Identifier
Mp00044:
Integer partitions
—conjugate⟶
Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Images
[1] => [1] => [[1],[]]
[2] => [1,1] => [[1,1],[]]
[1,1] => [2] => [[2],[]]
[3] => [1,1,1] => [[1,1,1],[]]
[2,1] => [2,1] => [[2,1],[]]
[1,1,1] => [3] => [[3],[]]
[4] => [1,1,1,1] => [[1,1,1,1],[]]
[3,1] => [2,1,1] => [[2,1,1],[]]
[2,2] => [2,2] => [[2,2],[]]
[2,1,1] => [3,1] => [[3,1],[]]
[1,1,1,1] => [4] => [[4],[]]
[5] => [1,1,1,1,1] => [[1,1,1,1,1],[]]
[4,1] => [2,1,1,1] => [[2,1,1,1],[]]
[3,2] => [2,2,1] => [[2,2,1],[]]
[3,1,1] => [3,1,1] => [[3,1,1],[]]
[2,2,1] => [3,2] => [[3,2],[]]
[2,1,1,1] => [4,1] => [[4,1],[]]
[1,1,1,1,1] => [5] => [[5],[]]
[6] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]]
[5,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]]
[4,2] => [2,2,1,1] => [[2,2,1,1],[]]
[4,1,1] => [3,1,1,1] => [[3,1,1,1],[]]
[3,3] => [2,2,2] => [[2,2,2],[]]
[3,2,1] => [3,2,1] => [[3,2,1],[]]
[3,1,1,1] => [4,1,1] => [[4,1,1],[]]
[2,2,2] => [3,3] => [[3,3],[]]
[2,2,1,1] => [4,2] => [[4,2],[]]
[2,1,1,1,1] => [5,1] => [[5,1],[]]
[1,1,1,1,1,1] => [6] => [[6],[]]
[7] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]]
[6,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]]
[5,2] => [2,2,1,1,1] => [[2,2,1,1,1],[]]
[5,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]]
[4,3] => [2,2,2,1] => [[2,2,2,1],[]]
[4,2,1] => [3,2,1,1] => [[3,2,1,1],[]]
[4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]]
[3,3,1] => [3,2,2] => [[3,2,2],[]]
[3,2,2] => [3,3,1] => [[3,3,1],[]]
[3,2,1,1] => [4,2,1] => [[4,2,1],[]]
[3,1,1,1,1] => [5,1,1] => [[5,1,1],[]]
[2,2,2,1] => [4,3] => [[4,3],[]]
[2,2,1,1,1] => [5,2] => [[5,2],[]]
[2,1,1,1,1,1] => [6,1] => [[6,1],[]]
[1,1,1,1,1,1,1] => [7] => [[7],[]]
[8] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]]
[7,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]]
[6,2] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]]
[6,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]]
[5,3] => [2,2,2,1,1] => [[2,2,2,1,1],[]]
[5,2,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]]
[5,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]]
[4,4] => [2,2,2,2] => [[2,2,2,2],[]]
[4,3,1] => [3,2,2,1] => [[3,2,2,1],[]]
[4,2,2] => [3,3,1,1] => [[3,3,1,1],[]]
[4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]]
[4,1,1,1,1] => [5,1,1,1] => [[5,1,1,1],[]]
[3,3,2] => [3,3,2] => [[3,3,2],[]]
[3,3,1,1] => [4,2,2] => [[4,2,2],[]]
[3,2,2,1] => [4,3,1] => [[4,3,1],[]]
[3,2,1,1,1] => [5,2,1] => [[5,2,1],[]]
[3,1,1,1,1,1] => [6,1,1] => [[6,1,1],[]]
[2,2,2,2] => [4,4] => [[4,4],[]]
[2,2,2,1,1] => [5,3] => [[5,3],[]]
[2,2,1,1,1,1] => [6,2] => [[6,2],[]]
[2,1,1,1,1,1,1] => [7,1] => [[7,1],[]]
[1,1,1,1,1,1,1,1] => [8] => [[8],[]]
[9] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]]
[8,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]]
[7,2] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]]
[7,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]]
[6,3] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]]
[6,2,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]]
[6,1,1,1] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]]
[5,4] => [2,2,2,2,1] => [[2,2,2,2,1],[]]
[5,3,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]]
[5,2,2] => [3,3,1,1,1] => [[3,3,1,1,1],[]]
[5,2,1,1] => [4,2,1,1,1] => [[4,2,1,1,1],[]]
[5,1,1,1,1] => [5,1,1,1,1] => [[5,1,1,1,1],[]]
[4,4,1] => [3,2,2,2] => [[3,2,2,2],[]]
[4,3,2] => [3,3,2,1] => [[3,3,2,1],[]]
[4,3,1,1] => [4,2,2,1] => [[4,2,2,1],[]]
[4,2,2,1] => [4,3,1,1] => [[4,3,1,1],[]]
[4,2,1,1,1] => [5,2,1,1] => [[5,2,1,1],[]]
[4,1,1,1,1,1] => [6,1,1,1] => [[6,1,1,1],[]]
[3,3,3] => [3,3,3] => [[3,3,3],[]]
[3,3,2,1] => [4,3,2] => [[4,3,2],[]]
[3,3,1,1,1] => [5,2,2] => [[5,2,2],[]]
[3,2,2,2] => [4,4,1] => [[4,4,1],[]]
[3,2,2,1,1] => [5,3,1] => [[5,3,1],[]]
[3,2,1,1,1,1] => [6,2,1] => [[6,2,1],[]]
[3,1,1,1,1,1,1] => [7,1,1] => [[7,1,1],[]]
[2,2,2,2,1] => [5,4] => [[5,4],[]]
[2,2,2,1,1,1] => [6,3] => [[6,3],[]]
[2,2,1,1,1,1,1] => [7,2] => [[7,2],[]]
[2,1,1,1,1,1,1,1] => [8,1] => [[8,1],[]]
[1,1,1,1,1,1,1,1,1] => [9] => [[9],[]]
[10] => [1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1],[]]
[9,1] => [2,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1],[]]
[8,2] => [2,2,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1],[]]
[8,1,1] => [3,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1],[]]
[7,3] => [2,2,2,1,1,1,1] => [[2,2,2,1,1,1,1],[]]
>>> Load all 1438 entries. <<<
[7,2,1] => [3,2,1,1,1,1,1] => [[3,2,1,1,1,1,1],[]]
[7,1,1,1] => [4,1,1,1,1,1,1] => [[4,1,1,1,1,1,1],[]]
[6,4] => [2,2,2,2,1,1] => [[2,2,2,2,1,1],[]]
[6,3,1] => [3,2,2,1,1,1] => [[3,2,2,1,1,1],[]]
[6,2,2] => [3,3,1,1,1,1] => [[3,3,1,1,1,1],[]]
[6,2,1,1] => [4,2,1,1,1,1] => [[4,2,1,1,1,1],[]]
[6,1,1,1,1] => [5,1,1,1,1,1] => [[5,1,1,1,1,1],[]]
[5,5] => [2,2,2,2,2] => [[2,2,2,2,2],[]]
[5,4,1] => [3,2,2,2,1] => [[3,2,2,2,1],[]]
[5,3,2] => [3,3,2,1,1] => [[3,3,2,1,1],[]]
[5,3,1,1] => [4,2,2,1,1] => [[4,2,2,1,1],[]]
[5,2,2,1] => [4,3,1,1,1] => [[4,3,1,1,1],[]]
[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] => [[6,1,1,1,1],[]]
[4,4,2] => [3,3,2,2] => [[3,3,2,2],[]]
[4,4,1,1] => [4,2,2,2] => [[4,2,2,2],[]]
[4,3,3] => [3,3,3,1] => [[3,3,3,1],[]]
[4,3,2,1] => [4,3,2,1] => [[4,3,2,1],[]]
[4,3,1,1,1] => [5,2,2,1] => [[5,2,2,1],[]]
[4,2,2,2] => [4,4,1,1] => [[4,4,1,1],[]]
[4,2,2,1,1] => [5,3,1,1] => [[5,3,1,1],[]]
[4,2,1,1,1,1] => [6,2,1,1] => [[6,2,1,1],[]]
[4,1,1,1,1,1,1] => [7,1,1,1] => [[7,1,1,1],[]]
[3,3,3,1] => [4,3,3] => [[4,3,3],[]]
[3,3,2,2] => [4,4,2] => [[4,4,2],[]]
[3,3,2,1,1] => [5,3,2] => [[5,3,2],[]]
[3,3,1,1,1,1] => [6,2,2] => [[6,2,2],[]]
[3,2,2,2,1] => [5,4,1] => [[5,4,1],[]]
[3,2,2,1,1,1] => [6,3,1] => [[6,3,1],[]]
[3,2,1,1,1,1,1] => [7,2,1] => [[7,2,1],[]]
[3,1,1,1,1,1,1,1] => [8,1,1] => [[8,1,1],[]]
[2,2,2,2,2] => [5,5] => [[5,5],[]]
[2,2,2,2,1,1] => [6,4] => [[6,4],[]]
[2,2,2,1,1,1,1] => [7,3] => [[7,3],[]]
[2,2,1,1,1,1,1,1] => [8,2] => [[8,2],[]]
[2,1,1,1,1,1,1,1,1] => [9,1] => [[9,1],[]]
[1,1,1,1,1,1,1,1,1,1] => [10] => [[10],[]]
[11] => [1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1],[]]
[10,1] => [2,1,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1,1],[]]
[9,2] => [2,2,1,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1,1],[]]
[9,1,1] => [3,1,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1,1],[]]
[8,3] => [2,2,2,1,1,1,1,1] => [[2,2,2,1,1,1,1,1],[]]
[8,2,1] => [3,2,1,1,1,1,1,1] => [[3,2,1,1,1,1,1,1],[]]
[8,1,1,1] => [4,1,1,1,1,1,1,1] => [[4,1,1,1,1,1,1,1],[]]
[7,4] => [2,2,2,2,1,1,1] => [[2,2,2,2,1,1,1],[]]
[7,3,1] => [3,2,2,1,1,1,1] => [[3,2,2,1,1,1,1],[]]
[7,2,2] => [3,3,1,1,1,1,1] => [[3,3,1,1,1,1,1],[]]
[7,2,1,1] => [4,2,1,1,1,1,1] => [[4,2,1,1,1,1,1],[]]
[7,1,1,1,1] => [5,1,1,1,1,1,1] => [[5,1,1,1,1,1,1],[]]
[6,5] => [2,2,2,2,2,1] => [[2,2,2,2,2,1],[]]
[6,4,1] => [3,2,2,2,1,1] => [[3,2,2,2,1,1],[]]
[6,3,2] => [3,3,2,1,1,1] => [[3,3,2,1,1,1],[]]
[6,3,1,1] => [4,2,2,1,1,1] => [[4,2,2,1,1,1],[]]
[6,2,2,1] => [4,3,1,1,1,1] => [[4,3,1,1,1,1],[]]
[6,2,1,1,1] => [5,2,1,1,1,1] => [[5,2,1,1,1,1],[]]
[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] => [[3,2,2,2,2],[]]
[5,4,2] => [3,3,2,2,1] => [[3,3,2,2,1],[]]
[5,4,1,1] => [4,2,2,2,1] => [[4,2,2,2,1],[]]
[5,3,3] => [3,3,3,1,1] => [[3,3,3,1,1],[]]
[5,3,2,1] => [4,3,2,1,1] => [[4,3,2,1,1],[]]
[5,3,1,1,1] => [5,2,2,1,1] => [[5,2,2,1,1],[]]
[5,2,2,2] => [4,4,1,1,1] => [[4,4,1,1,1],[]]
[5,2,2,1,1] => [5,3,1,1,1] => [[5,3,1,1,1],[]]
[5,2,1,1,1,1] => [6,2,1,1,1] => [[6,2,1,1,1],[]]
[5,1,1,1,1,1,1] => [7,1,1,1,1] => [[7,1,1,1,1],[]]
[4,4,3] => [3,3,3,2] => [[3,3,3,2],[]]
[4,4,2,1] => [4,3,2,2] => [[4,3,2,2],[]]
[4,4,1,1,1] => [5,2,2,2] => [[5,2,2,2],[]]
[4,3,3,1] => [4,3,3,1] => [[4,3,3,1],[]]
[4,3,2,2] => [4,4,2,1] => [[4,4,2,1],[]]
[4,3,2,1,1] => [5,3,2,1] => [[5,3,2,1],[]]
[4,3,1,1,1,1] => [6,2,2,1] => [[6,2,2,1],[]]
[4,2,2,2,1] => [5,4,1,1] => [[5,4,1,1],[]]
[4,2,2,1,1,1] => [6,3,1,1] => [[6,3,1,1],[]]
[4,2,1,1,1,1,1] => [7,2,1,1] => [[7,2,1,1],[]]
[4,1,1,1,1,1,1,1] => [8,1,1,1] => [[8,1,1,1],[]]
[3,3,3,2] => [4,4,3] => [[4,4,3],[]]
[3,3,3,1,1] => [5,3,3] => [[5,3,3],[]]
[3,3,2,2,1] => [5,4,2] => [[5,4,2],[]]
[3,3,2,1,1,1] => [6,3,2] => [[6,3,2],[]]
[3,3,1,1,1,1,1] => [7,2,2] => [[7,2,2],[]]
[3,2,2,2,2] => [5,5,1] => [[5,5,1],[]]
[3,2,2,2,1,1] => [6,4,1] => [[6,4,1],[]]
[3,2,2,1,1,1,1] => [7,3,1] => [[7,3,1],[]]
[3,2,1,1,1,1,1,1] => [8,2,1] => [[8,2,1],[]]
[3,1,1,1,1,1,1,1,1] => [9,1,1] => [[9,1,1],[]]
[2,2,2,2,2,1] => [6,5] => [[6,5],[]]
[2,2,2,2,1,1,1] => [7,4] => [[7,4],[]]
[2,2,2,1,1,1,1,1] => [8,3] => [[8,3],[]]
[2,2,1,1,1,1,1,1,1] => [9,2] => [[9,2],[]]
[2,1,1,1,1,1,1,1,1,1] => [10,1] => [[10,1],[]]
[1,1,1,1,1,1,1,1,1,1,1] => [11] => [[11],[]]
[12] => [1,1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1,1],[]]
[11,1] => [2,1,1,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1,1,1],[]]
[10,2] => [2,2,1,1,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1,1,1],[]]
[10,1,1] => [3,1,1,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1,1,1],[]]
[9,3] => [2,2,2,1,1,1,1,1,1] => [[2,2,2,1,1,1,1,1,1],[]]
[9,2,1] => [3,2,1,1,1,1,1,1,1] => [[3,2,1,1,1,1,1,1,1],[]]
[9,1,1,1] => [4,1,1,1,1,1,1,1,1] => [[4,1,1,1,1,1,1,1,1],[]]
[8,4] => [2,2,2,2,1,1,1,1] => [[2,2,2,2,1,1,1,1],[]]
[8,3,1] => [3,2,2,1,1,1,1,1] => [[3,2,2,1,1,1,1,1],[]]
[8,2,2] => [3,3,1,1,1,1,1,1] => [[3,3,1,1,1,1,1,1],[]]
[8,2,1,1] => [4,2,1,1,1,1,1,1] => [[4,2,1,1,1,1,1,1],[]]
[8,1,1,1,1] => [5,1,1,1,1,1,1,1] => [[5,1,1,1,1,1,1,1],[]]
[7,5] => [2,2,2,2,2,1,1] => [[2,2,2,2,2,1,1],[]]
[7,4,1] => [3,2,2,2,1,1,1] => [[3,2,2,2,1,1,1],[]]
[7,3,2] => [3,3,2,1,1,1,1] => [[3,3,2,1,1,1,1],[]]
[7,3,1,1] => [4,2,2,1,1,1,1] => [[4,2,2,1,1,1,1],[]]
[7,2,2,1] => [4,3,1,1,1,1,1] => [[4,3,1,1,1,1,1],[]]
[7,2,1,1,1] => [5,2,1,1,1,1,1] => [[5,2,1,1,1,1,1],[]]
[7,1,1,1,1,1] => [6,1,1,1,1,1,1] => [[6,1,1,1,1,1,1],[]]
[6,6] => [2,2,2,2,2,2] => [[2,2,2,2,2,2],[]]
[6,5,1] => [3,2,2,2,2,1] => [[3,2,2,2,2,1],[]]
[6,4,2] => [3,3,2,2,1,1] => [[3,3,2,2,1,1],[]]
[6,4,1,1] => [4,2,2,2,1,1] => [[4,2,2,2,1,1],[]]
[6,3,3] => [3,3,3,1,1,1] => [[3,3,3,1,1,1],[]]
[6,3,2,1] => [4,3,2,1,1,1] => [[4,3,2,1,1,1],[]]
[6,3,1,1,1] => [5,2,2,1,1,1] => [[5,2,2,1,1,1],[]]
[6,2,2,2] => [4,4,1,1,1,1] => [[4,4,1,1,1,1],[]]
[6,2,2,1,1] => [5,3,1,1,1,1] => [[5,3,1,1,1,1],[]]
[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] => [[7,1,1,1,1,1],[]]
[5,5,2] => [3,3,2,2,2] => [[3,3,2,2,2],[]]
[5,5,1,1] => [4,2,2,2,2] => [[4,2,2,2,2],[]]
[5,4,3] => [3,3,3,2,1] => [[3,3,3,2,1],[]]
[5,4,2,1] => [4,3,2,2,1] => [[4,3,2,2,1],[]]
[5,4,1,1,1] => [5,2,2,2,1] => [[5,2,2,2,1],[]]
[5,3,3,1] => [4,3,3,1,1] => [[4,3,3,1,1],[]]
[5,3,2,2] => [4,4,2,1,1] => [[4,4,2,1,1],[]]
[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] => [[6,2,2,1,1],[]]
[5,2,2,2,1] => [5,4,1,1,1] => [[5,4,1,1,1],[]]
[5,2,2,1,1,1] => [6,3,1,1,1] => [[6,3,1,1,1],[]]
[5,2,1,1,1,1,1] => [7,2,1,1,1] => [[7,2,1,1,1],[]]
[5,1,1,1,1,1,1,1] => [8,1,1,1,1] => [[8,1,1,1,1],[]]
[4,4,4] => [3,3,3,3] => [[3,3,3,3],[]]
[4,4,3,1] => [4,3,3,2] => [[4,3,3,2],[]]
[4,4,2,2] => [4,4,2,2] => [[4,4,2,2],[]]
[4,4,2,1,1] => [5,3,2,2] => [[5,3,2,2],[]]
[4,4,1,1,1,1] => [6,2,2,2] => [[6,2,2,2],[]]
[4,3,3,2] => [4,4,3,1] => [[4,4,3,1],[]]
[4,3,3,1,1] => [5,3,3,1] => [[5,3,3,1],[]]
[4,3,2,2,1] => [5,4,2,1] => [[5,4,2,1],[]]
[4,3,2,1,1,1] => [6,3,2,1] => [[6,3,2,1],[]]
[4,3,1,1,1,1,1] => [7,2,2,1] => [[7,2,2,1],[]]
[4,2,2,2,2] => [5,5,1,1] => [[5,5,1,1],[]]
[4,2,2,2,1,1] => [6,4,1,1] => [[6,4,1,1],[]]
[4,2,2,1,1,1,1] => [7,3,1,1] => [[7,3,1,1],[]]
[4,2,1,1,1,1,1,1] => [8,2,1,1] => [[8,2,1,1],[]]
[4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [[9,1,1,1],[]]
[3,3,3,3] => [4,4,4] => [[4,4,4],[]]
[3,3,3,2,1] => [5,4,3] => [[5,4,3],[]]
[3,3,3,1,1,1] => [6,3,3] => [[6,3,3],[]]
[3,3,2,2,2] => [5,5,2] => [[5,5,2],[]]
[3,3,2,2,1,1] => [6,4,2] => [[6,4,2],[]]
[3,3,2,1,1,1,1] => [7,3,2] => [[7,3,2],[]]
[3,3,1,1,1,1,1,1] => [8,2,2] => [[8,2,2],[]]
[3,2,2,2,2,1] => [6,5,1] => [[6,5,1],[]]
[3,2,2,2,1,1,1] => [7,4,1] => [[7,4,1],[]]
[3,2,2,1,1,1,1,1] => [8,3,1] => [[8,3,1],[]]
[3,2,1,1,1,1,1,1,1] => [9,2,1] => [[9,2,1],[]]
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [[10,1,1],[]]
[2,2,2,2,2,2] => [6,6] => [[6,6],[]]
[2,2,2,2,2,1,1] => [7,5] => [[7,5],[]]
[2,2,2,2,1,1,1,1] => [8,4] => [[8,4],[]]
[2,2,2,1,1,1,1,1,1] => [9,3] => [[9,3],[]]
[2,2,1,1,1,1,1,1,1,1] => [10,2] => [[10,2],[]]
[2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [[11,1],[]]
[1,1,1,1,1,1,1,1,1,1,1,1] => [12] => [[12],[]]
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[12,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [[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] => [[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] => [[3,1,1,1,1,1,1,1,1,1,1],[]]
[10,3] => [2,2,2,1,1,1,1,1,1,1] => [[2,2,2,1,1,1,1,1,1,1],[]]
[10,2,1] => [3,2,1,1,1,1,1,1,1,1] => [[3,2,1,1,1,1,1,1,1,1],[]]
[10,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [[4,1,1,1,1,1,1,1,1,1],[]]
[9,4] => [2,2,2,2,1,1,1,1,1] => [[2,2,2,2,1,1,1,1,1],[]]
[9,3,1] => [3,2,2,1,1,1,1,1,1] => [[3,2,2,1,1,1,1,1,1],[]]
[9,2,2] => [3,3,1,1,1,1,1,1,1] => [[3,3,1,1,1,1,1,1,1],[]]
[9,2,1,1] => [4,2,1,1,1,1,1,1,1] => [[4,2,1,1,1,1,1,1,1],[]]
[9,1,1,1,1] => [5,1,1,1,1,1,1,1,1] => [[5,1,1,1,1,1,1,1,1],[]]
[8,5] => [2,2,2,2,2,1,1,1] => [[2,2,2,2,2,1,1,1],[]]
[8,4,1] => [3,2,2,2,1,1,1,1] => [[3,2,2,2,1,1,1,1],[]]
[8,3,2] => [3,3,2,1,1,1,1,1] => [[3,3,2,1,1,1,1,1],[]]
[8,3,1,1] => [4,2,2,1,1,1,1,1] => [[4,2,2,1,1,1,1,1],[]]
[8,2,2,1] => [4,3,1,1,1,1,1,1] => [[4,3,1,1,1,1,1,1],[]]
[8,2,1,1,1] => [5,2,1,1,1,1,1,1] => [[5,2,1,1,1,1,1,1],[]]
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => [[6,1,1,1,1,1,1,1],[]]
[7,6] => [2,2,2,2,2,2,1] => [[2,2,2,2,2,2,1],[]]
[7,5,1] => [3,2,2,2,2,1,1] => [[3,2,2,2,2,1,1],[]]
[7,4,2] => [3,3,2,2,1,1,1] => [[3,3,2,2,1,1,1],[]]
[7,4,1,1] => [4,2,2,2,1,1,1] => [[4,2,2,2,1,1,1],[]]
[7,3,3] => [3,3,3,1,1,1,1] => [[3,3,3,1,1,1,1],[]]
[7,3,2,1] => [4,3,2,1,1,1,1] => [[4,3,2,1,1,1,1],[]]
[7,3,1,1,1] => [5,2,2,1,1,1,1] => [[5,2,2,1,1,1,1],[]]
[7,2,2,2] => [4,4,1,1,1,1,1] => [[4,4,1,1,1,1,1],[]]
[7,2,2,1,1] => [5,3,1,1,1,1,1] => [[5,3,1,1,1,1,1],[]]
[7,2,1,1,1,1] => [6,2,1,1,1,1,1] => [[6,2,1,1,1,1,1],[]]
[7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [[7,1,1,1,1,1,1],[]]
[6,6,1] => [3,2,2,2,2,2] => [[3,2,2,2,2,2],[]]
[6,5,2] => [3,3,2,2,2,1] => [[3,3,2,2,2,1],[]]
[6,5,1,1] => [4,2,2,2,2,1] => [[4,2,2,2,2,1],[]]
[6,4,3] => [3,3,3,2,1,1] => [[3,3,3,2,1,1],[]]
[6,4,2,1] => [4,3,2,2,1,1] => [[4,3,2,2,1,1],[]]
[6,4,1,1,1] => [5,2,2,2,1,1] => [[5,2,2,2,1,1],[]]
[6,3,3,1] => [4,3,3,1,1,1] => [[4,3,3,1,1,1],[]]
[6,3,2,2] => [4,4,2,1,1,1] => [[4,4,2,1,1,1],[]]
[6,3,2,1,1] => [5,3,2,1,1,1] => [[5,3,2,1,1,1],[]]
[6,3,1,1,1,1] => [6,2,2,1,1,1] => [[6,2,2,1,1,1],[]]
[6,2,2,2,1] => [5,4,1,1,1,1] => [[5,4,1,1,1,1],[]]
[6,2,2,1,1,1] => [6,3,1,1,1,1] => [[6,3,1,1,1,1],[]]
[6,2,1,1,1,1,1] => [7,2,1,1,1,1] => [[7,2,1,1,1,1],[]]
[6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => [[8,1,1,1,1,1],[]]
[5,5,3] => [3,3,3,2,2] => [[3,3,3,2,2],[]]
[5,5,2,1] => [4,3,2,2,2] => [[4,3,2,2,2],[]]
[5,5,1,1,1] => [5,2,2,2,2] => [[5,2,2,2,2],[]]
[5,4,4] => [3,3,3,3,1] => [[3,3,3,3,1],[]]
[5,4,3,1] => [4,3,3,2,1] => [[4,3,3,2,1],[]]
[5,4,2,2] => [4,4,2,2,1] => [[4,4,2,2,1],[]]
[5,4,2,1,1] => [5,3,2,2,1] => [[5,3,2,2,1],[]]
[5,4,1,1,1,1] => [6,2,2,2,1] => [[6,2,2,2,1],[]]
[5,3,3,2] => [4,4,3,1,1] => [[4,4,3,1,1],[]]
[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] => [[5,4,2,1,1],[]]
[5,3,2,1,1,1] => [6,3,2,1,1] => [[6,3,2,1,1],[]]
[5,3,1,1,1,1,1] => [7,2,2,1,1] => [[7,2,2,1,1],[]]
[5,2,2,2,2] => [5,5,1,1,1] => [[5,5,1,1,1],[]]
[5,2,2,2,1,1] => [6,4,1,1,1] => [[6,4,1,1,1],[]]
[5,2,2,1,1,1,1] => [7,3,1,1,1] => [[7,3,1,1,1],[]]
[5,2,1,1,1,1,1,1] => [8,2,1,1,1] => [[8,2,1,1,1],[]]
[5,1,1,1,1,1,1,1,1] => [9,1,1,1,1] => [[9,1,1,1,1],[]]
[4,4,4,1] => [4,3,3,3] => [[4,3,3,3],[]]
[4,4,3,2] => [4,4,3,2] => [[4,4,3,2],[]]
[4,4,3,1,1] => [5,3,3,2] => [[5,3,3,2],[]]
[4,4,2,2,1] => [5,4,2,2] => [[5,4,2,2],[]]
[4,4,2,1,1,1] => [6,3,2,2] => [[6,3,2,2],[]]
[4,4,1,1,1,1,1] => [7,2,2,2] => [[7,2,2,2],[]]
[4,3,3,3] => [4,4,4,1] => [[4,4,4,1],[]]
[4,3,3,2,1] => [5,4,3,1] => [[5,4,3,1],[]]
[4,3,3,1,1,1] => [6,3,3,1] => [[6,3,3,1],[]]
[4,3,2,2,2] => [5,5,2,1] => [[5,5,2,1],[]]
[4,3,2,2,1,1] => [6,4,2,1] => [[6,4,2,1],[]]
[4,3,2,1,1,1,1] => [7,3,2,1] => [[7,3,2,1],[]]
[4,3,1,1,1,1,1,1] => [8,2,2,1] => [[8,2,2,1],[]]
[4,2,2,2,2,1] => [6,5,1,1] => [[6,5,1,1],[]]
[4,2,2,2,1,1,1] => [7,4,1,1] => [[7,4,1,1],[]]
[4,2,2,1,1,1,1,1] => [8,3,1,1] => [[8,3,1,1],[]]
[4,2,1,1,1,1,1,1,1] => [9,2,1,1] => [[9,2,1,1],[]]
[4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => [[10,1,1,1],[]]
[3,3,3,3,1] => [5,4,4] => [[5,4,4],[]]
[3,3,3,2,2] => [5,5,3] => [[5,5,3],[]]
[3,3,3,2,1,1] => [6,4,3] => [[6,4,3],[]]
[3,3,3,1,1,1,1] => [7,3,3] => [[7,3,3],[]]
[3,3,2,2,2,1] => [6,5,2] => [[6,5,2],[]]
[3,3,2,2,1,1,1] => [7,4,2] => [[7,4,2],[]]
[3,3,2,1,1,1,1,1] => [8,3,2] => [[8,3,2],[]]
[3,3,1,1,1,1,1,1,1] => [9,2,2] => [[9,2,2],[]]
[3,2,2,2,2,2] => [6,6,1] => [[6,6,1],[]]
[3,2,2,2,2,1,1] => [7,5,1] => [[7,5,1],[]]
[3,2,2,2,1,1,1,1] => [8,4,1] => [[8,4,1],[]]
[3,2,2,1,1,1,1,1,1] => [9,3,1] => [[9,3,1],[]]
[3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [[10,2,1],[]]
[3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [[11,1,1],[]]
[2,2,2,2,2,2,1] => [7,6] => [[7,6],[]]
[2,2,2,2,2,1,1,1] => [8,5] => [[8,5],[]]
[2,2,2,2,1,1,1,1,1] => [9,4] => [[9,4],[]]
[2,2,2,1,1,1,1,1,1,1] => [10,3] => [[10,3],[]]
[2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [[11,2],[]]
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => [[12,1],[]]
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => [[13],[]]
[14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[13,1] => [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],[]]
[12,2] => [2,2,1,1,1,1,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1,1,1,1,1],[]]
[12,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [[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] => [[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] => [[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] => [[4,1,1,1,1,1,1,1,1,1,1],[]]
[10,4] => [2,2,2,2,1,1,1,1,1,1] => [[2,2,2,2,1,1,1,1,1,1],[]]
[10,3,1] => [3,2,2,1,1,1,1,1,1,1] => [[3,2,2,1,1,1,1,1,1,1],[]]
[10,2,2] => [3,3,1,1,1,1,1,1,1,1] => [[3,3,1,1,1,1,1,1,1,1],[]]
[10,2,1,1] => [4,2,1,1,1,1,1,1,1,1] => [[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] => [[5,1,1,1,1,1,1,1,1,1],[]]
[9,5] => [2,2,2,2,2,1,1,1,1] => [[2,2,2,2,2,1,1,1,1],[]]
[9,4,1] => [3,2,2,2,1,1,1,1,1] => [[3,2,2,2,1,1,1,1,1],[]]
[9,3,2] => [3,3,2,1,1,1,1,1,1] => [[3,3,2,1,1,1,1,1,1],[]]
[9,3,1,1] => [4,2,2,1,1,1,1,1,1] => [[4,2,2,1,1,1,1,1,1],[]]
[9,2,2,1] => [4,3,1,1,1,1,1,1,1] => [[4,3,1,1,1,1,1,1,1],[]]
[9,2,1,1,1] => [5,2,1,1,1,1,1,1,1] => [[5,2,1,1,1,1,1,1,1],[]]
[9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => [[6,1,1,1,1,1,1,1,1],[]]
[8,6] => [2,2,2,2,2,2,1,1] => [[2,2,2,2,2,2,1,1],[]]
[8,5,1] => [3,2,2,2,2,1,1,1] => [[3,2,2,2,2,1,1,1],[]]
[8,4,2] => [3,3,2,2,1,1,1,1] => [[3,3,2,2,1,1,1,1],[]]
[8,4,1,1] => [4,2,2,2,1,1,1,1] => [[4,2,2,2,1,1,1,1],[]]
[8,3,3] => [3,3,3,1,1,1,1,1] => [[3,3,3,1,1,1,1,1],[]]
[8,3,2,1] => [4,3,2,1,1,1,1,1] => [[4,3,2,1,1,1,1,1],[]]
[8,3,1,1,1] => [5,2,2,1,1,1,1,1] => [[5,2,2,1,1,1,1,1],[]]
[8,2,2,2] => [4,4,1,1,1,1,1,1] => [[4,4,1,1,1,1,1,1],[]]
[8,2,2,1,1] => [5,3,1,1,1,1,1,1] => [[5,3,1,1,1,1,1,1],[]]
[8,2,1,1,1,1] => [6,2,1,1,1,1,1,1] => [[6,2,1,1,1,1,1,1],[]]
[8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => [[7,1,1,1,1,1,1,1],[]]
[7,7] => [2,2,2,2,2,2,2] => [[2,2,2,2,2,2,2],[]]
[7,6,1] => [3,2,2,2,2,2,1] => [[3,2,2,2,2,2,1],[]]
[7,5,2] => [3,3,2,2,2,1,1] => [[3,3,2,2,2,1,1],[]]
[7,5,1,1] => [4,2,2,2,2,1,1] => [[4,2,2,2,2,1,1],[]]
[7,4,3] => [3,3,3,2,1,1,1] => [[3,3,3,2,1,1,1],[]]
[7,4,2,1] => [4,3,2,2,1,1,1] => [[4,3,2,2,1,1,1],[]]
[7,4,1,1,1] => [5,2,2,2,1,1,1] => [[5,2,2,2,1,1,1],[]]
[7,3,3,1] => [4,3,3,1,1,1,1] => [[4,3,3,1,1,1,1],[]]
[7,3,2,2] => [4,4,2,1,1,1,1] => [[4,4,2,1,1,1,1],[]]
[7,3,2,1,1] => [5,3,2,1,1,1,1] => [[5,3,2,1,1,1,1],[]]
[7,3,1,1,1,1] => [6,2,2,1,1,1,1] => [[6,2,2,1,1,1,1],[]]
[7,2,2,2,1] => [5,4,1,1,1,1,1] => [[5,4,1,1,1,1,1],[]]
[7,2,2,1,1,1] => [6,3,1,1,1,1,1] => [[6,3,1,1,1,1,1],[]]
[7,2,1,1,1,1,1] => [7,2,1,1,1,1,1] => [[7,2,1,1,1,1,1],[]]
[7,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1] => [[8,1,1,1,1,1,1],[]]
[6,6,2] => [3,3,2,2,2,2] => [[3,3,2,2,2,2],[]]
[6,6,1,1] => [4,2,2,2,2,2] => [[4,2,2,2,2,2],[]]
[6,5,3] => [3,3,3,2,2,1] => [[3,3,3,2,2,1],[]]
[6,5,2,1] => [4,3,2,2,2,1] => [[4,3,2,2,2,1],[]]
[6,5,1,1,1] => [5,2,2,2,2,1] => [[5,2,2,2,2,1],[]]
[6,4,4] => [3,3,3,3,1,1] => [[3,3,3,3,1,1],[]]
[6,4,3,1] => [4,3,3,2,1,1] => [[4,3,3,2,1,1],[]]
[6,4,2,2] => [4,4,2,2,1,1] => [[4,4,2,2,1,1],[]]
[6,4,2,1,1] => [5,3,2,2,1,1] => [[5,3,2,2,1,1],[]]
[6,4,1,1,1,1] => [6,2,2,2,1,1] => [[6,2,2,2,1,1],[]]
[6,3,3,2] => [4,4,3,1,1,1] => [[4,4,3,1,1,1],[]]
[6,3,3,1,1] => [5,3,3,1,1,1] => [[5,3,3,1,1,1],[]]
[6,3,2,2,1] => [5,4,2,1,1,1] => [[5,4,2,1,1,1],[]]
[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] => [[7,2,2,1,1,1],[]]
[6,2,2,2,2] => [5,5,1,1,1,1] => [[5,5,1,1,1,1],[]]
[6,2,2,2,1,1] => [6,4,1,1,1,1] => [[6,4,1,1,1,1],[]]
[6,2,2,1,1,1,1] => [7,3,1,1,1,1] => [[7,3,1,1,1,1],[]]
[6,2,1,1,1,1,1,1] => [8,2,1,1,1,1] => [[8,2,1,1,1,1],[]]
[6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1] => [[9,1,1,1,1,1],[]]
[5,5,4] => [3,3,3,3,2] => [[3,3,3,3,2],[]]
[5,5,3,1] => [4,3,3,2,2] => [[4,3,3,2,2],[]]
[5,5,2,2] => [4,4,2,2,2] => [[4,4,2,2,2],[]]
[5,5,2,1,1] => [5,3,2,2,2] => [[5,3,2,2,2],[]]
[5,5,1,1,1,1] => [6,2,2,2,2] => [[6,2,2,2,2],[]]
[5,4,4,1] => [4,3,3,3,1] => [[4,3,3,3,1],[]]
[5,4,3,2] => [4,4,3,2,1] => [[4,4,3,2,1],[]]
[5,4,3,1,1] => [5,3,3,2,1] => [[5,3,3,2,1],[]]
[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] => [[6,3,2,2,1],[]]
[5,4,1,1,1,1,1] => [7,2,2,2,1] => [[7,2,2,2,1],[]]
[5,3,3,3] => [4,4,4,1,1] => [[4,4,4,1,1],[]]
[5,3,3,2,1] => [5,4,3,1,1] => [[5,4,3,1,1],[]]
[5,3,3,1,1,1] => [6,3,3,1,1] => [[6,3,3,1,1],[]]
[5,3,2,2,2] => [5,5,2,1,1] => [[5,5,2,1,1],[]]
[5,3,2,2,1,1] => [6,4,2,1,1] => [[6,4,2,1,1],[]]
[5,3,2,1,1,1,1] => [7,3,2,1,1] => [[7,3,2,1,1],[]]
[5,3,1,1,1,1,1,1] => [8,2,2,1,1] => [[8,2,2,1,1],[]]
[5,2,2,2,2,1] => [6,5,1,1,1] => [[6,5,1,1,1],[]]
[5,2,2,2,1,1,1] => [7,4,1,1,1] => [[7,4,1,1,1],[]]
[5,2,2,1,1,1,1,1] => [8,3,1,1,1] => [[8,3,1,1,1],[]]
[5,2,1,1,1,1,1,1,1] => [9,2,1,1,1] => [[9,2,1,1,1],[]]
[5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1] => [[10,1,1,1,1],[]]
[4,4,4,2] => [4,4,3,3] => [[4,4,3,3],[]]
[4,4,4,1,1] => [5,3,3,3] => [[5,3,3,3],[]]
[4,4,3,3] => [4,4,4,2] => [[4,4,4,2],[]]
[4,4,3,2,1] => [5,4,3,2] => [[5,4,3,2],[]]
[4,4,3,1,1,1] => [6,3,3,2] => [[6,3,3,2],[]]
[4,4,2,2,2] => [5,5,2,2] => [[5,5,2,2],[]]
[4,4,2,2,1,1] => [6,4,2,2] => [[6,4,2,2],[]]
[4,4,2,1,1,1,1] => [7,3,2,2] => [[7,3,2,2],[]]
[4,4,1,1,1,1,1,1] => [8,2,2,2] => [[8,2,2,2],[]]
[4,3,3,3,1] => [5,4,4,1] => [[5,4,4,1],[]]
[4,3,3,2,2] => [5,5,3,1] => [[5,5,3,1],[]]
[4,3,3,2,1,1] => [6,4,3,1] => [[6,4,3,1],[]]
[4,3,3,1,1,1,1] => [7,3,3,1] => [[7,3,3,1],[]]
[4,3,2,2,2,1] => [6,5,2,1] => [[6,5,2,1],[]]
[4,3,2,2,1,1,1] => [7,4,2,1] => [[7,4,2,1],[]]
[4,3,2,1,1,1,1,1] => [8,3,2,1] => [[8,3,2,1],[]]
[4,3,1,1,1,1,1,1,1] => [9,2,2,1] => [[9,2,2,1],[]]
[4,2,2,2,2,2] => [6,6,1,1] => [[6,6,1,1],[]]
[4,2,2,2,2,1,1] => [7,5,1,1] => [[7,5,1,1],[]]
[4,2,2,2,1,1,1,1] => [8,4,1,1] => [[8,4,1,1],[]]
[4,2,2,1,1,1,1,1,1] => [9,3,1,1] => [[9,3,1,1],[]]
[4,2,1,1,1,1,1,1,1,1] => [10,2,1,1] => [[10,2,1,1],[]]
[4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1] => [[11,1,1,1],[]]
[3,3,3,3,2] => [5,5,4] => [[5,5,4],[]]
[3,3,3,3,1,1] => [6,4,4] => [[6,4,4],[]]
[3,3,3,2,2,1] => [6,5,3] => [[6,5,3],[]]
[3,3,3,2,1,1,1] => [7,4,3] => [[7,4,3],[]]
[3,3,3,1,1,1,1,1] => [8,3,3] => [[8,3,3],[]]
[3,3,2,2,2,2] => [6,6,2] => [[6,6,2],[]]
[3,3,2,2,2,1,1] => [7,5,2] => [[7,5,2],[]]
[3,3,2,2,1,1,1,1] => [8,4,2] => [[8,4,2],[]]
[3,3,2,1,1,1,1,1,1] => [9,3,2] => [[9,3,2],[]]
[3,3,1,1,1,1,1,1,1,1] => [10,2,2] => [[10,2,2],[]]
[3,2,2,2,2,2,1] => [7,6,1] => [[7,6,1],[]]
[3,2,2,2,2,1,1,1] => [8,5,1] => [[8,5,1],[]]
[3,2,2,2,1,1,1,1,1] => [9,4,1] => [[9,4,1],[]]
[3,2,2,1,1,1,1,1,1,1] => [10,3,1] => [[10,3,1],[]]
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => [[11,2,1],[]]
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => [[12,1,1],[]]
[2,2,2,2,2,2,2] => [7,7] => [[7,7],[]]
[2,2,2,2,2,2,1,1] => [8,6] => [[8,6],[]]
[2,2,2,2,2,1,1,1,1] => [9,5] => [[9,5],[]]
[2,2,2,2,1,1,1,1,1,1] => [10,4] => [[10,4],[]]
[2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [[11,3],[]]
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => [[12,2],[]]
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => [[13,1],[]]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => [[14],[]]
[15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[14,1] => [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],[]]
[13,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1,1,1,1,1,1],[]]
[13,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[12,3] => [2,2,2,1,1,1,1,1,1,1,1,1] => [[2,2,2,1,1,1,1,1,1,1,1,1],[]]
[12,2,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[5,1,1,1,1,1,1,1,1,1,1],[]]
[10,5] => [2,2,2,2,2,1,1,1,1,1] => [[2,2,2,2,2,1,1,1,1,1],[]]
[10,4,1] => [3,2,2,2,1,1,1,1,1,1] => [[3,2,2,2,1,1,1,1,1,1],[]]
[10,3,2] => [3,3,2,1,1,1,1,1,1,1] => [[3,3,2,1,1,1,1,1,1,1],[]]
[10,3,1,1] => [4,2,2,1,1,1,1,1,1,1] => [[4,2,2,1,1,1,1,1,1,1],[]]
[10,2,2,1] => [4,3,1,1,1,1,1,1,1,1] => [[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] => [[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] => [[6,1,1,1,1,1,1,1,1,1],[]]
[9,6] => [2,2,2,2,2,2,1,1,1] => [[2,2,2,2,2,2,1,1,1],[]]
[9,5,1] => [3,2,2,2,2,1,1,1,1] => [[3,2,2,2,2,1,1,1,1],[]]
[9,4,2] => [3,3,2,2,1,1,1,1,1] => [[3,3,2,2,1,1,1,1,1],[]]
[9,4,1,1] => [4,2,2,2,1,1,1,1,1] => [[4,2,2,2,1,1,1,1,1],[]]
[9,3,3] => [3,3,3,1,1,1,1,1,1] => [[3,3,3,1,1,1,1,1,1],[]]
[9,3,2,1] => [4,3,2,1,1,1,1,1,1] => [[4,3,2,1,1,1,1,1,1],[]]
[9,3,1,1,1] => [5,2,2,1,1,1,1,1,1] => [[5,2,2,1,1,1,1,1,1],[]]
[9,2,2,2] => [4,4,1,1,1,1,1,1,1] => [[4,4,1,1,1,1,1,1,1],[]]
[9,2,2,1,1] => [5,3,1,1,1,1,1,1,1] => [[5,3,1,1,1,1,1,1,1],[]]
[9,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1] => [[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] => [[7,1,1,1,1,1,1,1,1],[]]
[8,7] => [2,2,2,2,2,2,2,1] => [[2,2,2,2,2,2,2,1],[]]
[8,6,1] => [3,2,2,2,2,2,1,1] => [[3,2,2,2,2,2,1,1],[]]
[8,5,2] => [3,3,2,2,2,1,1,1] => [[3,3,2,2,2,1,1,1],[]]
[8,5,1,1] => [4,2,2,2,2,1,1,1] => [[4,2,2,2,2,1,1,1],[]]
[8,4,3] => [3,3,3,2,1,1,1,1] => [[3,3,3,2,1,1,1,1],[]]
[8,4,2,1] => [4,3,2,2,1,1,1,1] => [[4,3,2,2,1,1,1,1],[]]
[8,4,1,1,1] => [5,2,2,2,1,1,1,1] => [[5,2,2,2,1,1,1,1],[]]
[8,3,3,1] => [4,3,3,1,1,1,1,1] => [[4,3,3,1,1,1,1,1],[]]
[8,3,2,2] => [4,4,2,1,1,1,1,1] => [[4,4,2,1,1,1,1,1],[]]
[8,3,2,1,1] => [5,3,2,1,1,1,1,1] => [[5,3,2,1,1,1,1,1],[]]
[8,3,1,1,1,1] => [6,2,2,1,1,1,1,1] => [[6,2,2,1,1,1,1,1],[]]
[8,2,2,2,1] => [5,4,1,1,1,1,1,1] => [[5,4,1,1,1,1,1,1],[]]
[8,2,2,1,1,1] => [6,3,1,1,1,1,1,1] => [[6,3,1,1,1,1,1,1],[]]
[8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => [[7,2,1,1,1,1,1,1],[]]
[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] => [[3,2,2,2,2,2,2],[]]
[7,6,2] => [3,3,2,2,2,2,1] => [[3,3,2,2,2,2,1],[]]
[7,6,1,1] => [4,2,2,2,2,2,1] => [[4,2,2,2,2,2,1],[]]
[7,5,3] => [3,3,3,2,2,1,1] => [[3,3,3,2,2,1,1],[]]
[7,5,2,1] => [4,3,2,2,2,1,1] => [[4,3,2,2,2,1,1],[]]
[7,5,1,1,1] => [5,2,2,2,2,1,1] => [[5,2,2,2,2,1,1],[]]
[7,4,4] => [3,3,3,3,1,1,1] => [[3,3,3,3,1,1,1],[]]
[7,4,3,1] => [4,3,3,2,1,1,1] => [[4,3,3,2,1,1,1],[]]
[7,4,2,2] => [4,4,2,2,1,1,1] => [[4,4,2,2,1,1,1],[]]
[7,4,2,1,1] => [5,3,2,2,1,1,1] => [[5,3,2,2,1,1,1],[]]
[7,4,1,1,1,1] => [6,2,2,2,1,1,1] => [[6,2,2,2,1,1,1],[]]
[7,3,3,2] => [4,4,3,1,1,1,1] => [[4,4,3,1,1,1,1],[]]
[7,3,3,1,1] => [5,3,3,1,1,1,1] => [[5,3,3,1,1,1,1],[]]
[7,3,2,2,1] => [5,4,2,1,1,1,1] => [[5,4,2,1,1,1,1],[]]
[7,3,2,1,1,1] => [6,3,2,1,1,1,1] => [[6,3,2,1,1,1,1],[]]
[7,3,1,1,1,1,1] => [7,2,2,1,1,1,1] => [[7,2,2,1,1,1,1],[]]
[7,2,2,2,2] => [5,5,1,1,1,1,1] => [[5,5,1,1,1,1,1],[]]
[7,2,2,2,1,1] => [6,4,1,1,1,1,1] => [[6,4,1,1,1,1,1],[]]
[7,2,2,1,1,1,1] => [7,3,1,1,1,1,1] => [[7,3,1,1,1,1,1],[]]
[7,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1] => [[8,2,1,1,1,1,1],[]]
[7,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1] => [[9,1,1,1,1,1,1],[]]
[6,6,3] => [3,3,3,2,2,2] => [[3,3,3,2,2,2],[]]
[6,6,2,1] => [4,3,2,2,2,2] => [[4,3,2,2,2,2],[]]
[6,6,1,1,1] => [5,2,2,2,2,2] => [[5,2,2,2,2,2],[]]
[6,5,4] => [3,3,3,3,2,1] => [[3,3,3,3,2,1],[]]
[6,5,3,1] => [4,3,3,2,2,1] => [[4,3,3,2,2,1],[]]
[6,5,2,2] => [4,4,2,2,2,1] => [[4,4,2,2,2,1],[]]
[6,5,2,1,1] => [5,3,2,2,2,1] => [[5,3,2,2,2,1],[]]
[6,5,1,1,1,1] => [6,2,2,2,2,1] => [[6,2,2,2,2,1],[]]
[6,4,4,1] => [4,3,3,3,1,1] => [[4,3,3,3,1,1],[]]
[6,4,3,2] => [4,4,3,2,1,1] => [[4,4,3,2,1,1],[]]
[6,4,3,1,1] => [5,3,3,2,1,1] => [[5,3,3,2,1,1],[]]
[6,4,2,2,1] => [5,4,2,2,1,1] => [[5,4,2,2,1,1],[]]
[6,4,2,1,1,1] => [6,3,2,2,1,1] => [[6,3,2,2,1,1],[]]
[6,4,1,1,1,1,1] => [7,2,2,2,1,1] => [[7,2,2,2,1,1],[]]
[6,3,3,3] => [4,4,4,1,1,1] => [[4,4,4,1,1,1],[]]
[6,3,3,2,1] => [5,4,3,1,1,1] => [[5,4,3,1,1,1],[]]
[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] => [[5,5,2,1,1,1],[]]
[6,3,2,2,1,1] => [6,4,2,1,1,1] => [[6,4,2,1,1,1],[]]
[6,3,2,1,1,1,1] => [7,3,2,1,1,1] => [[7,3,2,1,1,1],[]]
[6,3,1,1,1,1,1,1] => [8,2,2,1,1,1] => [[8,2,2,1,1,1],[]]
[6,2,2,2,2,1] => [6,5,1,1,1,1] => [[6,5,1,1,1,1],[]]
[6,2,2,2,1,1,1] => [7,4,1,1,1,1] => [[7,4,1,1,1,1],[]]
[6,2,2,1,1,1,1,1] => [8,3,1,1,1,1] => [[8,3,1,1,1,1],[]]
[6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1] => [[9,2,1,1,1,1],[]]
[6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1] => [[10,1,1,1,1,1],[]]
[5,5,5] => [3,3,3,3,3] => [[3,3,3,3,3],[]]
[5,5,4,1] => [4,3,3,3,2] => [[4,3,3,3,2],[]]
[5,5,3,2] => [4,4,3,2,2] => [[4,4,3,2,2],[]]
[5,5,3,1,1] => [5,3,3,2,2] => [[5,3,3,2,2],[]]
[5,5,2,2,1] => [5,4,2,2,2] => [[5,4,2,2,2],[]]
[5,5,2,1,1,1] => [6,3,2,2,2] => [[6,3,2,2,2],[]]
[5,5,1,1,1,1,1] => [7,2,2,2,2] => [[7,2,2,2,2],[]]
[5,4,4,2] => [4,4,3,3,1] => [[4,4,3,3,1],[]]
[5,4,4,1,1] => [5,3,3,3,1] => [[5,3,3,3,1],[]]
[5,4,3,3] => [4,4,4,2,1] => [[4,4,4,2,1],[]]
[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] => [[6,3,3,2,1],[]]
[5,4,2,2,2] => [5,5,2,2,1] => [[5,5,2,2,1],[]]
[5,4,2,2,1,1] => [6,4,2,2,1] => [[6,4,2,2,1],[]]
[5,4,2,1,1,1,1] => [7,3,2,2,1] => [[7,3,2,2,1],[]]
[5,4,1,1,1,1,1,1] => [8,2,2,2,1] => [[8,2,2,2,1],[]]
[5,3,3,3,1] => [5,4,4,1,1] => [[5,4,4,1,1],[]]
[5,3,3,2,2] => [5,5,3,1,1] => [[5,5,3,1,1],[]]
[5,3,3,2,1,1] => [6,4,3,1,1] => [[6,4,3,1,1],[]]
[5,3,3,1,1,1,1] => [7,3,3,1,1] => [[7,3,3,1,1],[]]
[5,3,2,2,2,1] => [6,5,2,1,1] => [[6,5,2,1,1],[]]
[5,3,2,2,1,1,1] => [7,4,2,1,1] => [[7,4,2,1,1],[]]
[5,3,2,1,1,1,1,1] => [8,3,2,1,1] => [[8,3,2,1,1],[]]
[5,3,1,1,1,1,1,1,1] => [9,2,2,1,1] => [[9,2,2,1,1],[]]
[5,2,2,2,2,2] => [6,6,1,1,1] => [[6,6,1,1,1],[]]
[5,2,2,2,2,1,1] => [7,5,1,1,1] => [[7,5,1,1,1],[]]
[5,2,2,2,1,1,1,1] => [8,4,1,1,1] => [[8,4,1,1,1],[]]
[5,2,2,1,1,1,1,1,1] => [9,3,1,1,1] => [[9,3,1,1,1],[]]
[5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1] => [[10,2,1,1,1],[]]
[5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1] => [[11,1,1,1,1],[]]
[4,4,4,3] => [4,4,4,3] => [[4,4,4,3],[]]
[4,4,4,2,1] => [5,4,3,3] => [[5,4,3,3],[]]
[4,4,4,1,1,1] => [6,3,3,3] => [[6,3,3,3],[]]
[4,4,3,3,1] => [5,4,4,2] => [[5,4,4,2],[]]
[4,4,3,2,2] => [5,5,3,2] => [[5,5,3,2],[]]
[4,4,3,2,1,1] => [6,4,3,2] => [[6,4,3,2],[]]
[4,4,3,1,1,1,1] => [7,3,3,2] => [[7,3,3,2],[]]
[4,4,2,2,2,1] => [6,5,2,2] => [[6,5,2,2],[]]
[4,4,2,2,1,1,1] => [7,4,2,2] => [[7,4,2,2],[]]
[4,4,2,1,1,1,1,1] => [8,3,2,2] => [[8,3,2,2],[]]
[4,4,1,1,1,1,1,1,1] => [9,2,2,2] => [[9,2,2,2],[]]
[4,3,3,3,2] => [5,5,4,1] => [[5,5,4,1],[]]
[4,3,3,3,1,1] => [6,4,4,1] => [[6,4,4,1],[]]
[4,3,3,2,2,1] => [6,5,3,1] => [[6,5,3,1],[]]
[4,3,3,2,1,1,1] => [7,4,3,1] => [[7,4,3,1],[]]
[4,3,3,1,1,1,1,1] => [8,3,3,1] => [[8,3,3,1],[]]
[4,3,2,2,2,2] => [6,6,2,1] => [[6,6,2,1],[]]
[4,3,2,2,2,1,1] => [7,5,2,1] => [[7,5,2,1],[]]
[4,3,2,2,1,1,1,1] => [8,4,2,1] => [[8,4,2,1],[]]
[4,3,2,1,1,1,1,1,1] => [9,3,2,1] => [[9,3,2,1],[]]
[4,3,1,1,1,1,1,1,1,1] => [10,2,2,1] => [[10,2,2,1],[]]
[4,2,2,2,2,2,1] => [7,6,1,1] => [[7,6,1,1],[]]
[4,2,2,2,2,1,1,1] => [8,5,1,1] => [[8,5,1,1],[]]
[4,2,2,2,1,1,1,1,1] => [9,4,1,1] => [[9,4,1,1],[]]
[4,2,2,1,1,1,1,1,1,1] => [10,3,1,1] => [[10,3,1,1],[]]
[4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1] => [[11,2,1,1],[]]
[4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => [[12,1,1,1],[]]
[3,3,3,3,3] => [5,5,5] => [[5,5,5],[]]
[3,3,3,3,2,1] => [6,5,4] => [[6,5,4],[]]
[3,3,3,3,1,1,1] => [7,4,4] => [[7,4,4],[]]
[3,3,3,2,2,2] => [6,6,3] => [[6,6,3],[]]
[3,3,3,2,2,1,1] => [7,5,3] => [[7,5,3],[]]
[3,3,3,2,1,1,1,1] => [8,4,3] => [[8,4,3],[]]
[3,3,3,1,1,1,1,1,1] => [9,3,3] => [[9,3,3],[]]
[3,3,2,2,2,2,1] => [7,6,2] => [[7,6,2],[]]
[3,3,2,2,2,1,1,1] => [8,5,2] => [[8,5,2],[]]
[3,3,2,2,1,1,1,1,1] => [9,4,2] => [[9,4,2],[]]
[3,3,2,1,1,1,1,1,1,1] => [10,3,2] => [[10,3,2],[]]
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => [[11,2,2],[]]
[3,2,2,2,2,2,2] => [7,7,1] => [[7,7,1],[]]
[3,2,2,2,2,2,1,1] => [8,6,1] => [[8,6,1],[]]
[3,2,2,2,2,1,1,1,1] => [9,5,1] => [[9,5,1],[]]
[3,2,2,2,1,1,1,1,1,1] => [10,4,1] => [[10,4,1],[]]
[3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => [[11,3,1],[]]
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => [[12,2,1],[]]
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => [[13,1,1],[]]
[2,2,2,2,2,2,2,1] => [8,7] => [[8,7],[]]
[2,2,2,2,2,2,1,1,1] => [9,6] => [[9,6],[]]
[2,2,2,2,2,1,1,1,1,1] => [10,5] => [[10,5],[]]
[2,2,2,2,1,1,1,1,1,1,1] => [11,4] => [[11,4],[]]
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => [[12,3],[]]
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => [[13,2],[]]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => [[14,1],[]]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => [[15],[]]
[16] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[15,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[14,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[14,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[13,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[6,1,1,1,1,1,1,1,1,1,1],[]]
[10,6] => [2,2,2,2,2,2,1,1,1,1] => [[2,2,2,2,2,2,1,1,1,1],[]]
[10,5,1] => [3,2,2,2,2,1,1,1,1,1] => [[3,2,2,2,2,1,1,1,1,1],[]]
[10,4,2] => [3,3,2,2,1,1,1,1,1,1] => [[3,3,2,2,1,1,1,1,1,1],[]]
[10,4,1,1] => [4,2,2,2,1,1,1,1,1,1] => [[4,2,2,2,1,1,1,1,1,1],[]]
[10,3,3] => [3,3,3,1,1,1,1,1,1,1] => [[3,3,3,1,1,1,1,1,1,1],[]]
[10,3,2,1] => [4,3,2,1,1,1,1,1,1,1] => [[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] => [[5,2,2,1,1,1,1,1,1,1],[]]
[10,2,2,2] => [4,4,1,1,1,1,1,1,1,1] => [[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] => [[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] => [[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] => [[7,1,1,1,1,1,1,1,1,1],[]]
[9,7] => [2,2,2,2,2,2,2,1,1] => [[2,2,2,2,2,2,2,1,1],[]]
[9,6,1] => [3,2,2,2,2,2,1,1,1] => [[3,2,2,2,2,2,1,1,1],[]]
[9,5,2] => [3,3,2,2,2,1,1,1,1] => [[3,3,2,2,2,1,1,1,1],[]]
[9,5,1,1] => [4,2,2,2,2,1,1,1,1] => [[4,2,2,2,2,1,1,1,1],[]]
[9,4,3] => [3,3,3,2,1,1,1,1,1] => [[3,3,3,2,1,1,1,1,1],[]]
[9,4,2,1] => [4,3,2,2,1,1,1,1,1] => [[4,3,2,2,1,1,1,1,1],[]]
[9,4,1,1,1] => [5,2,2,2,1,1,1,1,1] => [[5,2,2,2,1,1,1,1,1],[]]
[9,3,3,1] => [4,3,3,1,1,1,1,1,1] => [[4,3,3,1,1,1,1,1,1],[]]
[9,3,2,2] => [4,4,2,1,1,1,1,1,1] => [[4,4,2,1,1,1,1,1,1],[]]
[9,3,2,1,1] => [5,3,2,1,1,1,1,1,1] => [[5,3,2,1,1,1,1,1,1],[]]
[9,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1] => [[6,2,2,1,1,1,1,1,1],[]]
[9,2,2,2,1] => [5,4,1,1,1,1,1,1,1] => [[5,4,1,1,1,1,1,1,1],[]]
[9,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1] => [[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] => [[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] => [[8,1,1,1,1,1,1,1,1],[]]
[8,8] => [2,2,2,2,2,2,2,2] => [[2,2,2,2,2,2,2,2],[]]
[8,7,1] => [3,2,2,2,2,2,2,1] => [[3,2,2,2,2,2,2,1],[]]
[8,6,2] => [3,3,2,2,2,2,1,1] => [[3,3,2,2,2,2,1,1],[]]
[8,6,1,1] => [4,2,2,2,2,2,1,1] => [[4,2,2,2,2,2,1,1],[]]
[8,5,3] => [3,3,3,2,2,1,1,1] => [[3,3,3,2,2,1,1,1],[]]
[8,5,2,1] => [4,3,2,2,2,1,1,1] => [[4,3,2,2,2,1,1,1],[]]
[8,5,1,1,1] => [5,2,2,2,2,1,1,1] => [[5,2,2,2,2,1,1,1],[]]
[8,4,4] => [3,3,3,3,1,1,1,1] => [[3,3,3,3,1,1,1,1],[]]
[8,4,3,1] => [4,3,3,2,1,1,1,1] => [[4,3,3,2,1,1,1,1],[]]
[8,4,2,2] => [4,4,2,2,1,1,1,1] => [[4,4,2,2,1,1,1,1],[]]
[8,4,2,1,1] => [5,3,2,2,1,1,1,1] => [[5,3,2,2,1,1,1,1],[]]
[8,4,1,1,1,1] => [6,2,2,2,1,1,1,1] => [[6,2,2,2,1,1,1,1],[]]
[8,3,3,2] => [4,4,3,1,1,1,1,1] => [[4,4,3,1,1,1,1,1],[]]
[8,3,3,1,1] => [5,3,3,1,1,1,1,1] => [[5,3,3,1,1,1,1,1],[]]
[8,3,2,2,1] => [5,4,2,1,1,1,1,1] => [[5,4,2,1,1,1,1,1],[]]
[8,3,2,1,1,1] => [6,3,2,1,1,1,1,1] => [[6,3,2,1,1,1,1,1],[]]
[8,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1] => [[7,2,2,1,1,1,1,1],[]]
[8,2,2,2,2] => [5,5,1,1,1,1,1,1] => [[5,5,1,1,1,1,1,1],[]]
[8,2,2,2,1,1] => [6,4,1,1,1,1,1,1] => [[6,4,1,1,1,1,1,1],[]]
[8,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1] => [[7,3,1,1,1,1,1,1],[]]
[8,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1] => [[8,2,1,1,1,1,1,1],[]]
[8,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1] => [[9,1,1,1,1,1,1,1],[]]
[7,7,2] => [3,3,2,2,2,2,2] => [[3,3,2,2,2,2,2],[]]
[7,7,1,1] => [4,2,2,2,2,2,2] => [[4,2,2,2,2,2,2],[]]
[7,6,3] => [3,3,3,2,2,2,1] => [[3,3,3,2,2,2,1],[]]
[7,6,2,1] => [4,3,2,2,2,2,1] => [[4,3,2,2,2,2,1],[]]
[7,6,1,1,1] => [5,2,2,2,2,2,1] => [[5,2,2,2,2,2,1],[]]
[7,5,4] => [3,3,3,3,2,1,1] => [[3,3,3,3,2,1,1],[]]
[7,5,3,1] => [4,3,3,2,2,1,1] => [[4,3,3,2,2,1,1],[]]
[7,5,2,2] => [4,4,2,2,2,1,1] => [[4,4,2,2,2,1,1],[]]
[7,5,2,1,1] => [5,3,2,2,2,1,1] => [[5,3,2,2,2,1,1],[]]
[7,5,1,1,1,1] => [6,2,2,2,2,1,1] => [[6,2,2,2,2,1,1],[]]
[7,4,4,1] => [4,3,3,3,1,1,1] => [[4,3,3,3,1,1,1],[]]
[7,4,3,2] => [4,4,3,2,1,1,1] => [[4,4,3,2,1,1,1],[]]
[7,4,3,1,1] => [5,3,3,2,1,1,1] => [[5,3,3,2,1,1,1],[]]
[7,4,2,2,1] => [5,4,2,2,1,1,1] => [[5,4,2,2,1,1,1],[]]
[7,4,2,1,1,1] => [6,3,2,2,1,1,1] => [[6,3,2,2,1,1,1],[]]
[7,4,1,1,1,1,1] => [7,2,2,2,1,1,1] => [[7,2,2,2,1,1,1],[]]
[7,3,3,3] => [4,4,4,1,1,1,1] => [[4,4,4,1,1,1,1],[]]
[7,3,3,2,1] => [5,4,3,1,1,1,1] => [[5,4,3,1,1,1,1],[]]
[7,3,3,1,1,1] => [6,3,3,1,1,1,1] => [[6,3,3,1,1,1,1],[]]
[7,3,2,2,2] => [5,5,2,1,1,1,1] => [[5,5,2,1,1,1,1],[]]
[7,3,2,2,1,1] => [6,4,2,1,1,1,1] => [[6,4,2,1,1,1,1],[]]
[7,3,2,1,1,1,1] => [7,3,2,1,1,1,1] => [[7,3,2,1,1,1,1],[]]
[7,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1] => [[8,2,2,1,1,1,1],[]]
[7,2,2,2,2,1] => [6,5,1,1,1,1,1] => [[6,5,1,1,1,1,1],[]]
[7,2,2,2,1,1,1] => [7,4,1,1,1,1,1] => [[7,4,1,1,1,1,1],[]]
[7,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1] => [[8,3,1,1,1,1,1],[]]
[7,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1] => [[9,2,1,1,1,1,1],[]]
[7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => [[10,1,1,1,1,1,1],[]]
[6,6,4] => [3,3,3,3,2,2] => [[3,3,3,3,2,2],[]]
[6,6,3,1] => [4,3,3,2,2,2] => [[4,3,3,2,2,2],[]]
[6,6,2,2] => [4,4,2,2,2,2] => [[4,4,2,2,2,2],[]]
[6,6,2,1,1] => [5,3,2,2,2,2] => [[5,3,2,2,2,2],[]]
[6,6,1,1,1,1] => [6,2,2,2,2,2] => [[6,2,2,2,2,2],[]]
[6,5,5] => [3,3,3,3,3,1] => [[3,3,3,3,3,1],[]]
[6,5,4,1] => [4,3,3,3,2,1] => [[4,3,3,3,2,1],[]]
[6,5,3,2] => [4,4,3,2,2,1] => [[4,4,3,2,2,1],[]]
[6,5,3,1,1] => [5,3,3,2,2,1] => [[5,3,3,2,2,1],[]]
[6,5,2,2,1] => [5,4,2,2,2,1] => [[5,4,2,2,2,1],[]]
[6,5,2,1,1,1] => [6,3,2,2,2,1] => [[6,3,2,2,2,1],[]]
[6,5,1,1,1,1,1] => [7,2,2,2,2,1] => [[7,2,2,2,2,1],[]]
[6,4,4,2] => [4,4,3,3,1,1] => [[4,4,3,3,1,1],[]]
[6,4,4,1,1] => [5,3,3,3,1,1] => [[5,3,3,3,1,1],[]]
[6,4,3,3] => [4,4,4,2,1,1] => [[4,4,4,2,1,1],[]]
[6,4,3,2,1] => [5,4,3,2,1,1] => [[5,4,3,2,1,1],[]]
[6,4,3,1,1,1] => [6,3,3,2,1,1] => [[6,3,3,2,1,1],[]]
[6,4,2,2,2] => [5,5,2,2,1,1] => [[5,5,2,2,1,1],[]]
[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] => [[7,3,2,2,1,1],[]]
[6,4,1,1,1,1,1,1] => [8,2,2,2,1,1] => [[8,2,2,2,1,1],[]]
[6,3,3,3,1] => [5,4,4,1,1,1] => [[5,4,4,1,1,1],[]]
[6,3,3,2,2] => [5,5,3,1,1,1] => [[5,5,3,1,1,1],[]]
[6,3,3,2,1,1] => [6,4,3,1,1,1] => [[6,4,3,1,1,1],[]]
[6,3,3,1,1,1,1] => [7,3,3,1,1,1] => [[7,3,3,1,1,1],[]]
[6,3,2,2,2,1] => [6,5,2,1,1,1] => [[6,5,2,1,1,1],[]]
[6,3,2,2,1,1,1] => [7,4,2,1,1,1] => [[7,4,2,1,1,1],[]]
[6,3,2,1,1,1,1,1] => [8,3,2,1,1,1] => [[8,3,2,1,1,1],[]]
[6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1] => [[9,2,2,1,1,1],[]]
[6,2,2,2,2,2] => [6,6,1,1,1,1] => [[6,6,1,1,1,1],[]]
[6,2,2,2,2,1,1] => [7,5,1,1,1,1] => [[7,5,1,1,1,1],[]]
[6,2,2,2,1,1,1,1] => [8,4,1,1,1,1] => [[8,4,1,1,1,1],[]]
[6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1] => [[9,3,1,1,1,1],[]]
[6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1] => [[10,2,1,1,1,1],[]]
[6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => [[11,1,1,1,1,1],[]]
[5,5,5,1] => [4,3,3,3,3] => [[4,3,3,3,3],[]]
[5,5,4,2] => [4,4,3,3,2] => [[4,4,3,3,2],[]]
[5,5,4,1,1] => [5,3,3,3,2] => [[5,3,3,3,2],[]]
[5,5,3,3] => [4,4,4,2,2] => [[4,4,4,2,2],[]]
[5,5,3,2,1] => [5,4,3,2,2] => [[5,4,3,2,2],[]]
[5,5,3,1,1,1] => [6,3,3,2,2] => [[6,3,3,2,2],[]]
[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] => [[6,4,2,2,2],[]]
[5,5,2,1,1,1,1] => [7,3,2,2,2] => [[7,3,2,2,2],[]]
[5,5,1,1,1,1,1,1] => [8,2,2,2,2] => [[8,2,2,2,2],[]]
[5,4,4,3] => [4,4,4,3,1] => [[4,4,4,3,1],[]]
[5,4,4,2,1] => [5,4,3,3,1] => [[5,4,3,3,1],[]]
[5,4,4,1,1,1] => [6,3,3,3,1] => [[6,3,3,3,1],[]]
[5,4,3,3,1] => [5,4,4,2,1] => [[5,4,4,2,1],[]]
[5,4,3,2,2] => [5,5,3,2,1] => [[5,5,3,2,1],[]]
[5,4,3,2,1,1] => [6,4,3,2,1] => [[6,4,3,2,1],[]]
[5,4,3,1,1,1,1] => [7,3,3,2,1] => [[7,3,3,2,1],[]]
[5,4,2,2,2,1] => [6,5,2,2,1] => [[6,5,2,2,1],[]]
[5,4,2,2,1,1,1] => [7,4,2,2,1] => [[7,4,2,2,1],[]]
[5,4,2,1,1,1,1,1] => [8,3,2,2,1] => [[8,3,2,2,1],[]]
[5,4,1,1,1,1,1,1,1] => [9,2,2,2,1] => [[9,2,2,2,1],[]]
[5,3,3,3,2] => [5,5,4,1,1] => [[5,5,4,1,1],[]]
[5,3,3,3,1,1] => [6,4,4,1,1] => [[6,4,4,1,1],[]]
[5,3,3,2,2,1] => [6,5,3,1,1] => [[6,5,3,1,1],[]]
[5,3,3,2,1,1,1] => [7,4,3,1,1] => [[7,4,3,1,1],[]]
[5,3,3,1,1,1,1,1] => [8,3,3,1,1] => [[8,3,3,1,1],[]]
[5,3,2,2,2,2] => [6,6,2,1,1] => [[6,6,2,1,1],[]]
[5,3,2,2,2,1,1] => [7,5,2,1,1] => [[7,5,2,1,1],[]]
[5,3,2,2,1,1,1,1] => [8,4,2,1,1] => [[8,4,2,1,1],[]]
[5,3,2,1,1,1,1,1,1] => [9,3,2,1,1] => [[9,3,2,1,1],[]]
[5,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1] => [[10,2,2,1,1],[]]
[5,2,2,2,2,2,1] => [7,6,1,1,1] => [[7,6,1,1,1],[]]
[5,2,2,2,2,1,1,1] => [8,5,1,1,1] => [[8,5,1,1,1],[]]
[5,2,2,2,1,1,1,1,1] => [9,4,1,1,1] => [[9,4,1,1,1],[]]
[5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1] => [[10,3,1,1,1],[]]
[5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1] => [[11,2,1,1,1],[]]
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => [[12,1,1,1,1],[]]
[4,4,4,4] => [4,4,4,4] => [[4,4,4,4],[]]
[4,4,4,3,1] => [5,4,4,3] => [[5,4,4,3],[]]
[4,4,4,2,2] => [5,5,3,3] => [[5,5,3,3],[]]
[4,4,4,2,1,1] => [6,4,3,3] => [[6,4,3,3],[]]
[4,4,4,1,1,1,1] => [7,3,3,3] => [[7,3,3,3],[]]
[4,4,3,3,2] => [5,5,4,2] => [[5,5,4,2],[]]
[4,4,3,3,1,1] => [6,4,4,2] => [[6,4,4,2],[]]
[4,4,3,2,2,1] => [6,5,3,2] => [[6,5,3,2],[]]
[4,4,3,2,1,1,1] => [7,4,3,2] => [[7,4,3,2],[]]
[4,4,3,1,1,1,1,1] => [8,3,3,2] => [[8,3,3,2],[]]
[4,4,2,2,2,2] => [6,6,2,2] => [[6,6,2,2],[]]
[4,4,2,2,2,1,1] => [7,5,2,2] => [[7,5,2,2],[]]
[4,4,2,2,1,1,1,1] => [8,4,2,2] => [[8,4,2,2],[]]
[4,4,2,1,1,1,1,1,1] => [9,3,2,2] => [[9,3,2,2],[]]
[4,4,1,1,1,1,1,1,1,1] => [10,2,2,2] => [[10,2,2,2],[]]
[4,3,3,3,3] => [5,5,5,1] => [[5,5,5,1],[]]
[4,3,3,3,2,1] => [6,5,4,1] => [[6,5,4,1],[]]
[4,3,3,3,1,1,1] => [7,4,4,1] => [[7,4,4,1],[]]
[4,3,3,2,2,2] => [6,6,3,1] => [[6,6,3,1],[]]
[4,3,3,2,2,1,1] => [7,5,3,1] => [[7,5,3,1],[]]
[4,3,3,2,1,1,1,1] => [8,4,3,1] => [[8,4,3,1],[]]
[4,3,3,1,1,1,1,1,1] => [9,3,3,1] => [[9,3,3,1],[]]
[4,3,2,2,2,2,1] => [7,6,2,1] => [[7,6,2,1],[]]
[4,3,2,2,2,1,1,1] => [8,5,2,1] => [[8,5,2,1],[]]
[4,3,2,2,1,1,1,1,1] => [9,4,2,1] => [[9,4,2,1],[]]
[4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => [[10,3,2,1],[]]
[4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => [[11,2,2,1],[]]
[4,2,2,2,2,2,2] => [7,7,1,1] => [[7,7,1,1],[]]
[4,2,2,2,2,2,1,1] => [8,6,1,1] => [[8,6,1,1],[]]
[4,2,2,2,2,1,1,1,1] => [9,5,1,1] => [[9,5,1,1],[]]
[4,2,2,2,1,1,1,1,1,1] => [10,4,1,1] => [[10,4,1,1],[]]
[4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1] => [[11,3,1,1],[]]
[4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1] => [[12,2,1,1],[]]
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1] => [[13,1,1,1],[]]
[3,3,3,3,3,1] => [6,5,5] => [[6,5,5],[]]
[3,3,3,3,2,2] => [6,6,4] => [[6,6,4],[]]
[3,3,3,3,2,1,1] => [7,5,4] => [[7,5,4],[]]
[3,3,3,3,1,1,1,1] => [8,4,4] => [[8,4,4],[]]
[3,3,3,2,2,2,1] => [7,6,3] => [[7,6,3],[]]
[3,3,3,2,2,1,1,1] => [8,5,3] => [[8,5,3],[]]
[3,3,3,2,1,1,1,1,1] => [9,4,3] => [[9,4,3],[]]
[3,3,3,1,1,1,1,1,1,1] => [10,3,3] => [[10,3,3],[]]
[3,3,2,2,2,2,2] => [7,7,2] => [[7,7,2],[]]
[3,3,2,2,2,2,1,1] => [8,6,2] => [[8,6,2],[]]
[3,3,2,2,2,1,1,1,1] => [9,5,2] => [[9,5,2],[]]
[3,3,2,2,1,1,1,1,1,1] => [10,4,2] => [[10,4,2],[]]
[3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => [[11,3,2],[]]
[3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2] => [[12,2,2],[]]
[3,2,2,2,2,2,2,1] => [8,7,1] => [[8,7,1],[]]
[3,2,2,2,2,2,1,1,1] => [9,6,1] => [[9,6,1],[]]
[3,2,2,2,2,1,1,1,1,1] => [10,5,1] => [[10,5,1],[]]
[3,2,2,2,1,1,1,1,1,1,1] => [11,4,1] => [[11,4,1],[]]
[3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1] => [[12,3,1],[]]
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => [[13,2,1],[]]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1] => [[14,1,1],[]]
[2,2,2,2,2,2,2,2] => [8,8] => [[8,8],[]]
[2,2,2,2,2,2,2,1,1] => [9,7] => [[9,7],[]]
[2,2,2,2,2,2,1,1,1,1] => [10,6] => [[10,6],[]]
[2,2,2,2,2,1,1,1,1,1,1] => [11,5] => [[11,5],[]]
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => [[12,4],[]]
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => [[13,3],[]]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => [[14,2],[]]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => [[15,1],[]]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => [[16],[]]
[17] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[16,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[15,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[15,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[14,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[7,1,1,1,1,1,1,1,1,1,1],[]]
[10,7] => [2,2,2,2,2,2,2,1,1,1] => [[2,2,2,2,2,2,2,1,1,1],[]]
[10,6,1] => [3,2,2,2,2,2,1,1,1,1] => [[3,2,2,2,2,2,1,1,1,1],[]]
[10,5,2] => [3,3,2,2,2,1,1,1,1,1] => [[3,3,2,2,2,1,1,1,1,1],[]]
[10,5,1,1] => [4,2,2,2,2,1,1,1,1,1] => [[4,2,2,2,2,1,1,1,1,1],[]]
[10,4,3] => [3,3,3,2,1,1,1,1,1,1] => [[3,3,3,2,1,1,1,1,1,1],[]]
[10,4,2,1] => [4,3,2,2,1,1,1,1,1,1] => [[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] => [[5,2,2,2,1,1,1,1,1,1],[]]
[10,3,3,1] => [4,3,3,1,1,1,1,1,1,1] => [[4,3,3,1,1,1,1,1,1,1],[]]
[10,3,2,2] => [4,4,2,1,1,1,1,1,1,1] => [[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] => [[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] => [[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] => [[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] => [[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] => [[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] => [[8,1,1,1,1,1,1,1,1,1],[]]
[9,8] => [2,2,2,2,2,2,2,2,1] => [[2,2,2,2,2,2,2,2,1],[]]
[9,7,1] => [3,2,2,2,2,2,2,1,1] => [[3,2,2,2,2,2,2,1,1],[]]
[9,6,2] => [3,3,2,2,2,2,1,1,1] => [[3,3,2,2,2,2,1,1,1],[]]
[9,6,1,1] => [4,2,2,2,2,2,1,1,1] => [[4,2,2,2,2,2,1,1,1],[]]
[9,5,3] => [3,3,3,2,2,1,1,1,1] => [[3,3,3,2,2,1,1,1,1],[]]
[9,5,2,1] => [4,3,2,2,2,1,1,1,1] => [[4,3,2,2,2,1,1,1,1],[]]
[9,5,1,1,1] => [5,2,2,2,2,1,1,1,1] => [[5,2,2,2,2,1,1,1,1],[]]
[9,4,4] => [3,3,3,3,1,1,1,1,1] => [[3,3,3,3,1,1,1,1,1],[]]
[9,4,3,1] => [4,3,3,2,1,1,1,1,1] => [[4,3,3,2,1,1,1,1,1],[]]
[9,4,2,2] => [4,4,2,2,1,1,1,1,1] => [[4,4,2,2,1,1,1,1,1],[]]
[9,4,2,1,1] => [5,3,2,2,1,1,1,1,1] => [[5,3,2,2,1,1,1,1,1],[]]
[9,4,1,1,1,1] => [6,2,2,2,1,1,1,1,1] => [[6,2,2,2,1,1,1,1,1],[]]
[9,3,3,2] => [4,4,3,1,1,1,1,1,1] => [[4,4,3,1,1,1,1,1,1],[]]
[9,3,3,1,1] => [5,3,3,1,1,1,1,1,1] => [[5,3,3,1,1,1,1,1,1],[]]
[9,3,2,2,1] => [5,4,2,1,1,1,1,1,1] => [[5,4,2,1,1,1,1,1,1],[]]
[9,3,2,1,1,1] => [6,3,2,1,1,1,1,1,1] => [[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] => [[7,2,2,1,1,1,1,1,1],[]]
[9,2,2,2,2] => [5,5,1,1,1,1,1,1,1] => [[5,5,1,1,1,1,1,1,1],[]]
[9,2,2,2,1,1] => [6,4,1,1,1,1,1,1,1] => [[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] => [[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] => [[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] => [[9,1,1,1,1,1,1,1,1],[]]
[8,8,1] => [3,2,2,2,2,2,2,2] => [[3,2,2,2,2,2,2,2],[]]
[8,7,2] => [3,3,2,2,2,2,2,1] => [[3,3,2,2,2,2,2,1],[]]
[8,7,1,1] => [4,2,2,2,2,2,2,1] => [[4,2,2,2,2,2,2,1],[]]
[8,6,3] => [3,3,3,2,2,2,1,1] => [[3,3,3,2,2,2,1,1],[]]
[8,6,2,1] => [4,3,2,2,2,2,1,1] => [[4,3,2,2,2,2,1,1],[]]
[8,6,1,1,1] => [5,2,2,2,2,2,1,1] => [[5,2,2,2,2,2,1,1],[]]
[8,5,4] => [3,3,3,3,2,1,1,1] => [[3,3,3,3,2,1,1,1],[]]
[8,5,3,1] => [4,3,3,2,2,1,1,1] => [[4,3,3,2,2,1,1,1],[]]
[8,5,2,2] => [4,4,2,2,2,1,1,1] => [[4,4,2,2,2,1,1,1],[]]
[8,5,2,1,1] => [5,3,2,2,2,1,1,1] => [[5,3,2,2,2,1,1,1],[]]
[8,5,1,1,1,1] => [6,2,2,2,2,1,1,1] => [[6,2,2,2,2,1,1,1],[]]
[8,4,4,1] => [4,3,3,3,1,1,1,1] => [[4,3,3,3,1,1,1,1],[]]
[8,4,3,2] => [4,4,3,2,1,1,1,1] => [[4,4,3,2,1,1,1,1],[]]
[8,4,3,1,1] => [5,3,3,2,1,1,1,1] => [[5,3,3,2,1,1,1,1],[]]
[8,4,2,2,1] => [5,4,2,2,1,1,1,1] => [[5,4,2,2,1,1,1,1],[]]
[8,4,2,1,1,1] => [6,3,2,2,1,1,1,1] => [[6,3,2,2,1,1,1,1],[]]
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1] => [[7,2,2,2,1,1,1,1],[]]
[8,3,3,3] => [4,4,4,1,1,1,1,1] => [[4,4,4,1,1,1,1,1],[]]
[8,3,3,2,1] => [5,4,3,1,1,1,1,1] => [[5,4,3,1,1,1,1,1],[]]
[8,3,3,1,1,1] => [6,3,3,1,1,1,1,1] => [[6,3,3,1,1,1,1,1],[]]
[8,3,2,2,2] => [5,5,2,1,1,1,1,1] => [[5,5,2,1,1,1,1,1],[]]
[8,3,2,2,1,1] => [6,4,2,1,1,1,1,1] => [[6,4,2,1,1,1,1,1],[]]
[8,3,2,1,1,1,1] => [7,3,2,1,1,1,1,1] => [[7,3,2,1,1,1,1,1],[]]
[8,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1,1] => [[8,2,2,1,1,1,1,1],[]]
[8,2,2,2,2,1] => [6,5,1,1,1,1,1,1] => [[6,5,1,1,1,1,1,1],[]]
[8,2,2,2,1,1,1] => [7,4,1,1,1,1,1,1] => [[7,4,1,1,1,1,1,1],[]]
[8,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1,1] => [[8,3,1,1,1,1,1,1],[]]
[8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => [[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] => [[10,1,1,1,1,1,1,1],[]]
[7,7,3] => [3,3,3,2,2,2,2] => [[3,3,3,2,2,2,2],[]]
[7,7,2,1] => [4,3,2,2,2,2,2] => [[4,3,2,2,2,2,2],[]]
[7,7,1,1,1] => [5,2,2,2,2,2,2] => [[5,2,2,2,2,2,2],[]]
[7,6,4] => [3,3,3,3,2,2,1] => [[3,3,3,3,2,2,1],[]]
[7,6,3,1] => [4,3,3,2,2,2,1] => [[4,3,3,2,2,2,1],[]]
[7,6,2,2] => [4,4,2,2,2,2,1] => [[4,4,2,2,2,2,1],[]]
[7,6,2,1,1] => [5,3,2,2,2,2,1] => [[5,3,2,2,2,2,1],[]]
[7,6,1,1,1,1] => [6,2,2,2,2,2,1] => [[6,2,2,2,2,2,1],[]]
[7,5,5] => [3,3,3,3,3,1,1] => [[3,3,3,3,3,1,1],[]]
[7,5,4,1] => [4,3,3,3,2,1,1] => [[4,3,3,3,2,1,1],[]]
[7,5,3,2] => [4,4,3,2,2,1,1] => [[4,4,3,2,2,1,1],[]]
[7,5,3,1,1] => [5,3,3,2,2,1,1] => [[5,3,3,2,2,1,1],[]]
[7,5,2,2,1] => [5,4,2,2,2,1,1] => [[5,4,2,2,2,1,1],[]]
[7,5,2,1,1,1] => [6,3,2,2,2,1,1] => [[6,3,2,2,2,1,1],[]]
[7,5,1,1,1,1,1] => [7,2,2,2,2,1,1] => [[7,2,2,2,2,1,1],[]]
[7,4,4,2] => [4,4,3,3,1,1,1] => [[4,4,3,3,1,1,1],[]]
[7,4,4,1,1] => [5,3,3,3,1,1,1] => [[5,3,3,3,1,1,1],[]]
[7,4,3,3] => [4,4,4,2,1,1,1] => [[4,4,4,2,1,1,1],[]]
[7,4,3,2,1] => [5,4,3,2,1,1,1] => [[5,4,3,2,1,1,1],[]]
[7,4,3,1,1,1] => [6,3,3,2,1,1,1] => [[6,3,3,2,1,1,1],[]]
[7,4,2,2,2] => [5,5,2,2,1,1,1] => [[5,5,2,2,1,1,1],[]]
[7,4,2,2,1,1] => [6,4,2,2,1,1,1] => [[6,4,2,2,1,1,1],[]]
[7,4,2,1,1,1,1] => [7,3,2,2,1,1,1] => [[7,3,2,2,1,1,1],[]]
[7,4,1,1,1,1,1,1] => [8,2,2,2,1,1,1] => [[8,2,2,2,1,1,1],[]]
[7,3,3,3,1] => [5,4,4,1,1,1,1] => [[5,4,4,1,1,1,1],[]]
[7,3,3,2,2] => [5,5,3,1,1,1,1] => [[5,5,3,1,1,1,1],[]]
[7,3,3,2,1,1] => [6,4,3,1,1,1,1] => [[6,4,3,1,1,1,1],[]]
[7,3,3,1,1,1,1] => [7,3,3,1,1,1,1] => [[7,3,3,1,1,1,1],[]]
[7,3,2,2,2,1] => [6,5,2,1,1,1,1] => [[6,5,2,1,1,1,1],[]]
[7,3,2,2,1,1,1] => [7,4,2,1,1,1,1] => [[7,4,2,1,1,1,1],[]]
[7,3,2,1,1,1,1,1] => [8,3,2,1,1,1,1] => [[8,3,2,1,1,1,1],[]]
[7,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1,1] => [[9,2,2,1,1,1,1],[]]
[7,2,2,2,2,2] => [6,6,1,1,1,1,1] => [[6,6,1,1,1,1,1],[]]
[7,2,2,2,2,1,1] => [7,5,1,1,1,1,1] => [[7,5,1,1,1,1,1],[]]
[7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1] => [[8,4,1,1,1,1,1],[]]
[7,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1] => [[9,3,1,1,1,1,1],[]]
[7,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1,1] => [[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] => [[11,1,1,1,1,1,1],[]]
[6,6,5] => [3,3,3,3,3,2] => [[3,3,3,3,3,2],[]]
[6,6,4,1] => [4,3,3,3,2,2] => [[4,3,3,3,2,2],[]]
[6,6,3,2] => [4,4,3,2,2,2] => [[4,4,3,2,2,2],[]]
[6,6,3,1,1] => [5,3,3,2,2,2] => [[5,3,3,2,2,2],[]]
[6,6,2,2,1] => [5,4,2,2,2,2] => [[5,4,2,2,2,2],[]]
[6,6,2,1,1,1] => [6,3,2,2,2,2] => [[6,3,2,2,2,2],[]]
[6,6,1,1,1,1,1] => [7,2,2,2,2,2] => [[7,2,2,2,2,2],[]]
[6,5,5,1] => [4,3,3,3,3,1] => [[4,3,3,3,3,1],[]]
[6,5,4,2] => [4,4,3,3,2,1] => [[4,4,3,3,2,1],[]]
[6,5,4,1,1] => [5,3,3,3,2,1] => [[5,3,3,3,2,1],[]]
[6,5,3,3] => [4,4,4,2,2,1] => [[4,4,4,2,2,1],[]]
[6,5,3,2,1] => [5,4,3,2,2,1] => [[5,4,3,2,2,1],[]]
[6,5,3,1,1,1] => [6,3,3,2,2,1] => [[6,3,3,2,2,1],[]]
[6,5,2,2,2] => [5,5,2,2,2,1] => [[5,5,2,2,2,1],[]]
[6,5,2,2,1,1] => [6,4,2,2,2,1] => [[6,4,2,2,2,1],[]]
[6,5,2,1,1,1,1] => [7,3,2,2,2,1] => [[7,3,2,2,2,1],[]]
[6,5,1,1,1,1,1,1] => [8,2,2,2,2,1] => [[8,2,2,2,2,1],[]]
[6,4,4,3] => [4,4,4,3,1,1] => [[4,4,4,3,1,1],[]]
[6,4,4,2,1] => [5,4,3,3,1,1] => [[5,4,3,3,1,1],[]]
[6,4,4,1,1,1] => [6,3,3,3,1,1] => [[6,3,3,3,1,1],[]]
[6,4,3,3,1] => [5,4,4,2,1,1] => [[5,4,4,2,1,1],[]]
[6,4,3,2,2] => [5,5,3,2,1,1] => [[5,5,3,2,1,1],[]]
[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] => [[7,3,3,2,1,1],[]]
[6,4,2,2,2,1] => [6,5,2,2,1,1] => [[6,5,2,2,1,1],[]]
[6,4,2,2,1,1,1] => [7,4,2,2,1,1] => [[7,4,2,2,1,1],[]]
[6,4,2,1,1,1,1,1] => [8,3,2,2,1,1] => [[8,3,2,2,1,1],[]]
[6,4,1,1,1,1,1,1,1] => [9,2,2,2,1,1] => [[9,2,2,2,1,1],[]]
[6,3,3,3,2] => [5,5,4,1,1,1] => [[5,5,4,1,1,1],[]]
[6,3,3,3,1,1] => [6,4,4,1,1,1] => [[6,4,4,1,1,1],[]]
[6,3,3,2,2,1] => [6,5,3,1,1,1] => [[6,5,3,1,1,1],[]]
[6,3,3,2,1,1,1] => [7,4,3,1,1,1] => [[7,4,3,1,1,1],[]]
[6,3,3,1,1,1,1,1] => [8,3,3,1,1,1] => [[8,3,3,1,1,1],[]]
[6,3,2,2,2,2] => [6,6,2,1,1,1] => [[6,6,2,1,1,1],[]]
[6,3,2,2,2,1,1] => [7,5,2,1,1,1] => [[7,5,2,1,1,1],[]]
[6,3,2,2,1,1,1,1] => [8,4,2,1,1,1] => [[8,4,2,1,1,1],[]]
[6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1] => [[9,3,2,1,1,1],[]]
[6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1] => [[10,2,2,1,1,1],[]]
[6,2,2,2,2,2,1] => [7,6,1,1,1,1] => [[7,6,1,1,1,1],[]]
[6,2,2,2,2,1,1,1] => [8,5,1,1,1,1] => [[8,5,1,1,1,1],[]]
[6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1] => [[9,4,1,1,1,1],[]]
[6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1] => [[10,3,1,1,1,1],[]]
[6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1] => [[11,2,1,1,1,1],[]]
[6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => [[12,1,1,1,1,1],[]]
[5,5,5,2] => [4,4,3,3,3] => [[4,4,3,3,3],[]]
[5,5,5,1,1] => [5,3,3,3,3] => [[5,3,3,3,3],[]]
[5,5,4,3] => [4,4,4,3,2] => [[4,4,4,3,2],[]]
[5,5,4,2,1] => [5,4,3,3,2] => [[5,4,3,3,2],[]]
[5,5,4,1,1,1] => [6,3,3,3,2] => [[6,3,3,3,2],[]]
[5,5,3,3,1] => [5,4,4,2,2] => [[5,4,4,2,2],[]]
[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] => [[6,4,3,2,2],[]]
[5,5,3,1,1,1,1] => [7,3,3,2,2] => [[7,3,3,2,2],[]]
[5,5,2,2,2,1] => [6,5,2,2,2] => [[6,5,2,2,2],[]]
[5,5,2,2,1,1,1] => [7,4,2,2,2] => [[7,4,2,2,2],[]]
[5,5,2,1,1,1,1,1] => [8,3,2,2,2] => [[8,3,2,2,2],[]]
[5,5,1,1,1,1,1,1,1] => [9,2,2,2,2] => [[9,2,2,2,2],[]]
[5,4,4,4] => [4,4,4,4,1] => [[4,4,4,4,1],[]]
[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] => [[5,5,3,3,1],[]]
[5,4,4,2,1,1] => [6,4,3,3,1] => [[6,4,3,3,1],[]]
[5,4,4,1,1,1,1] => [7,3,3,3,1] => [[7,3,3,3,1],[]]
[5,4,3,3,2] => [5,5,4,2,1] => [[5,5,4,2,1],[]]
[5,4,3,3,1,1] => [6,4,4,2,1] => [[6,4,4,2,1],[]]
[5,4,3,2,2,1] => [6,5,3,2,1] => [[6,5,3,2,1],[]]
[5,4,3,2,1,1,1] => [7,4,3,2,1] => [[7,4,3,2,1],[]]
[5,4,3,1,1,1,1,1] => [8,3,3,2,1] => [[8,3,3,2,1],[]]
[5,4,2,2,2,2] => [6,6,2,2,1] => [[6,6,2,2,1],[]]
[5,4,2,2,2,1,1] => [7,5,2,2,1] => [[7,5,2,2,1],[]]
[5,4,2,2,1,1,1,1] => [8,4,2,2,1] => [[8,4,2,2,1],[]]
[5,4,2,1,1,1,1,1,1] => [9,3,2,2,1] => [[9,3,2,2,1],[]]
[5,4,1,1,1,1,1,1,1,1] => [10,2,2,2,1] => [[10,2,2,2,1],[]]
[5,3,3,3,3] => [5,5,5,1,1] => [[5,5,5,1,1],[]]
[5,3,3,3,2,1] => [6,5,4,1,1] => [[6,5,4,1,1],[]]
[5,3,3,3,1,1,1] => [7,4,4,1,1] => [[7,4,4,1,1],[]]
[5,3,3,2,2,2] => [6,6,3,1,1] => [[6,6,3,1,1],[]]
[5,3,3,2,2,1,1] => [7,5,3,1,1] => [[7,5,3,1,1],[]]
[5,3,3,2,1,1,1,1] => [8,4,3,1,1] => [[8,4,3,1,1],[]]
[5,3,3,1,1,1,1,1,1] => [9,3,3,1,1] => [[9,3,3,1,1],[]]
[5,3,2,2,2,2,1] => [7,6,2,1,1] => [[7,6,2,1,1],[]]
[5,3,2,2,2,1,1,1] => [8,5,2,1,1] => [[8,5,2,1,1],[]]
[5,3,2,2,1,1,1,1,1] => [9,4,2,1,1] => [[9,4,2,1,1],[]]
[5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1] => [[10,3,2,1,1],[]]
[5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1] => [[11,2,2,1,1],[]]
[5,2,2,2,2,2,2] => [7,7,1,1,1] => [[7,7,1,1,1],[]]
[5,2,2,2,2,2,1,1] => [8,6,1,1,1] => [[8,6,1,1,1],[]]
[5,2,2,2,2,1,1,1,1] => [9,5,1,1,1] => [[9,5,1,1,1],[]]
[5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1] => [[10,4,1,1,1],[]]
[5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1] => [[11,3,1,1,1],[]]
[5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => [[12,2,1,1,1],[]]
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => [[13,1,1,1,1],[]]
[4,4,4,4,1] => [5,4,4,4] => [[5,4,4,4],[]]
[4,4,4,3,2] => [5,5,4,3] => [[5,5,4,3],[]]
[4,4,4,3,1,1] => [6,4,4,3] => [[6,4,4,3],[]]
[4,4,4,2,2,1] => [6,5,3,3] => [[6,5,3,3],[]]
[4,4,4,2,1,1,1] => [7,4,3,3] => [[7,4,3,3],[]]
[4,4,4,1,1,1,1,1] => [8,3,3,3] => [[8,3,3,3],[]]
[4,4,3,3,3] => [5,5,5,2] => [[5,5,5,2],[]]
[4,4,3,3,2,1] => [6,5,4,2] => [[6,5,4,2],[]]
[4,4,3,3,1,1,1] => [7,4,4,2] => [[7,4,4,2],[]]
[4,4,3,2,2,2] => [6,6,3,2] => [[6,6,3,2],[]]
[4,4,3,2,2,1,1] => [7,5,3,2] => [[7,5,3,2],[]]
[4,4,3,2,1,1,1,1] => [8,4,3,2] => [[8,4,3,2],[]]
[4,4,3,1,1,1,1,1,1] => [9,3,3,2] => [[9,3,3,2],[]]
[4,4,2,2,2,2,1] => [7,6,2,2] => [[7,6,2,2],[]]
[4,4,2,2,2,1,1,1] => [8,5,2,2] => [[8,5,2,2],[]]
[4,4,2,2,1,1,1,1,1] => [9,4,2,2] => [[9,4,2,2],[]]
[4,4,2,1,1,1,1,1,1,1] => [10,3,2,2] => [[10,3,2,2],[]]
[4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2] => [[11,2,2,2],[]]
[4,3,3,3,3,1] => [6,5,5,1] => [[6,5,5,1],[]]
[4,3,3,3,2,2] => [6,6,4,1] => [[6,6,4,1],[]]
[4,3,3,3,2,1,1] => [7,5,4,1] => [[7,5,4,1],[]]
[4,3,3,3,1,1,1,1] => [8,4,4,1] => [[8,4,4,1],[]]
[4,3,3,2,2,2,1] => [7,6,3,1] => [[7,6,3,1],[]]
[4,3,3,2,2,1,1,1] => [8,5,3,1] => [[8,5,3,1],[]]
[4,3,3,2,1,1,1,1,1] => [9,4,3,1] => [[9,4,3,1],[]]
[4,3,3,1,1,1,1,1,1,1] => [10,3,3,1] => [[10,3,3,1],[]]
[4,3,2,2,2,2,2] => [7,7,2,1] => [[7,7,2,1],[]]
[4,3,2,2,2,2,1,1] => [8,6,2,1] => [[8,6,2,1],[]]
[4,3,2,2,2,1,1,1,1] => [9,5,2,1] => [[9,5,2,1],[]]
[4,3,2,2,1,1,1,1,1,1] => [10,4,2,1] => [[10,4,2,1],[]]
[4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1] => [[11,3,2,1],[]]
[4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1] => [[12,2,2,1],[]]
[4,2,2,2,2,2,2,1] => [8,7,1,1] => [[8,7,1,1],[]]
[4,2,2,2,2,2,1,1,1] => [9,6,1,1] => [[9,6,1,1],[]]
[4,2,2,2,2,1,1,1,1,1] => [10,5,1,1] => [[10,5,1,1],[]]
[4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1] => [[11,4,1,1],[]]
[4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1] => [[12,3,1,1],[]]
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1] => [[13,2,1,1],[]]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1] => [[14,1,1,1],[]]
[3,3,3,3,3,2] => [6,6,5] => [[6,6,5],[]]
[3,3,3,3,3,1,1] => [7,5,5] => [[7,5,5],[]]
[3,3,3,3,2,2,1] => [7,6,4] => [[7,6,4],[]]
[3,3,3,3,2,1,1,1] => [8,5,4] => [[8,5,4],[]]
[3,3,3,3,1,1,1,1,1] => [9,4,4] => [[9,4,4],[]]
[3,3,3,2,2,2,2] => [7,7,3] => [[7,7,3],[]]
[3,3,3,2,2,2,1,1] => [8,6,3] => [[8,6,3],[]]
[3,3,3,2,2,1,1,1,1] => [9,5,3] => [[9,5,3],[]]
[3,3,3,2,1,1,1,1,1,1] => [10,4,3] => [[10,4,3],[]]
[3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => [[11,3,3],[]]
[3,3,2,2,2,2,2,1] => [8,7,2] => [[8,7,2],[]]
[3,3,2,2,2,2,1,1,1] => [9,6,2] => [[9,6,2],[]]
[3,3,2,2,2,1,1,1,1,1] => [10,5,2] => [[10,5,2],[]]
[3,3,2,2,1,1,1,1,1,1,1] => [11,4,2] => [[11,4,2],[]]
[3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => [[12,3,2],[]]
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => [[13,2,2],[]]
[3,2,2,2,2,2,2,2] => [8,8,1] => [[8,8,1],[]]
[3,2,2,2,2,2,2,1,1] => [9,7,1] => [[9,7,1],[]]
[3,2,2,2,2,2,1,1,1,1] => [10,6,1] => [[10,6,1],[]]
[3,2,2,2,2,1,1,1,1,1,1] => [11,5,1] => [[11,5,1],[]]
[3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1] => [[12,4,1],[]]
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1] => [[13,3,1],[]]
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1] => [[14,2,1],[]]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1] => [[15,1,1],[]]
[2,2,2,2,2,2,2,2,1] => [9,8] => [[9,8],[]]
[2,2,2,2,2,2,2,1,1,1] => [10,7] => [[10,7],[]]
[2,2,2,2,2,2,1,1,1,1,1] => [11,6] => [[11,6],[]]
[2,2,2,2,2,1,1,1,1,1,1,1] => [12,5] => [[12,5],[]]
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4] => [[13,4],[]]
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => [[14,3],[]]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => [[15,2],[]]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => [[16,1],[]]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => [[17],[]]
[] => [] => [[],[]]
[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] => [[6,5,4,3,2],[]]
[6,4,4,3,2,1] => [6,5,4,3,1,1] => [[6,5,4,3,1,1],[]]
[5,4,4,3,2,1] => [6,5,4,3,1] => [[6,5,4,3,1],[]]
[4,4,4,3,2,1] => [6,5,4,3] => [[6,5,4,3],[]]
[6,5,3,3,2,1] => [6,5,4,2,2,1] => [[6,5,4,2,2,1],[]]
[5,5,3,3,2,1] => [6,5,4,2,2] => [[6,5,4,2,2],[]]
[6,4,3,3,2,1] => [6,5,4,2,1,1] => [[6,5,4,2,1,1],[]]
[5,4,3,3,2,1] => [6,5,4,2,1] => [[6,5,4,2,1],[]]
[6,3,3,3,2,1] => [6,5,4,1,1,1] => [[6,5,4,1,1,1],[]]
[6,5,4,2,2,1] => [6,5,3,3,2,1] => [[6,5,3,3,2,1],[]]
[5,5,4,2,2,1] => [6,5,3,3,2] => [[6,5,3,3,2],[]]
[6,4,4,2,2,1] => [6,5,3,3,1,1] => [[6,5,3,3,1,1],[]]
[5,4,4,2,2,1] => [6,5,3,3,1] => [[6,5,3,3,1],[]]
[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] => [[6,5,3,2,2],[]]
[6,4,3,2,2,1] => [6,5,3,2,1,1] => [[6,5,3,2,1,1],[]]
[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] => [[6,4,4,3,2,1],[]]
[5,5,4,3,1,1] => [6,4,4,3,2] => [[6,4,4,3,2],[]]
[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] => [[6,4,4,3,1],[]]
[6,5,3,3,1,1] => [6,4,4,2,2,1] => [[6,4,4,2,2,1],[]]
[5,5,3,3,1,1] => [6,4,4,2,2] => [[6,4,4,2,2],[]]
[6,4,3,3,1,1] => [6,4,4,2,1,1] => [[6,4,4,2,1,1],[]]
[6,5,4,2,1,1] => [6,4,3,3,2,1] => [[6,4,3,3,2,1],[]]
[5,5,4,2,1,1] => [6,4,3,3,2] => [[6,4,3,3,2],[]]
[6,4,4,2,1,1] => [6,4,3,3,1,1] => [[6,4,3,3,1,1],[]]
[6,5,3,2,1,1] => [6,4,3,2,2,1] => [[6,4,3,2,2,1],[]]
[6,5,4,1,1,1] => [6,3,3,3,2,1] => [[6,3,3,3,2,1],[]]
[6,5,4,3,2] => [5,5,4,3,2,1] => [[5,5,4,3,2,1],[]]
[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] => [[5,5,4,3,1,1],[]]
[5,4,4,3,2] => [5,5,4,3,1] => [[5,5,4,3,1],[]]
[6,5,3,3,2] => [5,5,4,2,2,1] => [[5,5,4,2,2,1],[]]
[5,5,3,3,2] => [5,5,4,2,2] => [[5,5,4,2,2],[]]
[6,4,3,3,2] => [5,5,4,2,1,1] => [[5,5,4,2,1,1],[]]
[6,5,4,2,2] => [5,5,3,3,2,1] => [[5,5,3,3,2,1],[]]
[5,5,4,2,2] => [5,5,3,3,2] => [[5,5,3,3,2],[]]
[6,4,4,2,2] => [5,5,3,3,1,1] => [[5,5,3,3,1,1],[]]
[6,5,3,2,2] => [5,5,3,2,2,1] => [[5,5,3,2,2,1],[]]
[6,5,4,3,1] => [5,4,4,3,2,1] => [[5,4,4,3,2,1],[]]
[5,5,4,3,1] => [5,4,4,3,2] => [[5,4,4,3,2],[]]
[6,4,4,3,1] => [5,4,4,3,1,1] => [[5,4,4,3,1,1],[]]
[6,5,3,3,1] => [5,4,4,2,2,1] => [[5,4,4,2,2,1],[]]
[6,5,4,2,1] => [5,4,3,3,2,1] => [[5,4,3,3,2,1],[]]
[6,5,4,3] => [4,4,4,3,2,1] => [[4,4,4,3,2,1],[]]
[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] => [[7,6,5,4,3,2],[]]
[7,5,5,4,3,2,1] => [7,6,5,4,3,1,1] => [[7,6,5,4,3,1,1],[]]
[6,5,5,4,3,2,1] => [7,6,5,4,3,1] => [[7,6,5,4,3,1],[]]
[5,5,5,4,3,2,1] => [7,6,5,4,3] => [[7,6,5,4,3],[]]
[6,5,4,4,3,2,1] => [7,6,5,4,2,1] => [[7,6,5,4,2,1],[]]
[5,5,4,4,3,2,1] => [7,6,5,4,2] => [[7,6,5,4,2],[]]
[7,4,4,4,3,2,1] => [7,6,5,4,1,1,1] => [[7,6,5,4,1,1,1],[]]
[6,4,4,4,3,2,1] => [7,6,5,4,1,1] => [[7,6,5,4,1,1],[]]
[5,4,4,4,3,2,1] => [7,6,5,4,1] => [[7,6,5,4,1],[]]
[4,4,4,4,3,2,1] => [7,6,5,4] => [[7,6,5,4],[]]
[6,5,4,3,3,2,1] => [7,6,5,3,2,1] => [[7,6,5,3,2,1],[]]
[7,6,3,3,3,2,1] => [7,6,5,2,2,2,1] => [[7,6,5,2,2,2,1],[]]
[6,6,3,3,3,2,1] => [7,6,5,2,2,2] => [[7,6,5,2,2,2],[]]
[6,5,3,3,3,2,1] => [7,6,5,2,2,1] => [[7,6,5,2,2,1],[]]
[6,4,3,3,3,2,1] => [7,6,5,2,1,1] => [[7,6,5,2,1,1],[]]
[6,3,3,3,3,2,1] => [7,6,5,1,1,1] => [[7,6,5,1,1,1],[]]
[3,3,3,3,3,2,1] => [7,6,5] => [[7,6,5],[]]
[7,6,5,4,2,2,1] => [7,6,4,4,3,2,1] => [[7,6,4,4,3,2,1],[]]
[6,6,5,4,2,2,1] => [7,6,4,4,3,2] => [[7,6,4,4,3,2],[]]
[6,5,4,3,2,2,1] => [7,6,4,3,2,1] => [[7,6,4,3,2,1],[]]
[6,5,4,2,2,2,1] => [7,6,3,3,2,1] => [[7,6,3,3,2,1],[]]
[6,5,3,2,2,2,1] => [7,6,3,2,2,1] => [[7,6,3,2,2,1],[]]
[6,4,3,2,2,2,1] => [7,6,3,2,1,1] => [[7,6,3,2,1,1],[]]
[6,5,2,2,2,2,1] => [7,6,2,2,2,1] => [[7,6,2,2,2,1],[]]
[7,2,2,2,2,2,1] => [7,6,1,1,1,1,1] => [[7,6,1,1,1,1,1],[]]
[7,6,5,4,3,1,1] => [7,5,5,4,3,2,1] => [[7,5,5,4,3,2,1],[]]
[6,6,5,4,3,1,1] => [7,5,5,4,3,2] => [[7,5,5,4,3,2],[]]
[6,5,4,3,2,1,1] => [7,5,4,3,2,1] => [[7,5,4,3,2,1],[]]
[5,5,4,3,2,1,1] => [7,5,4,3,2] => [[7,5,4,3,2],[]]
[7,6,5,4,1,1,1] => [7,4,4,4,3,2,1] => [[7,4,4,4,3,2,1],[]]
[6,5,4,3,1,1,1] => [7,4,4,3,2,1] => [[7,4,4,3,2,1],[]]
[6,5,4,2,1,1,1] => [7,4,3,3,2,1] => [[7,4,3,3,2,1],[]]
[7,4,3,2,1,1,1] => [7,4,3,2,1,1,1] => [[7,4,3,2,1,1,1],[]]
[6,4,3,2,1,1,1] => [7,4,3,2,1,1] => [[7,4,3,2,1,1],[]]
[5,5,5,1,1,1,1] => [7,3,3,3,3] => [[7,3,3,3,3],[]]
[6,5,4,1,1,1,1] => [7,3,3,3,2,1] => [[7,3,3,3,2,1],[]]
[7,6,1,1,1,1,1] => [7,2,2,2,2,2,1] => [[7,2,2,2,2,2,1],[]]
[7,6,5,4,3,2] => [6,6,5,4,3,2,1] => [[6,6,5,4,3,2,1],[]]
[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] => [[6,6,5,4,3,1,1],[]]
[6,5,5,4,3,2] => [6,6,5,4,3,1] => [[6,6,5,4,3,1],[]]
[5,5,5,4,3,2] => [6,6,5,4,3] => [[6,6,5,4,3],[]]
[7,6,4,4,3,2] => [6,6,5,4,2,2,1] => [[6,6,5,4,2,2,1],[]]
[7,6,5,4,2,2] => [6,6,4,4,3,2,1] => [[6,6,4,4,3,2,1],[]]
[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] => [[6,5,5,4,3,2,1],[]]
[6,6,5,4,3,1] => [6,5,5,4,3,2] => [[6,5,5,4,3,2],[]]
[6,5,5,4,3,1] => [6,5,5,4,3,1] => [[6,5,5,4,3,1],[]]
[4,4,4,4,3,1] => [6,5,5,4] => [[6,5,5,4],[]]
[7,6,5,4,2,1] => [6,5,4,4,3,2,1] => [[6,5,4,4,3,2,1],[]]
[7,6,5,3,2,1] => [6,5,4,3,3,2,1] => [[6,5,4,3,3,2,1],[]]
[7,6,4,3,2,1] => [6,5,4,3,2,2,1] => [[6,5,4,3,2,2,1],[]]
[6,6,4,3,2,1] => [6,5,4,3,2,2] => [[6,5,4,3,2,2],[]]
[7,5,4,3,2,1] => [6,5,4,3,2,1,1] => [[6,5,4,3,2,1,1],[]]
[7,4,4,3,2,1] => [6,5,4,3,1,1,1] => [[6,5,4,3,1,1,1],[]]
[7,6,3,3,2,1] => [6,5,4,2,2,2,1] => [[6,5,4,2,2,2,1],[]]
[7,3,3,3,2,1] => [6,5,4,1,1,1,1] => [[6,5,4,1,1,1,1],[]]
[7,6,5,2,2,1] => [6,5,3,3,3,2,1] => [[6,5,3,3,3,2,1],[]]
[7,6,2,2,2,1] => [6,5,2,2,2,2,1] => [[6,5,2,2,2,2,1],[]]
[7,6,5,4,1,1] => [6,4,4,4,3,2,1] => [[6,4,4,4,3,2,1],[]]
[7,6,5,1,1,1] => [6,3,3,3,3,2,1] => [[6,3,3,3,3,2,1],[]]
[7,6,5,4,3] => [5,5,5,4,3,2,1] => [[5,5,5,4,3,2,1],[]]
[6,6,5,4,3] => [5,5,5,4,3,2] => [[5,5,5,4,3,2],[]]
[7,5,4,3,2] => [5,5,4,3,2,1,1] => [[5,5,4,3,2,1,1],[]]
[7,6,5,4,1] => [5,4,4,4,3,2,1] => [[5,4,4,4,3,2,1],[]]
[7,5,4,3,1] => [5,4,4,3,2,1,1] => [[5,4,4,3,2,1,1],[]]
[7,6,5,2,1] => [5,4,3,3,3,2,1] => [[5,4,3,3,3,2,1],[]]
[7,6,3,2,1] => [5,4,3,2,2,2,1] => [[5,4,3,2,2,2,1],[]]
[6,6,3,2,1] => [5,4,3,2,2,2] => [[5,4,3,2,2,2],[]]
[7,6,5,4] => [4,4,4,4,3,2,1] => [[4,4,4,4,3,2,1],[]]
[6,5,4,4] => [4,4,4,4,2,1] => [[4,4,4,4,2,1],[]]
[5,5,4,4] => [4,4,4,4,2] => [[4,4,4,4,2],[]]
[7,6,5] => [3,3,3,3,3,2,1] => [[3,3,3,3,3,2,1],[]]
[2,2,2,2,2,2,2,2,2] => [9,9] => [[9,9],[]]
[3,3,3,3,3,3] => [6,6,6] => [[6,6,6],[]]
[3,3,3,3,3,3,3,3] => [8,8,8] => [[8,8,8],[]]
[3,3,3,3,3,3,1] => [7,6,6] => [[7,6,6],[]]
[3,3,3,3,3,3,3] => [7,7,7] => [[7,7,7],[]]
[4,3,3,3,3,3] => [6,6,6,1] => [[6,6,6,1],[]]
[4,4,4,4,4] => [5,5,5,5] => [[5,5,5,5],[]]
[4,4,4,4,4,4] => [6,6,6,6] => [[6,6,6,6],[]]
[5,5,5,5] => [4,4,4,4,4] => [[4,4,4,4,4],[]]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [16,16] => [[16,16],[]]
[6,6,6,6] => [4,4,4,4,4,4] => [[4,4,4,4,4,4],[]]
[6,2,2,2,2,2,2] => [7,7,1,1,1,1] => [[7,7,1,1,1,1],[]]
[6,6,6] => [3,3,3,3,3,3] => [[3,3,3,3,3,3],[]]
[7,6,6] => [3,3,3,3,3,3,1] => [[3,3,3,3,3,3,1],[]]
[10,4,4] => [3,3,3,3,1,1,1,1,1,1] => [[3,3,3,3,1,1,1,1,1,1],[]]
[10,10] => [2,2,2,2,2,2,2,2,2,2] => [[2,2,2,2,2,2,2,2,2,2],[]]
[6,6,6,6,6] => [5,5,5,5,5,5] => [[5,5,5,5,5,5],[]]
[8,2,2,2,2,2,2] => [7,7,1,1,1,1,1,1] => [[7,7,1,1,1,1,1,1],[]]
[10,10,10,10] => [4,4,4,4,4,4,4,4,4,4] => [[4,4,4,4,4,4,4,4,4,4],[]]
[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] => [[24,24,24,24,24],[]]
[5,5,5,5,5,5,5,5,5,5,5,5] => [12,12,12,12,12] => [[12,12,12,12,12],[]]
[15,15] => [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],[]]
[5,5,5,5,5,5] => [6,6,6,6,6] => [[6,6,6,6,6],[]]
[15,5,5] => [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => [[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1],[]]
[7,7,7] => [3,3,3,3,3,3,3] => [[3,3,3,3,3,3,3],[]]
[11,7,5,1] => [4,3,3,3,3,2,2,1,1,1,1] => [[4,3,3,3,3,2,2,1,1,1,1],[]]
[9,7,5,3,1] => [5,4,4,3,3,2,2,1,1] => [[5,4,4,3,3,2,2,1,1],[]]
[11,9,7,5,3,1] => [6,5,5,4,4,3,3,2,2,1,1] => [[6,5,5,4,4,3,3,2,2,1,1],[]]
[9,7,5,5,3,1] => [6,5,5,4,4,2,2,1,1] => [[6,5,5,4,4,2,2,1,1],[]]
[11,8,7,5,4,1] => [6,5,5,5,4,3,3,2,1,1,1] => [[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] => [[8,7,6,5,4,3,2,1],[]]
[7,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2] => [[8,7,6,5,4,3,2],[]]
[7,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1] => [[8,7,6,5,4,3,1],[]]
[7,6,5,5,4,3,2,1] => [8,7,6,5,4,2,1] => [[8,7,6,5,4,2,1],[]]
[7,6,5,4,4,3,2,1] => [8,7,6,5,3,2,1] => [[8,7,6,5,3,2,1],[]]
[7,6,5,4,3,3,2,1] => [8,7,6,4,3,2,1] => [[8,7,6,4,3,2,1],[]]
[7,6,5,4,3,2,2,1] => [8,7,5,4,3,2,1] => [[8,7,5,4,3,2,1],[]]
[7,6,5,4,3,2,1,1] => [8,6,5,4,3,2,1] => [[8,6,5,4,3,2,1],[]]
[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] => [[9,8,7,6,5,4,3,2],[]]
[6,6,6,5,4,3,2,1] => [8,7,6,5,4,3] => [[8,7,6,5,4,3],[]]
[8,7,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1] => [[9,8,7,6,5,4,3,1],[]]
[7,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1] => [[8,7,6,5,4,1,1],[]]
[8,7,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,1] => [[9,8,7,6,5,4,2,1],[]]
[7,6,4,4,4,3,2,1] => [8,7,6,5,2,2,1] => [[8,7,6,5,2,2,1],[]]
[8,7,6,5,5,4,3,2,1] => [9,8,7,6,5,3,2,1] => [[9,8,7,6,5,3,2,1],[]]
[7,6,5,3,3,3,2,1] => [8,7,6,3,3,2,1] => [[8,7,6,3,3,2,1],[]]
[8,7,6,5,4,4,3,2,1] => [9,8,7,6,4,3,2,1] => [[9,8,7,6,4,3,2,1],[]]
[7,6,5,4,2,2,2,1] => [8,7,4,4,3,2,1] => [[8,7,4,4,3,2,1],[]]
[8,7,6,5,4,3,3,2,1] => [9,8,7,5,4,3,2,1] => [[9,8,7,5,4,3,2,1],[]]
[7,6,5,4,3,1,1,1] => [8,5,5,4,3,2,1] => [[8,5,5,4,3,2,1],[]]
[8,7,6,5,4,3,2,2,1] => [9,8,6,5,4,3,2,1] => [[9,8,6,5,4,3,2,1],[]]
[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] => [7,7,6,5,4,3,2,1] => [[7,7,6,5,4,3,2,1],[]]
[8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1] => [[7,6,6,5,4,3,2,1],[]]
[8,7,6,5,4,2,1] => [7,6,5,5,4,3,2,1] => [[7,6,5,5,4,3,2,1],[]]
[8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1] => [[7,6,5,4,4,3,2,1],[]]
[8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1] => [[7,6,5,4,3,3,2,1],[]]
[8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1] => [[7,6,5,4,3,2,2,1],[]]
[8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1] => [[7,6,5,4,3,2,1,1],[]]
[9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1] => [[8,8,7,6,5,4,3,2,1],[]]
[8,7,6,5,4,3] => [6,6,6,5,4,3,2,1] => [[6,6,6,5,4,3,2,1],[]]
[8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1] => [[7,5,5,5,4,3,2,1],[]]
[8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1] => [[7,6,4,4,4,3,2,1],[]]
[8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1] => [[7,6,5,3,3,3,2,1],[]]
[8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1] => [[7,6,5,4,2,2,2,1],[]]
[8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1] => [[7,6,5,4,3,1,1,1],[]]
[9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,1] => [[8,7,6,5,4,3,2,1,1],[]]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15] => [[15,15],[]]
[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] => [[6,2,2,2,2,2,2],[]]
[8,5,4,3,2,1] => [6,5,4,3,2,1,1,1] => [[6,5,4,3,2,1,1,1],[]]
[9,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1,1] => [[7,6,5,4,3,2,1,1,1],[]]
[8,7,4,3,2,1] => [6,5,4,3,2,2,2,1] => [[6,5,4,3,2,2,2,1],[]]
[6,5,4,3,2,1,1,1] => [8,5,4,3,2,1] => [[8,5,4,3,2,1],[]]
[8,6,5,4,3,2] => [6,6,5,4,3,2,1,1] => [[6,6,5,4,3,2,1,1],[]]
[7,5,4,3,2,1,1,1] => [8,5,4,3,2,1,1] => [[8,5,4,3,2,1,1],[]]
[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] => [[4,4,4,4,4,1],[]]
[5,4,4,4,4] => [5,5,5,5,1] => [[5,5,5,5,1],[]]
[8,7,6,3,2,1] => [6,5,4,3,3,3,2,1] => [[6,5,4,3,3,3,2,1],[]]
[8,7,6,5,2,1] => [6,5,4,4,4,3,2,1] => [[6,5,4,4,4,3,2,1],[]]
[8,7,6,5,4,1] => [6,5,5,5,4,3,2,1] => [[6,5,5,5,4,3,2,1],[]]
[7,6,6,5,4,3,2] => [7,7,6,5,4,3,1] => [[7,7,6,5,4,3,1],[]]
[7,6,6,5,4,3,1] => [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] => [[7,6,6,5,4,3,2],[]]
[7,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2] => [[8,6,6,5,4,3,2],[]]
[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] => [[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] => [[9,9,8,7,6,5,4,3,2,1],[]]
[8,6,6,5,4,3,2] => [7,7,6,5,4,3,1,1] => [[7,7,6,5,4,3,1,1],[]]
[4,4,4,4,4,1] => [6,5,5,5] => [[6,5,5,5],[]]
[5,5,5,5,1] => [5,4,4,4,4] => [[5,4,4,4,4],[]]
[6,6,6,1] => [4,3,3,3,3,3] => [[4,3,3,3,3,3],[]]
[8,7,6,5,4,2,2] => [7,7,5,5,4,3,2,1] => [[7,7,5,5,4,3,2,1],[]]
[3,3,3,3,2,2,1,1,1,1] => [10,6,4] => [[10,6,4],[]]
[4,4,3,3,2,2,1,1] => [8,6,4,2] => [[8,6,4,2],[]]
[5,5,4,4,3,3,2,2,1,1] => [10,8,6,4,2] => [[10,8,6,4,2],[]]
[3,3,3,3,3,3,2,1] => [8,7,6] => [[8,7,6],[]]
[4,4,4,4,4,3,2,1] => [8,7,6,5] => [[8,7,6,5],[]]
[5,5,5,5,4,3,2,1] => [8,7,6,5,4] => [[8,7,6,5,4],[]]
[8,7,6,4,4,3,2,1] => [8,7,6,5,3,3,2,1] => [[8,7,6,5,3,3,2,1],[]]
[8,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2,1] => [[8,7,6,5,4,2,2,1],[]]
[9,8,7,6,5,3,3,2,1] => [9,8,7,5,5,4,3,2,1] => [[9,8,7,5,5,4,3,2,1],[]]
[8,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1,1] => [[8,7,6,5,4,1,1,1],[]]
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.
Map
to skew partition
Description
The partition regarded as a skew partition.
searching the database
Sorry, this map was not found in the database.