Identifier
Images
[] => []
[1] => [1]
[2] => [1,1]
[1,1] => [2]
[3] => [1,1,1]
[2,1] => [2,1]
[1,1,1] => [3]
[4] => [1,1,1,1]
[3,1] => [2,1,1]
[2,2] => [2,2]
[2,1,1] => [3,1]
[1,1,1,1] => [4]
[5] => [1,1,1,1,1]
[4,1] => [2,1,1,1]
[3,2] => [2,2,1]
[3,1,1] => [3,1,1]
[2,2,1] => [3,2]
[2,1,1,1] => [4,1]
[1,1,1,1,1] => [5]
[6] => [1,1,1,1,1,1]
[5,1] => [2,1,1,1,1]
[4,2] => [2,2,1,1]
[4,1,1] => [3,1,1,1]
[3,3] => [2,2,2]
[3,2,1] => [3,2,1]
[3,1,1,1] => [4,1,1]
[2,2,2] => [3,3]
[2,2,1,1] => [4,2]
[2,1,1,1,1] => [5,1]
[1,1,1,1,1,1] => [6]
[7] => [1,1,1,1,1,1,1]
[6,1] => [2,1,1,1,1,1]
[5,2] => [2,2,1,1,1]
[5,1,1] => [3,1,1,1,1]
[4,3] => [2,2,2,1]
[4,2,1] => [3,2,1,1]
[4,1,1,1] => [4,1,1,1]
[3,3,1] => [3,2,2]
[3,2,2] => [3,3,1]
[3,2,1,1] => [4,2,1]
[3,1,1,1,1] => [5,1,1]
[2,2,2,1] => [4,3]
[2,2,1,1,1] => [5,2]
[2,1,1,1,1,1] => [6,1]
[1,1,1,1,1,1,1] => [7]
[8] => [1,1,1,1,1,1,1,1]
[7,1] => [2,1,1,1,1,1,1]
[6,2] => [2,2,1,1,1,1]
[6,1,1] => [3,1,1,1,1,1]
[5,3] => [2,2,2,1,1]
[5,2,1] => [3,2,1,1,1]
[5,1,1,1] => [4,1,1,1,1]
[4,4] => [2,2,2,2]
[4,3,1] => [3,2,2,1]
[4,2,2] => [3,3,1,1]
[4,2,1,1] => [4,2,1,1]
[4,1,1,1,1] => [5,1,1,1]
[3,3,2] => [3,3,2]
[3,3,1,1] => [4,2,2]
[3,2,2,1] => [4,3,1]
[3,2,1,1,1] => [5,2,1]
[3,1,1,1,1,1] => [6,1,1]
[2,2,2,2] => [4,4]
[2,2,2,1,1] => [5,3]
[2,2,1,1,1,1] => [6,2]
[2,1,1,1,1,1,1] => [7,1]
[1,1,1,1,1,1,1,1] => [8]
[9] => [1,1,1,1,1,1,1,1,1]
[8,1] => [2,1,1,1,1,1,1,1]
[7,2] => [2,2,1,1,1,1,1]
[7,1,1] => [3,1,1,1,1,1,1]
[6,3] => [2,2,2,1,1,1]
[6,2,1] => [3,2,1,1,1,1]
[6,1,1,1] => [4,1,1,1,1,1]
[5,4] => [2,2,2,2,1]
[5,3,1] => [3,2,2,1,1]
[5,2,2] => [3,3,1,1,1]
[5,2,1,1] => [4,2,1,1,1]
[5,1,1,1,1] => [5,1,1,1,1]
[4,4,1] => [3,2,2,2]
[4,3,2] => [3,3,2,1]
[4,3,1,1] => [4,2,2,1]
[4,2,2,1] => [4,3,1,1]
[4,2,1,1,1] => [5,2,1,1]
[4,1,1,1,1,1] => [6,1,1,1]
[3,3,3] => [3,3,3]
[3,3,2,1] => [4,3,2]
[3,3,1,1,1] => [5,2,2]
[3,2,2,2] => [4,4,1]
[3,2,2,1,1] => [5,3,1]
[3,2,1,1,1,1] => [6,2,1]
[3,1,1,1,1,1,1] => [7,1,1]
[2,2,2,2,1] => [5,4]
[2,2,2,1,1,1] => [6,3]
[2,2,1,1,1,1,1] => [7,2]
[2,1,1,1,1,1,1,1] => [8,1]
[1,1,1,1,1,1,1,1,1] => [9]
[10] => [1,1,1,1,1,1,1,1,1,1]
[9,1] => [2,1,1,1,1,1,1,1,1]
[8,2] => [2,2,1,1,1,1,1,1]
[8,1,1] => [3,1,1,1,1,1,1,1]
>>> Load all 1744 entries. <<<
[7,3] => [2,2,2,1,1,1,1]
[7,2,1] => [3,2,1,1,1,1,1]
[7,1,1,1] => [4,1,1,1,1,1,1]
[6,4] => [2,2,2,2,1,1]
[6,3,1] => [3,2,2,1,1,1]
[6,2,2] => [3,3,1,1,1,1]
[6,2,1,1] => [4,2,1,1,1,1]
[6,1,1,1,1] => [5,1,1,1,1,1]
[5,5] => [2,2,2,2,2]
[5,4,1] => [3,2,2,2,1]
[5,3,2] => [3,3,2,1,1]
[5,3,1,1] => [4,2,2,1,1]
[5,2,2,1] => [4,3,1,1,1]
[5,2,1,1,1] => [5,2,1,1,1]
[5,1,1,1,1,1] => [6,1,1,1,1]
[4,4,2] => [3,3,2,2]
[4,4,1,1] => [4,2,2,2]
[4,3,3] => [3,3,3,1]
[4,3,2,1] => [4,3,2,1]
[4,3,1,1,1] => [5,2,2,1]
[4,2,2,2] => [4,4,1,1]
[4,2,2,1,1] => [5,3,1,1]
[4,2,1,1,1,1] => [6,2,1,1]
[4,1,1,1,1,1,1] => [7,1,1,1]
[3,3,3,1] => [4,3,3]
[3,3,2,2] => [4,4,2]
[3,3,2,1,1] => [5,3,2]
[3,3,1,1,1,1] => [6,2,2]
[3,2,2,2,1] => [5,4,1]
[3,2,2,1,1,1] => [6,3,1]
[3,2,1,1,1,1,1] => [7,2,1]
[3,1,1,1,1,1,1,1] => [8,1,1]
[2,2,2,2,2] => [5,5]
[2,2,2,2,1,1] => [6,4]
[2,2,2,1,1,1,1] => [7,3]
[2,2,1,1,1,1,1,1] => [8,2]
[2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,1,1,1,1,1,1,1,1] => [10]
[11] => [1,1,1,1,1,1,1,1,1,1,1]
[10,1] => [2,1,1,1,1,1,1,1,1,1]
[9,2] => [2,2,1,1,1,1,1,1,1]
[9,1,1] => [3,1,1,1,1,1,1,1,1]
[8,3] => [2,2,2,1,1,1,1,1]
[8,2,1] => [3,2,1,1,1,1,1,1]
[8,1,1,1] => [4,1,1,1,1,1,1,1]
[7,4] => [2,2,2,2,1,1,1]
[7,3,1] => [3,2,2,1,1,1,1]
[7,2,2] => [3,3,1,1,1,1,1]
[7,2,1,1] => [4,2,1,1,1,1,1]
[7,1,1,1,1] => [5,1,1,1,1,1,1]
[6,5] => [2,2,2,2,2,1]
[6,4,1] => [3,2,2,2,1,1]
[6,3,2] => [3,3,2,1,1,1]
[6,3,1,1] => [4,2,2,1,1,1]
[6,2,2,1] => [4,3,1,1,1,1]
[6,2,1,1,1] => [5,2,1,1,1,1]
[6,1,1,1,1,1] => [6,1,1,1,1,1]
[5,5,1] => [3,2,2,2,2]
[5,4,2] => [3,3,2,2,1]
[5,4,1,1] => [4,2,2,2,1]
[5,3,3] => [3,3,3,1,1]
[5,3,2,1] => [4,3,2,1,1]
[5,3,1,1,1] => [5,2,2,1,1]
[5,2,2,2] => [4,4,1,1,1]
[5,2,2,1,1] => [5,3,1,1,1]
[5,2,1,1,1,1] => [6,2,1,1,1]
[5,1,1,1,1,1,1] => [7,1,1,1,1]
[4,4,3] => [3,3,3,2]
[4,4,2,1] => [4,3,2,2]
[4,4,1,1,1] => [5,2,2,2]
[4,3,3,1] => [4,3,3,1]
[4,3,2,2] => [4,4,2,1]
[4,3,2,1,1] => [5,3,2,1]
[4,3,1,1,1,1] => [6,2,2,1]
[4,2,2,2,1] => [5,4,1,1]
[4,2,2,1,1,1] => [6,3,1,1]
[4,2,1,1,1,1,1] => [7,2,1,1]
[4,1,1,1,1,1,1,1] => [8,1,1,1]
[3,3,3,2] => [4,4,3]
[3,3,3,1,1] => [5,3,3]
[3,3,2,2,1] => [5,4,2]
[3,3,2,1,1,1] => [6,3,2]
[3,3,1,1,1,1,1] => [7,2,2]
[3,2,2,2,2] => [5,5,1]
[3,2,2,2,1,1] => [6,4,1]
[3,2,2,1,1,1,1] => [7,3,1]
[3,2,1,1,1,1,1,1] => [8,2,1]
[3,1,1,1,1,1,1,1,1] => [9,1,1]
[2,2,2,2,2,1] => [6,5]
[2,2,2,2,1,1,1] => [7,4]
[2,2,2,1,1,1,1,1] => [8,3]
[2,2,1,1,1,1,1,1,1] => [9,2]
[2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,1,1,1,1,1,1,1,1,1,1] => [11]
[12] => [1,1,1,1,1,1,1,1,1,1,1,1]
[11,1] => [2,1,1,1,1,1,1,1,1,1,1]
[10,2] => [2,2,1,1,1,1,1,1,1,1]
[10,1,1] => [3,1,1,1,1,1,1,1,1,1]
[9,3] => [2,2,2,1,1,1,1,1,1]
[9,2,1] => [3,2,1,1,1,1,1,1,1]
[9,1,1,1] => [4,1,1,1,1,1,1,1,1]
[8,4] => [2,2,2,2,1,1,1,1]
[8,3,1] => [3,2,2,1,1,1,1,1]
[8,2,2] => [3,3,1,1,1,1,1,1]
[8,2,1,1] => [4,2,1,1,1,1,1,1]
[8,1,1,1,1] => [5,1,1,1,1,1,1,1]
[7,5] => [2,2,2,2,2,1,1]
[7,4,1] => [3,2,2,2,1,1,1]
[7,3,2] => [3,3,2,1,1,1,1]
[7,3,1,1] => [4,2,2,1,1,1,1]
[7,2,2,1] => [4,3,1,1,1,1,1]
[7,2,1,1,1] => [5,2,1,1,1,1,1]
[7,1,1,1,1,1] => [6,1,1,1,1,1,1]
[6,6] => [2,2,2,2,2,2]
[6,5,1] => [3,2,2,2,2,1]
[6,4,2] => [3,3,2,2,1,1]
[6,4,1,1] => [4,2,2,2,1,1]
[6,3,3] => [3,3,3,1,1,1]
[6,3,2,1] => [4,3,2,1,1,1]
[6,3,1,1,1] => [5,2,2,1,1,1]
[6,2,2,2] => [4,4,1,1,1,1]
[6,2,2,1,1] => [5,3,1,1,1,1]
[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]
[5,5,2] => [3,3,2,2,2]
[5,5,1,1] => [4,2,2,2,2]
[5,4,3] => [3,3,3,2,1]
[5,4,2,1] => [4,3,2,2,1]
[5,4,1,1,1] => [5,2,2,2,1]
[5,3,3,1] => [4,3,3,1,1]
[5,3,2,2] => [4,4,2,1,1]
[5,3,2,1,1] => [5,3,2,1,1]
[5,3,1,1,1,1] => [6,2,2,1,1]
[5,2,2,2,1] => [5,4,1,1,1]
[5,2,2,1,1,1] => [6,3,1,1,1]
[5,2,1,1,1,1,1] => [7,2,1,1,1]
[5,1,1,1,1,1,1,1] => [8,1,1,1,1]
[4,4,4] => [3,3,3,3]
[4,4,3,1] => [4,3,3,2]
[4,4,2,2] => [4,4,2,2]
[4,4,2,1,1] => [5,3,2,2]
[4,4,1,1,1,1] => [6,2,2,2]
[4,3,3,2] => [4,4,3,1]
[4,3,3,1,1] => [5,3,3,1]
[4,3,2,2,1] => [5,4,2,1]
[4,3,2,1,1,1] => [6,3,2,1]
[4,3,1,1,1,1,1] => [7,2,2,1]
[4,2,2,2,2] => [5,5,1,1]
[4,2,2,2,1,1] => [6,4,1,1]
[4,2,2,1,1,1,1] => [7,3,1,1]
[4,2,1,1,1,1,1,1] => [8,2,1,1]
[4,1,1,1,1,1,1,1,1] => [9,1,1,1]
[3,3,3,3] => [4,4,4]
[3,3,3,2,1] => [5,4,3]
[3,3,3,1,1,1] => [6,3,3]
[3,3,2,2,2] => [5,5,2]
[3,3,2,2,1,1] => [6,4,2]
[3,3,2,1,1,1,1] => [7,3,2]
[3,3,1,1,1,1,1,1] => [8,2,2]
[3,2,2,2,2,1] => [6,5,1]
[3,2,2,2,1,1,1] => [7,4,1]
[3,2,2,1,1,1,1,1] => [8,3,1]
[3,2,1,1,1,1,1,1,1] => [9,2,1]
[3,1,1,1,1,1,1,1,1,1] => [10,1,1]
[2,2,2,2,2,2] => [6,6]
[2,2,2,2,2,1,1] => [7,5]
[2,2,2,2,1,1,1,1] => [8,4]
[2,2,2,1,1,1,1,1,1] => [9,3]
[2,2,1,1,1,1,1,1,1,1] => [10,2]
[2,1,1,1,1,1,1,1,1,1,1] => [11,1]
[1,1,1,1,1,1,1,1,1,1,1,1] => [12]
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1]
[12,1] => [2,1,1,1,1,1,1,1,1,1,1,1]
[11,2] => [2,2,1,1,1,1,1,1,1,1,1]
[11,1,1] => [3,1,1,1,1,1,1,1,1,1,1]
[10,3] => [2,2,2,1,1,1,1,1,1,1]
[10,2,1] => [3,2,1,1,1,1,1,1,1,1]
[10,1,1,1] => [4,1,1,1,1,1,1,1,1,1]
[9,4] => [2,2,2,2,1,1,1,1,1]
[9,3,1] => [3,2,2,1,1,1,1,1,1]
[9,2,2] => [3,3,1,1,1,1,1,1,1]
[9,2,1,1] => [4,2,1,1,1,1,1,1,1]
[9,1,1,1,1] => [5,1,1,1,1,1,1,1,1]
[8,5] => [2,2,2,2,2,1,1,1]
[8,4,1] => [3,2,2,2,1,1,1,1]
[8,3,2] => [3,3,2,1,1,1,1,1]
[8,3,1,1] => [4,2,2,1,1,1,1,1]
[8,2,2,1] => [4,3,1,1,1,1,1,1]
[8,2,1,1,1] => [5,2,1,1,1,1,1,1]
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1]
[7,6] => [2,2,2,2,2,2,1]
[7,5,1] => [3,2,2,2,2,1,1]
[7,4,2] => [3,3,2,2,1,1,1]
[7,4,1,1] => [4,2,2,2,1,1,1]
[7,3,3] => [3,3,3,1,1,1,1]
[7,3,2,1] => [4,3,2,1,1,1,1]
[7,3,1,1,1] => [5,2,2,1,1,1,1]
[7,2,2,2] => [4,4,1,1,1,1,1]
[7,2,2,1,1] => [5,3,1,1,1,1,1]
[7,2,1,1,1,1] => [6,2,1,1,1,1,1]
[7,1,1,1,1,1,1] => [7,1,1,1,1,1,1]
[6,6,1] => [3,2,2,2,2,2]
[6,5,2] => [3,3,2,2,2,1]
[6,5,1,1] => [4,2,2,2,2,1]
[6,4,3] => [3,3,3,2,1,1]
[6,4,2,1] => [4,3,2,2,1,1]
[6,4,1,1,1] => [5,2,2,2,1,1]
[6,3,3,1] => [4,3,3,1,1,1]
[6,3,2,2] => [4,4,2,1,1,1]
[6,3,2,1,1] => [5,3,2,1,1,1]
[6,3,1,1,1,1] => [6,2,2,1,1,1]
[6,2,2,2,1] => [5,4,1,1,1,1]
[6,2,2,1,1,1] => [6,3,1,1,1,1]
[6,2,1,1,1,1,1] => [7,2,1,1,1,1]
[6,1,1,1,1,1,1,1] => [8,1,1,1,1,1]
[5,5,3] => [3,3,3,2,2]
[5,5,2,1] => [4,3,2,2,2]
[5,5,1,1,1] => [5,2,2,2,2]
[5,4,4] => [3,3,3,3,1]
[5,4,3,1] => [4,3,3,2,1]
[5,4,2,2] => [4,4,2,2,1]
[5,4,2,1,1] => [5,3,2,2,1]
[5,4,1,1,1,1] => [6,2,2,2,1]
[5,3,3,2] => [4,4,3,1,1]
[5,3,3,1,1] => [5,3,3,1,1]
[5,3,2,2,1] => [5,4,2,1,1]
[5,3,2,1,1,1] => [6,3,2,1,1]
[5,3,1,1,1,1,1] => [7,2,2,1,1]
[5,2,2,2,2] => [5,5,1,1,1]
[5,2,2,2,1,1] => [6,4,1,1,1]
[5,2,2,1,1,1,1] => [7,3,1,1,1]
[5,2,1,1,1,1,1,1] => [8,2,1,1,1]
[5,1,1,1,1,1,1,1,1] => [9,1,1,1,1]
[4,4,4,1] => [4,3,3,3]
[4,4,3,2] => [4,4,3,2]
[4,4,3,1,1] => [5,3,3,2]
[4,4,2,2,1] => [5,4,2,2]
[4,4,2,1,1,1] => [6,3,2,2]
[4,4,1,1,1,1,1] => [7,2,2,2]
[4,3,3,3] => [4,4,4,1]
[4,3,3,2,1] => [5,4,3,1]
[4,3,3,1,1,1] => [6,3,3,1]
[4,3,2,2,2] => [5,5,2,1]
[4,3,2,2,1,1] => [6,4,2,1]
[4,3,2,1,1,1,1] => [7,3,2,1]
[4,3,1,1,1,1,1,1] => [8,2,2,1]
[4,2,2,2,2,1] => [6,5,1,1]
[4,2,2,2,1,1,1] => [7,4,1,1]
[4,2,2,1,1,1,1,1] => [8,3,1,1]
[4,2,1,1,1,1,1,1,1] => [9,2,1,1]
[4,1,1,1,1,1,1,1,1,1] => [10,1,1,1]
[3,3,3,3,1] => [5,4,4]
[3,3,3,2,2] => [5,5,3]
[3,3,3,2,1,1] => [6,4,3]
[3,3,3,1,1,1,1] => [7,3,3]
[3,3,2,2,2,1] => [6,5,2]
[3,3,2,2,1,1,1] => [7,4,2]
[3,3,2,1,1,1,1,1] => [8,3,2]
[3,3,1,1,1,1,1,1,1] => [9,2,2]
[3,2,2,2,2,2] => [6,6,1]
[3,2,2,2,2,1,1] => [7,5,1]
[3,2,2,2,1,1,1,1] => [8,4,1]
[3,2,2,1,1,1,1,1,1] => [9,3,1]
[3,2,1,1,1,1,1,1,1,1] => [10,2,1]
[3,1,1,1,1,1,1,1,1,1,1] => [11,1,1]
[2,2,2,2,2,2,1] => [7,6]
[2,2,2,2,2,1,1,1] => [8,5]
[2,2,2,2,1,1,1,1,1] => [9,4]
[2,2,2,1,1,1,1,1,1,1] => [10,3]
[2,2,1,1,1,1,1,1,1,1,1] => [11,2]
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [13]
[14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[13,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1]
[12,2] => [2,2,1,1,1,1,1,1,1,1,1,1]
[12,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1]
[11,3] => [2,2,2,1,1,1,1,1,1,1,1]
[11,2,1] => [3,2,1,1,1,1,1,1,1,1,1]
[11,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1]
[10,4] => [2,2,2,2,1,1,1,1,1,1]
[10,3,1] => [3,2,2,1,1,1,1,1,1,1]
[10,2,2] => [3,3,1,1,1,1,1,1,1,1]
[10,2,1,1] => [4,2,1,1,1,1,1,1,1,1]
[10,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1]
[9,5] => [2,2,2,2,2,1,1,1,1]
[9,4,1] => [3,2,2,2,1,1,1,1,1]
[9,3,2] => [3,3,2,1,1,1,1,1,1]
[9,3,1,1] => [4,2,2,1,1,1,1,1,1]
[9,2,2,1] => [4,3,1,1,1,1,1,1,1]
[9,2,1,1,1] => [5,2,1,1,1,1,1,1,1]
[9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1]
[8,6] => [2,2,2,2,2,2,1,1]
[8,5,1] => [3,2,2,2,2,1,1,1]
[8,4,2] => [3,3,2,2,1,1,1,1]
[8,4,1,1] => [4,2,2,2,1,1,1,1]
[8,3,3] => [3,3,3,1,1,1,1,1]
[8,3,2,1] => [4,3,2,1,1,1,1,1]
[8,3,1,1,1] => [5,2,2,1,1,1,1,1]
[8,2,2,2] => [4,4,1,1,1,1,1,1]
[8,2,2,1,1] => [5,3,1,1,1,1,1,1]
[8,2,1,1,1,1] => [6,2,1,1,1,1,1,1]
[8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1]
[7,7] => [2,2,2,2,2,2,2]
[7,6,1] => [3,2,2,2,2,2,1]
[7,5,2] => [3,3,2,2,2,1,1]
[7,5,1,1] => [4,2,2,2,2,1,1]
[7,4,3] => [3,3,3,2,1,1,1]
[7,4,2,1] => [4,3,2,2,1,1,1]
[7,4,1,1,1] => [5,2,2,2,1,1,1]
[7,3,3,1] => [4,3,3,1,1,1,1]
[7,3,2,2] => [4,4,2,1,1,1,1]
[7,3,2,1,1] => [5,3,2,1,1,1,1]
[7,3,1,1,1,1] => [6,2,2,1,1,1,1]
[7,2,2,2,1] => [5,4,1,1,1,1,1]
[7,2,2,1,1,1] => [6,3,1,1,1,1,1]
[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]
[6,6,2] => [3,3,2,2,2,2]
[6,6,1,1] => [4,2,2,2,2,2]
[6,5,3] => [3,3,3,2,2,1]
[6,5,2,1] => [4,3,2,2,2,1]
[6,5,1,1,1] => [5,2,2,2,2,1]
[6,4,4] => [3,3,3,3,1,1]
[6,4,3,1] => [4,3,3,2,1,1]
[6,4,2,2] => [4,4,2,2,1,1]
[6,4,2,1,1] => [5,3,2,2,1,1]
[6,4,1,1,1,1] => [6,2,2,2,1,1]
[6,3,3,2] => [4,4,3,1,1,1]
[6,3,3,1,1] => [5,3,3,1,1,1]
[6,3,2,2,1] => [5,4,2,1,1,1]
[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]
[6,2,2,2,2] => [5,5,1,1,1,1]
[6,2,2,2,1,1] => [6,4,1,1,1,1]
[6,2,2,1,1,1,1] => [7,3,1,1,1,1]
[6,2,1,1,1,1,1,1] => [8,2,1,1,1,1]
[6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1]
[5,5,4] => [3,3,3,3,2]
[5,5,3,1] => [4,3,3,2,2]
[5,5,2,2] => [4,4,2,2,2]
[5,5,2,1,1] => [5,3,2,2,2]
[5,5,1,1,1,1] => [6,2,2,2,2]
[5,4,4,1] => [4,3,3,3,1]
[5,4,3,2] => [4,4,3,2,1]
[5,4,3,1,1] => [5,3,3,2,1]
[5,4,2,2,1] => [5,4,2,2,1]
[5,4,2,1,1,1] => [6,3,2,2,1]
[5,4,1,1,1,1,1] => [7,2,2,2,1]
[5,3,3,3] => [4,4,4,1,1]
[5,3,3,2,1] => [5,4,3,1,1]
[5,3,3,1,1,1] => [6,3,3,1,1]
[5,3,2,2,2] => [5,5,2,1,1]
[5,3,2,2,1,1] => [6,4,2,1,1]
[5,3,2,1,1,1,1] => [7,3,2,1,1]
[5,3,1,1,1,1,1,1] => [8,2,2,1,1]
[5,2,2,2,2,1] => [6,5,1,1,1]
[5,2,2,2,1,1,1] => [7,4,1,1,1]
[5,2,2,1,1,1,1,1] => [8,3,1,1,1]
[5,2,1,1,1,1,1,1,1] => [9,2,1,1,1]
[5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1]
[4,4,4,2] => [4,4,3,3]
[4,4,4,1,1] => [5,3,3,3]
[4,4,3,3] => [4,4,4,2]
[4,4,3,2,1] => [5,4,3,2]
[4,4,3,1,1,1] => [6,3,3,2]
[4,4,2,2,2] => [5,5,2,2]
[4,4,2,2,1,1] => [6,4,2,2]
[4,4,2,1,1,1,1] => [7,3,2,2]
[4,4,1,1,1,1,1,1] => [8,2,2,2]
[4,3,3,3,1] => [5,4,4,1]
[4,3,3,2,2] => [5,5,3,1]
[4,3,3,2,1,1] => [6,4,3,1]
[4,3,3,1,1,1,1] => [7,3,3,1]
[4,3,2,2,2,1] => [6,5,2,1]
[4,3,2,2,1,1,1] => [7,4,2,1]
[4,3,2,1,1,1,1,1] => [8,3,2,1]
[4,3,1,1,1,1,1,1,1] => [9,2,2,1]
[4,2,2,2,2,2] => [6,6,1,1]
[4,2,2,2,2,1,1] => [7,5,1,1]
[4,2,2,2,1,1,1,1] => [8,4,1,1]
[4,2,2,1,1,1,1,1,1] => [9,3,1,1]
[4,2,1,1,1,1,1,1,1,1] => [10,2,1,1]
[4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1]
[3,3,3,3,2] => [5,5,4]
[3,3,3,3,1,1] => [6,4,4]
[3,3,3,2,2,1] => [6,5,3]
[3,3,3,2,1,1,1] => [7,4,3]
[3,3,3,1,1,1,1,1] => [8,3,3]
[3,3,2,2,2,2] => [6,6,2]
[3,3,2,2,2,1,1] => [7,5,2]
[3,3,2,2,1,1,1,1] => [8,4,2]
[3,3,2,1,1,1,1,1,1] => [9,3,2]
[3,3,1,1,1,1,1,1,1,1] => [10,2,2]
[3,2,2,2,2,2,1] => [7,6,1]
[3,2,2,2,2,1,1,1] => [8,5,1]
[3,2,2,2,1,1,1,1,1] => [9,4,1]
[3,2,2,1,1,1,1,1,1,1] => [10,3,1]
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1]
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1]
[2,2,2,2,2,2,2] => [7,7]
[2,2,2,2,2,2,1,1] => [8,6]
[2,2,2,2,2,1,1,1,1] => [9,5]
[2,2,2,2,1,1,1,1,1,1] => [10,4]
[2,2,2,1,1,1,1,1,1,1,1] => [11,3]
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2]
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14]
[15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[14,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1]
[13,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1]
[13,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1]
[12,3] => [2,2,2,1,1,1,1,1,1,1,1,1]
[12,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1]
[12,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1]
[11,4] => [2,2,2,2,1,1,1,1,1,1,1]
[11,3,1] => [3,2,2,1,1,1,1,1,1,1,1]
[11,2,2] => [3,3,1,1,1,1,1,1,1,1,1]
[11,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1]
[11,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1]
[10,5] => [2,2,2,2,2,1,1,1,1,1]
[10,4,1] => [3,2,2,2,1,1,1,1,1,1]
[10,3,2] => [3,3,2,1,1,1,1,1,1,1]
[10,3,1,1] => [4,2,2,1,1,1,1,1,1,1]
[10,2,2,1] => [4,3,1,1,1,1,1,1,1,1]
[10,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1]
[10,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1]
[9,6] => [2,2,2,2,2,2,1,1,1]
[9,5,1] => [3,2,2,2,2,1,1,1,1]
[9,4,2] => [3,3,2,2,1,1,1,1,1]
[9,4,1,1] => [4,2,2,2,1,1,1,1,1]
[9,3,3] => [3,3,3,1,1,1,1,1,1]
[9,3,2,1] => [4,3,2,1,1,1,1,1,1]
[9,3,1,1,1] => [5,2,2,1,1,1,1,1,1]
[9,2,2,2] => [4,4,1,1,1,1,1,1,1]
[9,2,2,1,1] => [5,3,1,1,1,1,1,1,1]
[9,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1]
[9,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1]
[8,7] => [2,2,2,2,2,2,2,1]
[8,6,1] => [3,2,2,2,2,2,1,1]
[8,5,2] => [3,3,2,2,2,1,1,1]
[8,5,1,1] => [4,2,2,2,2,1,1,1]
[8,4,3] => [3,3,3,2,1,1,1,1]
[8,4,2,1] => [4,3,2,2,1,1,1,1]
[8,4,1,1,1] => [5,2,2,2,1,1,1,1]
[8,3,3,1] => [4,3,3,1,1,1,1,1]
[8,3,2,2] => [4,4,2,1,1,1,1,1]
[8,3,2,1,1] => [5,3,2,1,1,1,1,1]
[8,3,1,1,1,1] => [6,2,2,1,1,1,1,1]
[8,2,2,2,1] => [5,4,1,1,1,1,1,1]
[8,2,2,1,1,1] => [6,3,1,1,1,1,1,1]
[8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1]
[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]
[7,6,2] => [3,3,2,2,2,2,1]
[7,6,1,1] => [4,2,2,2,2,2,1]
[7,5,3] => [3,3,3,2,2,1,1]
[7,5,2,1] => [4,3,2,2,2,1,1]
[7,5,1,1,1] => [5,2,2,2,2,1,1]
[7,4,4] => [3,3,3,3,1,1,1]
[7,4,3,1] => [4,3,3,2,1,1,1]
[7,4,2,2] => [4,4,2,2,1,1,1]
[7,4,2,1,1] => [5,3,2,2,1,1,1]
[7,4,1,1,1,1] => [6,2,2,2,1,1,1]
[7,3,3,2] => [4,4,3,1,1,1,1]
[7,3,3,1,1] => [5,3,3,1,1,1,1]
[7,3,2,2,1] => [5,4,2,1,1,1,1]
[7,3,2,1,1,1] => [6,3,2,1,1,1,1]
[7,3,1,1,1,1,1] => [7,2,2,1,1,1,1]
[7,2,2,2,2] => [5,5,1,1,1,1,1]
[7,2,2,2,1,1] => [6,4,1,1,1,1,1]
[7,2,2,1,1,1,1] => [7,3,1,1,1,1,1]
[7,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1]
[6,6,3] => [3,3,3,2,2,2]
[6,6,2,1] => [4,3,2,2,2,2]
[6,6,1,1,1] => [5,2,2,2,2,2]
[6,5,4] => [3,3,3,3,2,1]
[6,5,3,1] => [4,3,3,2,2,1]
[6,5,2,2] => [4,4,2,2,2,1]
[6,5,2,1,1] => [5,3,2,2,2,1]
[6,5,1,1,1,1] => [6,2,2,2,2,1]
[6,4,4,1] => [4,3,3,3,1,1]
[6,4,3,2] => [4,4,3,2,1,1]
[6,4,3,1,1] => [5,3,3,2,1,1]
[6,4,2,2,1] => [5,4,2,2,1,1]
[6,4,2,1,1,1] => [6,3,2,2,1,1]
[6,4,1,1,1,1,1] => [7,2,2,2,1,1]
[6,3,3,3] => [4,4,4,1,1,1]
[6,3,3,2,1] => [5,4,3,1,1,1]
[6,3,3,1,1,1] => [6,3,3,1,1,1]
[6,3,2,2,2] => [5,5,2,1,1,1]
[6,3,2,2,1,1] => [6,4,2,1,1,1]
[6,3,2,1,1,1,1] => [7,3,2,1,1,1]
[6,3,1,1,1,1,1,1] => [8,2,2,1,1,1]
[6,2,2,2,2,1] => [6,5,1,1,1,1]
[6,2,2,2,1,1,1] => [7,4,1,1,1,1]
[6,2,2,1,1,1,1,1] => [8,3,1,1,1,1]
[6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1]
[5,5,5] => [3,3,3,3,3]
[5,5,4,1] => [4,3,3,3,2]
[5,5,3,2] => [4,4,3,2,2]
[5,5,3,1,1] => [5,3,3,2,2]
[5,5,2,2,1] => [5,4,2,2,2]
[5,5,2,1,1,1] => [6,3,2,2,2]
[5,5,1,1,1,1,1] => [7,2,2,2,2]
[5,4,4,2] => [4,4,3,3,1]
[5,4,4,1,1] => [5,3,3,3,1]
[5,4,3,3] => [4,4,4,2,1]
[5,4,3,2,1] => [5,4,3,2,1]
[5,4,3,1,1,1] => [6,3,3,2,1]
[5,4,2,2,2] => [5,5,2,2,1]
[5,4,2,2,1,1] => [6,4,2,2,1]
[5,4,2,1,1,1,1] => [7,3,2,2,1]
[5,4,1,1,1,1,1,1] => [8,2,2,2,1]
[5,3,3,3,1] => [5,4,4,1,1]
[5,3,3,2,2] => [5,5,3,1,1]
[5,3,3,2,1,1] => [6,4,3,1,1]
[5,3,3,1,1,1,1] => [7,3,3,1,1]
[5,3,2,2,2,1] => [6,5,2,1,1]
[5,3,2,2,1,1,1] => [7,4,2,1,1]
[5,3,2,1,1,1,1,1] => [8,3,2,1,1]
[5,3,1,1,1,1,1,1,1] => [9,2,2,1,1]
[5,2,2,2,2,2] => [6,6,1,1,1]
[5,2,2,2,2,1,1] => [7,5,1,1,1]
[5,2,2,2,1,1,1,1] => [8,4,1,1,1]
[5,2,2,1,1,1,1,1,1] => [9,3,1,1,1]
[5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1]
[4,4,4,3] => [4,4,4,3]
[4,4,4,2,1] => [5,4,3,3]
[4,4,4,1,1,1] => [6,3,3,3]
[4,4,3,3,1] => [5,4,4,2]
[4,4,3,2,2] => [5,5,3,2]
[4,4,3,2,1,1] => [6,4,3,2]
[4,4,3,1,1,1,1] => [7,3,3,2]
[4,4,2,2,2,1] => [6,5,2,2]
[4,4,2,2,1,1,1] => [7,4,2,2]
[4,4,2,1,1,1,1,1] => [8,3,2,2]
[4,4,1,1,1,1,1,1,1] => [9,2,2,2]
[4,3,3,3,2] => [5,5,4,1]
[4,3,3,3,1,1] => [6,4,4,1]
[4,3,3,2,2,1] => [6,5,3,1]
[4,3,3,2,1,1,1] => [7,4,3,1]
[4,3,3,1,1,1,1,1] => [8,3,3,1]
[4,3,2,2,2,2] => [6,6,2,1]
[4,3,2,2,2,1,1] => [7,5,2,1]
[4,3,2,2,1,1,1,1] => [8,4,2,1]
[4,3,2,1,1,1,1,1,1] => [9,3,2,1]
[4,3,1,1,1,1,1,1,1,1] => [10,2,2,1]
[4,2,2,2,2,2,1] => [7,6,1,1]
[4,2,2,2,2,1,1,1] => [8,5,1,1]
[4,2,2,2,1,1,1,1,1] => [9,4,1,1]
[4,2,2,1,1,1,1,1,1,1] => [10,3,1,1]
[4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1]
[3,3,3,3,3] => [5,5,5]
[3,3,3,3,2,1] => [6,5,4]
[3,3,3,3,1,1,1] => [7,4,4]
[3,3,3,2,2,2] => [6,6,3]
[3,3,3,2,2,1,1] => [7,5,3]
[3,3,3,2,1,1,1,1] => [8,4,3]
[3,3,3,1,1,1,1,1,1] => [9,3,3]
[3,3,2,2,2,2,1] => [7,6,2]
[3,3,2,2,2,1,1,1] => [8,5,2]
[3,3,2,2,1,1,1,1,1] => [9,4,2]
[3,3,2,1,1,1,1,1,1,1] => [10,3,2]
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2]
[3,2,2,2,2,2,2] => [7,7,1]
[3,2,2,2,2,2,1,1] => [8,6,1]
[3,2,2,2,2,1,1,1,1] => [9,5,1]
[3,2,2,2,1,1,1,1,1,1] => [10,4,1]
[3,2,2,1,1,1,1,1,1,1,1] => [11,3,1]
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1]
[2,2,2,2,2,2,2,1] => [8,7]
[2,2,2,2,2,2,1,1,1] => [9,6]
[2,2,2,2,2,1,1,1,1,1] => [10,5]
[2,2,2,2,1,1,1,1,1,1,1] => [11,4]
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3]
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15]
[16] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[15,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[14,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1]
[14,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1]
[13,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1]
[13,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1]
[13,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1]
[12,4] => [2,2,2,2,1,1,1,1,1,1,1,1]
[12,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1]
[12,2,2] => [3,3,1,1,1,1,1,1,1,1,1,1]
[12,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1]
[12,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1]
[11,5] => [2,2,2,2,2,1,1,1,1,1,1]
[11,4,1] => [3,2,2,2,1,1,1,1,1,1,1]
[11,3,2] => [3,3,2,1,1,1,1,1,1,1,1]
[11,3,1,1] => [4,2,2,1,1,1,1,1,1,1,1]
[11,2,2,1] => [4,3,1,1,1,1,1,1,1,1,1]
[11,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1]
[11,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1]
[10,6] => [2,2,2,2,2,2,1,1,1,1]
[10,5,1] => [3,2,2,2,2,1,1,1,1,1]
[10,4,2] => [3,3,2,2,1,1,1,1,1,1]
[10,4,1,1] => [4,2,2,2,1,1,1,1,1,1]
[10,3,3] => [3,3,3,1,1,1,1,1,1,1]
[10,3,2,1] => [4,3,2,1,1,1,1,1,1,1]
[10,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1]
[10,2,2,2] => [4,4,1,1,1,1,1,1,1,1]
[10,2,2,1,1] => [5,3,1,1,1,1,1,1,1,1]
[10,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1]
[10,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1]
[9,7] => [2,2,2,2,2,2,2,1,1]
[9,6,1] => [3,2,2,2,2,2,1,1,1]
[9,5,2] => [3,3,2,2,2,1,1,1,1]
[9,5,1,1] => [4,2,2,2,2,1,1,1,1]
[9,4,3] => [3,3,3,2,1,1,1,1,1]
[9,4,2,1] => [4,3,2,2,1,1,1,1,1]
[9,4,1,1,1] => [5,2,2,2,1,1,1,1,1]
[9,3,3,1] => [4,3,3,1,1,1,1,1,1]
[9,3,2,2] => [4,4,2,1,1,1,1,1,1]
[9,3,2,1,1] => [5,3,2,1,1,1,1,1,1]
[9,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1]
[9,2,2,2,1] => [5,4,1,1,1,1,1,1,1]
[9,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1]
[9,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1]
[9,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1]
[8,8] => [2,2,2,2,2,2,2,2]
[8,7,1] => [3,2,2,2,2,2,2,1]
[8,6,2] => [3,3,2,2,2,2,1,1]
[8,6,1,1] => [4,2,2,2,2,2,1,1]
[8,5,3] => [3,3,3,2,2,1,1,1]
[8,5,2,1] => [4,3,2,2,2,1,1,1]
[8,5,1,1,1] => [5,2,2,2,2,1,1,1]
[8,4,4] => [3,3,3,3,1,1,1,1]
[8,4,3,1] => [4,3,3,2,1,1,1,1]
[8,4,2,2] => [4,4,2,2,1,1,1,1]
[8,4,2,1,1] => [5,3,2,2,1,1,1,1]
[8,4,1,1,1,1] => [6,2,2,2,1,1,1,1]
[8,3,3,2] => [4,4,3,1,1,1,1,1]
[8,3,3,1,1] => [5,3,3,1,1,1,1,1]
[8,3,2,2,1] => [5,4,2,1,1,1,1,1]
[8,3,2,1,1,1] => [6,3,2,1,1,1,1,1]
[8,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1]
[8,2,2,2,2] => [5,5,1,1,1,1,1,1]
[8,2,2,2,1,1] => [6,4,1,1,1,1,1,1]
[8,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1]
[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]
[7,7,2] => [3,3,2,2,2,2,2]
[7,7,1,1] => [4,2,2,2,2,2,2]
[7,6,3] => [3,3,3,2,2,2,1]
[7,6,2,1] => [4,3,2,2,2,2,1]
[7,6,1,1,1] => [5,2,2,2,2,2,1]
[7,5,4] => [3,3,3,3,2,1,1]
[7,5,3,1] => [4,3,3,2,2,1,1]
[7,5,2,2] => [4,4,2,2,2,1,1]
[7,5,2,1,1] => [5,3,2,2,2,1,1]
[7,5,1,1,1,1] => [6,2,2,2,2,1,1]
[7,4,4,1] => [4,3,3,3,1,1,1]
[7,4,3,2] => [4,4,3,2,1,1,1]
[7,4,3,1,1] => [5,3,3,2,1,1,1]
[7,4,2,2,1] => [5,4,2,2,1,1,1]
[7,4,2,1,1,1] => [6,3,2,2,1,1,1]
[7,4,1,1,1,1,1] => [7,2,2,2,1,1,1]
[7,3,3,3] => [4,4,4,1,1,1,1]
[7,3,3,2,1] => [5,4,3,1,1,1,1]
[7,3,3,1,1,1] => [6,3,3,1,1,1,1]
[7,3,2,2,2] => [5,5,2,1,1,1,1]
[7,3,2,2,1,1] => [6,4,2,1,1,1,1]
[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]
[7,2,2,2,2,1] => [6,5,1,1,1,1,1]
[7,2,2,2,1,1,1] => [7,4,1,1,1,1,1]
[7,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1]
[7,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1]
[6,6,4] => [3,3,3,3,2,2]
[6,6,3,1] => [4,3,3,2,2,2]
[6,6,2,2] => [4,4,2,2,2,2]
[6,6,2,1,1] => [5,3,2,2,2,2]
[6,6,1,1,1,1] => [6,2,2,2,2,2]
[6,5,5] => [3,3,3,3,3,1]
[6,5,4,1] => [4,3,3,3,2,1]
[6,5,3,2] => [4,4,3,2,2,1]
[6,5,3,1,1] => [5,3,3,2,2,1]
[6,5,2,2,1] => [5,4,2,2,2,1]
[6,5,2,1,1,1] => [6,3,2,2,2,1]
[6,5,1,1,1,1,1] => [7,2,2,2,2,1]
[6,4,4,2] => [4,4,3,3,1,1]
[6,4,4,1,1] => [5,3,3,3,1,1]
[6,4,3,3] => [4,4,4,2,1,1]
[6,4,3,2,1] => [5,4,3,2,1,1]
[6,4,3,1,1,1] => [6,3,3,2,1,1]
[6,4,2,2,2] => [5,5,2,2,1,1]
[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]
[6,4,1,1,1,1,1,1] => [8,2,2,2,1,1]
[6,3,3,3,1] => [5,4,4,1,1,1]
[6,3,3,2,2] => [5,5,3,1,1,1]
[6,3,3,2,1,1] => [6,4,3,1,1,1]
[6,3,3,1,1,1,1] => [7,3,3,1,1,1]
[6,3,2,2,2,1] => [6,5,2,1,1,1]
[6,3,2,2,1,1,1] => [7,4,2,1,1,1]
[6,3,2,1,1,1,1,1] => [8,3,2,1,1,1]
[6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1]
[6,2,2,2,2,2] => [6,6,1,1,1,1]
[6,2,2,2,2,1,1] => [7,5,1,1,1,1]
[6,2,2,2,1,1,1,1] => [8,4,1,1,1,1]
[6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1]
[6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1]
[5,5,5,1] => [4,3,3,3,3]
[5,5,4,2] => [4,4,3,3,2]
[5,5,4,1,1] => [5,3,3,3,2]
[5,5,3,3] => [4,4,4,2,2]
[5,5,3,2,1] => [5,4,3,2,2]
[5,5,3,1,1,1] => [6,3,3,2,2]
[5,5,2,2,2] => [5,5,2,2,2]
[5,5,2,2,1,1] => [6,4,2,2,2]
[5,5,2,1,1,1,1] => [7,3,2,2,2]
[5,5,1,1,1,1,1,1] => [8,2,2,2,2]
[5,4,4,3] => [4,4,4,3,1]
[5,4,4,2,1] => [5,4,3,3,1]
[5,4,4,1,1,1] => [6,3,3,3,1]
[5,4,3,3,1] => [5,4,4,2,1]
[5,4,3,2,2] => [5,5,3,2,1]
[5,4,3,2,1,1] => [6,4,3,2,1]
[5,4,3,1,1,1,1] => [7,3,3,2,1]
[5,4,2,2,2,1] => [6,5,2,2,1]
[5,4,2,2,1,1,1] => [7,4,2,2,1]
[5,4,2,1,1,1,1,1] => [8,3,2,2,1]
[5,4,1,1,1,1,1,1,1] => [9,2,2,2,1]
[5,3,3,3,2] => [5,5,4,1,1]
[5,3,3,3,1,1] => [6,4,4,1,1]
[5,3,3,2,2,1] => [6,5,3,1,1]
[5,3,3,2,1,1,1] => [7,4,3,1,1]
[5,3,3,1,1,1,1,1] => [8,3,3,1,1]
[5,3,2,2,2,2] => [6,6,2,1,1]
[5,3,2,2,2,1,1] => [7,5,2,1,1]
[5,3,2,2,1,1,1,1] => [8,4,2,1,1]
[5,3,2,1,1,1,1,1,1] => [9,3,2,1,1]
[5,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1]
[5,2,2,2,2,2,1] => [7,6,1,1,1]
[5,2,2,2,2,1,1,1] => [8,5,1,1,1]
[5,2,2,2,1,1,1,1,1] => [9,4,1,1,1]
[5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1]
[5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1]
[4,4,4,4] => [4,4,4,4]
[4,4,4,3,1] => [5,4,4,3]
[4,4,4,2,2] => [5,5,3,3]
[4,4,4,2,1,1] => [6,4,3,3]
[4,4,4,1,1,1,1] => [7,3,3,3]
[4,4,3,3,2] => [5,5,4,2]
[4,4,3,3,1,1] => [6,4,4,2]
[4,4,3,2,2,1] => [6,5,3,2]
[4,4,3,2,1,1,1] => [7,4,3,2]
[4,4,3,1,1,1,1,1] => [8,3,3,2]
[4,4,2,2,2,2] => [6,6,2,2]
[4,4,2,2,2,1,1] => [7,5,2,2]
[4,4,2,2,1,1,1,1] => [8,4,2,2]
[4,4,2,1,1,1,1,1,1] => [9,3,2,2]
[4,4,1,1,1,1,1,1,1,1] => [10,2,2,2]
[4,3,3,3,3] => [5,5,5,1]
[4,3,3,3,2,1] => [6,5,4,1]
[4,3,3,3,1,1,1] => [7,4,4,1]
[4,3,3,2,2,2] => [6,6,3,1]
[4,3,3,2,2,1,1] => [7,5,3,1]
[4,3,3,2,1,1,1,1] => [8,4,3,1]
[4,3,3,1,1,1,1,1,1] => [9,3,3,1]
[4,3,2,2,2,2,1] => [7,6,2,1]
[4,3,2,2,2,1,1,1] => [8,5,2,1]
[4,3,2,2,1,1,1,1,1] => [9,4,2,1]
[4,3,2,1,1,1,1,1,1,1] => [10,3,2,1]
[4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1]
[4,2,2,2,2,2,2] => [7,7,1,1]
[4,2,2,2,2,2,1,1] => [8,6,1,1]
[4,2,2,2,2,1,1,1,1] => [9,5,1,1]
[4,2,2,2,1,1,1,1,1,1] => [10,4,1,1]
[4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1]
[3,3,3,3,3,1] => [6,5,5]
[3,3,3,3,2,2] => [6,6,4]
[3,3,3,3,2,1,1] => [7,5,4]
[3,3,3,3,1,1,1,1] => [8,4,4]
[3,3,3,2,2,2,1] => [7,6,3]
[3,3,3,2,2,1,1,1] => [8,5,3]
[3,3,3,2,1,1,1,1,1] => [9,4,3]
[3,3,3,1,1,1,1,1,1,1] => [10,3,3]
[3,3,2,2,2,2,2] => [7,7,2]
[3,3,2,2,2,2,1,1] => [8,6,2]
[3,3,2,2,2,1,1,1,1] => [9,5,2]
[3,3,2,2,1,1,1,1,1,1] => [10,4,2]
[3,3,2,1,1,1,1,1,1,1,1] => [11,3,2]
[3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2]
[3,2,2,2,2,2,2,1] => [8,7,1]
[3,2,2,2,2,2,1,1,1] => [9,6,1]
[3,2,2,2,2,1,1,1,1,1] => [10,5,1]
[3,2,2,2,1,1,1,1,1,1,1] => [11,4,1]
[3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1]
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1]
[2,2,2,2,2,2,2,2] => [8,8]
[2,2,2,2,2,2,2,1,1] => [9,7]
[2,2,2,2,2,2,1,1,1,1] => [10,6]
[2,2,2,2,2,1,1,1,1,1,1] => [11,5]
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4]
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16]
[17] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[16,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[15,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]
[15,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[14,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1]
[14,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1,1]
[14,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1]
[13,4] => [2,2,2,2,1,1,1,1,1,1,1,1,1]
[13,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1,1]
[13,2,2] => [3,3,1,1,1,1,1,1,1,1,1,1,1]
[13,2,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1,1]
[13,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1]
[12,5] => [2,2,2,2,2,1,1,1,1,1,1,1]
[12,4,1] => [3,2,2,2,1,1,1,1,1,1,1,1]
[12,3,2] => [3,3,2,1,1,1,1,1,1,1,1,1]
[12,3,1,1] => [4,2,2,1,1,1,1,1,1,1,1,1]
[12,2,2,1] => [4,3,1,1,1,1,1,1,1,1,1,1]
[12,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1]
[12,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1,1]
[11,6] => [2,2,2,2,2,2,1,1,1,1,1]
[11,5,1] => [3,2,2,2,2,1,1,1,1,1,1]
[11,4,2] => [3,3,2,2,1,1,1,1,1,1,1]
[11,4,1,1] => [4,2,2,2,1,1,1,1,1,1,1]
[11,3,3] => [3,3,3,1,1,1,1,1,1,1,1]
[11,3,2,1] => [4,3,2,1,1,1,1,1,1,1,1]
[11,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1,1]
[11,2,2,2] => [4,4,1,1,1,1,1,1,1,1,1]
[11,2,2,1,1] => [5,3,1,1,1,1,1,1,1,1,1]
[11,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1,1]
[11,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1,1]
[10,7] => [2,2,2,2,2,2,2,1,1,1]
[10,6,1] => [3,2,2,2,2,2,1,1,1,1]
[10,5,2] => [3,3,2,2,2,1,1,1,1,1]
[10,5,1,1] => [4,2,2,2,2,1,1,1,1,1]
[10,4,3] => [3,3,3,2,1,1,1,1,1,1]
[10,4,2,1] => [4,3,2,2,1,1,1,1,1,1]
[10,4,1,1,1] => [5,2,2,2,1,1,1,1,1,1]
[10,3,3,1] => [4,3,3,1,1,1,1,1,1,1]
[10,3,2,2] => [4,4,2,1,1,1,1,1,1,1]
[10,3,2,1,1] => [5,3,2,1,1,1,1,1,1,1]
[10,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1,1]
[10,2,2,2,1] => [5,4,1,1,1,1,1,1,1,1]
[10,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1,1]
[10,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1]
[10,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1,1]
[9,8] => [2,2,2,2,2,2,2,2,1]
[9,7,1] => [3,2,2,2,2,2,2,1,1]
[9,6,2] => [3,3,2,2,2,2,1,1,1]
[9,6,1,1] => [4,2,2,2,2,2,1,1,1]
[9,5,3] => [3,3,3,2,2,1,1,1,1]
[9,5,2,1] => [4,3,2,2,2,1,1,1,1]
[9,5,1,1,1] => [5,2,2,2,2,1,1,1,1]
[9,4,4] => [3,3,3,3,1,1,1,1,1]
[9,4,3,1] => [4,3,3,2,1,1,1,1,1]
[9,4,2,2] => [4,4,2,2,1,1,1,1,1]
[9,4,2,1,1] => [5,3,2,2,1,1,1,1,1]
[9,4,1,1,1,1] => [6,2,2,2,1,1,1,1,1]
[9,3,3,2] => [4,4,3,1,1,1,1,1,1]
[9,3,3,1,1] => [5,3,3,1,1,1,1,1,1]
[9,3,2,2,1] => [5,4,2,1,1,1,1,1,1]
[9,3,2,1,1,1] => [6,3,2,1,1,1,1,1,1]
[9,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1,1]
[9,2,2,2,2] => [5,5,1,1,1,1,1,1,1]
[9,2,2,2,1,1] => [6,4,1,1,1,1,1,1,1]
[9,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1,1]
[9,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1,1]
[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]
[8,7,2] => [3,3,2,2,2,2,2,1]
[8,7,1,1] => [4,2,2,2,2,2,2,1]
[8,6,3] => [3,3,3,2,2,2,1,1]
[8,6,2,1] => [4,3,2,2,2,2,1,1]
[8,6,1,1,1] => [5,2,2,2,2,2,1,1]
[8,5,4] => [3,3,3,3,2,1,1,1]
[8,5,3,1] => [4,3,3,2,2,1,1,1]
[8,5,2,2] => [4,4,2,2,2,1,1,1]
[8,5,2,1,1] => [5,3,2,2,2,1,1,1]
[8,5,1,1,1,1] => [6,2,2,2,2,1,1,1]
[8,4,4,1] => [4,3,3,3,1,1,1,1]
[8,4,3,2] => [4,4,3,2,1,1,1,1]
[8,4,3,1,1] => [5,3,3,2,1,1,1,1]
[8,4,2,2,1] => [5,4,2,2,1,1,1,1]
[8,4,2,1,1,1] => [6,3,2,2,1,1,1,1]
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1]
[8,3,3,3] => [4,4,4,1,1,1,1,1]
[8,3,3,2,1] => [5,4,3,1,1,1,1,1]
[8,3,3,1,1,1] => [6,3,3,1,1,1,1,1]
[8,3,2,2,2] => [5,5,2,1,1,1,1,1]
[8,3,2,2,1,1] => [6,4,2,1,1,1,1,1]
[8,3,2,1,1,1,1] => [7,3,2,1,1,1,1,1]
[8,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1,1]
[8,2,2,2,2,1] => [6,5,1,1,1,1,1,1]
[8,2,2,2,1,1,1] => [7,4,1,1,1,1,1,1]
[8,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1,1]
[8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1]
[8,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1]
[7,7,3] => [3,3,3,2,2,2,2]
[7,7,2,1] => [4,3,2,2,2,2,2]
[7,7,1,1,1] => [5,2,2,2,2,2,2]
[7,6,4] => [3,3,3,3,2,2,1]
[7,6,3,1] => [4,3,3,2,2,2,1]
[7,6,2,2] => [4,4,2,2,2,2,1]
[7,6,2,1,1] => [5,3,2,2,2,2,1]
[7,6,1,1,1,1] => [6,2,2,2,2,2,1]
[7,5,5] => [3,3,3,3,3,1,1]
[7,5,4,1] => [4,3,3,3,2,1,1]
[7,5,3,2] => [4,4,3,2,2,1,1]
[7,5,3,1,1] => [5,3,3,2,2,1,1]
[7,5,2,2,1] => [5,4,2,2,2,1,1]
[7,5,2,1,1,1] => [6,3,2,2,2,1,1]
[7,5,1,1,1,1,1] => [7,2,2,2,2,1,1]
[7,4,4,2] => [4,4,3,3,1,1,1]
[7,4,4,1,1] => [5,3,3,3,1,1,1]
[7,4,3,3] => [4,4,4,2,1,1,1]
[7,4,3,2,1] => [5,4,3,2,1,1,1]
[7,4,3,1,1,1] => [6,3,3,2,1,1,1]
[7,4,2,2,2] => [5,5,2,2,1,1,1]
[7,4,2,2,1,1] => [6,4,2,2,1,1,1]
[7,4,2,1,1,1,1] => [7,3,2,2,1,1,1]
[7,4,1,1,1,1,1,1] => [8,2,2,2,1,1,1]
[7,3,3,3,1] => [5,4,4,1,1,1,1]
[7,3,3,2,2] => [5,5,3,1,1,1,1]
[7,3,3,2,1,1] => [6,4,3,1,1,1,1]
[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]
[7,3,2,2,1,1,1] => [7,4,2,1,1,1,1]
[7,3,2,1,1,1,1,1] => [8,3,2,1,1,1,1]
[7,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1,1]
[7,2,2,2,2,2] => [6,6,1,1,1,1,1]
[7,2,2,2,2,1,1] => [7,5,1,1,1,1,1]
[7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1]
[7,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1]
[7,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1]
[6,6,5] => [3,3,3,3,3,2]
[6,6,4,1] => [4,3,3,3,2,2]
[6,6,3,2] => [4,4,3,2,2,2]
[6,6,3,1,1] => [5,3,3,2,2,2]
[6,6,2,2,1] => [5,4,2,2,2,2]
[6,6,2,1,1,1] => [6,3,2,2,2,2]
[6,6,1,1,1,1,1] => [7,2,2,2,2,2]
[6,5,5,1] => [4,3,3,3,3,1]
[6,5,4,2] => [4,4,3,3,2,1]
[6,5,4,1,1] => [5,3,3,3,2,1]
[6,5,3,3] => [4,4,4,2,2,1]
[6,5,3,2,1] => [5,4,3,2,2,1]
[6,5,3,1,1,1] => [6,3,3,2,2,1]
[6,5,2,2,2] => [5,5,2,2,2,1]
[6,5,2,2,1,1] => [6,4,2,2,2,1]
[6,5,2,1,1,1,1] => [7,3,2,2,2,1]
[6,5,1,1,1,1,1,1] => [8,2,2,2,2,1]
[6,4,4,3] => [4,4,4,3,1,1]
[6,4,4,2,1] => [5,4,3,3,1,1]
[6,4,4,1,1,1] => [6,3,3,3,1,1]
[6,4,3,3,1] => [5,4,4,2,1,1]
[6,4,3,2,2] => [5,5,3,2,1,1]
[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]
[6,4,2,2,2,1] => [6,5,2,2,1,1]
[6,4,2,2,1,1,1] => [7,4,2,2,1,1]
[6,4,2,1,1,1,1,1] => [8,3,2,2,1,1]
[6,4,1,1,1,1,1,1,1] => [9,2,2,2,1,1]
[6,3,3,3,2] => [5,5,4,1,1,1]
[6,3,3,3,1,1] => [6,4,4,1,1,1]
[6,3,3,2,2,1] => [6,5,3,1,1,1]
[6,3,3,2,1,1,1] => [7,4,3,1,1,1]
[6,3,3,1,1,1,1,1] => [8,3,3,1,1,1]
[6,3,2,2,2,2] => [6,6,2,1,1,1]
[6,3,2,2,2,1,1] => [7,5,2,1,1,1]
[6,3,2,2,1,1,1,1] => [8,4,2,1,1,1]
[6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1]
[6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1]
[6,2,2,2,2,2,1] => [7,6,1,1,1,1]
[6,2,2,2,2,1,1,1] => [8,5,1,1,1,1]
[6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1]
[6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1]
[6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1]
[5,5,5,2] => [4,4,3,3,3]
[5,5,5,1,1] => [5,3,3,3,3]
[5,5,4,3] => [4,4,4,3,2]
[5,5,4,2,1] => [5,4,3,3,2]
[5,5,4,1,1,1] => [6,3,3,3,2]
[5,5,3,3,1] => [5,4,4,2,2]
[5,5,3,2,2] => [5,5,3,2,2]
[5,5,3,2,1,1] => [6,4,3,2,2]
[5,5,3,1,1,1,1] => [7,3,3,2,2]
[5,5,2,2,2,1] => [6,5,2,2,2]
[5,5,2,2,1,1,1] => [7,4,2,2,2]
[5,5,2,1,1,1,1,1] => [8,3,2,2,2]
[5,5,1,1,1,1,1,1,1] => [9,2,2,2,2]
[5,4,4,4] => [4,4,4,4,1]
[5,4,4,3,1] => [5,4,4,3,1]
[5,4,4,2,2] => [5,5,3,3,1]
[5,4,4,2,1,1] => [6,4,3,3,1]
[5,4,4,1,1,1,1] => [7,3,3,3,1]
[5,4,3,3,2] => [5,5,4,2,1]
[5,4,3,3,1,1] => [6,4,4,2,1]
[5,4,3,2,2,1] => [6,5,3,2,1]
[5,4,3,2,1,1,1] => [7,4,3,2,1]
[5,4,3,1,1,1,1,1] => [8,3,3,2,1]
[5,4,2,2,2,2] => [6,6,2,2,1]
[5,4,2,2,2,1,1] => [7,5,2,2,1]
[5,4,2,2,1,1,1,1] => [8,4,2,2,1]
[5,4,2,1,1,1,1,1,1] => [9,3,2,2,1]
[5,4,1,1,1,1,1,1,1,1] => [10,2,2,2,1]
[5,3,3,3,3] => [5,5,5,1,1]
[5,3,3,3,2,1] => [6,5,4,1,1]
[5,3,3,3,1,1,1] => [7,4,4,1,1]
[5,3,3,2,2,2] => [6,6,3,1,1]
[5,3,3,2,2,1,1] => [7,5,3,1,1]
[5,3,3,2,1,1,1,1] => [8,4,3,1,1]
[5,3,3,1,1,1,1,1,1] => [9,3,3,1,1]
[5,3,2,2,2,2,1] => [7,6,2,1,1]
[5,3,2,2,2,1,1,1] => [8,5,2,1,1]
[5,3,2,2,1,1,1,1,1] => [9,4,2,1,1]
[5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1]
[5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1]
[5,2,2,2,2,2,2] => [7,7,1,1,1]
[5,2,2,2,2,2,1,1] => [8,6,1,1,1]
[5,2,2,2,2,1,1,1,1] => [9,5,1,1,1]
[5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1]
[5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1]
[5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1]
[4,4,4,4,1] => [5,4,4,4]
[4,4,4,3,2] => [5,5,4,3]
[4,4,4,3,1,1] => [6,4,4,3]
[4,4,4,2,2,1] => [6,5,3,3]
[4,4,4,2,1,1,1] => [7,4,3,3]
[4,4,4,1,1,1,1,1] => [8,3,3,3]
[4,4,3,3,3] => [5,5,5,2]
[4,4,3,3,2,1] => [6,5,4,2]
[4,4,3,3,1,1,1] => [7,4,4,2]
[4,4,3,2,2,2] => [6,6,3,2]
[4,4,3,2,2,1,1] => [7,5,3,2]
[4,4,3,2,1,1,1,1] => [8,4,3,2]
[4,4,3,1,1,1,1,1,1] => [9,3,3,2]
[4,4,2,2,2,2,1] => [7,6,2,2]
[4,4,2,2,2,1,1,1] => [8,5,2,2]
[4,4,2,2,1,1,1,1,1] => [9,4,2,2]
[4,4,2,1,1,1,1,1,1,1] => [10,3,2,2]
[4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2]
[4,3,3,3,3,1] => [6,5,5,1]
[4,3,3,3,2,2] => [6,6,4,1]
[4,3,3,3,2,1,1] => [7,5,4,1]
[4,3,3,3,1,1,1,1] => [8,4,4,1]
[4,3,3,2,2,2,1] => [7,6,3,1]
[4,3,3,2,2,1,1,1] => [8,5,3,1]
[4,3,3,2,1,1,1,1,1] => [9,4,3,1]
[4,3,3,1,1,1,1,1,1,1] => [10,3,3,1]
[4,3,2,2,2,2,2] => [7,7,2,1]
[4,3,2,2,2,2,1,1] => [8,6,2,1]
[4,3,2,2,2,1,1,1,1] => [9,5,2,1]
[4,3,2,2,1,1,1,1,1,1] => [10,4,2,1]
[4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1]
[4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1]
[4,2,2,2,2,2,2,1] => [8,7,1,1]
[4,2,2,2,2,2,1,1,1] => [9,6,1,1]
[4,2,2,2,2,1,1,1,1,1] => [10,5,1,1]
[4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1]
[4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1]
[3,3,3,3,3,2] => [6,6,5]
[3,3,3,3,3,1,1] => [7,5,5]
[3,3,3,3,2,2,1] => [7,6,4]
[3,3,3,3,2,1,1,1] => [8,5,4]
[3,3,3,3,1,1,1,1,1] => [9,4,4]
[3,3,3,2,2,2,2] => [7,7,3]
[3,3,3,2,2,2,1,1] => [8,6,3]
[3,3,3,2,2,1,1,1,1] => [9,5,3]
[3,3,3,2,1,1,1,1,1,1] => [10,4,3]
[3,3,3,1,1,1,1,1,1,1,1] => [11,3,3]
[3,3,2,2,2,2,2,1] => [8,7,2]
[3,3,2,2,2,2,1,1,1] => [9,6,2]
[3,3,2,2,2,1,1,1,1,1] => [10,5,2]
[3,3,2,2,1,1,1,1,1,1,1] => [11,4,2]
[3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2]
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2]
[3,2,2,2,2,2,2,2] => [8,8,1]
[3,2,2,2,2,2,2,1,1] => [9,7,1]
[3,2,2,2,2,2,1,1,1,1] => [10,6,1]
[3,2,2,2,2,1,1,1,1,1,1] => [11,5,1]
[3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1]
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1]
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1]
[2,2,2,2,2,2,2,2,1] => [9,8]
[2,2,2,2,2,2,2,1,1,1] => [10,7]
[2,2,2,2,2,2,1,1,1,1,1] => [11,6]
[2,2,2,2,2,1,1,1,1,1,1,1] => [12,5]
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4]
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17]
[4,4,4,3,2,1] => [6,5,4,3]
[5,4,3,3,2,1] => [6,5,4,2,1]
[6,3,3,3,2,1] => [6,5,4,1,1,1]
[5,4,4,2,2,1] => [6,5,3,3,1]
[5,5,3,2,2,1] => [6,5,3,2,2]
[6,4,3,2,2,1] => [6,5,3,2,1,1]
[6,5,2,2,2,1] => [6,5,2,2,2,1]
[5,4,4,3,1,1] => [6,4,4,3,1]
[5,5,3,3,1,1] => [6,4,4,2,2]
[6,4,3,3,1,1] => [6,4,4,2,1,1]
[5,5,4,2,1,1] => [6,4,3,3,2]
[6,4,4,2,1,1] => [6,4,3,3,1,1]
[6,5,3,2,1,1] => [6,4,3,2,2,1]
[6,5,4,1,1,1] => [6,3,3,3,2,1]
[5,4,4,3,2] => [5,5,4,3,1]
[5,5,3,3,2] => [5,5,4,2,2]
[6,4,3,3,2] => [5,5,4,2,1,1]
[5,5,4,2,2] => [5,5,3,3,2]
[6,4,4,2,2] => [5,5,3,3,1,1]
[6,5,3,2,2] => [5,5,3,2,2,1]
[5,5,4,3,1] => [5,4,4,3,2]
[6,4,4,3,1] => [5,4,4,3,1,1]
[6,5,3,3,1] => [5,4,4,2,2,1]
[6,5,4,2,1] => [5,4,3,3,2,1]
[6,5,4,3] => [4,4,4,3,2,1]
[3,3,3,3,3,2,1] => [7,6,5]
[4,4,3,2,2,2,1] => [7,6,3,2]
[6,3,2,2,2,2,1] => [7,6,2,1,1,1]
[7,2,2,2,2,2,1] => [7,6,1,1,1,1,1]
[6,4,3,2,1,1,1] => [7,4,3,2,1,1]
[6,5,2,2,1,1,1] => [7,4,2,2,2,1]
[6,6,2,1,1,1,1] => [7,3,2,2,2,2]
[7,6,1,1,1,1,1] => [7,2,2,2,2,2,1]
[4,4,3,3,3,1] => [6,5,5,2]
[4,4,4,4,1,1] => [6,4,4,4]
[6,6,3,1,1,1] => [6,3,3,2,2,2]
[5,4,3,3,3] => [5,5,5,2,1]
[4,4,4,4,2] => [5,5,4,4]
[5,4,4,4,1] => [5,4,4,4,1]
[6,6,3,2,1] => [5,4,3,2,2,2]
[5,5,4,4] => [4,4,4,4,2]
[6,4,4,4] => [4,4,4,4,1,1]
[7,6,5] => [3,3,3,3,3,2,1]
[2,2,2,2,2,2,2,2,2] => [9,9]
[3,3,3,3,3,3] => [6,6,6]
[18] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[6,2,2,2,2,2,2] => [7,7,1,1,1,1]
[6,6,6] => [3,3,3,3,3,3]
[4,2,2,2,2,2,2,2] => [8,8,1,1]
[10,4,4] => [3,3,3,3,1,1,1,1,1,1]
[9,6,3] => [3,3,3,2,2,2,1,1,1]
[8,6,4] => [3,3,3,3,2,2,1,1]
[10,8] => [2,2,2,2,2,2,2,2,1,1]
[7,7,1,1,1,1] => [6,2,2,2,2,2,2]
[5,4,3,2,1,1,1,1] => [8,4,3,2,1]
[5,4,4,3,2,1] => [6,5,4,3,1]
[5,5,3,3,2,1] => [6,5,4,2,2]
[6,4,3,3,2,1] => [6,5,4,2,1,1]
[5,5,4,2,2,1] => [6,5,3,3,2]
[6,4,4,2,2,1] => [6,5,3,3,1,1]
[6,5,3,2,2,1] => [6,5,3,2,2,1]
[5,5,4,3,1,1] => [6,4,4,3,2]
[6,4,4,3,1,1] => [6,4,4,3,1,1]
[6,5,3,3,1,1] => [6,4,4,2,2,1]
[6,5,4,2,1,1] => [6,4,3,3,2,1]
[5,5,4,3,2] => [5,5,4,3,2]
[6,4,4,3,2] => [5,5,4,3,1,1]
[6,5,3,3,2] => [5,5,4,2,2,1]
[6,5,4,2,2] => [5,5,3,3,2,1]
[6,5,4,3,1] => [5,4,4,3,2,1]
[4,3,3,3,3,2,1] => [7,6,5,1]
[6,3,3,2,2,2,1] => [7,6,3,1,1,1]
[4,4,4,4,1,1,1] => [7,4,4,4]
[6,5,3,2,1,1,1] => [7,4,3,2,2,1]
[7,4,3,2,1,1,1] => [7,4,3,2,1,1,1]
[7,5,2,2,1,1,1] => [7,4,2,2,2,1,1]
[5,5,5,1,1,1,1] => [7,3,3,3,3]
[6,5,4,1,1,1,1] => [7,3,3,3,2,1]
[4,4,4,3,2,2] => [6,6,4,3]
[4,4,4,4,2,1] => [6,5,4,4]
[7,3,3,3,2,1] => [6,5,4,1,1,1,1]
[4,4,4,4,3] => [5,5,5,4]
[7,3,3,3,3] => [5,5,5,1,1,1,1]
[7,6,3,2,1] => [5,4,3,2,2,2,1]
[5,5,5,4] => [4,4,4,4,3]
[6,5,4,4] => [4,4,4,4,2,1]
[7,5,4,3] => [4,4,4,3,2,1,1]
[3,3,3,3,3,3,1] => [7,6,6]
[3,3,3,3,3,2,2] => [7,7,5]
[4,3,3,3,3,3] => [6,6,6,1]
[19] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[7,2,2,2,2,2,2] => [7,7,1,1,1,1,1]
[7,6,6] => [3,3,3,3,3,3,1]
[5,2,2,2,2,2,2,2] => [8,8,1,1,1]
[13,6] => [2,2,2,2,2,2,1,1,1,1,1,1,1]
[11,4,4] => [3,3,3,3,1,1,1,1,1,1,1]
[9,6,4] => [3,3,3,3,2,2,1,1,1]
[8,5,4,2] => [4,4,3,3,2,1,1,1]
[8,5,5,1] => [4,3,3,3,3,1,1,1]
[5,4,3,2,1,1,1,1,1] => [9,4,3,2,1]
[6,6,6,1] => [4,3,3,3,3,3]
[5,5,4,3,2,1] => [6,5,4,3,2]
[6,4,4,3,2,1] => [6,5,4,3,1,1]
[6,5,3,3,2,1] => [6,5,4,2,2,1]
[6,5,4,2,2,1] => [6,5,3,3,2,1]
[6,5,4,3,1,1] => [6,4,4,3,2,1]
[6,5,4,3,2] => [5,5,4,3,2,1]
[6,4,3,2,2,2,1] => [7,6,3,2,1,1]
[6,5,2,2,2,2,1] => [7,6,2,2,2,1]
[4,4,4,4,2,1,1] => [7,5,4,4]
[5,5,5,2,1,1,1] => [7,4,3,3,3]
[6,5,4,2,1,1,1] => [7,4,3,3,2,1]
[4,4,4,4,2,2] => [6,6,4,4]
[6,6,2,2,2,2] => [6,6,2,2,2,2]
[4,4,4,4,3,1] => [6,5,5,4]
[5,5,3,3,3,1] => [6,5,5,2,2]
[7,6,2,2,2,1] => [6,5,2,2,2,2,1]
[6,4,4,4,1,1] => [6,4,4,4,1,1]
[5,5,5,3,1,1] => [6,4,4,3,3]
[6,6,3,3,1,1] => [6,4,4,2,2,2]
[7,5,3,3,1,1] => [6,4,4,2,2,1,1]
[5,5,4,4,2] => [5,5,4,4,2]
[7,5,4,3,1] => [5,4,4,3,2,1,1]
[6,6,4,4] => [4,4,4,4,2,2]
[4,4,4,4,4] => [5,5,5,5]
[5,5,5,5] => [4,4,4,4,4]
[20] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[10,10] => [2,2,2,2,2,2,2,2,2,2]
[8,2,2,2,2,2,2] => [7,7,1,1,1,1,1,1]
[8,6,4,2] => [4,4,3,3,2,2,1,1]
[8,6,6] => [3,3,3,3,3,3,1,1]
[10,6,4] => [3,3,3,3,2,2,1,1,1,1]
[6,6,6,2] => [4,4,3,3,3,3]
[10,7,3] => [3,3,3,2,2,2,2,1,1,1]
[9,7,4] => [3,3,3,3,2,2,2,1,1]
[9,5,5,1] => [4,3,3,3,3,1,1,1,1]
[3,3,3,3,3,3,1,1] => [8,6,6]
[7,4,2,2,2,1,1,1] => [8,5,2,2,1,1,1]
[18,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[6,6,6,1,1] => [5,3,3,3,3,3]
[3,3,3,3,2,2,1,1,1,1] => [10,6,4]
[4,4,3,3,2,2,1,1] => [8,6,4,2]
[6,5,4,3,2,1] => [6,5,4,3,2,1]
[6,3,3,3,3,2,1] => [7,6,5,1,1,1]
[4,4,4,4,2,2,1] => [7,6,4,4]
[6,5,3,2,2,2,1] => [7,6,3,2,2,1]
[6,6,2,2,2,2,1] => [7,6,2,2,2,2]
[4,4,4,4,3,1,1] => [7,5,5,4]
[7,3,3,3,3,1,1] => [7,5,5,1,1,1,1]
[5,5,4,3,2,1,1] => [7,5,4,3,2]
[6,4,4,3,2,1,1] => [7,5,4,3,1,1]
[6,5,3,3,2,1,1] => [7,5,4,2,2,1]
[6,5,4,2,2,1,1] => [7,5,3,3,2,1]
[7,5,3,2,2,1,1] => [7,5,3,2,2,1,1]
[6,5,4,3,1,1,1] => [7,4,4,3,2,1]
[7,5,3,3,1,1,1] => [7,4,4,2,2,1,1]
[7,6,3,2,1,1,1] => [7,4,3,2,2,2,1]
[4,4,4,4,3,2] => [6,6,5,4]
[5,4,4,4,2,2] => [6,6,4,4,1]
[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]
[7,4,4,3,2,1] => [6,5,4,3,1,1,1]
[7,6,5,1,1,1] => [6,3,3,3,3,2,1]
[7,5,4,3,2] => [5,5,4,3,2,1,1]
[6,5,5,4,1] => [5,4,4,4,3,1]
[6,6,4,4,1] => [5,4,4,4,2,2]
[7,5,5,3,1] => [5,4,4,3,3,1,1]
[7,6,5,2,1] => [5,4,3,3,3,2,1]
[6,6,5,4] => [4,4,4,4,3,2]
[3,3,3,3,3,3,3] => [7,7,7]
[4,4,4,3,3,3] => [6,6,6,3]
[21] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[11,7,3] => [3,3,3,2,2,2,2,1,1,1,1]
[5,4,2,2,2,2,2,2] => [8,8,2,2,1]
[11,10] => [2,2,2,2,2,2,2,2,2,2,1]
[13,4,4] => [3,3,3,3,1,1,1,1,1,1,1,1,1]
[7,7,7] => [3,3,3,3,3,3,3]
[6,5,5,5] => [4,4,4,4,4,1]
[5,4,4,4,4] => [5,5,5,5,1]
[20,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[4,4,4,4,4,1] => [6,5,5,5]
[5,5,5,5,1] => [5,4,4,4,4]
[3,3,3,3,3,3,2,1] => [8,7,6]
[4,4,4,4,3,2,1] => [7,6,5,4]
[6,4,3,3,3,2,1] => [7,6,5,2,1,1]
[7,3,3,3,3,2,1] => [7,6,5,1,1,1,1]
[5,5,5,2,2,2,1] => [7,6,3,3,3]
[6,5,4,2,2,2,1] => [7,6,3,3,2,1]
[7,6,2,2,2,2,1] => [7,6,2,2,2,2,1]
[6,5,4,3,2,1,1] => [7,5,4,3,2,1]
[7,4,4,3,2,1,1] => [7,5,4,3,1,1,1]
[7,4,4,4,1,1,1] => [7,4,4,4,1,1,1]
[7,6,5,1,1,1,1] => [7,3,3,3,3,2,1]
[7,5,3,3,3,1] => [6,5,5,2,2,1,1]
[6,5,4,4,2,1] => [6,5,4,4,2,1]
[6,6,4,3,2,1] => [6,5,4,3,2,2]
[7,5,4,3,2,1] => [6,5,4,3,2,1,1]
[7,6,3,3,2,1] => [6,5,4,2,2,2,1]
[6,6,4,4,1,1] => [6,4,4,4,2,2]
[6,6,5,3,1,1] => [6,4,4,3,3,2]
[7,5,5,3,1,1] => [6,4,4,3,3,1,1]
[5,5,5,4,3] => [5,5,5,4,3]
[7,6,5,4] => [4,4,4,4,3,2,1]
[8,6,2,2,2,2] => [6,6,2,2,2,2,1,1]
[22] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[9,6,4,3] => [4,4,4,3,2,2,1,1,1]
[6,5,4,3,1,1,1,1] => [8,4,4,3,2,1]
[7,4,2,2,2,2,2,1] => [8,7,2,2,1,1,1]
[7,4,3,3,2,1,1,1] => [8,5,4,2,1,1,1]
[7,6,2,2,2,1,1,1] => [8,5,2,2,2,2,1]
[3,3,3,3,1,1,1,1,1,1,1,1,1,1] => [14,4,4]
[5,4,4,4,3,2,1] => [7,6,5,4,1]
[6,5,3,3,3,2,1] => [7,6,5,2,2,1]
[6,5,4,3,2,2,1] => [7,6,4,3,2,1]
[7,6,3,2,2,2,1] => [7,6,3,2,2,2,1]
[5,5,5,3,3,1,1] => [7,5,5,3,3]
[7,5,4,3,2,1,1] => [7,5,4,3,2,1,1]
[7,6,3,3,2,1,1] => [7,5,4,2,2,2,1]
[6,5,5,4,1,1,1] => [7,4,4,4,3,1]
[6,6,4,4,1,1,1] => [7,4,4,4,2,2]
[7,5,5,3,1,1,1] => [7,4,4,3,3,1,1]
[7,6,5,2,1,1,1] => [7,4,3,3,3,2,1]
[7,4,4,4,2,2] => [6,6,4,4,1,1,1]
[6,5,5,4,2,1] => [6,5,4,4,3,1]
[7,5,5,3,2,1] => [6,5,4,3,3,1,1]
[7,6,4,3,2,1] => [6,5,4,3,2,2,1]
[7,6,5,2,2,1] => [6,5,3,3,3,2,1]
[7,6,5,3,1,1] => [6,4,4,3,3,2,1]
[6,5,5,4,3] => [5,5,5,4,3,1]
[7,6,5,4,1] => [5,4,4,4,3,2,1]
[15,2,2,2,2] => [5,5,1,1,1,1,1,1,1,1,1,1,1,1,1]
[9,6,5,3] => [4,4,4,3,3,2,1,1,1]
[8,6,5,3,1] => [5,4,4,3,3,2,1,1]
[8,5,4,3,2,1] => [6,5,4,3,2,1,1,1]
[6,5,4,3,2,1,1,1] => [8,5,4,3,2,1]
[5,5,4,4,3,2,1] => [7,6,5,4,2]
[6,4,4,4,3,2,1] => [7,6,5,4,1,1]
[5,5,5,3,3,2,1] => [7,6,5,3,3]
[6,5,4,3,3,2,1] => [7,6,5,3,2,1]
[7,4,4,3,3,2,1] => [7,6,5,3,1,1,1]
[6,6,3,3,3,2,1] => [7,6,5,2,2,2]
[6,5,4,4,2,2,1] => [7,6,4,4,2,1]
[7,6,3,3,2,2,1] => [7,6,4,2,2,2,1]
[7,6,3,3,3,1,1] => [7,5,5,2,2,2,1]
[6,5,5,4,2,1,1] => [7,5,4,4,3,1]
[7,5,4,4,2,1,1] => [7,5,4,4,2,1,1]
[7,6,5,2,2,1,1] => [7,5,3,3,3,2,1]
[5,5,5,4,3,2] => [6,6,5,4,3]
[6,5,4,4,3,2] => [6,6,5,4,2,1]
[6,6,4,4,2,2] => [6,6,4,4,2,2]
[7,6,5,2,2,2] => [6,6,3,3,3,2,1]
[6,5,5,4,3,1] => [6,5,5,4,3,1]
[7,5,5,3,3,1] => [6,5,5,3,3,1,1]
[7,6,5,3,2,1] => [6,5,4,3,3,2,1]
[7,6,5,4,1,1] => [6,4,4,4,3,2,1]
[6,6,5,4,3] => [5,5,5,4,3,2]
[3,3,3,3,3,3,3,3] => [8,8,8]
[4,4,4,4,4,4] => [6,6,6,6]
[6,6,6,6] => [4,4,4,4,4,4]
[24] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[11,7,5,1] => [4,3,3,3,3,2,2,1,1,1,1]
[9,7,5,3] => [4,4,4,3,3,2,2,1,1]
[6,5,4,3,2,1,1,1,1] => [9,5,4,3,2,1]
[7,5,4,3,2,1,1,1] => [8,5,4,3,2,1,1]
[7,4,3,3,2,2,2,1] => [8,7,4,2,1,1,1]
[7,6,2,2,2,2,2,1] => [8,7,2,2,2,2,1]
[7,6,3,3,2,1,1,1] => [8,5,4,2,2,2,1]
[8,5,3,3,3,1,1] => [7,5,5,2,2,1,1,1]
[20,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[5,5,5,5,1,1,1,1] => [8,4,4,4,4]
[5,5,4,4,2,2,1,1] => [8,6,4,4,2]
[5,5,5,4,3,2,1] => [7,6,5,4,3]
[6,5,4,4,3,2,1] => [7,6,5,4,2,1]
[7,4,4,4,3,2,1] => [7,6,5,4,1,1,1]
[7,6,3,3,3,2,1] => [7,6,5,2,2,2,1]
[6,5,5,4,2,2,1] => [7,6,4,4,3,1]
[6,6,4,4,2,2,1] => [7,6,4,4,2,2]
[7,6,4,3,2,2,1] => [7,6,4,3,2,2,1]
[7,6,5,2,2,2,1] => [7,6,3,3,3,2,1]
[6,5,5,4,3,1,1] => [7,5,5,4,3,1]
[7,5,5,3,3,1,1] => [7,5,5,3,3,1,1]
[6,6,5,4,2,1,1] => [7,5,4,4,3,2]
[7,6,5,4,1,1,1] => [7,4,4,4,3,2,1]
[6,5,5,4,3,2] => [6,6,5,4,3,1]
[7,6,4,4,2,2] => [6,6,4,4,2,2,1]
[6,6,5,4,3,1] => [6,5,5,4,3,2]
[7,6,5,4,2,1] => [6,5,4,4,3,2,1]
[7,6,5,4,3] => [5,5,5,4,3,2,1]
[7,6,6,6] => [4,4,4,4,4,4,1]
[5,4,4,4,2,2,2,2] => [8,8,4,4,1]
[13,12] => [2,2,2,2,2,2,2,2,2,2,2,2,1]
[25] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[15,5,5] => [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]
[9,7,5,3,1] => [5,4,4,3,3,2,2,1,1]
[10,7,5,3] => [4,4,4,3,3,2,2,1,1,1]
[5,5,5,5,5] => [5,5,5,5,5]
[8,7,4,3,2,1] => [6,5,4,3,2,2,2,1]
[23,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[8,7,5,4,1] => [5,4,4,4,3,2,2,1]
[6,5,5,4,3,2,1] => [7,6,5,4,3,1]
[6,6,4,4,3,2,1] => [7,6,5,4,2,2]
[6,6,5,3,3,2,1] => [7,6,5,3,3,2]
[6,6,5,4,2,2,1] => [7,6,4,4,3,2]
[7,6,4,4,2,2,1] => [7,6,4,4,2,2,1]
[6,6,5,4,3,1,1] => [7,5,5,4,3,2]
[7,5,5,4,3,1,1] => [7,5,5,4,3,1,1]
[7,6,5,3,3,1,1] => [7,5,5,3,3,2,1]
[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]
[7,6,4,4,3,2] => [6,6,5,4,2,2,1]
[7,6,5,4,2,2] => [6,6,4,4,3,2,1]
[7,6,5,4,3,1] => [6,5,5,4,3,2,1]
[6,6,4,3,3,2,2] => [7,7,5,3,2,2]
[8,6,6,6] => [4,4,4,4,4,4,1,1]
[9,7,5,4,1] => [5,4,4,4,3,2,2,1,1]
[7,4,3,3,3,3,2,1] => [8,7,6,2,1,1,1]
[7,6,3,3,2,2,2,1] => [8,7,4,2,2,2,1]
[7,6,5,3,2,1,1,1] => [8,5,4,3,3,2,1]
[8,5,5,3,3,1,1] => [7,5,5,3,3,1,1,1]
[8,6,6,3,1,1,1] => [7,4,4,3,3,3,1,1]
[4,4,4,4,4,3,2,1] => [8,7,6,5]
[6,6,5,4,3,2,1] => [7,6,5,4,3,2]
[7,5,5,4,3,2,1] => [7,6,5,4,3,1,1]
[7,6,4,4,3,2,1] => [7,6,5,4,2,2,1]
[7,6,5,3,3,2,1] => [7,6,5,3,3,2,1]
[7,6,5,4,2,2,1] => [7,6,4,4,3,2,1]
[7,6,5,4,3,1,1] => [7,5,5,4,3,2,1]
[7,6,5,4,3,2] => [6,6,5,4,3,2,1]
[15,6,6] => [3,3,3,3,3,3,1,1,1,1,1,1,1,1,1]
[7,6,4,3,2,2,2,1] => [8,7,4,3,2,2,1]
[8,7,6,3,2,1] => [6,5,4,3,3,3,2,1]
[7,7,5,3,3,1,1] => [7,5,5,3,3,2,2]
[7,5,5,5,3,1,1] => [7,5,5,4,4,1,1]
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[6,6,6,4,3,3] => [6,6,6,4,3,3]
[4,3,3,3,3,3,3,3,3] => [9,9,9,1]
[7,6,5,4,3,1,1,1] => [8,5,5,4,3,2,1]
[8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1]
[10,7,6,4,1] => [5,4,4,4,3,3,2,1,1,1]
[9,7,6,4,2] => [5,5,4,4,3,3,2,1,1]
[10,8,5,4,1] => [5,4,4,4,3,2,2,2,1,1]
[8,6,5,4,3,2] => [6,6,5,4,3,2,1,1]
[7,6,3,3,3,3,2,1] => [8,7,6,2,2,2,1]
[7,6,5,3,2,2,2,1] => [8,7,4,3,3,2,1]
[8,6,6,3,3,1,1] => [7,5,5,3,3,3,1,1]
[8,7,5,3,3,1,1] => [7,5,5,3,3,2,2,1]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [14,14]
[15,14] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]
[7,6,5,4,3,2,1,1] => [8,6,5,4,3,2,1]
[7,6,5,4,2,2,2,1] => [8,7,4,4,3,2,1]
[8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1]
[8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1]
[10,8,6,4,1] => [5,4,4,4,3,3,2,2,1,1]
[8,7,6,5,2,1] => [6,5,4,4,4,3,2,1]
[7,7,5,5,3,1,1] => [7,5,5,4,4,2,2]
[7,7,5,3,3,3,1] => [7,6,6,3,3,2,2]
[6,6,6,6,6] => [5,5,5,5,5,5]
[30] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[15,15] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
[5,5,5,5,5,5] => [6,6,6,6,6]
[6,6,6,6,3,3] => [6,6,6,4,4,4]
[10,10,10] => [3,3,3,3,3,3,3,3,3,3]
[9,7,5,5,3,1] => [6,5,5,4,4,2,2,1,1]
[7,6,5,4,3,2,2,1] => [8,7,5,4,3,2,1]
[7,6,5,3,3,3,2,1] => [8,7,6,3,3,2,1]
[8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1]
[8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1]
[11,8,6,4,1] => [5,4,4,4,3,3,2,2,1,1,1]
[10,8,6,4,2] => [5,5,4,4,3,3,2,2,1,1]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15]
[9,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1,1]
[7,6,5,4,3,2,1,1,1] => [9,6,5,4,3,2,1]
[8,6,6,4,4,1,1] => [7,5,5,5,3,3,1,1]
[7,7,5,5,3,1,1,1] => [8,5,5,4,4,2,2]
[28,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[7,6,5,5,4,2,1] => [7,6,5,5,4,2,1]
[7,7,5,5,3,3] => [6,6,6,4,4,2,2]
[5,5,4,4,3,3,2,2,1,1] => [10,8,6,4,2]
[5,5,5,5,4,3,2,1] => [8,7,6,5,4]
[6,6,6,4,4,2,2] => [7,7,5,5,3,3]
[5,5,5,4,3,3,2,1,1,1] => [10,7,6,4,3]
[7,6,6,6,6] => [5,5,5,5,5,5,1]
[7,6,5,4,3,3,2,1] => [8,7,6,4,3,2,1]
[7,6,4,4,4,3,2,1] => [8,7,6,5,2,2,1]
[8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1]
[8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1]
[11,8,6,5,1] => [5,4,4,4,4,3,2,2,1,1,1]
[8,7,6,5,4,1] => [6,5,5,5,4,3,2,1]
[7,7,5,5,3,3,1] => [7,6,6,4,4,2,2]
[7,7,5,5,2,2,2,1] => [8,7,4,4,4,2,2]
[8,7,4,4,4,2,2] => [7,7,5,5,2,2,2,1]
[8,5,5,5,3,3,1,1] => [8,6,6,4,4,1,1,1]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [16,16]
[7,6,5,4,4,3,2,1] => [8,7,6,5,3,2,1]
[7,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1]
[8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1]
[8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1]
[7,6,5,5,4,2,2,1] => [8,7,5,5,4,2,1]
[6,4,4,4,4,2,2,2,2,2] => [10,10,5,5,1,1]
[7,6,6,5,4,3,1] => [7,6,6,5,4,3,1]
[8,6,6,4,4,2,2] => [7,7,5,5,3,3,1,1]
[7,7,5,5,3,3,1,1] => [8,6,6,4,4,2,2]
[7,7,4,4,4,3,2,1] => [8,7,6,5,2,2,2]
[8,7,6,5,2,2,2] => [7,7,4,4,4,3,2,1]
[8,7,6,3,3,3,1,1] => [8,6,6,3,3,3,2,1]
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [16,16,1]
[5,4,4,4,4,4,4,4] => [8,8,8,8,1]
[7,6,5,5,4,3,2,1] => [8,7,6,5,4,2,1]
[6,6,6,5,4,3,2,1] => [8,7,6,5,4,3]
[8,7,6,5,4,2,1] => [7,6,5,5,4,3,2,1]
[8,7,6,5,4,3] => [6,6,6,5,4,3,2,1]
[7,6,6,5,4,3,1,1] => [8,6,6,5,4,3,1]
[7,6,6,5,4,3,2] => [7,7,6,5,4,3,1]
[7,7,6,5,4,3,1] => [7,6,6,5,4,3,2]
[8,7,6,5,4,1,1,1] => [8,5,5,5,4,3,2,1]
[7,7,5,5,3,3,2,1] => [8,7,6,4,4,2,2]
[8,7,6,5,2,2,2,1] => [8,7,4,4,4,3,2,1]
[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]
[8,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1,1]
[8,7,6,4,4,2,2] => [7,7,5,5,3,3,2,1]
[8,7,5,5,3,3,1,1] => [8,6,6,4,4,2,2,1]
[4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [16,16,1,1]
[7,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1]
[8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1]
[12,9,7,5,1] => [5,4,4,4,4,3,3,2,2,1,1,1]
[7,7,6,5,4,3,2] => [7,7,6,5,4,3,2]
[7,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2]
[8,7,6,5,3,3,1,1] => [8,6,6,4,4,3,2,1]
[8,8,5,5,3,3,1,1] => [8,6,6,4,4,2,2,2]
[9,7,5,5,3,3,1,1] => [8,6,6,4,4,2,2,1,1]
[8,6,6,5,4,3,2] => [7,7,6,5,4,3,1,1]
[7,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2]
[8,7,6,5,4,2,2] => [7,7,5,5,4,3,2,1]
[7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15,1,1,1,1,1]
[7,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2]
[8,7,6,5,4,3,2] => [7,7,6,5,4,3,2,1]
[13,9,7,5,1] => [5,4,4,4,4,3,3,2,2,1,1,1,1]
[8,7,6,5,3,3,2,1] => [8,7,6,4,4,3,2,1]
[8,7,6,5,4,2,2,1] => [8,7,5,5,4,3,2,1]
[8,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2,1]
[8,7,6,4,4,3,2,1] => [8,7,6,5,3,3,2,1]
[8,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2,1]
[8,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1,1]
[18,18] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
[24,12] => [2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1]
[36] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[11,9,7,5,3,1] => [6,5,5,4,4,3,3,2,2,1,1]
[11,8,7,5,4,1] => [6,5,5,5,4,3,3,2,1,1,1]
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[8,8,6,6,3,3,1,1] => [8,6,6,4,4,4,2,2]
[9,7,7,5,3,3,1,1] => [8,6,6,4,4,3,3,1,1]
[34,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[33,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[4,4,4,4,4,4,4,4,4] => [9,9,9,9]
[7,6,2,2,2,2,2,2,2,2,2,2,2,2] => [14,14,2,2,2,2,1]
[7,6,6,6,6,6] => [6,6,6,6,6,6,1]
[8,7,6,5,4,3,2,1,1] => [9,7,6,5,4,3,2,1]
[9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,1]
[8,7,6,5,4,3,2,2,1] => [9,8,6,5,4,3,2,1]
[8,8,6,6,4,4,1,1] => [8,6,6,6,4,4,2,2]
[9,7,7,5,5,3,1,1] => [8,6,6,5,5,3,3,1,1]
[8,7,6,5,4,3,3,2,1] => [9,8,7,5,4,3,2,1]
[10,10,10,10] => [4,4,4,4,4,4,4,4,4,4]
[12,12,12,4] => [4,4,4,4,3,3,3,3,3,3,3,3]
[8,7,6,5,4,4,3,2,1] => [9,8,7,6,4,3,2,1]
[11,9,7,5,5,3] => [6,6,6,5,5,3,3,2,2,1,1]
[8,8,6,6,4,4,2,2] => [8,8,6,6,4,4,2,2]
[9,7,7,5,5,3,3,1] => [8,7,7,5,5,3,3,1,1]
[7,6,6,6,2,2,2,2,2,2,2,2] => [12,12,4,4,4,4,1]
[8,7,6,5,5,4,3,2,1] => [9,8,7,6,5,3,2,1]
[9,7,7,5,5,3,3,1,1] => [9,7,7,5,5,3,3,1,1]
[8,8,6,6,4,4,2,2,1] => [9,8,6,6,4,4,2,2]
[9,8,6,6,4,4,2,2] => [8,8,6,6,4,4,2,2,1]
[8,7,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,1]
[8,7,7,6,5,4,3,2] => [8,8,7,6,5,4,3,1]
[10,10,10,5,5,2] => [6,6,5,5,5,3,3,3,3,3]
[9,8,7,6,5,4,3] => [7,7,7,6,5,4,3,2,1]
[8,8,6,6,4,4,3,2,1] => [9,8,7,6,4,4,2,2]
[9,8,7,6,4,4,2,2] => [8,8,6,6,4,4,3,2,1]
[9,8,7,5,5,3,3,1,1] => [9,7,7,5,5,3,3,2,1]
[8,7,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1]
[8,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2]
[8,8,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,2]
[9,8,7,6,5,4,2,2] => [8,8,6,6,5,4,3,2,1]
[9,8,7,6,5,3,3,1,1] => [9,7,7,5,5,4,3,2,1]
[8,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2]
[9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1]
[9,8,7,5,5,4,3,2,1] => [9,8,7,6,5,3,3,2,1]
[9,8,7,6,5,4,3,1,1] => [9,7,7,6,5,4,3,2,1]
[9,8,7,6,5,4,2,2,1] => [9,8,6,6,5,4,3,2,1]
[9,8,7,6,5,3,3,2,1] => [9,8,7,5,5,4,3,2,1]
[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]
[9,7,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,1]
[18,18,9] => [3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2]
[9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1]
[11,9,7,7,5,3,3] => [7,7,7,5,5,4,4,2,2,1,1]
[12,12,12,12] => [4,4,4,4,4,4,4,4,4,4,4,4]
[48] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[7,6,6,6,6,6,6,6] => [8,8,8,8,8,8,1]
[6,6,6,6,6,6,6,3,3,2] => [10,10,9,7,7,7]
[9,8,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1]
[9,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2]
[10,9,8,7,6,5,4,3,2] => [9,9,8,7,6,5,4,3,2,1]
[5,5,5,5,5,5,5,5,5,5,5] => [11,11,11,11,11]
[6,6,6,6,6,6,6,6,6,6] => [10,10,10,10,10,10]
[5,5,5,5,5,5,5,5,5,5,5,5] => [12,12,12,12,12]
[7,5,5,5,5,5,3,3,3,3,3,3,3,3,3,1,1,1,1,1] => [20,15,15,6,6,1,1]
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [32,32,1]
[8,8,8,8,8,8,8,8,4,2] => [10,10,9,9,8,8,8,8]
[24,24,24] => [3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]
[12,12,12,12,12,12,4,4] => [8,8,8,8,6,6,6,6,6,6,6,6]
[18,18,18,18,18] => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
[18,18,18,18,9,9] => [6,6,6,6,6,6,6,6,6,4,4,4,4,4,4,4,4,4]
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => [16,16,16,14,14,14]
[24,24,24,24] => [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4]
[12,12,12,12,12,12,12,12,4,3,2] => [11,11,10,9,8,8,8,8,8,8,8,8]
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => [23,23,23,23,23]
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => [24,24,24,24,24]
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => [20,20,20,20,20,20]
[12,12,12,12,12,12,12,12,12,12] => [10,10,10,10,10,10,10,10,10,10,10,10]
[12,12,12,12,12,12,12,12,12,6,6,6,4,2] => [14,14,13,13,12,12,9,9,9,9,9,9]
[24,24,24,24,24,24] => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
[18,18,18,18,18,18,18,18,18,18] => [10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10]
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => [30,30,30,30,30,30]
[16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2] => [17,17,16,16,15,15,15,15,7,7,7,7,7,7,7,7]
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => [20,20,20,20,20,20,20,20,20,20,20,20]
[10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2] => [26,26,25,25,25,25,25,25,25,25]
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => [60,60,60,60,60,60]
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2] => [34,34,33,33,33,33,33,28,28,28,28,28,28,28]
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => [120,120,120,120,120,120]
Identities
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Inverses
Mp00044conjugate ∘ Mp00044conjugate = id : Integer partitions ⟶ Integer partitions
Intertwining relations
Mp00060Robinson-Schensted tableau shape ∘ Mp00064reverse = Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape : Permutations ⟶ Integer partitions
Mp00060Robinson-Schensted tableau shape ∘ Mp00069complement = Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape : Permutations ⟶ Integer partitions
Mp00043to Dyck path ∘ Mp00044conjugate = Mp00028reverse ∘ Mp00043to Dyck path : Integer partitions ⟶ Dyck paths
Mp00187conjugate ∘ Mp00179to skew partition = Mp00179to skew partition ∘ Mp00044conjugate : Integer partitions ⟶ Skew partitions
Mp00027to partition ∘ Mp00028reverse = Mp00044conjugate ∘ Mp00027to partition : Dyck paths ⟶ Integer partitions
Mp00083shape ∘ Mp00084conjugate = Mp00044conjugate ∘ Mp00083shape : Standard tableaux ⟶ Integer partitions
Mp00183inner shape ∘ Mp00187conjugate = Mp00044conjugate ∘ Mp00183inner shape : Skew partitions ⟶ Integer partitions
Mp00182outer shape ∘ Mp00187conjugate = Mp00044conjugate ∘ Mp00182outer shape : Skew partitions ⟶ Integer partitions
Mp00105complement ∘ Mp00104reverse ∘ Mp00095to binary word = Mp00095to binary word ∘ Mp00044conjugate : Integer partitions ⟶ Binary words
Mp00044conjugate ∘ Mp00182outer shape ∘ Mp00189rotate = Mp00182outer shape ∘ Mp00189rotate ∘ Mp00187conjugate : Skew partitions ⟶ Integer partitions
Mp00044conjugate ∘ Mp00183inner shape ∘ Mp00189rotate = Mp00183inner shape ∘ Mp00189rotate ∘ Mp00187conjugate : Skew partitions ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00175inverse Foata bijection = Mp00060Robinson-Schensted tableau shape ∘ Mp00175inverse Foata bijection ∘ Mp00069complement : Permutations ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00089Inverse Kreweras complement = Mp00060Robinson-Schensted tableau shape ∘ Mp00089Inverse Kreweras complement ∘ Mp00064reverse : Permutations ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00088Kreweras complement = Mp00060Robinson-Schensted tableau shape ∘ Mp00088Kreweras complement ∘ Mp00069complement : Permutations ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00123Barnabei-Castronuovo involution = Mp00027to partition ∘ Mp00123Barnabei-Castronuovo involution ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00227Delest-Viennot-inverse = Mp00027to partition ∘ Mp00227Delest-Viennot-inverse ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00222peaks-to-valleys = Mp00027to partition ∘ Mp00222peaks-to-valleys ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00120Lalanne-Kreweras involution = Mp00027to partition ∘ Mp00120Lalanne-Kreweras involution ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00229Delest-Viennot = Mp00027to partition ∘ Mp00229Delest-Viennot ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00228reflect parallelogram polyomino ∘ Mp00028reverse ∘ Mp00230parallelogram polyomino = Mp00230parallelogram polyomino ∘ Mp00044conjugate : Integer partitions ⟶ Dyck paths
Mp00041conjugate ∘ Mp00178to composition ∘ Mp00095to binary word = Mp00178to composition ∘ Mp00095to binary word ∘ Mp00044conjugate : Integer partitions ⟶ Integer compositions
Mp00038reverse ∘ Mp00097delta morphism ∘ Mp00095to binary word = Mp00097delta morphism ∘ Mp00095to binary word ∘ Mp00044conjugate : Integer partitions ⟶ Integer compositions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00228reflect parallelogram polyomino = Mp00027to partition ∘ Mp00228reflect parallelogram polyomino ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00182outer shape ∘ Mp00180to ribbon = Mp00182outer shape ∘ Mp00180to ribbon ∘ Mp00041conjugate : Integer compositions ⟶ Integer partitions
Mp00044conjugate ∘ Mp00183inner shape ∘ Mp00180to ribbon = Mp00183inner shape ∘ Mp00180to ribbon ∘ Mp00041conjugate : Integer compositions ⟶ Integer partitions
Mp00204LLPS ∘ Mp00014to 132-avoiding permutation ∘ Mp00016left-right symmetry = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00014to 132-avoiding permutation : Binary trees ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00150to Dyck path = Mp00027to partition ∘ Mp00150to Dyck path ∘ Mp00113reverse : Perfect matchings ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00051to Dyck path = Mp00027to partition ∘ Mp00051to Dyck path ∘ Mp00048left-right symmetry : Ordered trees ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00163permutation = Mp00060Robinson-Schensted tableau shape ∘ Mp00163permutation ∘ Mp00161reverse : Signed permutations ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00310toric promotion = Mp00060Robinson-Schensted tableau shape ∘ Mp00310toric promotion ∘ Mp00064reverse : Permutations ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00252restriction = Mp00060Robinson-Schensted tableau shape ∘ Mp00252restriction ∘ Mp00064reverse : Permutations ⟶ Integer partitions
Mp00204LLPS ∘ Mp00025to 132-avoiding permutation ∘ Mp00030zeta map = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00025to 132-avoiding permutation : Dyck paths ⟶ Integer partitions
Mp00204LLPS ∘ Mp00025to 132-avoiding permutation ∘ Mp00101decomposition reverse = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00025to 132-avoiding permutation : Dyck paths ⟶ Integer partitions
Mp00204LLPS ∘ Mp00025to 132-avoiding permutation ∘ Mp00120Lalanne-Kreweras involution = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00025to 132-avoiding permutation : Dyck paths ⟶ Integer partitions
Mp00204LLPS ∘ Mp00025to 132-avoiding permutation ∘ Mp00032inverse zeta map = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00025to 132-avoiding permutation : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00231bounce path = Mp00027to partition ∘ Mp00231bounce path ∘ Mp00038reverse : Integer compositions ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00309inverse toric promotion = Mp00060Robinson-Schensted tableau shape ∘ Mp00309inverse toric promotion ∘ Mp00064reverse : Permutations ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00329Tanimoto = Mp00060Robinson-Schensted tableau shape ∘ Mp00329Tanimoto ∘ Mp00064reverse : Permutations ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00103peeling map = Mp00027to partition ∘ Mp00103peeling map ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00245standardize = Mp00060Robinson-Schensted tableau shape ∘ Mp00245standardize ∘ Mp00161reverse : Signed permutations ⟶ Integer partitions
Mp00204LLPS ∘ Mp00025to 132-avoiding permutation ∘ Mp00327inverse Kreweras complement = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00025to 132-avoiding permutation : Dyck paths ⟶ Integer partitions
Absorbing relations
Mp00185cell poset ∘ Mp00179to skew partition ∘ Mp00044conjugate = Mp00185cell poset ∘ Mp00179to skew partition : Integer partitions ⟶ Posets
Mp00262poset of factors ∘ Mp00095to binary word ∘ Mp00044conjugate = Mp00262poset of factors ∘ Mp00095to binary word : Integer partitions ⟶ Posets
Other relations
Mp00104reverse ∘ Mp00095to binary word ∘ Mp00044conjugate = Mp00105complement ∘ Mp00095to binary word : Integer partitions ⟶ Binary words
Mp00105complement ∘ Mp00095to binary word ∘ Mp00044conjugate = Mp00104reverse ∘ Mp00095to binary word : Integer partitions ⟶ Binary words
Mp00228reflect parallelogram polyomino ∘ Mp00230parallelogram polyomino = Mp00028reverse ∘ Mp00230parallelogram polyomino ∘ Mp00044conjugate : Integer partitions ⟶ Dyck paths
Mp00226row-to-column-descents ∘ Mp00042initial tableau = Mp00084conjugate ∘ Mp00042initial tableau ∘ Mp00044conjugate : Integer partitions ⟶ Standard tableaux
Mp00233skew partition ∘ Mp00230parallelogram polyomino = Mp00179to skew partition ∘ Mp00044conjugate : Integer partitions ⟶ Skew partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00142promotion = Mp00027to partition ∘ Mp00143inverse promotion ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00143inverse promotion = Mp00027to partition ∘ Mp00142promotion ∘ Mp00028reverse : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00023to non-crossing permutation = Mp00204LLPS ∘ Mp00023to non-crossing permutation : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00023to non-crossing permutation = Mp00060Robinson-Schensted tableau shape ∘ Mp00023to non-crossing permutation : Dyck paths ⟶ Integer partitions
Mp00186dominating partition ∘ Mp00180to ribbon = Mp00044conjugate ∘ Mp00040to partition ∘ Mp00039complement : Integer compositions ⟶ Integer partitions
Mp00070Robinson-Schensted recording tableau ∘ Mp00081reading word permutation ∘ Mp00084conjugate = Mp00045reading tableau ∘ Mp00044conjugate ∘ Mp00083shape : Standard tableaux ⟶ Standard tableaux
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00020to Tamari-corresponding Dyck path = Mp00027to partition ∘ Mp00012to Dyck path: up step, left tree, down step, right tree ∘ Mp00016left-right symmetry : Binary trees ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00017to 312-avoiding permutation = Mp00204LLPS ∘ Mp00017to 312-avoiding permutation : Binary trees ⟶ Integer partitions
Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00017to 312-avoiding permutation = Mp00060Robinson-Schensted tableau shape ∘ Mp00017to 312-avoiding permutation : Binary trees ⟶ Integer partitions
Mp00204LLPS ∘ Mp00064reverse ∘ Mp00017to 312-avoiding permutation = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00014to 132-avoiding permutation : Binary trees ⟶ Integer partitions
Mp00044conjugate ∘ Mp00186dominating partition ∘ Mp00187conjugate = Mp00040to partition ∘ Mp00181row lengths : Skew partitions ⟶ Integer partitions
Mp00044conjugate ∘ Mp00040to partition ∘ Mp00181row lengths = Mp00186dominating partition ∘ Mp00187conjugate : Skew partitions ⟶ Integer partitions
Mp00040to partition ∘ Mp00181row lengths ∘ Mp00187conjugate = Mp00044conjugate ∘ Mp00186dominating partition : Skew partitions ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00241invert Laguerre heap = Mp00060Robinson-Schensted tableau shape ∘ Mp00326weak order rowmotion : Permutations ⟶ Integer partitions
Mp00233skew partition ∘ Mp00028reverse ∘ Mp00230parallelogram polyomino = Mp00189rotate ∘ Mp00179to skew partition ∘ Mp00044conjugate : Integer partitions ⟶ Skew partitions
Mp00204LLPS ∘ Mp00014to 132-avoiding permutation ∘ Mp00029to binary tree: left tree, up step, right tree, down step = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00025to 132-avoiding permutation : Dyck paths ⟶ Integer partitions
Mp00060Robinson-Schensted tableau shape ∘ Mp00002to left key permutation ∘ Mp00035to alternating sign matrix = Mp00044conjugate ∘ Mp00204LLPS ∘ Mp00119to 321-avoiding permutation (Krattenthaler) : Dyck paths ⟶ Integer partitions
Mp00060Robinson-Schensted tableau shape ∘ Mp00002to left key permutation ∘ Mp00137to symmetric ASM = Mp00044conjugate ∘ Mp00079shape ∘ Mp00138to noncrossing partition : Dyck paths ⟶ Integer partitions
Mp00044conjugate ∘ Mp00027to partition ∘ Mp00012to Dyck path: up step, left tree, down step, right tree ∘ Mp00016left-right symmetry = Mp00027to partition ∘ Mp00020to Tamari-corresponding Dyck path : Binary trees ⟶ Integer partitions
Mp00060Robinson-Schensted tableau shape ∘ Mp00023to non-crossing permutation ∘ Mp00012to Dyck path: up step, left tree, down step, right tree = Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00014to 132-avoiding permutation : Binary trees ⟶ Integer partitions
Mp00044conjugate ∘ Mp00060Robinson-Schensted tableau shape ∘ Mp00326weak order rowmotion = Mp00060Robinson-Schensted tableau shape ∘ Mp00241invert Laguerre heap : Permutations ⟶ Integer partitions
Mp00232parallelogram poset ∘ Mp00028reverse ∘ Mp00230parallelogram polyomino = Mp00232parallelogram poset ∘ Mp00230parallelogram polyomino ∘ Mp00044conjugate : Integer partitions ⟶ Posets
Mp00204LLPS ∘ Mp00175inverse Foata bijection ∘ Mp00081reading word permutation ∘ Mp00042initial tableau = Mp00044conjugate : Integer partitions ⟶ Integer partitions
Mp00060Robinson-Schensted tableau shape ∘ Mp00023to non-crossing permutation ∘ Mp00231bounce path = Mp00044conjugate ∘ Mp00040to partition : Integer compositions ⟶ Integer partitions
Mp00322Loehr-Warrington ∘ Mp00037to partition of connected components ∘ Mp00154core = Mp00044conjugate ∘ Mp00037to partition of connected components ∘ Mp00154core : Graphs ⟶ Integer partitions
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.
Properties
bijective, graded, involutive
Sage code
def mapping(elt):
return elt.conjugate()
Weight
11
Created
Jan 19, 2020 at 07:27 by FindStatCrew
Updated
Jan 19, 2020 at 07:27 by Martin Rubey
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