1,1,1,1] => [8,2,2,2,1]
[8,2,2,1,1,1] => [6,3,1,1,1,1,1,1] => [8,2,2,1,1,1]
[8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1]
[8,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1]
[7,7,1] => [3,2,2,2,2,2,2] => [7,7,1]
[7,6,2] => [3,3,2,2,2,2,1] => [7,6,2]
[7,6,1,1] => [4,2,2,2,2,2,1] => [7,6,1,1]
[7,5,3] => [3,3,3,2,2,1,1] => [7,5,3]
[7,5,2,1] => [4,3,2,2,2,1,1] => [7,5,2,1]
[7,5,1,1,1] => [5,2,2,2,2,1,1] => [7,5,1,1,1]
[7,4,4] => [3,3,3,3,1,1,1] => [7,4,4]
[7,4,3,1] => [4,3,3,2,1,1,1] => [7,4,3,1]
[7,4,2,2] => [4,4,2,2,1,1,1] => [7,4,2,2]
[7,4,2,1,1] => [5,3,2,2,1,1,1] => [7,4,2,1,1]
[7,4,1,1,1,1] => [6,2,2,2,1,1,1] => [7,4,1,1,1,1]
[7,3,3,2] => [4,4,3,1,1,1,1] => [7,3,3,2]
[7,3,3,1,1] => [5,3,3,1,1,1,1] => [7,3,3,1,1]
[7,3,2,2,1] => [5,4,2,1,1,1,1] => [7,3,2,2,1]
[7,3,2,1,1,1] => [6,3,2,1,1,1,1] => [7,3,2,1,1,1]
[7,3,1,1,1,1,1] => [7,2,2,1,1,1,1] => [7,3,1,1,1,1,1]
[7,2,2,2,2] => [5,5,1,1,1,1,1] => [7,2,2,2,2]
[7,2,2,2,1,1] => [6,4,1,1,1,1,1] => [7,2,2,2,1,1]
[7,2,2,1,1,1,1] => [7,3,1,1,1,1,1] => [7,2,2,1,1,1,1]
[7,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1]
[6,6,3] => [3,3,3,2,2,2] => [6,6,3]
[6,6,2,1] => [4,3,2,2,2,2] => [6,6,2,1]
[6,6,1,1,1] => [5,2,2,2,2,2] => [6,6,1,1,1]
[6,5,4] => [3,3,3,3,2,1] => [6,5,4]
[6,5,3,1] => [4,3,3,2,2,1] => [6,5,3,1]
[6,5,2,2] => [4,4,2,2,2,1] => [6,5,2,2]
[6,5,2,1,1] => [5,3,2,2,2,1] => [6,5,2,1,1]
[6,5,1,1,1,1] => [6,2,2,2,2,1] => [6,5,1,1,1,1]
[6,4,4,1] => [4,3,3,3,1,1] => [6,4,4,1]
[6,4,3,2] => [4,4,3,2,1,1] => [6,4,3,2]
[6,4,3,1,1] => [5,3,3,2,1,1] => [6,4,3,1,1]
[6,4,2,2,1] => [5,4,2,2,1,1] => [6,4,2,2,1]
[6,4,2,1,1,1] => [6,3,2,2,1,1] => [6,4,2,1,1,1]
[6,4,1,1,1,1,1] => [7,2,2,2,1,1] => [6,4,1,1,1,1,1]
[6,3,3,3] => [4,4,4,1,1,1] => [6,3,3,3]
[6,3,3,2,1] => [5,4,3,1,1,1] => [6,3,3,2,1]
[6,3,3,1,1,1] => [6,3,3,1,1,1] => [6,3,3,1,1,1]
[6,3,2,2,2] => [5,5,2,1,1,1] => [6,3,2,2,2]
[6,3,2,2,1,1] => [6,4,2,1,1,1] => [6,3,2,2,1,1]
[6,3,2,1,1,1,1] => [7,3,2,1,1,1] => [6,3,2,1,1,1,1]
[6,3,1,1,1,1,1,1] => [8,2,2,1,1,1] => [6,3,1,1,1,1,1,1]
[6,2,2,2,2,1] => [6,5,1,1,1,1] => [6,2,2,2,2,1]
[6,2,2,2,1,1,1] => [7,4,1,1,1,1] => [6,2,2,2,1,1,1]
[6,2,2,1,1,1,1,1] => [8,3,1,1,1,1] => [6,2,2,1,1,1,1,1]
[6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1]
[5,5,5] => [3,3,3,3,3] => [5,5,5]
[5,5,4,1] => [4,3,3,3,2] => [5,5,4,1]
[5,5,3,2] => [4,4,3,2,2] => [5,5,3,2]
[5,5,3,1,1] => [5,3,3,2,2] => [5,5,3,1,1]
[5,5,2,2,1] => [5,4,2,2,2] => [5,5,2,2,1]
[5,5,2,1,1,1] => [6,3,2,2,2] => [5,5,2,1,1,1]
[5,5,1,1,1,1,1] => [7,2,2,2,2] => [5,5,1,1,1,1,1]
[5,4,4,2] => [4,4,3,3,1] => [5,4,4,2]
[5,4,4,1,1] => [5,3,3,3,1] => [5,4,4,1,1]
[5,4,3,3] => [4,4,4,2,1] => [5,4,3,3]
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1]
[5,4,3,1,1,1] => [6,3,3,2,1] => [5,4,3,1,1,1]
[5,4,2,2,2] => [5,5,2,2,1] => [5,4,2,2,2]
[5,4,2,2,1,1] => [6,4,2,2,1] => [5,4,2,2,1,1]
[5,4,2,1,1,1,1] => [7,3,2,2,1] => [5,4,2,1,1,1,1]
[5,4,1,1,1,1,1,1] => [8,2,2,2,1] => [5,4,1,1,1,1,1,1]
[5,3,3,3,1] => [5,4,4,1,1] => [5,3,3,3,1]
[5,3,3,2,2] => [5,5,3,1,1] => [5,3,3,2,2]
[5,3,3,2,1,1] => [6,4,3,1,1] => [5,3,3,2,1,1]
[5,3,3,1,1,1,1] => [7,3,3,1,1] => [5,3,3,1,1,1,1]
[5,3,2,2,2,1] => [6,5,2,1,1] => [5,3,2,2,2,1]
[5,3,2,2,1,1,1] => [7,4,2,1,1] => [5,3,2,2,1,1,1]
[5,3,2,1,1,1,1,1] => [8,3,2,1,1] => [5,3,2,1,1,1,1,1]
[5,3,1,1,1,1,1,1,1] => [9,2,2,1,1] => [5,3,1,1,1,1,1,1,1]
[5,2,2,2,2,2] => [6,6,1,1,1] => [5,2,2,2,2,2]
[5,2,2,2,2,1,1] => [7,5,1,1,1] => [5,2,2,2,2,1,1]
[5,2,2,2,1,1,1,1] => [8,4,1,1,1] => [5,2,2,2,1,1,1,1]
[5,2,2,1,1,1,1,1,1] => [9,3,1,1,1] => [5,2,2,1,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1]
[4,4,4,3] => [4,4,4,3] => [4,4,4,3]
[4,4,4,2,1] => [5,4,3,3] => [4,4,4,2,1]
[4,4,4,1,1,1] => [6,3,3,3] => [4,4,4,1,1,1]
[4,4,3,3,1] => [5,4,4,2] => [4,4,3,3,1]
[4,4,3,2,2] => [5,5,3,2] => [4,4,3,2,2]
[4,4,3,2,1,1] => [6,4,3,2] => [4,4,3,2,1,1]
[4,4,3,1,1,1,1] => [7,3,3,2] => [4,4,3,1,1,1,1]
[4,4,2,2,2,1] => [6,5,2,2] => [4,4,2,2,2,1]
[4,4,2,2,1,1,1] => [7,4,2,2] => [4,4,2,2,1,1,1]
[4,4,2,1,1,1,1,1] => [8,3,2,2] => [4,4,2,1,1,1,1,1]
[4,4,1,1,1,1,1,1,1] => [9,2,2,2] => [4,4,1,1,1,1,1,1,1]
[4,3,3,3,2] => [5,5,4,1] => [4,3,3,3,2]
[4,3,3,3,1,1] => [6,4,4,1] => [4,3,3,3,1,1]
[4,3,3,2,2,1] => [6,5,3,1] => [4,3,3,2,2,1]
[4,3,3,2,1,1,1] => [7,4,3,1] => [4,3,3,2,1,1,1]
[4,3,3,1,1,1,1,1] => [8,3,3,1] => [4,3,3,1,1,1,1,1]
[4,3,2,2,2,2] => [6,6,2,1] => [4,3,2,2,2,2]
[4,3,2,2,2,1,1] => [7,5,2,1] => [4,3,2,2,2,1,1]
[4,3,2,2,1,1,1,1] => [8,4,2,1] => [4,3,2,2,1,1,1,1]
[4,3,2,1,1,1,1,1,1] => [9,3,2,1] => [4,3,2,1,1,1,1,1,1]
[4,3,1,1,1,1,1,1,1,1] => [10,2,2,1] => [4,3,1,1,1,1,1,1,1,1]
[4,2,2,2,2,2,1] => [7,6,1,1] => [4,2,2,2,2,2,1]
[4,2,2,2,2,1,1,1] => [8,5,1,1] => [4,2,2,2,2,1,1,1]
[4,2,2,2,1,1,1,1,1] => [9,4,1,1] => [4,2,2,2,1,1,1,1,1]
[4,2,2,1,1,1,1,1,1,1] => [10,3,1,1] => [4,2,2,1,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,3] => [5,5,5] => [3,3,3,3,3]
[3,3,3,3,2,1] => [6,5,4] => [3,3,3,3,2,1]
[3,3,3,3,1,1,1] => [7,4,4] => [3,3,3,3,1,1,1]
[3,3,3,2,2,2] => [6,6,3] => [3,3,3,2,2,2]
[3,3,3,2,2,1,1] => [7,5,3] => [3,3,3,2,2,1,1]
[3,3,3,2,1,1,1,1] => [8,4,3] => [3,3,3,2,1,1,1,1]
[3,3,3,1,1,1,1,1,1] => [9,3,3] => [3,3,3,1,1,1,1,1,1]
[3,3,2,2,2,2,1] => [7,6,2] => [3,3,2,2,2,2,1]
[3,3,2,2,2,1,1,1] => [8,5,2] => [3,3,2,2,2,1,1,1]
[3,3,2,2,1,1,1,1,1] => [9,4,2] => [3,3,2,2,1,1,1,1,1]
[3,3,2,1,1,1,1,1,1,1] => [10,3,2] => [3,3,2,1,1,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => [3,3,1,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,2] => [7,7,1] => [3,2,2,2,2,2,2]
[3,2,2,2,2,2,1,1] => [8,6,1] => [3,2,2,2,2,2,1,1]
[3,2,2,2,2,1,1,1,1] => [9,5,1] => [3,2,2,2,2,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1] => [10,4,1] => [3,2,2,2,1,1,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => [3,2,2,1,1,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2,1] => [8,7] => [2,2,2,2,2,2,2,1]
[2,2,2,2,2,2,1,1,1] => [9,6] => [2,2,2,2,2,2,1,1,1]
[2,2,2,2,2,1,1,1,1,1] => [10,5] => [2,2,2,2,2,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1,1] => [11,4] => [2,2,2,2,1,1,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => [2,2,2,1,1,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => [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] => [15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[16] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16]
[15,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1]
[14,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2]
[14,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1]
[13,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3]
[13,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1]
[13,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1]
[12,4] => [2,2,2,2,1,1,1,1,1,1,1,1] => [12,4]
[12,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1]
[12,2,2] => [3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2]
[12,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1]
[12,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1]
[11,5] => [2,2,2,2,2,1,1,1,1,1,1] => [11,5]
[11,4,1] => [3,2,2,2,1,1,1,1,1,1,1] => [11,4,1]
[11,3,2] => [3,3,2,1,1,1,1,1,1,1,1] => [11,3,2]
[11,3,1,1] => [4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1]
[11,2,2,1] => [4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1]
[11,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1]
[11,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1]
[10,6] => [2,2,2,2,2,2,1,1,1,1] => [10,6]
[10,5,1] => [3,2,2,2,2,1,1,1,1,1] => [10,5,1]
[10,4,2] => [3,3,2,2,1,1,1,1,1,1] => [10,4,2]
[10,4,1,1] => [4,2,2,2,1,1,1,1,1,1] => [10,4,1,1]
[10,3,3] => [3,3,3,1,1,1,1,1,1,1] => [10,3,3]
[10,3,2,1] => [4,3,2,1,1,1,1,1,1,1] => [10,3,2,1]
[10,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1]
[10,2,2,2] => [4,4,1,1,1,1,1,1,1,1] => [10,2,2,2]
[10,2,2,1,1] => [5,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1]
[10,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1]
[10,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1]
[9,7] => [2,2,2,2,2,2,2,1,1] => [9,7]
[9,6,1] => [3,2,2,2,2,2,1,1,1] => [9,6,1]
[9,5,2] => [3,3,2,2,2,1,1,1,1] => [9,5,2]
[9,5,1,1] => [4,2,2,2,2,1,1,1,1] => [9,5,1,1]
[9,4,3] => [3,3,3,2,1,1,1,1,1] => [9,4,3]
[9,4,2,1] => [4,3,2,2,1,1,1,1,1] => [9,4,2,1]
[9,4,1,1,1] => [5,2,2,2,1,1,1,1,1] => [9,4,1,1,1]
[9,3,3,1] => [4,3,3,1,1,1,1,1,1] => [9,3,3,1]
[9,3,2,2] => [4,4,2,1,1,1,1,1,1] => [9,3,2,2]
[9,3,2,1,1] => [5,3,2,1,1,1,1,1,1] => [9,3,2,1,1]
[9,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1]
[9,2,2,2,1] => [5,4,1,1,1,1,1,1,1] => [9,2,2,2,1]
[9,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1]
[9,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1]
[9,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1]
[8,8] => [2,2,2,2,2,2,2,2] => [8,8]
[8,7,1] => [3,2,2,2,2,2,2,1] => [8,7,1]
[8,6,2] => [3,3,2,2,2,2,1,1] => [8,6,2]
[8,6,1,1] => [4,2,2,2,2,2,1,1] => [8,6,1,1]
[8,5,3] => [3,3,3,2,2,1,1,1] => [8,5,3]
[8,5,2,1] => [4,3,2,2,2,1,1,1] => [8,5,2,1]
[8,5,1,1,1] => [5,2,2,2,2,1,1,1] => [8,5,1,1,1]
[8,4,4] => [3,3,3,3,1,1,1,1] => [8,4,4]
[8,4,3,1] => [4,3,3,2,1,1,1,1] => [8,4,3,1]
[8,4,2,2] => [4,4,2,2,1,1,1,1] => [8,4,2,2]
[8,4,2,1,1] => [5,3,2,2,1,1,1,1] => [8,4,2,1,1]
[8,4,1,1,1,1] => [6,2,2,2,1,1,1,1] => [8,4,1,1,1,1]
[8,3,3,2] => [4,4,3,1,1,1,1,1] => [8,3,3,2]
[8,3,3,1,1] => [5,3,3,1,1,1,1,1] => [8,3,3,1,1]
[8,3,2,2,1] => [5,4,2,1,1,1,1,1] => [8,3,2,2,1]
[8,3,2,1,1,1] => [6,3,2,1,1,1,1,1] => [8,3,2,1,1,1]
[8,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1]
[8,2,2,2,2] => [5,5,1,1,1,1,1,1] => [8,2,2,2,2]
[8,2,2,2,1,1] => [6,4,1,1,1,1,1,1] => [8,2,2,2,1,1]
[8,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1]
[8,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1]
[8,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1]
[7,7,2] => [3,3,2,2,2,2,2] => [7,7,2]
[7,7,1,1] => [4,2,2,2,2,2,2] => [7,7,1,1]
[7,6,3] => [3,3,3,2,2,2,1] => [7,6,3]
[7,6,2,1] => [4,3,2,2,2,2,1] => [7,6,2,1]
[7,6,1,1,1] => [5,2,2,2,2,2,1] => [7,6,1,1,1]
[7,5,4] => [3,3,3,3,2,1,1] => [7,5,4]
[7,5,3,1] => [4,3,3,2,2,1,1] => [7,5,3,1]
[7,5,2,2] => [4,4,2,2,2,1,1] => [7,5,2,2]
[7,5,2,1,1] => [5,3,2,2,2,1,1] => [7,5,2,1,1]
[7,5,1,1,1,1] => [6,2,2,2,2,1,1] => [7,5,1,1,1,1]
[7,4,4,1] => [4,3,3,3,1,1,1] => [7,4,4,1]
[7,4,3,2] => [4,4,3,2,1,1,1] => [7,4,3,2]
[7,4,3,1,1] => [5,3,3,2,1,1,1] => [7,4,3,1,1]
[7,4,2,2,1] => [5,4,2,2,1,1,1] => [7,4,2,2,1]
[7,4,2,1,1,1] => [6,3,2,2,1,1,1] => [7,4,2,1,1,1]
[7,4,1,1,1,1,1] => [7,2,2,2,1,1,1] => [7,4,1,1,1,1,1]
[7,3,3,3] => [4,4,4,1,1,1,1] => [7,3,3,3]
[7,3,3,2,1] => [5,4,3,1,1,1,1] => [7,3,3,2,1]
[7,3,3,1,1,1] => [6,3,3,1,1,1,1] => [7,3,3,1,1,1]
[7,3,2,2,2] => [5,5,2,1,1,1,1] => [7,3,2,2,2]
[7,3,2,2,1,1] => [6,4,2,1,1,1,1] => [7,3,2,2,1,1]
[7,3,2,1,1,1,1] => [7,3,2,1,1,1,1] => [7,3,2,1,1,1,1]
[7,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1]
[7,2,2,2,2,1] => [6,5,1,1,1,1,1] => [7,2,2,2,2,1]
[7,2,2,2,1,1,1] => [7,4,1,1,1,1,1] => [7,2,2,2,1,1,1]
[7,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1]
[7,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1]
[6,6,4] => [3,3,3,3,2,2] => [6,6,4]
[6,6,3,1] => [4,3,3,2,2,2] => [6,6,3,1]
[6,6,2,2] => [4,4,2,2,2,2] => [6,6,2,2]
[6,6,2,1,1] => [5,3,2,2,2,2] => [6,6,2,1,1]
[6,6,1,1,1,1] => [6,2,2,2,2,2] => [6,6,1,1,1,1]
[6,5,5] => [3,3,3,3,3,1] => [6,5,5]
[6,5,4,1] => [4,3,3,3,2,1] => [6,5,4,1]
[6,5,3,2] => [4,4,3,2,2,1] => [6,5,3,2]
[6,5,3,1,1] => [5,3,3,2,2,1] => [6,5,3,1,1]
[6,5,2,2,1] => [5,4,2,2,2,1] => [6,5,2,2,1]
[6,5,2,1,1,1] => [6,3,2,2,2,1] => [6,5,2,1,1,1]
[6,5,1,1,1,1,1] => [7,2,2,2,2,1] => [6,5,1,1,1,1,1]
[6,4,4,2] => [4,4,3,3,1,1] => [6,4,4,2]
[6,4,4,1,1] => [5,3,3,3,1,1] => [6,4,4,1,1]
[6,4,3,3] => [4,4,4,2,1,1] => [6,4,3,3]
[6,4,3,2,1] => [5,4,3,2,1,1] => [6,4,3,2,1]
[6,4,3,1,1,1] => [6,3,3,2,1,1] => [6,4,3,1,1,1]
[6,4,2,2,2] => [5,5,2,2,1,1] => [6,4,2,2,2]
[6,4,2,2,1,1] => [6,4,2,2,1,1] => [6,4,2,2,1,1]
[6,4,2,1,1,1,1] => [7,3,2,2,1,1] => [6,4,2,1,1,1,1]
[6,4,1,1,1,1,1,1] => [8,2,2,2,1,1] => [6,4,1,1,1,1,1,1]
[6,3,3,3,1] => [5,4,4,1,1,1] => [6,3,3,3,1]
[6,3,3,2,2] => [5,5,3,1,1,1] => [6,3,3,2,2]
[6,3,3,2,1,1] => [6,4,3,1,1,1] => [6,3,3,2,1,1]
[6,3,3,1,1,1,1] => [7,3,3,1,1,1] => [6,3,3,1,1,1,1]
[6,3,2,2,2,1] => [6,5,2,1,1,1] => [6,3,2,2,2,1]
[6,3,2,2,1,1,1] => [7,4,2,1,1,1] => [6,3,2,2,1,1,1]
[6,3,2,1,1,1,1,1] => [8,3,2,1,1,1] => [6,3,2,1,1,1,1,1]
[6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1]
[6,2,2,2,2,2] => [6,6,1,1,1,1] => [6,2,2,2,2,2]
[6,2,2,2,2,1,1] => [7,5,1,1,1,1] => [6,2,2,2,2,1,1]
[6,2,2,2,1,1,1,1] => [8,4,1,1,1,1] => [6,2,2,2,1,1,1,1]
[6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1]
[6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1]
[5,5,5,1] => [4,3,3,3,3] => [5,5,5,1]
[5,5,4,2] => [4,4,3,3,2] => [5,5,4,2]
[5,5,4,1,1] => [5,3,3,3,2] => [5,5,4,1,1]
[5,5,3,3] => [4,4,4,2,2] => [5,5,3,3]
[5,5,3,2,1] => [5,4,3,2,2] => [5,5,3,2,1]
[5,5,3,1,1,1] => [6,3,3,2,2] => [5,5,3,1,1,1]
[5,5,2,2,2] => [5,5,2,2,2] => [5,5,2,2,2]
[5,5,2,2,1,1] => [6,4,2,2,2] => [5,5,2,2,1,1]
[5,5,2,1,1,1,1] => [7,3,2,2,2] => [5,5,2,1,1,1,1]
[5,5,1,1,1,1,1,1] => [8,2,2,2,2] => [5,5,1,1,1,1,1,1]
[5,4,4,3] => [4,4,4,3,1] => [5,4,4,3]
[5,4,4,2,1] => [5,4,3,3,1] => [5,4,4,2,1]
[5,4,4,1,1,1] => [6,3,3,3,1] => [5,4,4,1,1,1]
[5,4,3,3,1] => [5,4,4,2,1] => [5,4,3,3,1]
[5,4,3,2,2] => [5,5,3,2,1] => [5,4,3,2,2]
[5,4,3,2,1,1] => [6,4,3,2,1] => [5,4,3,2,1,1]
[5,4,3,1,1,1,1] => [7,3,3,2,1] => [5,4,3,1,1,1,1]
[5,4,2,2,2,1] => [6,5,2,2,1] => [5,4,2,2,2,1]
[5,4,2,2,1,1,1] => [7,4,2,2,1] => [5,4,2,2,1,1,1]
[5,4,2,1,1,1,1,1] => [8,3,2,2,1] => [5,4,2,1,1,1,1,1]
[5,4,1,1,1,1,1,1,1] => [9,2,2,2,1] => [5,4,1,1,1,1,1,1,1]
[5,3,3,3,2] => [5,5,4,1,1] => [5,3,3,3,2]
[5,3,3,3,1,1] => [6,4,4,1,1] => [5,3,3,3,1,1]
[5,3,3,2,2,1] => [6,5,3,1,1] => [5,3,3,2,2,1]
[5,3,3,2,1,1,1] => [7,4,3,1,1] => [5,3,3,2,1,1,1]
[5,3,3,1,1,1,1,1] => [8,3,3,1,1] => [5,3,3,1,1,1,1,1]
[5,3,2,2,2,2] => [6,6,2,1,1] => [5,3,2,2,2,2]
[5,3,2,2,2,1,1] => [7,5,2,1,1] => [5,3,2,2,2,1,1]
[5,3,2,2,1,1,1,1] => [8,4,2,1,1] => [5,3,2,2,1,1,1,1]
[5,3,2,1,1,1,1,1,1] => [9,3,2,1,1] => [5,3,2,1,1,1,1,1,1]
[5,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1] => [5,3,1,1,1,1,1,1,1,1]
[5,2,2,2,2,2,1] => [7,6,1,1,1] => [5,2,2,2,2,2,1]
[5,2,2,2,2,1,1,1] => [8,5,1,1,1] => [5,2,2,2,2,1,1,1]
[5,2,2,2,1,1,1,1,1] => [9,4,1,1,1] => [5,2,2,2,1,1,1,1,1]
[5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1]
[4,4,4,4] => [4,4,4,4] => [4,4,4,4]
[4,4,4,3,1] => [5,4,4,3] => [4,4,4,3,1]
[4,4,4,2,2] => [5,5,3,3] => [4,4,4,2,2]
[4,4,4,2,1,1] => [6,4,3,3] => [4,4,4,2,1,1]
[4,4,4,1,1,1,1] => [7,3,3,3] => [4,4,4,1,1,1,1]
[4,4,3,3,2] => [5,5,4,2] => [4,4,3,3,2]
[4,4,3,3,1,1] => [6,4,4,2] => [4,4,3,3,1,1]
[4,4,3,2,2,1] => [6,5,3,2] => [4,4,3,2,2,1]
[4,4,3,2,1,1,1] => [7,4,3,2] => [4,4,3,2,1,1,1]
[4,4,3,1,1,1,1,1] => [8,3,3,2] => [4,4,3,1,1,1,1,1]
[4,4,2,2,2,2] => [6,6,2,2] => [4,4,2,2,2,2]
[4,4,2,2,2,1,1] => [7,5,2,2] => [4,4,2,2,2,1,1]
[4,4,2,2,1,1,1,1] => [8,4,2,2] => [4,4,2,2,1,1,1,1]
[4,4,2,1,1,1,1,1,1] => [9,3,2,2] => [4,4,2,1,1,1,1,1,1]
[4,4,1,1,1,1,1,1,1,1] => [10,2,2,2] => [4,4,1,1,1,1,1,1,1,1]
[4,3,3,3,3] => [5,5,5,1] => [4,3,3,3,3]
[4,3,3,3,2,1] => [6,5,4,1] => [4,3,3,3,2,1]
[4,3,3,3,1,1,1] => [7,4,4,1] => [4,3,3,3,1,1,1]
[4,3,3,2,2,2] => [6,6,3,1] => [4,3,3,2,2,2]
[4,3,3,2,2,1,1] => [7,5,3,1] => [4,3,3,2,2,1,1]
[4,3,3,2,1,1,1,1] => [8,4,3,1] => [4,3,3,2,1,1,1,1]
[4,3,3,1,1,1,1,1,1] => [9,3,3,1] => [4,3,3,1,1,1,1,1,1]
[4,3,2,2,2,2,1] => [7,6,2,1] => [4,3,2,2,2,2,1]
[4,3,2,2,2,1,1,1] => [8,5,2,1] => [4,3,2,2,2,1,1,1]
[4,3,2,2,1,1,1,1,1] => [9,4,2,1] => [4,3,2,2,1,1,1,1,1]
[4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => [4,3,2,1,1,1,1,1,1,1]
[4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => [4,3,1,1,1,1,1,1,1,1,1]
[4,2,2,2,2,2,2] => [7,7,1,1] => [4,2,2,2,2,2,2]
[4,2,2,2,2,2,1,1] => [8,6,1,1] => [4,2,2,2,2,2,1,1]
[4,2,2,2,2,1,1,1,1] => [9,5,1,1] => [4,2,2,2,2,1,1,1,1]
[4,2,2,2,1,1,1,1,1,1] => [10,4,1,1] => [4,2,2,2,1,1,1,1,1,1]
[4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1] => [4,2,2,1,1,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,3,1] => [6,5,5] => [3,3,3,3,3,1]
[3,3,3,3,2,2] => [6,6,4] => [3,3,3,3,2,2]
[3,3,3,3,2,1,1] => [7,5,4] => [3,3,3,3,2,1,1]
[3,3,3,3,1,1,1,1] => [8,4,4] => [3,3,3,3,1,1,1,1]
[3,3,3,2,2,2,1] => [7,6,3] => [3,3,3,2,2,2,1]
[3,3,3,2,2,1,1,1] => [8,5,3] => [3,3,3,2,2,1,1,1]
[3,3,3,2,1,1,1,1,1] => [9,4,3] => [3,3,3,2,1,1,1,1,1]
[3,3,3,1,1,1,1,1,1,1] => [10,3,3] => [3,3,3,1,1,1,1,1,1,1]
[3,3,2,2,2,2,2] => [7,7,2] => [3,3,2,2,2,2,2]
[3,3,2,2,2,2,1,1] => [8,6,2] => [3,3,2,2,2,2,1,1]
[3,3,2,2,2,1,1,1,1] => [9,5,2] => [3,3,2,2,2,1,1,1,1]
[3,3,2,2,1,1,1,1,1,1] => [10,4,2] => [3,3,2,2,1,1,1,1,1,1]
[3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => [3,3,2,1,1,1,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2] => [3,3,1,1,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,2,1] => [8,7,1] => [3,2,2,2,2,2,2,1]
[3,2,2,2,2,2,1,1,1] => [9,6,1] => [3,2,2,2,2,2,1,1,1]
[3,2,2,2,2,1,1,1,1,1] => [10,5,1] => [3,2,2,2,2,1,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1,1] => [11,4,1] => [3,2,2,2,1,1,1,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2,2] => [8,8] => [2,2,2,2,2,2,2,2]
[2,2,2,2,2,2,2,1,1] => [9,7] => [2,2,2,2,2,2,2,1,1]
[2,2,2,2,2,2,1,1,1,1] => [10,6] => [2,2,2,2,2,2,1,1,1,1]
[2,2,2,2,2,1,1,1,1,1,1] => [11,5] => [2,2,2,2,2,1,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => [2,2,2,2,1,1,1,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => [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] => [15,1] => [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] => [16] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[17] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17]
[16,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1]
[15,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2]
[15,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1]
[14,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3]
[14,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1]
[14,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1]
[13,4] => [2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4]
[13,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1]
[13,2,2] => [3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2]
[13,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1]
[13,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1]
[12,5] => [2,2,2,2,2,1,1,1,1,1,1,1] => [12,5]
[12,4,1] => [3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1]
[12,3,2] => [3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2]
[12,3,1,1] => [4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1]
[12,2,2,1] => [4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1]
[12,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1]
[12,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1]
[11,6] => [2,2,2,2,2,2,1,1,1,1,1] => [11,6]
[11,5,1] => [3,2,2,2,2,1,1,1,1,1,1] => [11,5,1]
[11,4,2] => [3,3,2,2,1,1,1,1,1,1,1] => [11,4,2]
[11,4,1,1] => [4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1]
[11,3,3] => [3,3,3,1,1,1,1,1,1,1,1] => [11,3,3]
[11,3,2,1] => [4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1]
[11,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1]
[11,2,2,2] => [4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2]
[11,2,2,1,1] => [5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1]
[11,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1]
[11,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1]
[10,7] => [2,2,2,2,2,2,2,1,1,1] => [10,7]
[10,6,1] => [3,2,2,2,2,2,1,1,1,1] => [10,6,1]
[10,5,2] => [3,3,2,2,2,1,1,1,1,1] => [10,5,2]
[10,5,1,1] => [4,2,2,2,2,1,1,1,1,1] => [10,5,1,1]
[10,4,3] => [3,3,3,2,1,1,1,1,1,1] => [10,4,3]
[10,4,2,1] => [4,3,2,2,1,1,1,1,1,1] => [10,4,2,1]
[10,4,1,1,1] => [5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1]
[10,3,3,1] => [4,3,3,1,1,1,1,1,1,1] => [10,3,3,1]
[10,3,2,2] => [4,4,2,1,1,1,1,1,1,1] => [10,3,2,2]
[10,3,2,1,1] => [5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1]
[10,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1]
[10,2,2,2,1] => [5,4,1,1,1,1,1,1,1,1] => [10,2,2,2,1]
[10,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1]
[10,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1,1]
[10,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1]
[9,8] => [2,2,2,2,2,2,2,2,1] => [9,8]
[9,7,1] => [3,2,2,2,2,2,2,1,1] => [9,7,1]
[9,6,2] => [3,3,2,2,2,2,1,1,1] => [9,6,2]
[9,6,1,1] => [4,2,2,2,2,2,1,1,1] => [9,6,1,1]
[9,5,3] => [3,3,3,2,2,1,1,1,1] => [9,5,3]
[9,5,2,1] => [4,3,2,2,2,1,1,1,1] => [9,5,2,1]
[9,5,1,1,1] => [5,2,2,2,2,1,1,1,1] => [9,5,1,1,1]
[9,4,4] => [3,3,3,3,1,1,1,1,1] => [9,4,4]
[9,4,3,1] => [4,3,3,2,1,1,1,1,1] => [9,4,3,1]
[9,4,2,2] => [4,4,2,2,1,1,1,1,1] => [9,4,2,2]
[9,4,2,1,1] => [5,3,2,2,1,1,1,1,1] => [9,4,2,1,1]
[9,4,1,1,1,1] => [6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1]
[9,3,3,2] => [4,4,3,1,1,1,1,1,1] => [9,3,3,2]
[9,3,3,1,1] => [5,3,3,1,1,1,1,1,1] => [9,3,3,1,1]
[9,3,2,2,1] => [5,4,2,1,1,1,1,1,1] => [9,3,2,2,1]
[9,3,2,1,1,1] => [6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1]
[9,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1]
[9,2,2,2,2] => [5,5,1,1,1,1,1,1,1] => [9,2,2,2,2]
[9,2,2,2,1,1] => [6,4,1,1,1,1,1,1,1] => [9,2,2,2,1,1]
[9,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1,1]
[9,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1]
[9,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1,1]
[8,8,1] => [3,2,2,2,2,2,2,2] => [8,8,1]
[8,7,2] => [3,3,2,2,2,2,2,1] => [8,7,2]
[8,7,1,1] => [4,2,2,2,2,2,2,1] => [8,7,1,1]
[8,6,3] => [3,3,3,2,2,2,1,1] => [8,6,3]
[8,6,2,1] => [4,3,2,2,2,2,1,1] => [8,6,2,1]
[8,6,1,1,1] => [5,2,2,2,2,2,1,1] => [8,6,1,1,1]
[8,5,4] => [3,3,3,3,2,1,1,1] => [8,5,4]
[8,5,3,1] => [4,3,3,2,2,1,1,1] => [8,5,3,1]
[8,5,2,2] => [4,4,2,2,2,1,1,1] => [8,5,2,2]
[8,5,2,1,1] => [5,3,2,2,2,1,1,1] => [8,5,2,1,1]
[8,5,1,1,1,1] => [6,2,2,2,2,1,1,1] => [8,5,1,1,1,1]
[8,4,4,1] => [4,3,3,3,1,1,1,1] => [8,4,4,1]
[8,4,3,2] => [4,4,3,2,1,1,1,1] => [8,4,3,2]
[8,4,3,1,1] => [5,3,3,2,1,1,1,1] => [8,4,3,1,1]
[8,4,2,2,1] => [5,4,2,2,1,1,1,1] => [8,4,2,2,1]
[8,4,2,1,1,1] => [6,3,2,2,1,1,1,1] => [8,4,2,1,1,1]
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1]
[8,3,3,3] => [4,4,4,1,1,1,1,1] => [8,3,3,3]
[8,3,3,2,1] => [5,4,3,1,1,1,1,1] => [8,3,3,2,1]
[8,3,3,1,1,1] => [6,3,3,1,1,1,1,1] => [8,3,3,1,1,1]
[8,3,2,2,2] => [5,5,2,1,1,1,1,1] => [8,3,2,2,2]
[8,3,2,2,1,1] => [6,4,2,1,1,1,1,1] => [8,3,2,2,1,1]
[8,3,2,1,1,1,1] => [7,3,2,1,1,1,1,1] => [8,3,2,1,1,1,1]
[8,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1,1]
[8,2,2,2,2,1] => [6,5,1,1,1,1,1,1] => [8,2,2,2,2,1]
[8,2,2,2,1,1,1] => [7,4,1,1,1,1,1,1] => [8,2,2,2,1,1,1]
[8,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1,1]
[8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1,1]
[8,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1,1]
[7,7,3] => [3,3,3,2,2,2,2] => [7,7,3]
[7,7,2,1] => [4,3,2,2,2,2,2] => [7,7,2,1]
[7,7,1,1,1] => [5,2,2,2,2,2,2] => [7,7,1,1,1]
[7,6,4] => [3,3,3,3,2,2,1] => [7,6,4]
[7,6,3,1] => [4,3,3,2,2,2,1] => [7,6,3,1]
[7,6,2,2] => [4,4,2,2,2,2,1] => [7,6,2,2]
[7,6,2,1,1] => [5,3,2,2,2,2,1] => [7,6,2,1,1]
[7,6,1,1,1,1] => [6,2,2,2,2,2,1] => [7,6,1,1,1,1]
[7,5,5] => [3,3,3,3,3,1,1] => [7,5,5]
[7,5,4,1] => [4,3,3,3,2,1,1] => [7,5,4,1]
[7,5,3,2] => [4,4,3,2,2,1,1] => [7,5,3,2]
[7,5,3,1,1] => [5,3,3,2,2,1,1] => [7,5,3,1,1]
[7,5,2,2,1] => [5,4,2,2,2,1,1] => [7,5,2,2,1]
[7,5,2,1,1,1] => [6,3,2,2,2,1,1] => [7,5,2,1,1,1]
[7,5,1,1,1,1,1] => [7,2,2,2,2,1,1] => [7,5,1,1,1,1,1]
[7,4,4,2] => [4,4,3,3,1,1,1] => [7,4,4,2]
[7,4,4,1,1] => [5,3,3,3,1,1,1] => [7,4,4,1,1]
[7,4,3,3] => [4,4,4,2,1,1,1] => [7,4,3,3]
[7,4,3,2,1] => [5,4,3,2,1,1,1] => [7,4,3,2,1]
[7,4,3,1,1,1] => [6,3,3,2,1,1,1] => [7,4,3,1,1,1]
[7,4,2,2,2] => [5,5,2,2,1,1,1] => [7,4,2,2,2]
[7,4,2,2,1,1] => [6,4,2,2,1,1,1] => [7,4,2,2,1,1]
[7,4,2,1,1,1,1] => [7,3,2,2,1,1,1] => [7,4,2,1,1,1,1]
[7,4,1,1,1,1,1,1] => [8,2,2,2,1,1,1] => [7,4,1,1,1,1,1,1]
[7,3,3,3,1] => [5,4,4,1,1,1,1] => [7,3,3,3,1]
[7,3,3,2,2] => [5,5,3,1,1,1,1] => [7,3,3,2,2]
[7,3,3,2,1,1] => [6,4,3,1,1,1,1] => [7,3,3,2,1,1]
[7,3,3,1,1,1,1] => [7,3,3,1,1,1,1] => [7,3,3,1,1,1,1]
[7,3,2,2,2,1] => [6,5,2,1,1,1,1] => [7,3,2,2,2,1]
[7,3,2,2,1,1,1] => [7,4,2,1,1,1,1] => [7,3,2,2,1,1,1]
[7,3,2,1,1,1,1,1] => [8,3,2,1,1,1,1] => [7,3,2,1,1,1,1,1]
[7,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1,1]
[7,2,2,2,2,2] => [6,6,1,1,1,1,1] => [7,2,2,2,2,2]
[7,2,2,2,2,1,1] => [7,5,1,1,1,1,1] => [7,2,2,2,2,1,1]
[7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1]
[7,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1,1]
[7,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1,1]
[6,6,5] => [3,3,3,3,3,2] => [6,6,5]
[6,6,4,1] => [4,3,3,3,2,2] => [6,6,4,1]
[6,6,3,2] => [4,4,3,2,2,2] => [6,6,3,2]
[6,6,3,1,1] => [5,3,3,2,2,2] => [6,6,3,1,1]
[6,6,2,2,1] => [5,4,2,2,2,2] => [6,6,2,2,1]
[6,6,2,1,1,1] => [6,3,2,2,2,2] => [6,6,2,1,1,1]
[6,6,1,1,1,1,1] => [7,2,2,2,2,2] => [6,6,1,1,1,1,1]
[6,5,5,1] => [4,3,3,3,3,1] => [6,5,5,1]
[6,5,4,2] => [4,4,3,3,2,1] => [6,5,4,2]
[6,5,4,1,1] => [5,3,3,3,2,1] => [6,5,4,1,1]
[6,5,3,3] => [4,4,4,2,2,1] => [6,5,3,3]
[6,5,3,2,1] => [5,4,3,2,2,1] => [6,5,3,2,1]
[6,5,3,1,1,1] => [6,3,3,2,2,1] => [6,5,3,1,1,1]
[6,5,2,2,2] => [5,5,2,2,2,1] => [6,5,2,2,2]
[6,5,2,2,1,1] => [6,4,2,2,2,1] => [6,5,2,2,1,1]
[6,5,2,1,1,1,1] => [7,3,2,2,2,1] => [6,5,2,1,1,1,1]
[6,5,1,1,1,1,1,1] => [8,2,2,2,2,1] => [6,5,1,1,1,1,1,1]
[6,4,4,3] => [4,4,4,3,1,1] => [6,4,4,3]
[6,4,4,2,1] => [5,4,3,3,1,1] => [6,4,4,2,1]
[6,4,4,1,1,1] => [6,3,3,3,1,1] => [6,4,4,1,1,1]
[6,4,3,3,1] => [5,4,4,2,1,1] => [6,4,3,3,1]
[6,4,3,2,2] => [5,5,3,2,1,1] => [6,4,3,2,2]
[6,4,3,2,1,1] => [6,4,3,2,1,1] => [6,4,3,2,1,1]
[6,4,3,1,1,1,1] => [7,3,3,2,1,1] => [6,4,3,1,1,1,1]
[6,4,2,2,2,1] => [6,5,2,2,1,1] => [6,4,2,2,2,1]
[6,4,2,2,1,1,1] => [7,4,2,2,1,1] => [6,4,2,2,1,1,1]
[6,4,2,1,1,1,1,1] => [8,3,2,2,1,1] => [6,4,2,1,1,1,1,1]
[6,4,1,1,1,1,1,1,1] => [9,2,2,2,1,1] => [6,4,1,1,1,1,1,1,1]
[6,3,3,3,2] => [5,5,4,1,1,1] => [6,3,3,3,2]
[6,3,3,3,1,1] => [6,4,4,1,1,1] => [6,3,3,3,1,1]
[6,3,3,2,2,1] => [6,5,3,1,1,1] => [6,3,3,2,2,1]
[6,3,3,2,1,1,1] => [7,4,3,1,1,1] => [6,3,3,2,1,1,1]
[6,3,3,1,1,1,1,1] => [8,3,3,1,1,1] => [6,3,3,1,1,1,1,1]
[6,3,2,2,2,2] => [6,6,2,1,1,1] => [6,3,2,2,2,2]
[6,3,2,2,2,1,1] => [7,5,2,1,1,1] => [6,3,2,2,2,1,1]
[6,3,2,2,1,1,1,1] => [8,4,2,1,1,1] => [6,3,2,2,1,1,1,1]
[6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1] => [6,3,2,1,1,1,1,1,1]
[6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1,1]
[6,2,2,2,2,2,1] => [7,6,1,1,1,1] => [6,2,2,2,2,2,1]
[6,2,2,2,2,1,1,1] => [8,5,1,1,1,1] => [6,2,2,2,2,1,1,1]
[6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1] => [6,2,2,2,1,1,1,1,1]
[6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1,1]
[6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1,1]
[5,5,5,2] => [4,4,3,3,3] => [5,5,5,2]
[5,5,5,1,1] => [5,3,3,3,3] => [5,5,5,1,1]
[5,5,4,3] => [4,4,4,3,2] => [5,5,4,3]
[5,5,4,2,1] => [5,4,3,3,2] => [5,5,4,2,1]
[5,5,4,1,1,1] => [6,3,3,3,2] => [5,5,4,1,1,1]
[5,5,3,3,1] => [5,4,4,2,2] => [5,5,3,3,1]
[5,5,3,2,2] => [5,5,3,2,2] => [5,5,3,2,2]
[5,5,3,2,1,1] => [6,4,3,2,2] => [5,5,3,2,1,1]
[5,5,3,1,1,1,1] => [7,3,3,2,2] => [5,5,3,1,1,1,1]
[5,5,2,2,2,1] => [6,5,2,2,2] => [5,5,2,2,2,1]
[5,5,2,2,1,1,1] => [7,4,2,2,2] => [5,5,2,2,1,1,1]
[5,5,2,1,1,1,1,1] => [8,3,2,2,2] => [5,5,2,1,1,1,1,1]
[5,5,1,1,1,1,1,1,1] => [9,2,2,2,2] => [5,5,1,1,1,1,1,1,1]
[5,4,4,4] => [4,4,4,4,1] => [5,4,4,4]
[5,4,4,3,1] => [5,4,4,3,1] => [5,4,4,3,1]
[5,4,4,2,2] => [5,5,3,3,1] => [5,4,4,2,2]
[5,4,4,2,1,1] => [6,4,3,3,1] => [5,4,4,2,1,1]
[5,4,4,1,1,1,1] => [7,3,3,3,1] => [5,4,4,1,1,1,1]
[5,4,3,3,2] => [5,5,4,2,1] => [5,4,3,3,2]
[5,4,3,3,1,1] => [6,4,4,2,1] => [5,4,3,3,1,1]
[5,4,3,2,2,1] => [6,5,3,2,1] => [5,4,3,2,2,1]
[5,4,3,2,1,1,1] => [7,4,3,2,1] => [5,4,3,2,1,1,1]
[5,4,3,1,1,1,1,1] => [8,3,3,2,1] => [5,4,3,1,1,1,1,1]
[5,4,2,2,2,2] => [6,6,2,2,1] => [5,4,2,2,2,2]
[5,4,2,2,2,1,1] => [7,5,2,2,1] => [5,4,2,2,2,1,1]
[5,4,2,2,1,1,1,1] => [8,4,2,2,1] => [5,4,2,2,1,1,1,1]
[5,4,2,1,1,1,1,1,1] => [9,3,2,2,1] => [5,4,2,1,1,1,1,1,1]
[5,4,1,1,1,1,1,1,1,1] => [10,2,2,2,1] => [5,4,1,1,1,1,1,1,1,1]
[5,3,3,3,3] => [5,5,5,1,1] => [5,3,3,3,3]
[5,3,3,3,2,1] => [6,5,4,1,1] => [5,3,3,3,2,1]
[5,3,3,3,1,1,1] => [7,4,4,1,1] => [5,3,3,3,1,1,1]
[5,3,3,2,2,2] => [6,6,3,1,1] => [5,3,3,2,2,2]
[5,3,3,2,2,1,1] => [7,5,3,1,1] => [5,3,3,2,2,1,1]
[5,3,3,2,1,1,1,1] => [8,4,3,1,1] => [5,3,3,2,1,1,1,1]
[5,3,3,1,1,1,1,1,1] => [9,3,3,1,1] => [5,3,3,1,1,1,1,1,1]
[5,3,2,2,2,2,1] => [7,6,2,1,1] => [5,3,2,2,2,2,1]
[5,3,2,2,2,1,1,1] => [8,5,2,1,1] => [5,3,2,2,2,1,1,1]
[5,3,2,2,1,1,1,1,1] => [9,4,2,1,1] => [5,3,2,2,1,1,1,1,1]
[5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1] => [5,3,2,1,1,1,1,1,1,1]
[5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1] => [5,3,1,1,1,1,1,1,1,1,1]
[5,2,2,2,2,2,2] => [7,7,1,1,1] => [5,2,2,2,2,2,2]
[5,2,2,2,2,2,1,1] => [8,6,1,1,1] => [5,2,2,2,2,2,1,1]
[5,2,2,2,2,1,1,1,1] => [9,5,1,1,1] => [5,2,2,2,2,1,1,1,1]
[5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1] => [5,2,2,2,1,1,1,1,1,1]
[5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1]
[4,4,4,4,1] => [5,4,4,4] => [4,4,4,4,1]
[4,4,4,3,2] => [5,5,4,3] => [4,4,4,3,2]
[4,4,4,3,1,1] => [6,4,4,3] => [4,4,4,3,1,1]
[4,4,4,2,2,1] => [6,5,3,3] => [4,4,4,2,2,1]
[4,4,4,2,1,1,1] => [7,4,3,3] => [4,4,4,2,1,1,1]
[4,4,4,1,1,1,1,1] => [8,3,3,3] => [4,4,4,1,1,1,1,1]
[4,4,3,3,3] => [5,5,5,2] => [4,4,3,3,3]
[4,4,3,3,2,1] => [6,5,4,2] => [4,4,3,3,2,1]
[4,4,3,3,1,1,1] => [7,4,4,2] => [4,4,3,3,1,1,1]
[4,4,3,2,2,2] => [6,6,3,2] => [4,4,3,2,2,2]
[4,4,3,2,2,1,1] => [7,5,3,2] => [4,4,3,2,2,1,1]
[4,4,3,2,1,1,1,1] => [8,4,3,2] => [4,4,3,2,1,1,1,1]
[4,4,3,1,1,1,1,1,1] => [9,3,3,2] => [4,4,3,1,1,1,1,1,1]
[4,4,2,2,2,2,1] => [7,6,2,2] => [4,4,2,2,2,2,1]
[4,4,2,2,2,1,1,1] => [8,5,2,2] => [4,4,2,2,2,1,1,1]
[4,4,2,2,1,1,1,1,1] => [9,4,2,2] => [4,4,2,2,1,1,1,1,1]
[4,4,2,1,1,1,1,1,1,1] => [10,3,2,2] => [4,4,2,1,1,1,1,1,1,1]
[4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2] => [4,4,1,1,1,1,1,1,1,1,1]
[4,3,3,3,3,1] => [6,5,5,1] => [4,3,3,3,3,1]
[4,3,3,3,2,2] => [6,6,4,1] => [4,3,3,3,2,2]
[4,3,3,3,2,1,1] => [7,5,4,1] => [4,3,3,3,2,1,1]
[4,3,3,3,1,1,1,1] => [8,4,4,1] => [4,3,3,3,1,1,1,1]
[4,3,3,2,2,2,1] => [7,6,3,1] => [4,3,3,2,2,2,1]
[4,3,3,2,2,1,1,1] => [8,5,3,1] => [4,3,3,2,2,1,1,1]
[4,3,3,2,1,1,1,1,1] => [9,4,3,1] => [4,3,3,2,1,1,1,1,1]
[4,3,3,1,1,1,1,1,1,1] => [10,3,3,1] => [4,3,3,1,1,1,1,1,1,1]
[4,3,2,2,2,2,2] => [7,7,2,1] => [4,3,2,2,2,2,2]
[4,3,2,2,2,2,1,1] => [8,6,2,1] => [4,3,2,2,2,2,1,1]
[4,3,2,2,2,1,1,1,1] => [9,5,2,1] => [4,3,2,2,2,1,1,1,1]
[4,3,2,2,1,1,1,1,1,1] => [10,4,2,1] => [4,3,2,2,1,1,1,1,1,1]
[4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1] => [4,3,2,1,1,1,1,1,1,1,1]
[4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1] => [4,3,1,1,1,1,1,1,1,1,1,1]
[4,2,2,2,2,2,2,1] => [8,7,1,1] => [4,2,2,2,2,2,2,1]
[4,2,2,2,2,2,1,1,1] => [9,6,1,1] => [4,2,2,2,2,2,1,1,1]
[4,2,2,2,2,1,1,1,1,1] => [10,5,1,1] => [4,2,2,2,2,1,1,1,1,1]
[4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1] => [4,2,2,2,1,1,1,1,1,1,1]
[4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1] => [4,2,2,1,1,1,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,3,2] => [6,6,5] => [3,3,3,3,3,2]
[3,3,3,3,3,1,1] => [7,5,5] => [3,3,3,3,3,1,1]
[3,3,3,3,2,2,1] => [7,6,4] => [3,3,3,3,2,2,1]
[3,3,3,3,2,1,1,1] => [8,5,4] => [3,3,3,3,2,1,1,1]
[3,3,3,3,1,1,1,1,1] => [9,4,4] => [3,3,3,3,1,1,1,1,1]
[3,3,3,2,2,2,2] => [7,7,3] => [3,3,3,2,2,2,2]
[3,3,3,2,2,2,1,1] => [8,6,3] => [3,3,3,2,2,2,1,1]
[3,3,3,2,2,1,1,1,1] => [9,5,3] => [3,3,3,2,2,1,1,1,1]
[3,3,3,2,1,1,1,1,1,1] => [10,4,3] => [3,3,3,2,1,1,1,1,1,1]
[3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => [3,3,3,1,1,1,1,1,1,1,1]
[3,3,2,2,2,2,2,1] => [8,7,2] => [3,3,2,2,2,2,2,1]
[3,3,2,2,2,2,1,1,1] => [9,6,2] => [3,3,2,2,2,2,1,1,1]
[3,3,2,2,2,1,1,1,1,1] => [10,5,2] => [3,3,2,2,2,1,1,1,1,1]
[3,3,2,2,1,1,1,1,1,1,1] => [11,4,2] => [3,3,2,2,1,1,1,1,1,1,1]
[3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => [3,3,2,1,1,1,1,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => [3,3,1,1,1,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,2,2] => [8,8,1] => [3,2,2,2,2,2,2,2]
[3,2,2,2,2,2,2,1,1] => [9,7,1] => [3,2,2,2,2,2,2,1,1]
[3,2,2,2,2,2,1,1,1,1] => [10,6,1] => [3,2,2,2,2,2,1,1,1,1]
[3,2,2,2,2,1,1,1,1,1,1] => [11,5,1] => [3,2,2,2,2,1,1,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1] => [3,2,2,2,1,1,1,1,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2,2,1] => [9,8] => [2,2,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,1,1,1] => [10,7] => [2,2,2,2,2,2,2,1,1,1]
[2,2,2,2,2,2,1,1,1,1,1] => [11,6] => [2,2,2,2,2,2,1,1,1,1,1]
[2,2,2,2,2,1,1,1,1,1,1,1] => [12,5] => [2,2,2,2,2,1,1,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4] => [2,2,2,2,1,1,1,1,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => [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] => [17] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[] => [] => []
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[5,5,4,3,2,1] => [6,5,4,3,2] => [5,5,4,3,2,1]
[6,4,4,3,2,1] => [6,5,4,3,1,1] => [6,4,4,3,2,1]
[5,4,4,3,2,1] => [6,5,4,3,1] => [5,4,4,3,2,1]
[4,4,4,3,2,1] => [6,5,4,3] => [4,4,4,3,2,1]
[6,5,3,3,2,1] => [6,5,4,2,2,1] => [6,5,3,3,2,1]
[5,5,3,3,2,1] => [6,5,4,2,2] => [5,5,3,3,2,1]
[6,4,3,3,2,1] => [6,5,4,2,1,1] => [6,4,3,3,2,1]
[5,4,3,3,2,1] => [6,5,4,2,1] => [5,4,3,3,2,1]
[6,3,3,3,2,1] => [6,5,4,1,1,1] => [6,3,3,3,2,1]
[6,5,4,2,2,1] => [6,5,3,3,2,1] => [6,5,4,2,2,1]
[5,5,4,2,2,1] => [6,5,3,3,2] => [5,5,4,2,2,1]
[6,4,4,2,2,1] => [6,5,3,3,1,1] => [6,4,4,2,2,1]
[5,4,4,2,2,1] => [6,5,3,3,1] => [5,4,4,2,2,1]
[6,5,3,2,2,1] => [6,5,3,2,2,1] => [6,5,3,2,2,1]
[5,5,3,2,2,1] => [6,5,3,2,2] => [5,5,3,2,2,1]
[6,4,3,2,2,1] => [6,5,3,2,1,1] => [6,4,3,2,2,1]
[6,5,2,2,2,1] => [6,5,2,2,2,1] => [6,5,2,2,2,1]
[6,5,4,3,1,1] => [6,4,4,3,2,1] => [6,5,4,3,1,1]
[5,5,4,3,1,1] => [6,4,4,3,2] => [5,5,4,3,1,1]
[6,4,4,3,1,1] => [6,4,4,3,1,1] => [6,4,4,3,1,1]
[5,4,4,3,1,1] => [6,4,4,3,1] => [5,4,4,3,1,1]
[6,5,3,3,1,1] => [6,4,4,2,2,1] => [6,5,3,3,1,1]
[5,5,3,3,1,1] => [6,4,4,2,2] => [5,5,3,3,1,1]
[6,4,3,3,1,1] => [6,4,4,2,1,1] => [6,4,3,3,1,1]
[6,5,4,2,1,1] => [6,4,3,3,2,1] => [6,5,4,2,1,1]
[5,5,4,2,1,1] => [6,4,3,3,2] => [5,5,4,2,1,1]
[6,4,4,2,1,1] => [6,4,3,3,1,1] => [6,4,4,2,1,1]
[6,5,3,2,1,1] => [6,4,3,2,2,1] => [6,5,3,2,1,1]
[6,5,4,1,1,1] => [6,3,3,3,2,1] => [6,5,4,1,1,1]
[6,5,4,3,2] => [5,5,4,3,2,1] => [6,5,4,3,2]
[5,5,4,3,2] => [5,5,4,3,2] => [5,5,4,3,2]
[6,4,4,3,2] => [5,5,4,3,1,1] => [6,4,4,3,2]
[5,4,4,3,2] => [5,5,4,3,1] => [5,4,4,3,2]
[6,5,3,3,2] => [5,5,4,2,2,1] => [6,5,3,3,2]
[5,5,3,3,2] => [5,5,4,2,2] => [5,5,3,3,2]
[6,4,3,3,2] => [5,5,4,2,1,1] => [6,4,3,3,2]
[6,5,4,2,2] => [5,5,3,3,2,1] => [6,5,4,2,2]
[5,5,4,2,2] => [5,5,3,3,2] => [5,5,4,2,2]
[6,4,4,2,2] => [5,5,3,3,1,1] => [6,4,4,2,2]
[6,5,3,2,2] => [5,5,3,2,2,1] => [6,5,3,2,2]
[6,5,4,3,1] => [5,4,4,3,2,1] => [6,5,4,3,1]
[5,5,4,3,1] => [5,4,4,3,2] => [5,5,4,3,1]
[6,4,4,3,1] => [5,4,4,3,1,1] => [6,4,4,3,1]
[6,5,3,3,1] => [5,4,4,2,2,1] => [6,5,3,3,1]
[6,5,4,2,1] => [5,4,3,3,2,1] => [6,5,4,2,1]
[6,5,4,3] => [4,4,4,3,2,1] => [6,5,4,3]
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[6,6,5,4,3,2,1] => [7,6,5,4,3,2] => [6,6,5,4,3,2,1]
[7,5,5,4,3,2,1] => [7,6,5,4,3,1,1] => [7,5,5,4,3,2,1]
[6,5,5,4,3,2,1] => [7,6,5,4,3,1] => [6,5,5,4,3,2,1]
[5,5,5,4,3,2,1] => [7,6,5,4,3] => [5,5,5,4,3,2,1]
[7,6,4,4,3,2,1] => [7,6,5,4,2,2,1] => [7,6,4,4,3,2,1]
[6,6,4,4,3,2,1] => [7,6,5,4,2,2] => [6,6,4,4,3,2,1]
[6,5,4,4,3,2,1] => [7,6,5,4,2,1] => [6,5,4,4,3,2,1]
[7,4,4,4,3,2,1] => [7,6,5,4,1,1,1] => [7,4,4,4,3,2,1]
[6,4,4,4,3,2,1] => [7,6,5,4,1,1] => [6,4,4,4,3,2,1]
[5,4,4,4,3,2,1] => [7,6,5,4,1] => [5,4,4,4,3,2,1]
[4,4,4,4,3,2,1] => [7,6,5,4] => [4,4,4,4,3,2,1]
[7,6,5,3,3,2,1] => [7,6,5,3,3,2,1] => [7,6,5,3,3,2,1]
[6,5,4,3,3,2,1] => [7,6,5,3,2,1] => [6,5,4,3,3,2,1]
[7,6,3,3,3,2,1] => [7,6,5,2,2,2,1] => [7,6,3,3,3,2,1]
[6,6,3,3,3,2,1] => [7,6,5,2,2,2] => [6,6,3,3,3,2,1]
[6,5,3,3,3,2,1] => [7,6,5,2,2,1] => [6,5,3,3,3,2,1]
[7,3,3,3,3,2,1] => [7,6,5,1,1,1,1] => [7,3,3,3,3,2,1]
[6,3,3,3,3,2,1] => [7,6,5,1,1,1] => [6,3,3,3,3,2,1]
[3,3,3,3,3,2,1] => [7,6,5] => [3,3,3,3,3,2,1]
[7,6,5,4,2,2,1] => [7,6,4,4,3,2,1] => [7,6,5,4,2,2,1]
[6,6,5,4,2,2,1] => [7,6,4,4,3,2] => [6,6,5,4,2,2,1]
[7,6,4,4,2,2,1] => [7,6,4,4,2,2,1] => [7,6,4,4,2,2,1]
[6,6,4,4,2,2,1] => [7,6,4,4,2,2] => [6,6,4,4,2,2,1]
[7,6,4,3,2,2,1] => [7,6,4,3,2,2,1] => [7,6,4,3,2,2,1]
[6,5,4,3,2,2,1] => [7,6,4,3,2,1] => [6,5,4,3,2,2,1]
[7,6,5,2,2,2,1] => [7,6,3,3,3,2,1] => [7,6,5,2,2,2,1]
[6,5,4,2,2,2,1] => [7,6,3,3,2,1] => [6,5,4,2,2,2,1]
[7,6,3,2,2,2,1] => [7,6,3,2,2,2,1] => [7,6,3,2,2,2,1]
[7,6,2,2,2,2,1] => [7,6,2,2,2,2,1] => [7,6,2,2,2,2,1]
[6,6,2,2,2,2,1] => [7,6,2,2,2,2] => [6,6,2,2,2,2,1]
[6,5,2,2,2,2,1] => [7,6,2,2,2,1] => [6,5,2,2,2,2,1]
[7,2,2,2,2,2,1] => [7,6,1,1,1,1,1] => [7,2,2,2,2,2,1]
[7,6,5,4,3,1,1] => [7,5,5,4,3,2,1] => [7,6,5,4,3,1,1]
[6,6,5,4,3,1,1] => [7,5,5,4,3,2] => [6,6,5,4,3,1,1]
[7,5,5,4,3,1,1] => [7,5,5,4,3,1,1] => [7,5,5,4,3,1,1]
[7,5,5,3,3,1,1] => [7,5,5,3,3,1,1] => [7,5,5,3,3,1,1]
[7,5,4,4,2,1,1] => [7,5,4,4,2,1,1] => [7,5,4,4,2,1,1]
[7,5,4,3,2,1,1] => [7,5,4,3,2,1,1] => [7,5,4,3,2,1,1]
[6,5,4,3,2,1,1] => [7,5,4,3,2,1] => [6,5,4,3,2,1,1]
[5,5,4,3,2,1,1] => [7,5,4,3,2] => [5,5,4,3,2,1,1]
[7,5,3,2,2,1,1] => [7,5,3,2,2,1,1] => [7,5,3,2,2,1,1]
[7,6,5,4,1,1,1] => [7,4,4,4,3,2,1] => [7,6,5,4,1,1,1]
[6,6,4,4,1,1,1] => [7,4,4,4,2,2] => [6,6,4,4,1,1,1]
[7,4,4,4,1,1,1] => [7,4,4,4,1,1,1] => [7,4,4,4,1,1,1]
[6,5,4,3,1,1,1] => [7,4,4,3,2,1] => [6,5,4,3,1,1,1]
[7,4,3,2,1,1,1] => [7,4,3,2,1,1,1] => [7,4,3,2,1,1,1]
[7,6,5,1,1,1,1] => [7,3,3,3,3,2,1] => [7,6,5,1,1,1,1]
[5,5,5,1,1,1,1] => [7,3,3,3,3] => [5,5,5,1,1,1,1]
[6,5,4,1,1,1,1] => [7,3,3,3,2,1] => [6,5,4,1,1,1,1]
[7,6,1,1,1,1,1] => [7,2,2,2,2,2,1] => [7,6,1,1,1,1,1]
[7,6,5,4,3,2] => [6,6,5,4,3,2,1] => [7,6,5,4,3,2]
[6,6,5,4,3,2] => [6,6,5,4,3,2] => [6,6,5,4,3,2]
[7,5,5,4,3,2] => [6,6,5,4,3,1,1] => [7,5,5,4,3,2]
[6,5,5,4,3,2] => [6,6,5,4,3,1] => [6,5,5,4,3,2]
[5,5,5,4,3,2] => [6,6,5,4,3] => [5,5,5,4,3,2]
[7,6,4,4,3,2] => [6,6,5,4,2,2,1] => [7,6,4,4,3,2]
[4,4,4,4,3,2] => [6,6,5,4] => [4,4,4,4,3,2]
[7,6,5,4,2,2] => [6,6,4,4,3,2,1] => [7,6,5,4,2,2]
[7,6,4,4,2,2] => [6,6,4,4,2,2,1] => [7,6,4,4,2,2]
[6,6,4,4,2,2] => [6,6,4,4,2,2] => [6,6,4,4,2,2]
[7,4,4,4,2,2] => [6,6,4,4,1,1,1] => [7,4,4,4,2,2]
[5,4,4,4,2,2] => [6,6,4,4,1] => [5,4,4,4,2,2]
[4,4,4,4,2,2] => [6,6,4,4] => [4,4,4,4,2,2]
[7,6,5,2,2,2] => [6,6,3,3,3,2,1] => [7,6,5,2,2,2]
[6,6,3,2,2,2] => [6,6,3,2,2,2] => [6,6,3,2,2,2]
[7,6,2,2,2,2] => [6,6,2,2,2,2,1] => [7,6,2,2,2,2]
[6,6,2,2,2,2] => [6,6,2,2,2,2] => [6,6,2,2,2,2]
[7,6,5,4,3,1] => [6,5,5,4,3,2,1] => [7,6,5,4,3,1]
[6,6,5,4,3,1] => [6,5,5,4,3,2] => [6,6,5,4,3,1]
[6,5,5,4,3,1] => [6,5,5,4,3,1] => [6,5,5,4,3,1]
[7,6,5,4,2,1] => [6,5,4,4,3,2,1] => [7,6,5,4,2,1]
[6,5,4,4,2,1] => [6,5,4,4,2,1] => [6,5,4,4,2,1]
[4,4,4,4,2,1] => [6,5,4,4] => [4,4,4,4,2,1]
[7,6,5,3,2,1] => [6,5,4,3,3,2,1] => [7,6,5,3,2,1]
[7,6,4,3,2,1] => [6,5,4,3,2,2,1] => [7,6,4,3,2,1]
[7,5,4,3,2,1] => [6,5,4,3,2,1,1] => [7,5,4,3,2,1]
[7,4,4,3,2,1] => [6,5,4,3,1,1,1] => [7,4,4,3,2,1]
[7,6,3,3,2,1] => [6,5,4,2,2,2,1] => [7,6,3,3,2,1]
[7,3,3,3,2,1] => [6,5,4,1,1,1,1] => [7,3,3,3,2,1]
[7,6,5,2,2,1] => [6,5,3,3,3,2,1] => [7,6,5,2,2,1]
[7,6,2,2,2,1] => [6,5,2,2,2,2,1] => [7,6,2,2,2,1]
[7,6,5,4,1,1] => [6,4,4,4,3,2,1] => [7,6,5,4,1,1]
[6,4,4,4,1,1] => [6,4,4,4,1,1] => [6,4,4,4,1,1]
[4,4,4,4,1,1] => [6,4,4,4] => [4,4,4,4,1,1]
[7,6,5,1,1,1] => [6,3,3,3,3,2,1] => [7,6,5,1,1,1]
[7,6,5,4,3] => [5,5,5,4,3,2,1] => [7,6,5,4,3]
[6,6,5,4,3] => [5,5,5,4,3,2] => [6,6,5,4,3]
[5,5,5,4,3] => [5,5,5,4,3] => [5,5,5,4,3]
[4,4,4,4,3] => [5,5,5,4] => [4,4,4,4,3]
[7,3,3,3,3] => [5,5,5,1,1,1,1] => [7,3,3,3,3]
[5,5,4,4,2] => [5,5,4,4,2] => [5,5,4,4,2]
[4,4,4,4,2] => [5,5,4,4] => [4,4,4,4,2]
[7,5,4,3,2] => [5,5,4,3,2,1,1] => [7,5,4,3,2]
[7,6,5,4,1] => [5,4,4,4,3,2,1] => [7,6,5,4,1]
[6,6,4,4,1] => [5,4,4,4,2,2] => [6,6,4,4,1]
[5,4,4,4,1] => [5,4,4,4,1] => [5,4,4,4,1]
[7,6,5,4] => [4,4,4,4,3,2,1] => [7,6,5,4]
[6,6,5,4] => [4,4,4,4,3,2] => [6,6,5,4]
[5,5,5,4] => [4,4,4,4,3] => [5,5,5,4]
[6,6,4,4] => [4,4,4,4,2,2] => [6,6,4,4]
[6,5,4,4] => [4,4,4,4,2,1] => [6,5,4,4]
[5,5,4,4] => [4,4,4,4,2] => [5,5,4,4]
[6,4,4,4] => [4,4,4,4,1,1] => [6,4,4,4]
[7,6,5] => [3,3,3,3,3,2,1] => [7,6,5]
[3,3,3,3,3,3] => [6,6,6] => [3,3,3,3,3,3]
[3,3,3,3,3,3,1] => [7,6,6] => [3,3,3,3,3,3,1]
[3,3,3,3,3,3,3] => [7,7,7] => [3,3,3,3,3,3,3]
[4,3,3,3,3,3] => [6,6,6,1] => [4,3,3,3,3,3]
[4,4,4,4,4] => [5,5,5,5] => [4,4,4,4,4]
[4,4,4,4,4,4] => [6,6,6,6] => [4,4,4,4,4,4]
[5,5,5,5] => [4,4,4,4,4] => [5,5,5,5]
[6,6,6,6] => [4,4,4,4,4,4] => [6,6,6,6]
[6,2,2,2,2,2,2] => [7,7,1,1,1,1] => [6,2,2,2,2,2,2]
[6,6,6] => [3,3,3,3,3,3] => [6,6,6]
[7,6,6] => [3,3,3,3,3,3,1] => [7,6,6]
[6,6,6,6,6] => [5,5,5,5,5,5] => [6,6,6,6,6]
[6,6,6,4,3,3] => [6,6,6,4,3,3] => [6,6,6,4,3,3]
[8,6,4,2] => [4,4,3,3,2,2,1,1] => [8,6,4,2]
[8,6,6] => [3,3,3,3,3,3,1,1] => [8,6,6]
[10,6,4] => [3,3,3,3,2,2,1,1,1,1] => [10,6,4]
[15,15] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15]
[5,5,5,5,5,5] => [6,6,6,6,6] => [5,5,5,5,5,5]
[7,7,7] => [3,3,3,3,3,3,3] => [7,7,7]
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[7,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2] => [7,7,6,5,4,3,2,1]
[7,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1]
[7,6,5,5,4,3,2,1] => [8,7,6,5,4,2,1] => [7,6,5,5,4,3,2,1]
[7,6,5,4,4,3,2,1] => [8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1]
[7,6,5,4,3,3,2,1] => [8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1]
[7,6,5,4,3,2,2,1] => [8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1]
[7,6,5,4,3,2,1,1] => [8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1]
[9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1]
[8,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1]
[6,6,6,5,4,3,2,1] => [8,7,6,5,4,3] => [6,6,6,5,4,3,2,1]
[7,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1]
[7,6,4,4,4,3,2,1] => [8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1]
[7,6,5,3,3,3,2,1] => [8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1]
[7,6,5,4,2,2,2,1] => [8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1]
[7,6,5,4,3,1,1,1] => [8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1]
[8,7,6,5,4,3,2,1,1] => [9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,1]
[8,7,6,5,4,3,2] => [7,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2]
[8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1]
[8,7,6,5,4,2,1] => [7,6,5,5,4,3,2,1] => [8,7,6,5,4,2,1]
[8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1] => [8,7,6,5,3,2,1]
[8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1] => [8,7,6,4,3,2,1]
[8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1] => [8,7,5,4,3,2,1]
[8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1] => [8,6,5,4,3,2,1]
[9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2]
[8,7,6,5,4,3] => [6,6,6,5,4,3,2,1] => [8,7,6,5,4,3]
[8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1]
[8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1] => [8,7,6,5,2,2,1]
[8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1] => [8,7,6,3,3,2,1]
[8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1] => [8,7,4,4,3,2,1]
[8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1] => [8,5,5,4,3,2,1]
[9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,1] => [9,7,6,5,4,3,2,1]
[10,8,6,4,2] => [5,5,4,4,3,3,2,2,1,1] => [10,8,6,4,2]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
[5,5,5,5,5] => [5,5,5,5,5] => [5,5,5,5,5]
[7,7,1,1,1,1] => [6,2,2,2,2,2,2] => [7,7,1,1,1,1]
[8,5,4,3,2,1] => [6,5,4,3,2,1,1,1] => [8,5,4,3,2,1]
[9,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1,1] => [9,6,5,4,3,2,1]
[6,5,4,3,2,1,1,1] => [8,5,4,3,2,1] => [6,5,4,3,2,1,1,1]
[7,6,5,4,3,2,1,1,1] => [9,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1,1]
[7,7,6,5,4,3,2] => [7,7,6,5,4,3,2] => [7,7,6,5,4,3,2]
[6,5,5,5] => [4,4,4,4,4,1] => [6,5,5,5]
[5,4,4,4,4] => [5,5,5,5,1] => [5,4,4,4,4]
[7,6,6,5,4,3,2] => [7,7,6,5,4,3,1] => [7,6,6,5,4,3,2]
[7,6,6,5,4,3,1] => [7,6,6,5,4,3,1] => [7,6,6,5,4,3,1]
[7,7,6,5,4,3,1] => [7,6,6,5,4,3,2] => [7,7,6,5,4,3,1]
[7,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2] => [7,7,6,5,4,3,1,1]
[8,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2]
[9,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2] => [9,9,8,7,6,5,4,3,2,1]
[3,3,3,3,3,3,1,1] => [8,6,6] => [3,3,3,3,3,3,1,1]
[8,7,6,5,3,3,2,1] => [8,7,6,4,4,3,2,1] => [8,7,6,5,3,3,2,1]
[9,8,7,5,5,4,3,2,1] => [9,8,7,6,5,3,3,2,1] => [9,8,7,5,5,4,3,2,1]
[8,7,6,5,4,2,2,1] => [8,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2,1]
[8,6,6,4,4,2,2] => [7,7,5,5,3,3,1,1] => [8,6,6,4,4,2,2]
[7,7,5,5,3,3,1,1] => [8,6,6,4,4,2,2] => [7,7,5,5,3,3,1,1]
[8,8,6,6,4,4,2,2] => [8,8,6,6,4,4,2,2] => [8,8,6,6,4,4,2,2]
[9,7,7,5,5,3,3,1,1] => [9,7,7,5,5,3,3,1,1] => [9,7,7,5,5,3,3,1,1]
[8,7,6,5,4,1,1,1] => [8,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1,1]
[10,9,8,7,6,5,4,3,2] => [9,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2]
[8,6,6,5,4,3,2] => [7,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2]
[7,6,5,5,4,2,1] => [7,6,5,5,4,2,1] => [7,6,5,5,4,2,1]
[4,4,4,4,4,1] => [6,5,5,5] => [4,4,4,4,4,1]
[5,5,5,5,1] => [5,4,4,4,4] => [5,5,5,5,1]
[6,6,6,1] => [4,3,3,3,3,3] => [6,6,6,1]
[7,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2] => [7,7,5,5,4,3,2,1]
[7,7,5,5,3,3,2,1] => [8,7,6,4,4,2,2] => [7,7,5,5,3,3,2,1]
[8,8,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,2] => [8,8,6,6,5,4,3,2,1]
[7,7,4,4,4,3,2,1] => [8,7,6,5,2,2,2] => [7,7,4,4,4,3,2,1]
[8,8,6,6,4,4,3,2,1] => [9,8,7,6,4,4,2,2] => [8,8,6,6,4,4,3,2,1]
[7,7,5,5,2,2,2,1] => [8,7,4,4,4,2,2] => [7,7,5,5,2,2,2,1]
[8,8,6,6,4,4,2,2,1] => [9,8,6,6,4,4,2,2] => [8,8,6,6,4,4,2,2,1]
[7,7,5,5,3,3] => [6,6,6,4,4,2,2] => [7,7,5,5,3,3]
[8,7,6,5,4,2,2] => [7,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2]
[8,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1,1]
[3,3,3,3,2,2,1,1,1,1] => [10,6,4] => [3,3,3,3,2,2,1,1,1,1]
[4,4,3,3,2,2,1,1] => [8,6,4,2] => [4,4,3,3,2,2,1,1]
[5,5,4,4,3,3,2,2,1,1] => [10,8,6,4,2] => [5,5,4,4,3,3,2,2,1,1]
[8,7,6,4,4,3,2,1] => [8,7,6,5,3,3,2,1] => [8,7,6,4,4,3,2,1]
[8,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2,1] => [8,7,5,5,4,3,2,1]
[8,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2,1]
[9,8,7,6,5,4,3,1,1] => [9,7,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,1]
[9,8,7,6,5,4,2,2,1] => [9,8,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,2,1]
[9,8,7,6,5,3,3,2,1] => [9,8,7,5,5,4,3,2,1] => [9,8,7,6,5,3,3,2,1]
[9,8,7,6,4,4,3,2,1] => [9,8,7,6,4,4,3,2,1] => [9,8,7,6,4,4,3,2,1]
[9,8,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,2,1] => [9,8,6,6,5,4,3,2,1]
[9,7,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,1] => [9,7,7,6,5,4,3,2,1]
[8,7,6,5,2,2,2,1] => [8,7,4,4,4,3,2,1] => [8,7,6,5,2,2,2,1]
[8,7,6,3,3,3,2,1] => [8,7,6,3,3,3,2,1] => [8,7,6,3,3,3,2,1]
[8,7,4,4,4,3,2,1] => [8,7,6,5,2,2,2,1] => [8,7,4,4,4,3,2,1]
[8,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1,1] => [8,5,5,5,4,3,2,1]
[8,7,6,4,4,2,2] => [7,7,5,5,3,3,2,1] => [8,7,6,4,4,2,2]
[9,8,7,6,5,4,2,2] => [8,8,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,2]
[8,7,6,5,2,2,2] => [7,7,4,4,4,3,2,1] => [8,7,6,5,2,2,2]
[9,8,7,6,4,4,2,2] => [8,8,6,6,4,4,3,2,1] => [9,8,7,6,4,4,2,2]
[8,7,4,4,4,2,2] => [7,7,5,5,2,2,2,1] => [8,7,4,4,4,2,2]
[9,8,6,6,4,4,2,2] => [8,8,6,6,4,4,2,2,1] => [9,8,6,6,4,4,2,2]
[6,6,6,4,4,2,2] => [7,7,5,5,3,3] => [6,6,6,4,4,2,2]
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
searching the database
Sorry, this map was not found in the database.