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Identifier
Mp00040: Integer compositions —to partition⟶ Integer partitions
Images
[1] => [1]
[1,1] => [1,1]
[2] => [2]
[1,1,1] => [1,1,1]
[1,2] => [2,1]
[2,1] => [2,1]
[3] => [3]
[1,1,1,1] => [1,1,1,1]
[1,1,2] => [2,1,1]
[1,2,1] => [2,1,1]
[1,3] => [3,1]
[2,1,1] => [2,1,1]
[2,2] => [2,2]
[3,1] => [3,1]
[4] => [4]
[1,1,1,1,1] => [1,1,1,1,1]
[1,1,1,2] => [2,1,1,1]
[1,1,2,1] => [2,1,1,1]
[1,1,3] => [3,1,1]
[1,2,1,1] => [2,1,1,1]
[1,2,2] => [2,2,1]
[1,3,1] => [3,1,1]
[1,4] => [4,1]
[2,1,1,1] => [2,1,1,1]
[2,1,2] => [2,2,1]
[2,2,1] => [2,2,1]
[2,3] => [3,2]
[3,1,1] => [3,1,1]
[3,2] => [3,2]
[4,1] => [4,1]
[5] => [5]
[1,1,1,1,1,1] => [1,1,1,1,1,1]
[1,1,1,1,2] => [2,1,1,1,1]
[1,1,1,2,1] => [2,1,1,1,1]
[1,1,1,3] => [3,1,1,1]
[1,1,2,1,1] => [2,1,1,1,1]
[1,1,2,2] => [2,2,1,1]
[1,1,3,1] => [3,1,1,1]
[1,1,4] => [4,1,1]
[1,2,1,1,1] => [2,1,1,1,1]
[1,2,1,2] => [2,2,1,1]
[1,2,2,1] => [2,2,1,1]
[1,2,3] => [3,2,1]
[1,3,1,1] => [3,1,1,1]
[1,3,2] => [3,2,1]
[1,4,1] => [4,1,1]
[1,5] => [5,1]
[2,1,1,1,1] => [2,1,1,1,1]
[2,1,1,2] => [2,2,1,1]
[2,1,2,1] => [2,2,1,1]
[2,1,3] => [3,2,1]
[2,2,1,1] => [2,2,1,1]
[2,2,2] => [2,2,2]
[2,3,1] => [3,2,1]
[2,4] => [4,2]
[3,1,1,1] => [3,1,1,1]
[3,1,2] => [3,2,1]
[3,2,1] => [3,2,1]
[3,3] => [3,3]
[4,1,1] => [4,1,1]
[4,2] => [4,2]
[5,1] => [5,1]
[6] => [6]
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
[1,1,1,1,1,2] => [2,1,1,1,1,1]
[1,1,1,1,2,1] => [2,1,1,1,1,1]
[1,1,1,1,3] => [3,1,1,1,1]
[1,1,1,2,1,1] => [2,1,1,1,1,1]
[1,1,1,2,2] => [2,2,1,1,1]
[1,1,1,3,1] => [3,1,1,1,1]
[1,1,1,4] => [4,1,1,1]
[1,1,2,1,1,1] => [2,1,1,1,1,1]
[1,1,2,1,2] => [2,2,1,1,1]
[1,1,2,2,1] => [2,2,1,1,1]
[1,1,2,3] => [3,2,1,1]
[1,1,3,1,1] => [3,1,1,1,1]
[1,1,3,2] => [3,2,1,1]
[1,1,4,1] => [4,1,1,1]
[1,1,5] => [5,1,1]
[1,2,1,1,1,1] => [2,1,1,1,1,1]
[1,2,1,1,2] => [2,2,1,1,1]
[1,2,1,2,1] => [2,2,1,1,1]
[1,2,1,3] => [3,2,1,1]
[1,2,2,1,1] => [2,2,1,1,1]
[1,2,2,2] => [2,2,2,1]
[1,2,3,1] => [3,2,1,1]
[1,2,4] => [4,2,1]
[1,3,1,1,1] => [3,1,1,1,1]
[1,3,1,2] => [3,2,1,1]
[1,3,2,1] => [3,2,1,1]
[1,3,3] => [3,3,1]
[1,4,1,1] => [4,1,1,1]
[1,4,2] => [4,2,1]
[1,5,1] => [5,1,1]
[1,6] => [6,1]
[2,1,1,1,1,1] => [2,1,1,1,1,1]
[2,1,1,1,2] => [2,2,1,1,1]
[2,1,1,2,1] => [2,2,1,1,1]
[2,1,1,3] => [3,2,1,1]
[2,1,2,1,1] => [2,2,1,1,1]
[2,1,2,2] => [2,2,2,1]
>>> Load all 2280 entries. <<<
[2,1,3,1] => [3,2,1,1]
[2,1,4] => [4,2,1]
[2,2,1,1,1] => [2,2,1,1,1]
[2,2,1,2] => [2,2,2,1]
[2,2,2,1] => [2,2,2,1]
[2,2,3] => [3,2,2]
[2,3,1,1] => [3,2,1,1]
[2,3,2] => [3,2,2]
[2,4,1] => [4,2,1]
[2,5] => [5,2]
[3,1,1,1,1] => [3,1,1,1,1]
[3,1,1,2] => [3,2,1,1]
[3,1,2,1] => [3,2,1,1]
[3,1,3] => [3,3,1]
[3,2,1,1] => [3,2,1,1]
[3,2,2] => [3,2,2]
[3,3,1] => [3,3,1]
[3,4] => [4,3]
[4,1,1,1] => [4,1,1,1]
[4,1,2] => [4,2,1]
[4,2,1] => [4,2,1]
[4,3] => [4,3]
[5,1,1] => [5,1,1]
[5,2] => [5,2]
[6,1] => [6,1]
[7] => [7]
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1]
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1]
[1,1,1,1,1,3] => [3,1,1,1,1,1]
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1]
[1,1,1,1,2,2] => [2,2,1,1,1,1]
[1,1,1,1,3,1] => [3,1,1,1,1,1]
[1,1,1,1,4] => [4,1,1,1,1]
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1]
[1,1,1,2,1,2] => [2,2,1,1,1,1]
[1,1,1,2,2,1] => [2,2,1,1,1,1]
[1,1,1,2,3] => [3,2,1,1,1]
[1,1,1,3,1,1] => [3,1,1,1,1,1]
[1,1,1,3,2] => [3,2,1,1,1]
[1,1,1,4,1] => [4,1,1,1,1]
[1,1,1,5] => [5,1,1,1]
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1]
[1,1,2,1,1,2] => [2,2,1,1,1,1]
[1,1,2,1,2,1] => [2,2,1,1,1,1]
[1,1,2,1,3] => [3,2,1,1,1]
[1,1,2,2,1,1] => [2,2,1,1,1,1]
[1,1,2,2,2] => [2,2,2,1,1]
[1,1,2,3,1] => [3,2,1,1,1]
[1,1,2,4] => [4,2,1,1]
[1,1,3,1,1,1] => [3,1,1,1,1,1]
[1,1,3,1,2] => [3,2,1,1,1]
[1,1,3,2,1] => [3,2,1,1,1]
[1,1,3,3] => [3,3,1,1]
[1,1,4,1,1] => [4,1,1,1,1]
[1,1,4,2] => [4,2,1,1]
[1,1,5,1] => [5,1,1,1]
[1,1,6] => [6,1,1]
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1]
[1,2,1,1,1,2] => [2,2,1,1,1,1]
[1,2,1,1,2,1] => [2,2,1,1,1,1]
[1,2,1,1,3] => [3,2,1,1,1]
[1,2,1,2,1,1] => [2,2,1,1,1,1]
[1,2,1,2,2] => [2,2,2,1,1]
[1,2,1,3,1] => [3,2,1,1,1]
[1,2,1,4] => [4,2,1,1]
[1,2,2,1,1,1] => [2,2,1,1,1,1]
[1,2,2,1,2] => [2,2,2,1,1]
[1,2,2,2,1] => [2,2,2,1,1]
[1,2,2,3] => [3,2,2,1]
[1,2,3,1,1] => [3,2,1,1,1]
[1,2,3,2] => [3,2,2,1]
[1,2,4,1] => [4,2,1,1]
[1,2,5] => [5,2,1]
[1,3,1,1,1,1] => [3,1,1,1,1,1]
[1,3,1,1,2] => [3,2,1,1,1]
[1,3,1,2,1] => [3,2,1,1,1]
[1,3,1,3] => [3,3,1,1]
[1,3,2,1,1] => [3,2,1,1,1]
[1,3,2,2] => [3,2,2,1]
[1,3,3,1] => [3,3,1,1]
[1,3,4] => [4,3,1]
[1,4,1,1,1] => [4,1,1,1,1]
[1,4,1,2] => [4,2,1,1]
[1,4,2,1] => [4,2,1,1]
[1,4,3] => [4,3,1]
[1,5,1,1] => [5,1,1,1]
[1,5,2] => [5,2,1]
[1,6,1] => [6,1,1]
[1,7] => [7,1]
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1]
[2,1,1,1,1,2] => [2,2,1,1,1,1]
[2,1,1,1,2,1] => [2,2,1,1,1,1]
[2,1,1,1,3] => [3,2,1,1,1]
[2,1,1,2,1,1] => [2,2,1,1,1,1]
[2,1,1,2,2] => [2,2,2,1,1]
[2,1,1,3,1] => [3,2,1,1,1]
[2,1,1,4] => [4,2,1,1]
[2,1,2,1,1,1] => [2,2,1,1,1,1]
[2,1,2,1,2] => [2,2,2,1,1]
[2,1,2,2,1] => [2,2,2,1,1]
[2,1,2,3] => [3,2,2,1]
[2,1,3,1,1] => [3,2,1,1,1]
[2,1,3,2] => [3,2,2,1]
[2,1,4,1] => [4,2,1,1]
[2,1,5] => [5,2,1]
[2,2,1,1,1,1] => [2,2,1,1,1,1]
[2,2,1,1,2] => [2,2,2,1,1]
[2,2,1,2,1] => [2,2,2,1,1]
[2,2,1,3] => [3,2,2,1]
[2,2,2,1,1] => [2,2,2,1,1]
[2,2,2,2] => [2,2,2,2]
[2,2,3,1] => [3,2,2,1]
[2,2,4] => [4,2,2]
[2,3,1,1,1] => [3,2,1,1,1]
[2,3,1,2] => [3,2,2,1]
[2,3,2,1] => [3,2,2,1]
[2,3,3] => [3,3,2]
[2,4,1,1] => [4,2,1,1]
[2,4,2] => [4,2,2]
[2,5,1] => [5,2,1]
[2,6] => [6,2]
[3,1,1,1,1,1] => [3,1,1,1,1,1]
[3,1,1,1,2] => [3,2,1,1,1]
[3,1,1,2,1] => [3,2,1,1,1]
[3,1,1,3] => [3,3,1,1]
[3,1,2,1,1] => [3,2,1,1,1]
[3,1,2,2] => [3,2,2,1]
[3,1,3,1] => [3,3,1,1]
[3,1,4] => [4,3,1]
[3,2,1,1,1] => [3,2,1,1,1]
[3,2,1,2] => [3,2,2,1]
[3,2,2,1] => [3,2,2,1]
[3,2,3] => [3,3,2]
[3,3,1,1] => [3,3,1,1]
[3,3,2] => [3,3,2]
[3,4,1] => [4,3,1]
[3,5] => [5,3]
[4,1,1,1,1] => [4,1,1,1,1]
[4,1,1,2] => [4,2,1,1]
[4,1,2,1] => [4,2,1,1]
[4,1,3] => [4,3,1]
[4,2,1,1] => [4,2,1,1]
[4,2,2] => [4,2,2]
[4,3,1] => [4,3,1]
[4,4] => [4,4]
[5,1,1,1] => [5,1,1,1]
[5,1,2] => [5,2,1]
[5,2,1] => [5,2,1]
[5,3] => [5,3]
[6,1,1] => [6,1,1]
[6,2] => [6,2]
[7,1] => [7,1]
[8] => [8]
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1]
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1]
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,4] => [4,1,1,1,1,1]
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1]
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1]
[1,1,1,1,2,3] => [3,2,1,1,1,1]
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,3,2] => [3,2,1,1,1,1]
[1,1,1,1,4,1] => [4,1,1,1,1,1]
[1,1,1,1,5] => [5,1,1,1,1]
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1]
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1]
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1]
[1,1,1,2,1,3] => [3,2,1,1,1,1]
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1]
[1,1,1,2,2,2] => [2,2,2,1,1,1]
[1,1,1,2,3,1] => [3,2,1,1,1,1]
[1,1,1,2,4] => [4,2,1,1,1]
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1]
[1,1,1,3,1,2] => [3,2,1,1,1,1]
[1,1,1,3,2,1] => [3,2,1,1,1,1]
[1,1,1,3,3] => [3,3,1,1,1]
[1,1,1,4,1,1] => [4,1,1,1,1,1]
[1,1,1,4,2] => [4,2,1,1,1]
[1,1,1,5,1] => [5,1,1,1,1]
[1,1,1,6] => [6,1,1,1]
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1]
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1]
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1]
[1,1,2,1,1,3] => [3,2,1,1,1,1]
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1]
[1,1,2,1,2,2] => [2,2,2,1,1,1]
[1,1,2,1,3,1] => [3,2,1,1,1,1]
[1,1,2,1,4] => [4,2,1,1,1]
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1]
[1,1,2,2,1,2] => [2,2,2,1,1,1]
[1,1,2,2,2,1] => [2,2,2,1,1,1]
[1,1,2,2,3] => [3,2,2,1,1]
[1,1,2,3,1,1] => [3,2,1,1,1,1]
[1,1,2,3,2] => [3,2,2,1,1]
[1,1,2,4,1] => [4,2,1,1,1]
[1,1,2,5] => [5,2,1,1]
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1]
[1,1,3,1,1,2] => [3,2,1,1,1,1]
[1,1,3,1,2,1] => [3,2,1,1,1,1]
[1,1,3,1,3] => [3,3,1,1,1]
[1,1,3,2,1,1] => [3,2,1,1,1,1]
[1,1,3,2,2] => [3,2,2,1,1]
[1,1,3,3,1] => [3,3,1,1,1]
[1,1,3,4] => [4,3,1,1]
[1,1,4,1,1,1] => [4,1,1,1,1,1]
[1,1,4,1,2] => [4,2,1,1,1]
[1,1,4,2,1] => [4,2,1,1,1]
[1,1,4,3] => [4,3,1,1]
[1,1,5,1,1] => [5,1,1,1,1]
[1,1,5,2] => [5,2,1,1]
[1,1,6,1] => [6,1,1,1]
[1,1,7] => [7,1,1]
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1]
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1]
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1]
[1,2,1,1,1,3] => [3,2,1,1,1,1]
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1]
[1,2,1,1,2,2] => [2,2,2,1,1,1]
[1,2,1,1,3,1] => [3,2,1,1,1,1]
[1,2,1,1,4] => [4,2,1,1,1]
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1]
[1,2,1,2,1,2] => [2,2,2,1,1,1]
[1,2,1,2,2,1] => [2,2,2,1,1,1]
[1,2,1,2,3] => [3,2,2,1,1]
[1,2,1,3,1,1] => [3,2,1,1,1,1]
[1,2,1,3,2] => [3,2,2,1,1]
[1,2,1,4,1] => [4,2,1,1,1]
[1,2,1,5] => [5,2,1,1]
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1]
[1,2,2,1,1,2] => [2,2,2,1,1,1]
[1,2,2,1,2,1] => [2,2,2,1,1,1]
[1,2,2,1,3] => [3,2,2,1,1]
[1,2,2,2,1,1] => [2,2,2,1,1,1]
[1,2,2,2,2] => [2,2,2,2,1]
[1,2,2,3,1] => [3,2,2,1,1]
[1,2,2,4] => [4,2,2,1]
[1,2,3,1,1,1] => [3,2,1,1,1,1]
[1,2,3,1,2] => [3,2,2,1,1]
[1,2,3,2,1] => [3,2,2,1,1]
[1,2,3,3] => [3,3,2,1]
[1,2,4,1,1] => [4,2,1,1,1]
[1,2,4,2] => [4,2,2,1]
[1,2,5,1] => [5,2,1,1]
[1,2,6] => [6,2,1]
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1]
[1,3,1,1,1,2] => [3,2,1,1,1,1]
[1,3,1,1,2,1] => [3,2,1,1,1,1]
[1,3,1,1,3] => [3,3,1,1,1]
[1,3,1,2,1,1] => [3,2,1,1,1,1]
[1,3,1,2,2] => [3,2,2,1,1]
[1,3,1,3,1] => [3,3,1,1,1]
[1,3,1,4] => [4,3,1,1]
[1,3,2,1,1,1] => [3,2,1,1,1,1]
[1,3,2,1,2] => [3,2,2,1,1]
[1,3,2,2,1] => [3,2,2,1,1]
[1,3,2,3] => [3,3,2,1]
[1,3,3,1,1] => [3,3,1,1,1]
[1,3,3,2] => [3,3,2,1]
[1,3,4,1] => [4,3,1,1]
[1,3,5] => [5,3,1]
[1,4,1,1,1,1] => [4,1,1,1,1,1]
[1,4,1,1,2] => [4,2,1,1,1]
[1,4,1,2,1] => [4,2,1,1,1]
[1,4,1,3] => [4,3,1,1]
[1,4,2,1,1] => [4,2,1,1,1]
[1,4,2,2] => [4,2,2,1]
[1,4,3,1] => [4,3,1,1]
[1,4,4] => [4,4,1]
[1,5,1,1,1] => [5,1,1,1,1]
[1,5,1,2] => [5,2,1,1]
[1,5,2,1] => [5,2,1,1]
[1,5,3] => [5,3,1]
[1,6,1,1] => [6,1,1,1]
[1,6,2] => [6,2,1]
[1,7,1] => [7,1,1]
[1,8] => [8,1]
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1]
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1]
[2,1,1,1,1,3] => [3,2,1,1,1,1]
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1]
[2,1,1,1,2,2] => [2,2,2,1,1,1]
[2,1,1,1,3,1] => [3,2,1,1,1,1]
[2,1,1,1,4] => [4,2,1,1,1]
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1]
[2,1,1,2,1,2] => [2,2,2,1,1,1]
[2,1,1,2,2,1] => [2,2,2,1,1,1]
[2,1,1,2,3] => [3,2,2,1,1]
[2,1,1,3,1,1] => [3,2,1,1,1,1]
[2,1,1,3,2] => [3,2,2,1,1]
[2,1,1,4,1] => [4,2,1,1,1]
[2,1,1,5] => [5,2,1,1]
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1]
[2,1,2,1,1,2] => [2,2,2,1,1,1]
[2,1,2,1,2,1] => [2,2,2,1,1,1]
[2,1,2,1,3] => [3,2,2,1,1]
[2,1,2,2,1,1] => [2,2,2,1,1,1]
[2,1,2,2,2] => [2,2,2,2,1]
[2,1,2,3,1] => [3,2,2,1,1]
[2,1,2,4] => [4,2,2,1]
[2,1,3,1,1,1] => [3,2,1,1,1,1]
[2,1,3,1,2] => [3,2,2,1,1]
[2,1,3,2,1] => [3,2,2,1,1]
[2,1,3,3] => [3,3,2,1]
[2,1,4,1,1] => [4,2,1,1,1]
[2,1,4,2] => [4,2,2,1]
[2,1,5,1] => [5,2,1,1]
[2,1,6] => [6,2,1]
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1]
[2,2,1,1,1,2] => [2,2,2,1,1,1]
[2,2,1,1,2,1] => [2,2,2,1,1,1]
[2,2,1,1,3] => [3,2,2,1,1]
[2,2,1,2,1,1] => [2,2,2,1,1,1]
[2,2,1,2,2] => [2,2,2,2,1]
[2,2,1,3,1] => [3,2,2,1,1]
[2,2,1,4] => [4,2,2,1]
[2,2,2,1,1,1] => [2,2,2,1,1,1]
[2,2,2,1,2] => [2,2,2,2,1]
[2,2,2,2,1] => [2,2,2,2,1]
[2,2,2,3] => [3,2,2,2]
[2,2,3,1,1] => [3,2,2,1,1]
[2,2,3,2] => [3,2,2,2]
[2,2,4,1] => [4,2,2,1]
[2,2,5] => [5,2,2]
[2,3,1,1,1,1] => [3,2,1,1,1,1]
[2,3,1,1,2] => [3,2,2,1,1]
[2,3,1,2,1] => [3,2,2,1,1]
[2,3,1,3] => [3,3,2,1]
[2,3,2,1,1] => [3,2,2,1,1]
[2,3,2,2] => [3,2,2,2]
[2,3,3,1] => [3,3,2,1]
[2,3,4] => [4,3,2]
[2,4,1,1,1] => [4,2,1,1,1]
[2,4,1,2] => [4,2,2,1]
[2,4,2,1] => [4,2,2,1]
[2,4,3] => [4,3,2]
[2,5,1,1] => [5,2,1,1]
[2,5,2] => [5,2,2]
[2,6,1] => [6,2,1]
[2,7] => [7,2]
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1]
[3,1,1,1,1,2] => [3,2,1,1,1,1]
[3,1,1,1,2,1] => [3,2,1,1,1,1]
[3,1,1,1,3] => [3,3,1,1,1]
[3,1,1,2,1,1] => [3,2,1,1,1,1]
[3,1,1,2,2] => [3,2,2,1,1]
[3,1,1,3,1] => [3,3,1,1,1]
[3,1,1,4] => [4,3,1,1]
[3,1,2,1,1,1] => [3,2,1,1,1,1]
[3,1,2,1,2] => [3,2,2,1,1]
[3,1,2,2,1] => [3,2,2,1,1]
[3,1,2,3] => [3,3,2,1]
[3,1,3,1,1] => [3,3,1,1,1]
[3,1,3,2] => [3,3,2,1]
[3,1,4,1] => [4,3,1,1]
[3,1,5] => [5,3,1]
[3,2,1,1,1,1] => [3,2,1,1,1,1]
[3,2,1,1,2] => [3,2,2,1,1]
[3,2,1,2,1] => [3,2,2,1,1]
[3,2,1,3] => [3,3,2,1]
[3,2,2,1,1] => [3,2,2,1,1]
[3,2,2,2] => [3,2,2,2]
[3,2,3,1] => [3,3,2,1]
[3,2,4] => [4,3,2]
[3,3,1,1,1] => [3,3,1,1,1]
[3,3,1,2] => [3,3,2,1]
[3,3,2,1] => [3,3,2,1]
[3,3,3] => [3,3,3]
[3,4,1,1] => [4,3,1,1]
[3,4,2] => [4,3,2]
[3,5,1] => [5,3,1]
[3,6] => [6,3]
[4,1,1,1,1,1] => [4,1,1,1,1,1]
[4,1,1,1,2] => [4,2,1,1,1]
[4,1,1,2,1] => [4,2,1,1,1]
[4,1,1,3] => [4,3,1,1]
[4,1,2,1,1] => [4,2,1,1,1]
[4,1,2,2] => [4,2,2,1]
[4,1,3,1] => [4,3,1,1]
[4,1,4] => [4,4,1]
[4,2,1,1,1] => [4,2,1,1,1]
[4,2,1,2] => [4,2,2,1]
[4,2,2,1] => [4,2,2,1]
[4,2,3] => [4,3,2]
[4,3,1,1] => [4,3,1,1]
[4,3,2] => [4,3,2]
[4,4,1] => [4,4,1]
[4,5] => [5,4]
[5,1,1,1,1] => [5,1,1,1,1]
[5,1,1,2] => [5,2,1,1]
[5,1,2,1] => [5,2,1,1]
[5,1,3] => [5,3,1]
[5,2,1,1] => [5,2,1,1]
[5,2,2] => [5,2,2]
[5,3,1] => [5,3,1]
[5,4] => [5,4]
[6,1,1,1] => [6,1,1,1]
[6,1,2] => [6,2,1]
[6,2,1] => [6,2,1]
[6,3] => [6,3]
[7,1,1] => [7,1,1]
[7,2] => [7,2]
[8,1] => [8,1]
[9] => [9]
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1]
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1]
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1]
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1]
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1]
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1]
[1,1,1,1,1,5] => [5,1,1,1,1,1]
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1]
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1]
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1]
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1]
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1]
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1]
[1,1,1,1,2,4] => [4,2,1,1,1,1]
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1]
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1]
[1,1,1,1,3,3] => [3,3,1,1,1,1]
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1]
[1,1,1,1,4,2] => [4,2,1,1,1,1]
[1,1,1,1,5,1] => [5,1,1,1,1,1]
[1,1,1,1,6] => [6,1,1,1,1]
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1]
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1]
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1]
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1]
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1]
[1,1,1,2,1,4] => [4,2,1,1,1,1]
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1]
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1]
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1]
[1,1,1,2,2,3] => [3,2,2,1,1,1]
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1]
[1,1,1,2,3,2] => [3,2,2,1,1,1]
[1,1,1,2,4,1] => [4,2,1,1,1,1]
[1,1,1,2,5] => [5,2,1,1,1]
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1]
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1]
[1,1,1,3,1,3] => [3,3,1,1,1,1]
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1]
[1,1,1,3,2,2] => [3,2,2,1,1,1]
[1,1,1,3,3,1] => [3,3,1,1,1,1]
[1,1,1,3,4] => [4,3,1,1,1]
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1]
[1,1,1,4,1,2] => [4,2,1,1,1,1]
[1,1,1,4,2,1] => [4,2,1,1,1,1]
[1,1,1,4,3] => [4,3,1,1,1]
[1,1,1,5,1,1] => [5,1,1,1,1,1]
[1,1,1,5,2] => [5,2,1,1,1]
[1,1,1,6,1] => [6,1,1,1,1]
[1,1,1,7] => [7,1,1,1]
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1]
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1]
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1]
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1]
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1]
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1]
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1]
[1,1,2,1,1,4] => [4,2,1,1,1,1]
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1]
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1]
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1]
[1,1,2,1,2,3] => [3,2,2,1,1,1]
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1]
[1,1,2,1,3,2] => [3,2,2,1,1,1]
[1,1,2,1,4,1] => [4,2,1,1,1,1]
[1,1,2,1,5] => [5,2,1,1,1]
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1]
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1]
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1]
[1,1,2,2,1,3] => [3,2,2,1,1,1]
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1]
[1,1,2,2,2,2] => [2,2,2,2,1,1]
[1,1,2,2,3,1] => [3,2,2,1,1,1]
[1,1,2,2,4] => [4,2,2,1,1]
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1]
[1,1,2,3,1,2] => [3,2,2,1,1,1]
[1,1,2,3,2,1] => [3,2,2,1,1,1]
[1,1,2,3,3] => [3,3,2,1,1]
[1,1,2,4,1,1] => [4,2,1,1,1,1]
[1,1,2,4,2] => [4,2,2,1,1]
[1,1,2,5,1] => [5,2,1,1,1]
[1,1,2,6] => [6,2,1,1]
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1]
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1]
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1]
[1,1,3,1,1,3] => [3,3,1,1,1,1]
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1]
[1,1,3,1,2,2] => [3,2,2,1,1,1]
[1,1,3,1,3,1] => [3,3,1,1,1,1]
[1,1,3,1,4] => [4,3,1,1,1]
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1]
[1,1,3,2,1,2] => [3,2,2,1,1,1]
[1,1,3,2,2,1] => [3,2,2,1,1,1]
[1,1,3,2,3] => [3,3,2,1,1]
[1,1,3,3,1,1] => [3,3,1,1,1,1]
[1,1,3,3,2] => [3,3,2,1,1]
[1,1,3,4,1] => [4,3,1,1,1]
[1,1,3,5] => [5,3,1,1]
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1]
[1,1,4,1,1,2] => [4,2,1,1,1,1]
[1,1,4,1,2,1] => [4,2,1,1,1,1]
[1,1,4,1,3] => [4,3,1,1,1]
[1,1,4,2,1,1] => [4,2,1,1,1,1]
[1,1,4,2,2] => [4,2,2,1,1]
[1,1,4,3,1] => [4,3,1,1,1]
[1,1,4,4] => [4,4,1,1]
[1,1,5,1,1,1] => [5,1,1,1,1,1]
[1,1,5,1,2] => [5,2,1,1,1]
[1,1,5,2,1] => [5,2,1,1,1]
[1,1,5,3] => [5,3,1,1]
[1,1,6,1,1] => [6,1,1,1,1]
[1,1,6,2] => [6,2,1,1]
[1,1,7,1] => [7,1,1,1]
[1,1,8] => [8,1,1]
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1]
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1]
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1]
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1]
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1]
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1]
[1,2,1,1,1,4] => [4,2,1,1,1,1]
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1]
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1]
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1]
[1,2,1,1,2,3] => [3,2,2,1,1,1]
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1]
[1,2,1,1,3,2] => [3,2,2,1,1,1]
[1,2,1,1,4,1] => [4,2,1,1,1,1]
[1,2,1,1,5] => [5,2,1,1,1]
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1]
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1]
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1]
[1,2,1,2,1,3] => [3,2,2,1,1,1]
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1]
[1,2,1,2,2,2] => [2,2,2,2,1,1]
[1,2,1,2,3,1] => [3,2,2,1,1,1]
[1,2,1,2,4] => [4,2,2,1,1]
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1]
[1,2,1,3,1,2] => [3,2,2,1,1,1]
[1,2,1,3,2,1] => [3,2,2,1,1,1]
[1,2,1,3,3] => [3,3,2,1,1]
[1,2,1,4,1,1] => [4,2,1,1,1,1]
[1,2,1,4,2] => [4,2,2,1,1]
[1,2,1,5,1] => [5,2,1,1,1]
[1,2,1,6] => [6,2,1,1]
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1]
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1]
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1]
[1,2,2,1,1,3] => [3,2,2,1,1,1]
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1]
[1,2,2,1,2,2] => [2,2,2,2,1,1]
[1,2,2,1,3,1] => [3,2,2,1,1,1]
[1,2,2,1,4] => [4,2,2,1,1]
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1]
[1,2,2,2,1,2] => [2,2,2,2,1,1]
[1,2,2,2,2,1] => [2,2,2,2,1,1]
[1,2,2,2,3] => [3,2,2,2,1]
[1,2,2,3,1,1] => [3,2,2,1,1,1]
[1,2,2,3,2] => [3,2,2,2,1]
[1,2,2,4,1] => [4,2,2,1,1]
[1,2,2,5] => [5,2,2,1]
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1]
[1,2,3,1,1,2] => [3,2,2,1,1,1]
[1,2,3,1,2,1] => [3,2,2,1,1,1]
[1,2,3,1,3] => [3,3,2,1,1]
[1,2,3,2,1,1] => [3,2,2,1,1,1]
[1,2,3,2,2] => [3,2,2,2,1]
[1,2,3,3,1] => [3,3,2,1,1]
[1,2,3,4] => [4,3,2,1]
[1,2,4,1,1,1] => [4,2,1,1,1,1]
[1,2,4,1,2] => [4,2,2,1,1]
[1,2,4,2,1] => [4,2,2,1,1]
[1,2,4,3] => [4,3,2,1]
[1,2,5,1,1] => [5,2,1,1,1]
[1,2,5,2] => [5,2,2,1]
[1,2,6,1] => [6,2,1,1]
[1,2,7] => [7,2,1]
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1]
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1]
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1]
[1,3,1,1,1,3] => [3,3,1,1,1,1]
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1]
[1,3,1,1,2,2] => [3,2,2,1,1,1]
[1,3,1,1,3,1] => [3,3,1,1,1,1]
[1,3,1,1,4] => [4,3,1,1,1]
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1]
[1,3,1,2,1,2] => [3,2,2,1,1,1]
[1,3,1,2,2,1] => [3,2,2,1,1,1]
[1,3,1,2,3] => [3,3,2,1,1]
[1,3,1,3,1,1] => [3,3,1,1,1,1]
[1,3,1,3,2] => [3,3,2,1,1]
[1,3,1,4,1] => [4,3,1,1,1]
[1,3,1,5] => [5,3,1,1]
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1]
[1,3,2,1,1,2] => [3,2,2,1,1,1]
[1,3,2,1,2,1] => [3,2,2,1,1,1]
[1,3,2,1,3] => [3,3,2,1,1]
[1,3,2,2,1,1] => [3,2,2,1,1,1]
[1,3,2,2,2] => [3,2,2,2,1]
[1,3,2,3,1] => [3,3,2,1,1]
[1,3,2,4] => [4,3,2,1]
[1,3,3,1,1,1] => [3,3,1,1,1,1]
[1,3,3,1,2] => [3,3,2,1,1]
[1,3,3,2,1] => [3,3,2,1,1]
[1,3,3,3] => [3,3,3,1]
[1,3,4,1,1] => [4,3,1,1,1]
[1,3,4,2] => [4,3,2,1]
[1,3,5,1] => [5,3,1,1]
[1,3,6] => [6,3,1]
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1]
[1,4,1,1,1,2] => [4,2,1,1,1,1]
[1,4,1,1,2,1] => [4,2,1,1,1,1]
[1,4,1,1,3] => [4,3,1,1,1]
[1,4,1,2,1,1] => [4,2,1,1,1,1]
[1,4,1,2,2] => [4,2,2,1,1]
[1,4,1,3,1] => [4,3,1,1,1]
[1,4,1,4] => [4,4,1,1]
[1,4,2,1,1,1] => [4,2,1,1,1,1]
[1,4,2,1,2] => [4,2,2,1,1]
[1,4,2,2,1] => [4,2,2,1,1]
[1,4,2,3] => [4,3,2,1]
[1,4,3,1,1] => [4,3,1,1,1]
[1,4,3,2] => [4,3,2,1]
[1,4,4,1] => [4,4,1,1]
[1,4,5] => [5,4,1]
[1,5,1,1,1,1] => [5,1,1,1,1,1]
[1,5,1,1,2] => [5,2,1,1,1]
[1,5,1,2,1] => [5,2,1,1,1]
[1,5,1,3] => [5,3,1,1]
[1,5,2,1,1] => [5,2,1,1,1]
[1,5,2,2] => [5,2,2,1]
[1,5,3,1] => [5,3,1,1]
[1,5,4] => [5,4,1]
[1,6,1,1,1] => [6,1,1,1,1]
[1,6,1,2] => [6,2,1,1]
[1,6,2,1] => [6,2,1,1]
[1,6,3] => [6,3,1]
[1,7,1,1] => [7,1,1,1]
[1,7,2] => [7,2,1]
[1,8,1] => [8,1,1]
[1,9] => [9,1]
[2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1]
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1]
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1]
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1]
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1]
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1]
[2,1,1,1,1,4] => [4,2,1,1,1,1]
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1]
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1]
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1]
[2,1,1,1,2,3] => [3,2,2,1,1,1]
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1]
[2,1,1,1,3,2] => [3,2,2,1,1,1]
[2,1,1,1,4,1] => [4,2,1,1,1,1]
[2,1,1,1,5] => [5,2,1,1,1]
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1]
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1]
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1]
[2,1,1,2,1,3] => [3,2,2,1,1,1]
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1]
[2,1,1,2,2,2] => [2,2,2,2,1,1]
[2,1,1,2,3,1] => [3,2,2,1,1,1]
[2,1,1,2,4] => [4,2,2,1,1]
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1]
[2,1,1,3,1,2] => [3,2,2,1,1,1]
[2,1,1,3,2,1] => [3,2,2,1,1,1]
[2,1,1,3,3] => [3,3,2,1,1]
[2,1,1,4,1,1] => [4,2,1,1,1,1]
[2,1,1,4,2] => [4,2,2,1,1]
[2,1,1,5,1] => [5,2,1,1,1]
[2,1,1,6] => [6,2,1,1]
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1]
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1]
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1]
[2,1,2,1,1,3] => [3,2,2,1,1,1]
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1]
[2,1,2,1,2,2] => [2,2,2,2,1,1]
[2,1,2,1,3,1] => [3,2,2,1,1,1]
[2,1,2,1,4] => [4,2,2,1,1]
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1]
[2,1,2,2,1,2] => [2,2,2,2,1,1]
[2,1,2,2,2,1] => [2,2,2,2,1,1]
[2,1,2,2,3] => [3,2,2,2,1]
[2,1,2,3,1,1] => [3,2,2,1,1,1]
[2,1,2,3,2] => [3,2,2,2,1]
[2,1,2,4,1] => [4,2,2,1,1]
[2,1,2,5] => [5,2,2,1]
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1]
[2,1,3,1,1,2] => [3,2,2,1,1,1]
[2,1,3,1,2,1] => [3,2,2,1,1,1]
[2,1,3,1,3] => [3,3,2,1,1]
[2,1,3,2,1,1] => [3,2,2,1,1,1]
[2,1,3,2,2] => [3,2,2,2,1]
[2,1,3,3,1] => [3,3,2,1,1]
[2,1,3,4] => [4,3,2,1]
[2,1,4,1,1,1] => [4,2,1,1,1,1]
[2,1,4,1,2] => [4,2,2,1,1]
[2,1,4,2,1] => [4,2,2,1,1]
[2,1,4,3] => [4,3,2,1]
[2,1,5,1,1] => [5,2,1,1,1]
[2,1,5,2] => [5,2,2,1]
[2,1,6,1] => [6,2,1,1]
[2,1,7] => [7,2,1]
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1]
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1]
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1]
[2,2,1,1,1,3] => [3,2,2,1,1,1]
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1]
[2,2,1,1,2,2] => [2,2,2,2,1,1]
[2,2,1,1,3,1] => [3,2,2,1,1,1]
[2,2,1,1,4] => [4,2,2,1,1]
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1]
[2,2,1,2,1,2] => [2,2,2,2,1,1]
[2,2,1,2,2,1] => [2,2,2,2,1,1]
[2,2,1,2,3] => [3,2,2,2,1]
[2,2,1,3,1,1] => [3,2,2,1,1,1]
[2,2,1,3,2] => [3,2,2,2,1]
[2,2,1,4,1] => [4,2,2,1,1]
[2,2,1,5] => [5,2,2,1]
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1]
[2,2,2,1,1,2] => [2,2,2,2,1,1]
[2,2,2,1,2,1] => [2,2,2,2,1,1]
[2,2,2,1,3] => [3,2,2,2,1]
[2,2,2,2,1,1] => [2,2,2,2,1,1]
[2,2,2,2,2] => [2,2,2,2,2]
[2,2,2,3,1] => [3,2,2,2,1]
[2,2,2,4] => [4,2,2,2]
[2,2,3,1,1,1] => [3,2,2,1,1,1]
[2,2,3,1,2] => [3,2,2,2,1]
[2,2,3,2,1] => [3,2,2,2,1]
[2,2,3,3] => [3,3,2,2]
[2,2,4,1,1] => [4,2,2,1,1]
[2,2,4,2] => [4,2,2,2]
[2,2,5,1] => [5,2,2,1]
[2,2,6] => [6,2,2]
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1]
[2,3,1,1,1,2] => [3,2,2,1,1,1]
[2,3,1,1,2,1] => [3,2,2,1,1,1]
[2,3,1,1,3] => [3,3,2,1,1]
[2,3,1,2,1,1] => [3,2,2,1,1,1]
[2,3,1,2,2] => [3,2,2,2,1]
[2,3,1,3,1] => [3,3,2,1,1]
[2,3,1,4] => [4,3,2,1]
[2,3,2,1,1,1] => [3,2,2,1,1,1]
[2,3,2,1,2] => [3,2,2,2,1]
[2,3,2,2,1] => [3,2,2,2,1]
[2,3,2,3] => [3,3,2,2]
[2,3,3,1,1] => [3,3,2,1,1]
[2,3,3,2] => [3,3,2,2]
[2,3,4,1] => [4,3,2,1]
[2,3,5] => [5,3,2]
[2,4,1,1,1,1] => [4,2,1,1,1,1]
[2,4,1,1,2] => [4,2,2,1,1]
[2,4,1,2,1] => [4,2,2,1,1]
[2,4,1,3] => [4,3,2,1]
[2,4,2,1,1] => [4,2,2,1,1]
[2,4,2,2] => [4,2,2,2]
[2,4,3,1] => [4,3,2,1]
[2,4,4] => [4,4,2]
[2,5,1,1,1] => [5,2,1,1,1]
[2,5,1,2] => [5,2,2,1]
[2,5,2,1] => [5,2,2,1]
[2,5,3] => [5,3,2]
[2,6,1,1] => [6,2,1,1]
[2,6,2] => [6,2,2]
[2,7,1] => [7,2,1]
[2,8] => [8,2]
[3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1]
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1]
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1]
[3,1,1,1,1,3] => [3,3,1,1,1,1]
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1]
[3,1,1,1,2,2] => [3,2,2,1,1,1]
[3,1,1,1,3,1] => [3,3,1,1,1,1]
[3,1,1,1,4] => [4,3,1,1,1]
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1]
[3,1,1,2,1,2] => [3,2,2,1,1,1]
[3,1,1,2,2,1] => [3,2,2,1,1,1]
[3,1,1,2,3] => [3,3,2,1,1]
[3,1,1,3,1,1] => [3,3,1,1,1,1]
[3,1,1,3,2] => [3,3,2,1,1]
[3,1,1,4,1] => [4,3,1,1,1]
[3,1,1,5] => [5,3,1,1]
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1]
[3,1,2,1,1,2] => [3,2,2,1,1,1]
[3,1,2,1,2,1] => [3,2,2,1,1,1]
[3,1,2,1,3] => [3,3,2,1,1]
[3,1,2,2,1,1] => [3,2,2,1,1,1]
[3,1,2,2,2] => [3,2,2,2,1]
[3,1,2,3,1] => [3,3,2,1,1]
[3,1,2,4] => [4,3,2,1]
[3,1,3,1,1,1] => [3,3,1,1,1,1]
[3,1,3,1,2] => [3,3,2,1,1]
[3,1,3,2,1] => [3,3,2,1,1]
[3,1,3,3] => [3,3,3,1]
[3,1,4,1,1] => [4,3,1,1,1]
[3,1,4,2] => [4,3,2,1]
[3,1,5,1] => [5,3,1,1]
[3,1,6] => [6,3,1]
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1]
[3,2,1,1,1,2] => [3,2,2,1,1,1]
[3,2,1,1,2,1] => [3,2,2,1,1,1]
[3,2,1,1,3] => [3,3,2,1,1]
[3,2,1,2,1,1] => [3,2,2,1,1,1]
[3,2,1,2,2] => [3,2,2,2,1]
[3,2,1,3,1] => [3,3,2,1,1]
[3,2,1,4] => [4,3,2,1]
[3,2,2,1,1,1] => [3,2,2,1,1,1]
[3,2,2,1,2] => [3,2,2,2,1]
[3,2,2,2,1] => [3,2,2,2,1]
[3,2,2,3] => [3,3,2,2]
[3,2,3,1,1] => [3,3,2,1,1]
[3,2,3,2] => [3,3,2,2]
[3,2,4,1] => [4,3,2,1]
[3,2,5] => [5,3,2]
[3,3,1,1,1,1] => [3,3,1,1,1,1]
[3,3,1,1,2] => [3,3,2,1,1]
[3,3,1,2,1] => [3,3,2,1,1]
[3,3,1,3] => [3,3,3,1]
[3,3,2,1,1] => [3,3,2,1,1]
[3,3,2,2] => [3,3,2,2]
[3,3,3,1] => [3,3,3,1]
[3,3,4] => [4,3,3]
[3,4,1,1,1] => [4,3,1,1,1]
[3,4,1,2] => [4,3,2,1]
[3,4,2,1] => [4,3,2,1]
[3,4,3] => [4,3,3]
[3,5,1,1] => [5,3,1,1]
[3,5,2] => [5,3,2]
[3,6,1] => [6,3,1]
[3,7] => [7,3]
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1]
[4,1,1,1,1,2] => [4,2,1,1,1,1]
[4,1,1,1,2,1] => [4,2,1,1,1,1]
[4,1,1,1,3] => [4,3,1,1,1]
[4,1,1,2,1,1] => [4,2,1,1,1,1]
[4,1,1,2,2] => [4,2,2,1,1]
[4,1,1,3,1] => [4,3,1,1,1]
[4,1,1,4] => [4,4,1,1]
[4,1,2,1,1,1] => [4,2,1,1,1,1]
[4,1,2,1,2] => [4,2,2,1,1]
[4,1,2,2,1] => [4,2,2,1,1]
[4,1,2,3] => [4,3,2,1]
[4,1,3,1,1] => [4,3,1,1,1]
[4,1,3,2] => [4,3,2,1]
[4,1,4,1] => [4,4,1,1]
[4,1,5] => [5,4,1]
[4,2,1,1,1,1] => [4,2,1,1,1,1]
[4,2,1,1,2] => [4,2,2,1,1]
[4,2,1,2,1] => [4,2,2,1,1]
[4,2,1,3] => [4,3,2,1]
[4,2,2,1,1] => [4,2,2,1,1]
[4,2,2,2] => [4,2,2,2]
[4,2,3,1] => [4,3,2,1]
[4,2,4] => [4,4,2]
[4,3,1,1,1] => [4,3,1,1,1]
[4,3,1,2] => [4,3,2,1]
[4,3,2,1] => [4,3,2,1]
[4,3,3] => [4,3,3]
[4,4,1,1] => [4,4,1,1]
[4,4,2] => [4,4,2]
[4,5,1] => [5,4,1]
[4,6] => [6,4]
[5,1,1,1,1,1] => [5,1,1,1,1,1]
[5,1,1,1,2] => [5,2,1,1,1]
[5,1,1,2,1] => [5,2,1,1,1]
[5,1,1,3] => [5,3,1,1]
[5,1,2,1,1] => [5,2,1,1,1]
[5,1,2,2] => [5,2,2,1]
[5,1,3,1] => [5,3,1,1]
[5,1,4] => [5,4,1]
[5,2,1,1,1] => [5,2,1,1,1]
[5,2,1,2] => [5,2,2,1]
[5,2,2,1] => [5,2,2,1]
[5,2,3] => [5,3,2]
[5,3,1,1] => [5,3,1,1]
[5,3,2] => [5,3,2]
[5,4,1] => [5,4,1]
[5,5] => [5,5]
[6,1,1,1,1] => [6,1,1,1,1]
[6,1,1,2] => [6,2,1,1]
[6,1,2,1] => [6,2,1,1]
[6,1,3] => [6,3,1]
[6,2,1,1] => [6,2,1,1]
[6,2,2] => [6,2,2]
[6,3,1] => [6,3,1]
[6,4] => [6,4]
[7,1,1,1] => [7,1,1,1]
[7,1,2] => [7,2,1]
[7,2,1] => [7,2,1]
[7,3] => [7,3]
[8,1,1] => [8,1,1]
[8,2] => [8,2]
[9,1] => [9,1]
[10] => [10]
[1,10] => [10,1]
[1,8,1,1] => [8,1,1,1]
[1,7,2,1] => [7,2,1,1]
[1,6,3,1] => [6,3,1,1]
[1,5,4,1] => [5,4,1,1]
[1,4,5,1] => [5,4,1,1]
[1,3,6,1] => [6,3,1,1]
[1,2,7,1] => [7,2,1,1]
[1,1,8,1] => [8,1,1,1]
[10,1] => [10,1]
[1,8,2] => [8,2,1]
[1,7,1,2] => [7,2,1,1]
[1,6,1,1,2] => [6,2,1,1,1]
[1,5,1,1,1,2] => [5,2,1,1,1,1]
[1,4,1,1,1,1,2] => [4,2,1,1,1,1,1]
[1,3,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1]
[1,7,3] => [7,3,1]
[1,6,2,2] => [6,2,2,1]
[1,5,2,1,2] => [5,2,2,1,1]
[1,4,2,1,1,2] => [4,2,2,1,1,1]
[1,3,2,1,1,1,2] => [3,2,2,1,1,1,1]
[1,2,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1]
[1,1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1]
[1,2,2,2,2,2] => [2,2,2,2,2,1]
[1,2,2,2,1,3] => [3,2,2,2,1,1]
[1,2,2,1,3,2] => [3,2,2,2,1,1]
[1,2,2,1,2,3] => [3,2,2,2,1,1]
[1,2,2,1,1,4] => [4,2,2,1,1,1]
[1,2,1,3,2,2] => [3,2,2,2,1,1]
[1,2,1,3,1,3] => [3,3,2,1,1,1]
[1,2,1,2,3,2] => [3,2,2,2,1,1]
[1,2,1,2,2,3] => [3,2,2,2,1,1]
[1,2,1,2,1,4] => [4,2,2,1,1,1]
[1,2,1,1,4,2] => [4,2,2,1,1,1]
[1,2,1,1,3,3] => [3,3,2,1,1,1]
[1,2,1,1,2,4] => [4,2,2,1,1,1]
[1,2,1,1,1,5] => [5,2,1,1,1,1]
[1,1,3,2,2,2] => [3,2,2,2,1,1]
[1,1,3,2,1,3] => [3,3,2,1,1,1]
[1,1,3,1,3,2] => [3,3,2,1,1,1]
[1,1,3,1,2,3] => [3,3,2,1,1,1]
[1,1,3,1,1,4] => [4,3,1,1,1,1]
[1,1,2,3,2,2] => [3,2,2,2,1,1]
[1,1,2,3,1,3] => [3,3,2,1,1,1]
[1,1,2,2,3,2] => [3,2,2,2,1,1]
[1,1,2,2,2,3] => [3,2,2,2,1,1]
[1,1,2,2,1,4] => [4,2,2,1,1,1]
[1,1,2,1,4,2] => [4,2,2,1,1,1]
[1,1,2,1,3,3] => [3,3,2,1,1,1]
[1,1,2,1,2,4] => [4,2,2,1,1,1]
[1,1,2,1,1,5] => [5,2,1,1,1,1]
[1,1,1,4,2,2] => [4,2,2,1,1,1]
[1,1,1,4,1,3] => [4,3,1,1,1,1]
[1,1,1,3,3,2] => [3,3,2,1,1,1]
[1,1,1,3,2,3] => [3,3,2,1,1,1]
[1,1,1,3,1,4] => [4,3,1,1,1,1]
[1,1,1,2,4,2] => [4,2,2,1,1,1]
[1,1,1,2,3,3] => [3,3,2,1,1,1]
[1,1,1,2,2,4] => [4,2,2,1,1,1]
[1,1,1,2,1,5] => [5,2,1,1,1,1]
[1,1,1,1,5,2] => [5,2,1,1,1,1]
[1,1,1,1,4,3] => [4,3,1,1,1,1]
[1,1,1,1,3,4] => [4,3,1,1,1,1]
[1,1,1,1,2,5] => [5,2,1,1,1,1]
[1,1,1,1,1,6] => [6,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1]
[2,8,1] => [8,2,1]
[2,1,7,1] => [7,2,1,1]
[2,1,1,6,1] => [6,2,1,1,1]
[2,1,1,1,5,1] => [5,2,1,1,1,1]
[2,1,1,1,1,4,1] => [4,2,1,1,1,1,1]
[2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1]
[2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1]
[3,7,1] => [7,3,1]
[2,2,6,1] => [6,2,2,1]
[2,1,2,5,1] => [5,2,2,1,1]
[2,1,1,2,4,1] => [4,2,2,1,1,1]
[2,1,1,1,2,3,1] => [3,2,2,1,1,1,1]
[2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1]
[2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1]
[2,2,2,2,2,1] => [2,2,2,2,2,1]
[3,1,2,2,2,1] => [3,2,2,2,1,1]
[2,3,1,2,2,1] => [3,2,2,2,1,1]
[3,2,1,2,2,1] => [3,2,2,2,1,1]
[4,1,1,2,2,1] => [4,2,2,1,1,1]
[2,2,3,1,2,1] => [3,2,2,2,1,1]
[3,1,3,1,2,1] => [3,3,2,1,1,1]
[2,3,2,1,2,1] => [3,2,2,2,1,1]
[3,2,2,1,2,1] => [3,2,2,2,1,1]
[4,1,2,1,2,1] => [4,2,2,1,1,1]
[2,4,1,1,2,1] => [4,2,2,1,1,1]
[3,3,1,1,2,1] => [3,3,2,1,1,1]
[4,2,1,1,2,1] => [4,2,2,1,1,1]
[5,1,1,1,2,1] => [5,2,1,1,1,1]
[2,2,2,3,1,1] => [3,2,2,2,1,1]
[3,1,2,3,1,1] => [3,3,2,1,1,1]
[2,3,1,3,1,1] => [3,3,2,1,1,1]
[3,2,1,3,1,1] => [3,3,2,1,1,1]
[4,1,1,3,1,1] => [4,3,1,1,1,1]
[2,2,3,2,1,1] => [3,2,2,2,1,1]
[3,1,3,2,1,1] => [3,3,2,1,1,1]
[2,3,2,2,1,1] => [3,2,2,2,1,1]
[3,2,2,2,1,1] => [3,2,2,2,1,1]
[4,1,2,2,1,1] => [4,2,2,1,1,1]
[2,4,1,2,1,1] => [4,2,2,1,1,1]
[3,3,1,2,1,1] => [3,3,2,1,1,1]
[4,2,1,2,1,1] => [4,2,2,1,1,1]
[5,1,1,2,1,1] => [5,2,1,1,1,1]
[2,2,4,1,1,1] => [4,2,2,1,1,1]
[3,1,4,1,1,1] => [4,3,1,1,1,1]
[2,3,3,1,1,1] => [3,3,2,1,1,1]
[3,2,3,1,1,1] => [3,3,2,1,1,1]
[4,1,3,1,1,1] => [4,3,1,1,1,1]
[2,4,2,1,1,1] => [4,2,2,1,1,1]
[3,3,2,1,1,1] => [3,3,2,1,1,1]
[4,2,2,1,1,1] => [4,2,2,1,1,1]
[5,1,2,1,1,1] => [5,2,1,1,1,1]
[2,5,1,1,1,1] => [5,2,1,1,1,1]
[3,4,1,1,1,1] => [4,3,1,1,1,1]
[4,3,1,1,1,1] => [4,3,1,1,1,1]
[5,2,1,1,1,1] => [5,2,1,1,1,1]
[6,1,1,1,1,1] => [6,1,1,1,1,1]
[2,1,1,1,1,1,1,3] => [3,2,1,1,1,1,1,1]
[2,1,1,1,1,1,2,2] => [2,2,2,1,1,1,1,1]
[2,1,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1]
[2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1]
[2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1]
[2,1,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1]
[2,2,1,1,1,1,1,2] => [2,2,2,1,1,1,1,1]
[3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1]
[9,2] => [9,2]
[1,9,1] => [9,1,1]
[11] => [11]
[2,9] => [9,2]
[1,1,2,2,4,1] => [4,2,2,1,1,1]
[5,1,1,1,1,2] => [5,2,1,1,1,1]
[1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,5,1] => [5,1,1,1,1,1,1]
[1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1]
[1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1]
[1,1,1,3,1,3,1] => [3,3,1,1,1,1,1]
[1,1,1,5,1,1,1] => [5,1,1,1,1,1,1]
[1,1,1,7,1] => [7,1,1,1,1]
[1,1,1,4,1,2,1] => [4,2,1,1,1,1,1]
[1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1]
[1,1,1,2,1,4,1] => [4,2,1,1,1,1,1]
[1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1]
[1,1,1,2,3,2,1] => [3,2,2,1,1,1,1]
[1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1]
[1,3,1,1,1,3,1] => [3,3,1,1,1,1,1]
[1,3,1,3,1,1,1] => [3,3,1,1,1,1,1]
[1,3,1,5,1] => [5,3,1,1,1]
[1,3,1,2,1,2,1] => [3,2,2,1,1,1,1]
[1,5,1,1,1,1,1] => [5,1,1,1,1,1,1]
[1,5,1,3,1] => [5,3,1,1,1]
[1,7,1,1,1] => [7,1,1,1,1]
[1,6,1,2,1] => [6,2,1,1,1]
[1,4,1,2,1,1,1] => [4,2,1,1,1,1,1]
[1,4,1,4,1] => [4,4,1,1,1]
[1,4,1,1,1,2,1] => [4,2,1,1,1,1,1]
[1,4,3,2,1] => [4,3,2,1,1]
[1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1]
[1,2,1,2,1,3,1] => [3,2,2,1,1,1,1]
[1,2,1,4,1,1,1] => [4,2,1,1,1,1,1]
[1,2,1,6,1] => [6,2,1,1,1]
[1,2,1,3,1,2,1] => [3,2,2,1,1,1,1]
[1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1]
[1,2,1,1,1,4,1] => [4,2,1,1,1,1,1]
[1,2,1,1,3,2,1] => [3,2,2,1,1,1,1]
[1,2,3,2,1,1,1] => [3,2,2,1,1,1,1]
[1,2,3,4,1] => [4,3,2,1,1]
[1,2,3,1,1,2,1] => [3,2,2,1,1,1,1]
[1,2,5,2,1] => [5,2,2,1,1]
[1,2,2,1,2,2,1] => [2,2,2,2,1,1,1]
[1,1,9] => [9,1,1]
[1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1]
[1,6,4] => [6,4,1]
[1,5,5] => [5,5,1]
[1,4,6] => [6,4,1]
[1,3,7] => [7,3,1]
[1,2,8] => [8,2,1]
[1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1]
[1,1,2,2,2,2,1] => [2,2,2,2,1,1,1]
[1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1]
[1,1,2,2,3,1,1] => [3,2,2,1,1,1,1]
[1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1]
[1,1,2,3,2,1,1] => [3,2,2,1,1,1,1]
[1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1]
[1,1,3,2,2,1,1] => [3,2,2,1,1,1,1]
[1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1]
[1,2,2,2,2,1,1] => [2,2,2,2,1,1,1]
[1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1]
[1,1,2,5,1,1] => [5,2,1,1,1,1]
[1,1,5,2,1,1] => [5,2,1,1,1,1]
[1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1]
[1,4,2,2,1,1] => [4,2,2,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,3,3] => [3,3,1,1,1,1,1,1]
[1,1,1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,2,2,2,2] => [2,2,2,2,1,1,1,1]
[1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,2,1,2,3] => [3,2,2,1,1,1,1,1]
[1,1,1,1,3,3,1,1] => [3,3,1,1,1,1,1,1]
[1,1,1,1,3,2,1,2] => [3,2,2,1,1,1,1,1]
[1,1,1,1,3,1,1,3] => [3,3,1,1,1,1,1,1]
[1,1,1,1,4,4] => [4,4,1,1,1,1]
[1,1,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,2,1,1,2,2] => [2,2,2,2,1,1,1,1]
[1,1,2,2,2,2,1,1] => [2,2,2,2,1,1,1,1]
[1,1,2,2,2,1,1,2] => [2,2,2,2,1,1,1,1]
[1,1,2,2,3,3] => [3,3,2,2,1,1]
[1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,1,1,2,2,2] => [2,2,2,2,1,1,1,1]
[1,1,2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,1,1,1,2,3] => [3,2,2,1,1,1,1,1]
[1,1,2,1,2,3,1,1] => [3,2,2,1,1,1,1,1]
[1,1,2,1,2,2,1,2] => [2,2,2,2,1,1,1,1]
[1,1,2,1,2,1,1,3] => [3,2,2,1,1,1,1,1]
[1,1,2,1,3,4] => [4,3,2,1,1,1]
[1,1,3,3,1,1,1,1] => [3,3,1,1,1,1,1,1]
[1,1,3,3,2,2] => [3,3,2,2,1,1]
[1,1,3,2,1,2,1,1] => [3,2,2,1,1,1,1,1]
[1,1,3,2,1,1,1,2] => [3,2,2,1,1,1,1,1]
[1,1,3,2,2,3] => [3,3,2,2,1,1]
[1,1,3,1,1,3,1,1] => [3,3,1,1,1,1,1,1]
[1,1,3,1,1,2,1,2] => [3,2,2,1,1,1,1,1]
[1,1,3,1,1,1,1,3] => [3,3,1,1,1,1,1,1]
[1,1,3,1,2,4] => [4,3,2,1,1,1]
[1,1,4,4,1,1] => [4,4,1,1,1,1]
[1,1,4,3,1,2] => [4,3,2,1,1,1]
[1,1,4,2,1,3] => [4,3,2,1,1,1]
[1,1,4,1,1,4] => [4,4,1,1,1,1]
[1,1,5,5] => [5,5,1,1]
[2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[2,2,1,1,1,1,2,2] => [2,2,2,2,1,1,1,1]
[2,2,1,1,2,2,1,1] => [2,2,2,2,1,1,1,1]
[2,2,1,1,2,1,1,2] => [2,2,2,2,1,1,1,1]
[2,2,1,1,3,3] => [3,3,2,2,1,1]
[2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1]
[2,2,2,2,2,2] => [2,2,2,2,2,2]
[2,2,2,1,1,2,1,1] => [2,2,2,2,1,1,1,1]
[2,2,2,1,1,1,1,2] => [2,2,2,2,1,1,1,1]
[2,2,2,1,2,3] => [3,2,2,2,2,1]
[2,2,3,3,1,1] => [3,3,2,2,1,1]
[2,2,3,2,1,2] => [3,2,2,2,2,1]
[2,2,3,1,1,3] => [3,3,2,2,1,1]
[2,2,4,4] => [4,4,2,2]
[2,1,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[2,1,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1]
[2,1,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1]
[2,1,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1]
[2,1,1,2,3,3] => [3,3,2,2,1,1]
[2,1,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1]
[2,1,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,2,3] => [3,2,2,1,1,1,1,1]
[2,1,1,1,2,3,1,1] => [3,2,2,1,1,1,1,1]
[2,1,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1]
[2,1,1,1,2,1,1,3] => [3,2,2,1,1,1,1,1]
[2,1,1,1,3,4] => [4,3,2,1,1,1]
[2,1,2,3,1,1,1,1] => [3,2,2,1,1,1,1,1]
[2,1,2,3,2,2] => [3,2,2,2,2,1]
[2,1,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1]
[2,1,2,2,1,1,1,2] => [2,2,2,2,1,1,1,1]
[2,1,2,2,2,3] => [3,2,2,2,2,1]
[2,1,2,1,1,3,1,1] => [3,2,2,1,1,1,1,1]
[2,1,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1]
[2,1,2,1,1,1,1,3] => [3,2,2,1,1,1,1,1]
[2,1,2,1,2,4] => [4,2,2,2,1,1]
[2,1,3,4,1,1] => [4,3,2,1,1,1]
[2,1,3,3,1,2] => [3,3,2,2,1,1]
[2,1,3,2,1,3] => [3,3,2,2,1,1]
[2,1,3,1,1,4] => [4,3,2,1,1,1]
[2,1,4,5] => [5,4,2,1]
[3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1]
[3,3,1,1,2,2] => [3,3,2,2,1,1]
[3,3,2,2,1,1] => [3,3,2,2,1,1]
[3,3,2,1,1,2] => [3,3,2,2,1,1]
[3,3,3,3] => [3,3,3,3]
[3,2,1,2,1,1,1,1] => [3,2,2,1,1,1,1,1]
[3,2,1,2,2,2] => [3,2,2,2,2,1]
[3,2,1,1,1,2,1,1] => [3,2,2,1,1,1,1,1]
[3,2,1,1,1,1,1,2] => [3,2,2,1,1,1,1,1]
[3,2,1,1,2,3] => [3,3,2,2,1,1]
[3,2,2,3,1,1] => [3,3,2,2,1,1]
[3,2,2,2,1,2] => [3,2,2,2,2,1]
[3,2,2,1,1,3] => [3,3,2,2,1,1]
[3,2,3,4] => [4,3,3,2]
[3,1,1,3,1,1,1,1] => [3,3,1,1,1,1,1,1]
[3,1,1,3,2,2] => [3,3,2,2,1,1]
[3,1,1,2,1,2,1,1] => [3,2,2,1,1,1,1,1]
[3,1,1,2,1,1,1,2] => [3,2,2,1,1,1,1,1]
[3,1,1,2,2,3] => [3,3,2,2,1,1]
[3,1,1,1,1,3,1,1] => [3,3,1,1,1,1,1,1]
[3,1,1,1,1,2,1,2] => [3,2,2,1,1,1,1,1]
[3,1,1,1,1,1,1,3] => [3,3,1,1,1,1,1,1]
[3,1,1,1,2,4] => [4,3,2,1,1,1]
[3,1,2,4,1,1] => [4,3,2,1,1,1]
[3,1,2,3,1,2] => [3,3,2,2,1,1]
[3,1,2,2,1,3] => [3,3,2,2,1,1]
[3,1,2,1,1,4] => [4,3,2,1,1,1]
[3,1,3,5] => [5,3,3,1]
[4,4,1,1,1,1] => [4,4,1,1,1,1]
[4,4,2,2] => [4,4,2,2]
[4,3,1,2,1,1] => [4,3,2,1,1,1]
[4,3,1,1,1,2] => [4,3,2,1,1,1]
[4,3,2,3] => [4,3,3,2]
[4,2,1,3,1,1] => [4,3,2,1,1,1]
[4,2,1,2,1,2] => [4,2,2,2,1,1]
[4,2,1,1,1,3] => [4,3,2,1,1,1]
[4,2,2,4] => [4,4,2,2]
[4,1,1,4,1,1] => [4,4,1,1,1,1]
[4,1,1,3,1,2] => [4,3,2,1,1,1]
[4,1,1,2,1,3] => [4,3,2,1,1,1]
[4,1,1,1,1,4] => [4,4,1,1,1,1]
[4,1,2,5] => [5,4,2,1]
[5,5,1,1] => [5,5,1,1]
[5,4,1,2] => [5,4,2,1]
[5,3,1,3] => [5,3,3,1]
[5,2,1,4] => [5,4,2,1]
[5,1,1,5] => [5,5,1,1]
[6,6] => [6,6]
[1,2,2,2,2,2,1] => [2,2,2,2,2,1,1]
[1,2,2,2,3,2] => [3,2,2,2,2,1]
[1,2,2,3,3,1] => [3,3,2,2,1,1]
[1,2,2,3,2,2] => [3,2,2,2,2,1]
[1,2,2,4,3] => [4,3,2,2,1]
[1,2,3,3,2,1] => [3,3,2,2,1,1]
[1,2,3,4,2] => [4,3,2,2,1]
[1,2,3,2,3,1] => [3,3,2,2,1,1]
[1,2,3,2,2,2] => [3,2,2,2,2,1]
[1,2,3,3,3] => [3,3,3,2,1]
[1,2,4,4,1] => [4,4,2,1,1]
[1,2,4,3,2] => [4,3,2,2,1]
[1,2,4,2,3] => [4,3,2,2,1]
[1,2,5,4] => [5,4,2,1]
[1,3,3,2,2,1] => [3,3,2,2,1,1]
[1,3,3,3,2] => [3,3,3,2,1]
[1,3,4,3,1] => [4,3,3,1,1]
[1,3,4,2,2] => [4,3,2,2,1]
[1,3,5,3] => [5,3,3,1]
[1,3,2,3,2,1] => [3,3,2,2,1,1]
[1,3,2,4,2] => [4,3,2,2,1]
[1,3,2,2,3,1] => [3,3,2,2,1,1]
[1,3,2,2,2,2] => [3,2,2,2,2,1]
[1,3,2,3,3] => [3,3,3,2,1]
[1,3,3,4,1] => [4,3,3,1,1]
[1,3,3,2,3] => [3,3,3,2,1]
[1,3,4,4] => [4,4,3,1]
[1,4,4,2,1] => [4,4,2,1,1]
[1,4,5,2] => [5,4,2,1]
[1,4,3,3,1] => [4,3,3,1,1]
[1,4,3,2,2] => [4,3,2,2,1]
[1,4,4,3] => [4,4,3,1]
[1,4,2,4,1] => [4,4,2,1,1]
[1,4,2,3,2] => [4,3,2,2,1]
[1,4,2,2,3] => [4,3,2,2,1]
[1,4,3,4] => [4,4,3,1]
[1,5,5,1] => [5,5,1,1]
[1,5,4,2] => [5,4,2,1]
[1,5,3,3] => [5,3,3,1]
[1,5,2,4] => [5,4,2,1]
[1,6,5] => [6,5,1]
[2,3,2,2,2,1] => [3,2,2,2,2,1]
[2,3,2,3,2] => [3,3,2,2,2]
[2,3,3,3,1] => [3,3,3,2,1]
[2,3,3,2,2] => [3,3,2,2,2]
[2,3,4,3] => [4,3,3,2]
[2,4,3,2,1] => [4,3,2,2,1]
[2,4,4,2] => [4,4,2,2]
[2,4,2,3,1] => [4,3,2,2,1]
[2,4,2,2,2] => [4,2,2,2,2]
[2,4,3,3] => [4,3,3,2]
[2,5,4,1] => [5,4,2,1]
[2,5,3,2] => [5,3,2,2]
[2,5,2,3] => [5,3,2,2]
[2,6,4] => [6,4,2]
[2,2,3,2,2,1] => [3,2,2,2,2,1]
[2,2,3,3,2] => [3,3,2,2,2]
[2,2,4,3,1] => [4,3,2,2,1]
[2,2,4,2,2] => [4,2,2,2,2]
[2,2,5,3] => [5,3,2,2]
[2,2,2,3,2,1] => [3,2,2,2,2,1]
[2,2,2,4,2] => [4,2,2,2,2]
[2,2,2,2,3,1] => [3,2,2,2,2,1]
[2,2,2,3,3] => [3,3,2,2,2]
[2,2,3,4,1] => [4,3,2,2,1]
[2,2,3,2,3] => [3,3,2,2,2]
[2,3,4,2,1] => [4,3,2,2,1]
[2,3,5,2] => [5,3,2,2]
[2,3,2,4,1] => [4,3,2,2,1]
[2,3,2,2,3] => [3,3,2,2,2]
[2,3,3,4] => [4,3,3,2]
[2,4,5,1] => [5,4,2,1]
[2,4,2,4] => [4,4,2,2]
[2,5,5] => [5,5,2]
[3,4,2,2,1] => [4,3,2,2,1]
[3,4,3,2] => [4,3,3,2]
[3,5,3,1] => [5,3,3,1]
[3,5,2,2] => [5,3,2,2]
[3,6,3] => [6,3,3]
[3,3,3,2,1] => [3,3,3,2,1]
[3,3,4,2] => [4,3,3,2]
[3,3,2,3,1] => [3,3,3,2,1]
[3,3,2,2,2] => [3,3,2,2,2]
[3,4,4,1] => [4,4,3,1]
[3,4,2,3] => [4,3,3,2]
[3,5,4] => [5,4,3]
[3,2,4,2,1] => [4,3,2,2,1]
[3,2,5,2] => [5,3,2,2]
[3,2,3,3,1] => [3,3,3,2,1]
[3,2,3,2,2] => [3,3,2,2,2]
[3,2,4,3] => [4,3,3,2]
[3,2,2,4,1] => [4,3,2,2,1]
[3,2,2,3,2] => [3,3,2,2,2]
[3,2,2,2,3] => [3,3,2,2,2]
[3,3,5,1] => [5,3,3,1]
[3,3,2,4] => [4,3,3,2]
[3,4,5] => [5,4,3]
[4,5,2,1] => [5,4,2,1]
[4,6,2] => [6,4,2]
[4,4,3,1] => [4,4,3,1]
[4,5,3] => [5,4,3]
[4,3,4,1] => [4,4,3,1]
[4,3,3,2] => [4,3,3,2]
[4,4,4] => [4,4,4]
[4,2,5,1] => [5,4,2,1]
[4,2,4,2] => [4,4,2,2]
[4,2,3,3] => [4,3,3,2]
[4,3,5] => [5,4,3]
[5,6,1] => [6,5,1]
[5,5,2] => [5,5,2]
[5,4,3] => [5,4,3]
[5,3,4] => [5,4,3]
[5,2,5] => [5,5,2]
[1,11] => [11,1]
[1,9,2] => [9,2,1]
[1,8,1,2] => [8,2,1,1]
[1,7,1,1,2] => [7,2,1,1,1]
[1,6,1,1,1,2] => [6,2,1,1,1,1]
[1,5,1,1,1,1,2] => [5,2,1,1,1,1,1]
[1,4,1,1,1,1,1,2] => [4,2,1,1,1,1,1,1]
[1,3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1,1]
[12] => [12]
[1,2,9] => [9,2,1]
[3,2,7] => [7,3,2]
[1,4,7] => [7,4,1]
[1,1,2,1,7] => [7,2,1,1,1]
[1,2,2,2,5] => [5,2,2,2,1]
[1,1,2,3,5] => [5,3,2,1,1]
[3,1,2,1,5] => [5,3,2,1,1]
[1,3,2,1,5] => [5,3,2,1,1]
[1,1,4,1,5] => [5,4,1,1,1]
[1,1,1,2,1,1,5] => [5,2,1,1,1,1,1]
[7,2,3] => [7,3,2]
[1,1,2,1,2,2,3] => [3,2,2,2,1,1,1]
[1,8,3] => [8,3,1]
[1,1,2,5,3] => [5,3,2,1,1]
[3,1,2,3,3] => [3,3,3,2,1]
[1,1,4,3,3] => [4,3,3,1,1]
[1,1,1,2,1,3,3] => [3,3,2,1,1,1,1]
[5,1,2,1,3] => [5,3,2,1,1]
[1,2,2,1,2,1,3] => [3,2,2,2,1,1,1]
[3,3,2,1,3] => [3,3,3,2,1]
[1,5,2,1,3] => [5,3,2,1,1]
[1,1,2,2,2,1,3] => [3,2,2,2,1,1,1]
[3,1,4,1,3] => [4,3,3,1,1]
[1,3,4,1,3] => [4,3,3,1,1]
[1,1,6,1,3] => [6,3,1,1,1]
[1,1,1,2,3,1,3] => [3,3,2,1,1,1,1]
[3,1,1,2,1,1,3] => [3,3,2,1,1,1,1]
[1,3,1,2,1,1,3] => [3,3,2,1,1,1,1]
[1,1,3,2,1,1,3] => [3,3,2,1,1,1,1]
[1,1,1,4,1,1,3] => [4,3,1,1,1,1,1]
[1,1,1,1,2,1,1,1,3] => [3,2,1,1,1,1,1,1,1]
[9,2,1] => [9,2,1]
[1,2,6,2,1] => [6,2,2,1,1]
[1,1,2,1,4,2,1] => [4,2,2,1,1,1,1]
[5,2,2,2,1] => [5,2,2,2,1]
[1,6,2,2,1] => [6,2,2,1,1]
[1,1,2,3,2,2,1] => [3,2,2,2,1,1,1]
[3,1,2,1,2,2,1] => [3,2,2,2,1,1,1]
[1,3,2,1,2,2,1] => [3,2,2,2,1,1,1]
[1,1,4,1,2,2,1] => [4,2,2,1,1,1,1]
[1,1,1,2,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1]
[7,4,1] => [7,4,1]
[1,1,2,1,2,4,1] => [4,2,2,1,1,1,1]
[1,2,2,6,1] => [6,2,2,1,1]
[3,8,1] => [8,3,1]
[1,10,1] => [10,1,1]
[1,1,2,7,1] => [7,2,1,1,1]
[3,1,2,5,1] => [5,3,2,1,1]
[1,3,2,5,1] => [5,3,2,1,1]
[1,1,4,5,1] => [5,4,1,1,1]
[1,1,1,2,1,5,1] => [5,2,1,1,1,1,1]
[5,1,2,3,1] => [5,3,2,1,1]
[1,2,2,1,2,3,1] => [3,2,2,2,1,1,1]
[1,5,2,3,1] => [5,3,2,1,1]
[1,1,2,2,2,3,1] => [3,2,2,2,1,1,1]
[3,1,4,3,1] => [4,3,3,1,1]
[1,1,6,3,1] => [6,3,1,1,1]
[1,1,1,2,3,3,1] => [3,3,2,1,1,1,1]
[3,1,1,2,1,3,1] => [3,3,2,1,1,1,1]
[1,3,1,2,1,3,1] => [3,3,2,1,1,1,1]
[1,1,3,2,1,3,1] => [3,3,2,1,1,1,1]
[1,1,1,4,1,3,1] => [4,3,1,1,1,1,1]
[1,1,1,1,2,1,1,3,1] => [3,2,1,1,1,1,1,1,1]
[7,1,2,1,1] => [7,2,1,1,1]
[1,2,4,1,2,1,1] => [4,2,2,1,1,1,1]
[3,2,2,1,2,1,1] => [3,2,2,2,1,1,1]
[1,4,2,1,2,1,1] => [4,2,2,1,1,1,1]
[1,1,2,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[5,3,2,1,1] => [5,3,2,1,1]
[1,2,2,3,2,1,1] => [3,2,2,2,1,1,1]
[3,5,2,1,1] => [5,3,2,1,1]
[1,7,2,1,1] => [7,2,1,1,1]
[1,1,2,4,2,1,1] => [4,2,2,1,1,1,1]
[3,1,2,2,2,1,1] => [3,2,2,2,1,1,1]
[1,3,2,2,2,1,1] => [3,2,2,2,1,1,1]
[1,1,4,2,2,1,1] => [4,2,2,1,1,1,1]
[1,1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1]
[5,1,4,1,1] => [5,4,1,1,1]
[1,2,2,1,4,1,1] => [4,2,2,1,1,1,1]
[3,3,4,1,1] => [4,3,3,1,1]
[1,5,4,1,1] => [5,4,1,1,1]
[1,1,2,2,4,1,1] => [4,2,2,1,1,1,1]
[3,1,6,1,1] => [6,3,1,1,1]
[1,3,6,1,1] => [6,3,1,1,1]
[1,1,8,1,1] => [8,1,1,1,1]
[1,1,1,2,5,1,1] => [5,2,1,1,1,1,1]
[3,1,1,2,3,1,1] => [3,3,2,1,1,1,1]
[1,3,1,2,3,1,1] => [3,3,2,1,1,1,1]
[1,1,3,2,3,1,1] => [3,3,2,1,1,1,1]
[1,1,1,4,3,1,1] => [4,3,1,1,1,1,1]
[1,1,1,1,2,1,3,1,1] => [3,2,1,1,1,1,1,1,1]
[5,1,1,2,1,1,1] => [5,2,1,1,1,1,1]
[1,2,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[3,3,1,2,1,1,1] => [3,3,2,1,1,1,1]
[1,5,1,2,1,1,1] => [5,2,1,1,1,1,1]
[1,1,2,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[3,1,3,2,1,1,1] => [3,3,2,1,1,1,1]
[1,3,3,2,1,1,1] => [3,3,2,1,1,1,1]
[1,1,5,2,1,1,1] => [5,2,1,1,1,1,1]
[1,1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[3,1,1,4,1,1,1] => [4,3,1,1,1,1,1]
[1,3,1,4,1,1,1] => [4,3,1,1,1,1,1]
[1,1,3,4,1,1,1] => [4,3,1,1,1,1,1]
[1,1,1,6,1,1,1] => [6,1,1,1,1,1,1]
[1,1,1,1,2,3,1,1,1] => [3,2,1,1,1,1,1,1,1]
[3,1,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1]
[1,3,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1]
[1,1,3,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1]
[1,1,1,3,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1]
[1,1,1,1,4,1,1,1,1] => [4,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,1,2,1] => [2,2,2,2,2,1,1]
[2,2,2,1,2,1,2] => [2,2,2,2,2,1,1]
[2,2,2,1,2,2,1] => [2,2,2,2,2,1,1]
[2,2,2,1,1,2,2] => [2,2,2,2,2,1,1]
[2,2,1,2,1,2,2] => [2,2,2,2,2,1,1]
[2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1]
[2,2,1,2,2,1,2] => [2,2,2,2,2,1,1]
[2,2,1,2,2,2,1] => [2,2,2,2,2,1,1]
[2,2,1,1,2,2,2] => [2,2,2,2,2,1,1]
[2,2,1,1,2,1,2,1] => [2,2,2,2,1,1,1,1]
[2,2,1,1,1,2,2,1] => [2,2,2,2,1,1,1,1]
[2,1,2,1,2,2,2] => [2,2,2,2,2,1,1]
[2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1]
[2,1,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1]
[2,1,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1]
[2,1,2,2,1,2,2] => [2,2,2,2,2,1,1]
[2,1,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1]
[2,1,2,2,2,1,2] => [2,2,2,2,2,1,1]
[2,1,2,2,2,2,1] => [2,2,2,2,2,1,1]
[2,1,1,2,2,2,2] => [2,2,2,2,2,1,1]
[2,1,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1]
[2,1,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1]
[2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1]
[2,1,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1]
[2,1,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1]
[1,2,1,2,2,2,2] => [2,2,2,2,2,1,1]
[1,2,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1]
[1,2,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1]
[1,2,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1]
[1,2,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1]
[1,2,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1]
[1,2,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1]
[1,2,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1]
[1,2,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1]
[1,2,1,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1]
[1,2,2,1,2,2,2] => [2,2,2,2,2,1,1]
[1,2,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1]
[1,2,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1]
[1,2,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1]
[1,2,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1]
[1,2,2,2,1,2,2] => [2,2,2,2,2,1,1]
[1,2,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1]
[1,2,2,2,2,1,2] => [2,2,2,2,2,1,1]
[1,1,2,2,2,2,2] => [2,2,2,2,2,1,1]
[1,1,2,2,2,1,2,1] => [2,2,2,2,1,1,1,1]
[1,1,2,2,1,2,1,2] => [2,2,2,2,1,1,1,1]
[1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1]
[1,1,2,1,2,1,2,2] => [2,2,2,2,1,1,1,1]
[1,1,2,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,2,1,2,2,2,1] => [2,2,2,2,1,1,1,1]
[1,1,2,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,2,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,2,1,2,2] => [2,2,2,2,1,1,1,1]
[1,1,1,2,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,2,2,1,2] => [2,2,2,2,1,1,1,1]
[1,1,1,2,2,2,2,1] => [2,2,2,2,1,1,1,1]
[1,1,1,2,1,2,2,2] => [2,2,2,2,1,1,1,1]
[1,1,1,2,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,1,2,2,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,1,2,1,2,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,1,1,2,2,2,1] => [2,2,2,1,1,1,1,1,1]
[3,2,2,2,2,1] => [3,2,2,2,2,1]
[4,3,2,2,1] => [4,3,2,2,1]
[4,2,3,2,1] => [4,3,2,2,1]
[4,2,2,3,1] => [4,3,2,2,1]
[4,2,2,2,2] => [4,2,2,2,2]
[5,4,2,1] => [5,4,2,1]
[5,3,3,1] => [5,3,3,1]
[5,3,2,2] => [5,3,2,2]
[5,2,4,1] => [5,4,2,1]
[5,2,3,2] => [5,3,2,2]
[5,2,2,3] => [5,3,2,2]
[6,5,1] => [6,5,1]
[6,4,2] => [6,4,2]
[6,3,3] => [6,3,3]
[6,2,4] => [6,4,2]
[7,5] => [7,5]
[11,1] => [11,1]
[2,9,1] => [9,2,1]
[2,1,8,1] => [8,2,1,1]
[2,1,1,7,1] => [7,2,1,1,1]
[2,1,1,1,6,1] => [6,2,1,1,1,1]
[2,1,1,1,1,5,1] => [5,2,1,1,1,1,1]
[2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1]
[2,1,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[2,2,1,2,1,2,1,1] => [2,2,2,2,1,1,1,1]
[2,2,1,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[2,1,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[2,1,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1]
[2,1,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1]
[2,1,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[2,1,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[2,1,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[2,1,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[2,1,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1]
[2,1,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[2,1,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[2,1,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,2,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1]
[1,2,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1]
[1,2,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1]
[1,2,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1]
[1,2,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1]
[1,2,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1]
[1,1,2,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1]
[1,1,2,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,2,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,1,2,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1]
[1,1,2,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,1,2,2] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,2,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,2,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,2,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,2,2,4,2,1] => [4,2,2,2,1,1]
[1,2,4,2,2,1] => [4,2,2,2,1,1]
[1,2,5,2,2] => [5,2,2,2,1]
[1,3,5,2,1] => [5,3,2,1,1]
[1,4,2,2,2,1] => [4,2,2,2,1,1]
[1,5,2,2,2] => [5,2,2,2,1]
[1,5,3,2,1] => [5,3,2,1,1]
[2,5,2,2,1] => [5,2,2,2,1]
[2,6,2,2] => [6,2,2,2]
[2,2,5,2,1] => [5,2,2,2,1]
[6,2,2,2] => [6,2,2,2]
[2,2,2,2,2,1,1] => [2,2,2,2,2,1,1]
[1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1]
[1,2,2,1,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,1,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,1,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[10,2] => [10,2]
[1,1,1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1]
[1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1]
[1,2,2,2,3,1,1] => [3,2,2,2,1,1,1]
[1,2,2,3,1,2,1] => [3,2,2,2,1,1,1]
[1,2,2,4,1,1,1] => [4,2,2,1,1,1,1]
[1,2,3,1,2,2,1] => [3,2,2,2,1,1,1]
[1,2,3,1,3,1,1] => [3,3,2,1,1,1,1]
[1,2,3,2,1,2,1] => [3,2,2,2,1,1,1]
[1,2,4,1,1,2,1] => [4,2,2,1,1,1,1]
[1,2,3,2,2,1,1] => [3,2,2,2,1,1,1]
[1,2,3,3,1,1,1] => [3,3,2,1,1,1,1]
[1,2,4,2,1,1,1] => [4,2,2,1,1,1,1]
[1,2,5,1,1,1,1] => [5,2,1,1,1,1,1]
[1,3,1,2,2,2,1] => [3,2,2,2,1,1,1]
[1,3,1,3,1,2,1] => [3,3,2,1,1,1,1]
[1,3,1,3,2,1,1] => [3,3,2,1,1,1,1]
[1,3,2,1,3,1,1] => [3,3,2,1,1,1,1]
[1,4,1,1,2,2,1] => [4,2,2,1,1,1,1]
[1,4,1,1,3,1,1] => [4,3,1,1,1,1,1]
[1,3,2,2,1,2,1] => [3,2,2,2,1,1,1]
[1,3,3,1,1,2,1] => [3,3,2,1,1,1,1]
[1,4,1,2,1,2,1] => [4,2,2,1,1,1,1]
[1,4,2,1,1,2,1] => [4,2,2,1,1,1,1]
[1,5,1,1,1,2,1] => [5,2,1,1,1,1,1]
[1,3,2,3,1,1,1] => [3,3,2,1,1,1,1]
[1,3,3,1,2,1,1] => [3,3,2,1,1,1,1]
[1,3,4,1,1,1,1] => [4,3,1,1,1,1,1]
[1,4,1,2,2,1,1] => [4,2,2,1,1,1,1]
[1,4,1,3,1,1,1] => [4,3,1,1,1,1,1]
[1,5,1,1,2,1,1] => [5,2,1,1,1,1,1]
[1,4,2,2,1,1,1] => [4,2,2,1,1,1,1]
[1,4,3,1,1,1,1] => [4,3,1,1,1,1,1]
[1,5,2,1,1,1,1] => [5,2,1,1,1,1,1]
[1,6,1,1,1,1,1] => [6,1,1,1,1,1,1]
[2,1,2,2,3,1,1] => [3,2,2,2,1,1,1]
[2,1,2,3,1,2,1] => [3,2,2,2,1,1,1]
[2,1,2,3,2,1,1] => [3,2,2,2,1,1,1]
[2,1,2,4,1,1,1] => [4,2,2,1,1,1,1]
[2,1,3,1,2,2,1] => [3,2,2,2,1,1,1]
[2,1,3,1,3,1,1] => [3,3,2,1,1,1,1]
[2,1,3,2,1,2,1] => [3,2,2,2,1,1,1]
[2,1,4,1,1,2,1] => [4,2,2,1,1,1,1]
[2,1,3,2,2,1,1] => [3,2,2,2,1,1,1]
[2,1,3,3,1,1,1] => [3,3,2,1,1,1,1]
[2,1,4,1,2,1,1] => [4,2,2,1,1,1,1]
[2,1,4,2,1,1,1] => [4,2,2,1,1,1,1]
[2,1,5,1,1,1,1] => [5,2,1,1,1,1,1]
[2,2,1,2,3,1,1] => [3,2,2,2,1,1,1]
[2,2,1,3,1,2,1] => [3,2,2,2,1,1,1]
[2,2,1,3,2,1,1] => [3,2,2,2,1,1,1]
[2,2,1,4,1,1,1] => [4,2,2,1,1,1,1]
[3,1,1,2,2,2,1] => [3,2,2,2,1,1,1]
[3,1,1,3,1,2,1] => [3,3,2,1,1,1,1]
[3,1,1,3,2,1,1] => [3,3,2,1,1,1,1]
[2,2,2,1,3,1,1] => [3,2,2,2,1,1,1]
[2,3,1,1,2,2,1] => [3,2,2,2,1,1,1]
[2,3,1,1,3,1,1] => [3,3,2,1,1,1,1]
[3,1,2,1,3,1,1] => [3,3,2,1,1,1,1]
[3,2,1,1,2,2,1] => [3,2,2,2,1,1,1]
[3,2,1,1,3,1,1] => [3,3,2,1,1,1,1]
[4,1,1,1,2,2,1] => [4,2,2,1,1,1,1]
[4,1,1,1,3,1,1] => [4,3,1,1,1,1,1]
[2,2,3,1,1,2,1] => [3,2,2,2,1,1,1]
[2,3,1,2,1,2,1] => [3,2,2,2,1,1,1]
[2,3,2,1,1,2,1] => [3,2,2,2,1,1,1]
[2,4,1,1,1,2,1] => [4,2,2,1,1,1,1]
[3,1,2,2,1,2,1] => [3,2,2,2,1,1,1]
[3,1,3,1,1,2,1] => [3,3,2,1,1,1,1]
[3,2,1,2,1,2,1] => [3,2,2,2,1,1,1]
[4,1,1,2,1,2,1] => [4,2,2,1,1,1,1]
[3,2,2,1,1,2,1] => [3,2,2,2,1,1,1]
[3,3,1,1,1,2,1] => [3,3,2,1,1,1,1]
[4,1,2,1,1,2,1] => [4,2,2,1,1,1,1]
[4,2,1,1,1,2,1] => [4,2,2,1,1,1,1]
[5,1,1,1,1,2,1] => [5,2,1,1,1,1,1]
[2,2,2,3,1,1,1] => [3,2,2,2,1,1,1]
[2,2,3,1,2,1,1] => [3,2,2,2,1,1,1]
[2,2,3,2,1,1,1] => [3,2,2,2,1,1,1]
[2,2,4,1,1,1,1] => [4,2,2,1,1,1,1]
[2,3,1,2,2,1,1] => [3,2,2,2,1,1,1]
[2,3,1,3,1,1,1] => [3,3,2,1,1,1,1]
[2,3,2,1,2,1,1] => [3,2,2,2,1,1,1]
[2,4,1,1,2,1,1] => [4,2,2,1,1,1,1]
[2,3,2,2,1,1,1] => [3,2,2,2,1,1,1]
[2,3,3,1,1,1,1] => [3,3,2,1,1,1,1]
[2,4,1,2,1,1,1] => [4,2,2,1,1,1,1]
[2,4,2,1,1,1,1] => [4,2,2,1,1,1,1]
[2,5,1,1,1,1,1] => [5,2,1,1,1,1,1]
[3,1,2,3,1,1,1] => [3,3,2,1,1,1,1]
[3,1,3,1,2,1,1] => [3,3,2,1,1,1,1]
[3,1,4,1,1,1,1] => [4,3,1,1,1,1,1]
[3,2,1,2,2,1,1] => [3,2,2,2,1,1,1]
[3,2,1,3,1,1,1] => [3,3,2,1,1,1,1]
[4,1,1,2,2,1,1] => [4,2,2,1,1,1,1]
[4,1,1,3,1,1,1] => [4,3,1,1,1,1,1]
[3,3,1,1,2,1,1] => [3,3,2,1,1,1,1]
[4,1,2,1,2,1,1] => [4,2,2,1,1,1,1]
[4,2,1,1,2,1,1] => [4,2,2,1,1,1,1]
[5,1,1,1,2,1,1] => [5,2,1,1,1,1,1]
[3,2,2,2,1,1,1] => [3,2,2,2,1,1,1]
[3,2,3,1,1,1,1] => [3,3,2,1,1,1,1]
[3,3,2,1,1,1,1] => [3,3,2,1,1,1,1]
[3,4,1,1,1,1,1] => [4,3,1,1,1,1,1]
[4,1,2,2,1,1,1] => [4,2,2,1,1,1,1]
[4,1,3,1,1,1,1] => [4,3,1,1,1,1,1]
[4,2,1,2,1,1,1] => [4,2,2,1,1,1,1]
[4,2,2,1,1,1,1] => [4,2,2,1,1,1,1]
[4,3,1,1,1,1,1] => [4,3,1,1,1,1,1]
[5,1,2,1,1,1,1] => [5,2,1,1,1,1,1]
[5,2,1,1,1,1,1] => [5,2,1,1,1,1,1]
[6,1,1,1,1,1,1] => [6,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1]
[1,2,2,1,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,1,2,3,2,3] => [3,3,2,2,1,1]
[1,2,2,2,2,3] => [3,2,2,2,2,1]
[1,1,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,1,2,2,1,2,3] => [3,2,2,2,1,1,1]
[1,1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,2,2,2,3] => [3,2,2,2,1,1,1]
[1,2,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1,1]
[1,1,2,2,2,4] => [4,2,2,2,1,1]
[1,2,2,2,2,2,2] => [2,2,2,2,2,2,1]
[1,2,2,2,2,1,3] => [3,2,2,2,2,1,1]
[1,2,2,2,1,3,2] => [3,2,2,2,2,1,1]
[1,2,2,2,1,2,3] => [3,2,2,2,2,1,1]
[1,2,2,2,1,1,4] => [4,2,2,2,1,1,1]
[1,2,2,1,3,2,2] => [3,2,2,2,2,1,1]
[1,2,2,1,3,1,3] => [3,3,2,2,1,1,1]
[1,2,2,1,2,3,2] => [3,2,2,2,2,1,1]
[1,2,2,1,2,2,3] => [3,2,2,2,2,1,1]
[1,2,2,1,2,1,4] => [4,2,2,2,1,1,1]
[1,2,2,1,1,4,2] => [4,2,2,2,1,1,1]
[1,2,2,1,1,3,3] => [3,3,2,2,1,1,1]
[1,2,2,1,1,2,4] => [4,2,2,2,1,1,1]
[1,2,2,1,1,1,5] => [5,2,2,1,1,1,1]
[1,2,1,3,2,2,2] => [3,2,2,2,2,1,1]
[1,2,1,3,2,1,3] => [3,3,2,2,1,1,1]
[1,2,1,3,1,3,2] => [3,3,2,2,1,1,1]
[1,2,1,3,1,2,3] => [3,3,2,2,1,1,1]
[1,2,1,3,1,1,4] => [4,3,2,1,1,1,1]
[1,2,1,2,3,2,2] => [3,2,2,2,2,1,1]
[1,2,1,2,3,1,3] => [3,3,2,2,1,1,1]
[1,2,1,2,2,3,2] => [3,2,2,2,2,1,1]
[1,2,1,2,2,2,3] => [3,2,2,2,2,1,1]
[1,2,1,2,2,1,4] => [4,2,2,2,1,1,1]
[1,2,1,2,1,4,2] => [4,2,2,2,1,1,1]
[1,2,1,2,1,3,3] => [3,3,2,2,1,1,1]
[1,2,1,2,1,2,4] => [4,2,2,2,1,1,1]
[1,2,1,2,1,1,5] => [5,2,2,1,1,1,1]
[1,2,1,1,4,2,2] => [4,2,2,2,1,1,1]
[1,2,1,1,4,1,3] => [4,3,2,1,1,1,1]
[1,2,1,1,3,3,2] => [3,3,2,2,1,1,1]
[1,2,1,1,3,2,3] => [3,3,2,2,1,1,1]
[1,2,1,1,3,1,4] => [4,3,2,1,1,1,1]
[1,2,1,1,2,4,2] => [4,2,2,2,1,1,1]
[1,2,1,1,2,3,3] => [3,3,2,2,1,1,1]
[1,2,1,1,2,2,4] => [4,2,2,2,1,1,1]
[1,2,1,1,2,1,5] => [5,2,2,1,1,1,1]
[1,2,1,1,1,5,2] => [5,2,2,1,1,1,1]
[1,2,1,1,1,4,3] => [4,3,2,1,1,1,1]
[1,2,1,1,1,3,4] => [4,3,2,1,1,1,1]
[1,2,1,1,1,2,5] => [5,2,2,1,1,1,1]
[1,2,1,1,1,1,6] => [6,2,1,1,1,1,1]
[1,1,3,2,2,2,2] => [3,2,2,2,2,1,1]
[1,1,3,2,2,1,3] => [3,3,2,2,1,1,1]
[1,1,3,2,1,3,2] => [3,3,2,2,1,1,1]
[1,1,3,2,1,2,3] => [3,3,2,2,1,1,1]
[1,1,3,2,1,1,4] => [4,3,2,1,1,1,1]
[1,1,3,1,3,2,2] => [3,3,2,2,1,1,1]
[1,1,3,1,3,1,3] => [3,3,3,1,1,1,1]
[1,1,3,1,2,3,2] => [3,3,2,2,1,1,1]
[1,1,3,1,2,2,3] => [3,3,2,2,1,1,1]
[1,1,3,1,2,1,4] => [4,3,2,1,1,1,1]
[1,1,3,1,1,4,2] => [4,3,2,1,1,1,1]
[1,1,3,1,1,3,3] => [3,3,3,1,1,1,1]
[1,1,3,1,1,2,4] => [4,3,2,1,1,1,1]
[1,1,3,1,1,1,5] => [5,3,1,1,1,1,1]
[1,1,2,3,2,2,2] => [3,2,2,2,2,1,1]
[1,1,2,3,2,1,3] => [3,3,2,2,1,1,1]
[1,1,2,3,1,3,2] => [3,3,2,2,1,1,1]
[1,1,2,3,1,2,3] => [3,3,2,2,1,1,1]
[1,1,2,3,1,1,4] => [4,3,2,1,1,1,1]
[1,1,2,2,3,2,2] => [3,2,2,2,2,1,1]
[1,1,2,2,3,1,3] => [3,3,2,2,1,1,1]
[1,1,2,2,2,3,2] => [3,2,2,2,2,1,1]
[1,1,2,2,2,2,3] => [3,2,2,2,2,1,1]
[1,1,2,2,2,1,4] => [4,2,2,2,1,1,1]
[1,1,2,2,1,4,2] => [4,2,2,2,1,1,1]
[1,1,2,2,1,3,3] => [3,3,2,2,1,1,1]
[1,1,2,2,1,2,4] => [4,2,2,2,1,1,1]
[1,1,2,2,1,1,5] => [5,2,2,1,1,1,1]
[1,1,2,1,4,2,2] => [4,2,2,2,1,1,1]
[1,1,2,1,4,1,3] => [4,3,2,1,1,1,1]
[1,1,2,1,3,3,2] => [3,3,2,2,1,1,1]
[1,1,2,1,3,2,3] => [3,3,2,2,1,1,1]
[1,1,2,1,3,1,4] => [4,3,2,1,1,1,1]
[1,1,2,1,2,4,2] => [4,2,2,2,1,1,1]
[1,1,2,1,2,3,3] => [3,3,2,2,1,1,1]
[1,1,2,1,2,2,4] => [4,2,2,2,1,1,1]
[1,1,2,1,2,1,5] => [5,2,2,1,1,1,1]
[1,1,2,1,1,5,2] => [5,2,2,1,1,1,1]
[1,1,2,1,1,4,3] => [4,3,2,1,1,1,1]
[1,1,2,1,1,3,4] => [4,3,2,1,1,1,1]
[1,1,2,1,1,2,5] => [5,2,2,1,1,1,1]
[1,1,2,1,1,1,6] => [6,2,1,1,1,1,1]
[1,1,1,4,2,2,2] => [4,2,2,2,1,1,1]
[1,1,1,4,2,1,3] => [4,3,2,1,1,1,1]
[1,1,1,4,1,3,2] => [4,3,2,1,1,1,1]
[1,1,1,4,1,2,3] => [4,3,2,1,1,1,1]
[1,1,1,4,1,1,4] => [4,4,1,1,1,1,1]
[1,1,1,3,3,2,2] => [3,3,2,2,1,1,1]
[1,1,1,3,3,1,3] => [3,3,3,1,1,1,1]
[1,1,1,3,2,3,2] => [3,3,2,2,1,1,1]
[1,1,1,3,2,2,3] => [3,3,2,2,1,1,1]
[1,1,1,3,2,1,4] => [4,3,2,1,1,1,1]
[1,1,1,3,1,4,2] => [4,3,2,1,1,1,1]
[1,1,1,3,1,3,3] => [3,3,3,1,1,1,1]
[1,1,1,3,1,2,4] => [4,3,2,1,1,1,1]
[1,1,1,3,1,1,5] => [5,3,1,1,1,1,1]
[1,1,1,2,4,2,2] => [4,2,2,2,1,1,1]
[1,1,1,2,4,1,3] => [4,3,2,1,1,1,1]
[1,1,1,2,3,3,2] => [3,3,2,2,1,1,1]
[1,1,1,2,3,2,3] => [3,3,2,2,1,1,1]
[1,1,1,2,3,1,4] => [4,3,2,1,1,1,1]
[1,1,1,2,2,4,2] => [4,2,2,2,1,1,1]
[1,1,1,2,2,3,3] => [3,3,2,2,1,1,1]
[1,1,1,2,2,2,4] => [4,2,2,2,1,1,1]
[1,1,1,2,2,1,5] => [5,2,2,1,1,1,1]
[1,1,1,2,1,5,2] => [5,2,2,1,1,1,1]
[1,1,1,2,1,4,3] => [4,3,2,1,1,1,1]
[1,1,1,2,1,3,4] => [4,3,2,1,1,1,1]
[1,1,1,2,1,2,5] => [5,2,2,1,1,1,1]
[1,1,1,2,1,1,6] => [6,2,1,1,1,1,1]
[1,1,1,1,5,2,2] => [5,2,2,1,1,1,1]
[1,1,1,1,5,1,3] => [5,3,1,1,1,1,1]
[1,1,1,1,4,3,2] => [4,3,2,1,1,1,1]
[1,1,1,1,4,2,3] => [4,3,2,1,1,1,1]
[1,1,1,1,4,1,4] => [4,4,1,1,1,1,1]
[1,1,1,1,3,4,2] => [4,3,2,1,1,1,1]
[1,1,1,1,3,3,3] => [3,3,3,1,1,1,1]
[1,1,1,1,3,2,4] => [4,3,2,1,1,1,1]
[1,1,1,1,3,1,5] => [5,3,1,1,1,1,1]
[1,1,1,1,2,5,2] => [5,2,2,1,1,1,1]
[1,1,1,1,2,4,3] => [4,3,2,1,1,1,1]
[1,1,1,1,2,3,4] => [4,3,2,1,1,1,1]
[1,1,1,1,2,2,5] => [5,2,2,1,1,1,1]
[1,1,1,1,2,1,6] => [6,2,1,1,1,1,1]
[1,1,1,1,1,6,2] => [6,2,1,1,1,1,1]
[1,1,1,1,1,5,3] => [5,3,1,1,1,1,1]
[1,1,1,1,1,4,4] => [4,4,1,1,1,1,1]
[1,1,1,1,1,3,5] => [5,3,1,1,1,1,1]
[1,1,1,1,1,2,6] => [6,2,1,1,1,1,1]
[1,1,1,1,1,1,7] => [7,1,1,1,1,1,1]
[2,2,2,2,2,2,1] => [2,2,2,2,2,2,1]
[3,1,2,2,2,2,1] => [3,2,2,2,2,1,1]
[2,3,1,2,2,2,1] => [3,2,2,2,2,1,1]
[3,2,1,2,2,2,1] => [3,2,2,2,2,1,1]
[4,1,1,2,2,2,1] => [4,2,2,2,1,1,1]
[2,2,3,1,2,2,1] => [3,2,2,2,2,1,1]
[3,1,3,1,2,2,1] => [3,3,2,2,1,1,1]
[2,3,2,1,2,2,1] => [3,2,2,2,2,1,1]
[3,2,2,1,2,2,1] => [3,2,2,2,2,1,1]
[4,1,2,1,2,2,1] => [4,2,2,2,1,1,1]
[2,4,1,1,2,2,1] => [4,2,2,2,1,1,1]
[3,3,1,1,2,2,1] => [3,3,2,2,1,1,1]
[4,2,1,1,2,2,1] => [4,2,2,2,1,1,1]
[5,1,1,1,2,2,1] => [5,2,2,1,1,1,1]
[2,2,2,3,1,2,1] => [3,2,2,2,2,1,1]
[3,1,2,3,1,2,1] => [3,3,2,2,1,1,1]
[2,3,1,3,1,2,1] => [3,3,2,2,1,1,1]
[3,2,1,3,1,2,1] => [3,3,2,2,1,1,1]
[4,1,1,3,1,2,1] => [4,3,2,1,1,1,1]
[2,2,3,2,1,2,1] => [3,2,2,2,2,1,1]
[3,1,3,2,1,2,1] => [3,3,2,2,1,1,1]
[2,3,2,2,1,2,1] => [3,2,2,2,2,1,1]
[3,2,2,2,1,2,1] => [3,2,2,2,2,1,1]
[4,1,2,2,1,2,1] => [4,2,2,2,1,1,1]
[2,4,1,2,1,2,1] => [4,2,2,2,1,1,1]
[3,3,1,2,1,2,1] => [3,3,2,2,1,1,1]
[4,2,1,2,1,2,1] => [4,2,2,2,1,1,1]
[5,1,1,2,1,2,1] => [5,2,2,1,1,1,1]
[2,2,4,1,1,2,1] => [4,2,2,2,1,1,1]
[3,1,4,1,1,2,1] => [4,3,2,1,1,1,1]
[2,3,3,1,1,2,1] => [3,3,2,2,1,1,1]
[3,2,3,1,1,2,1] => [3,3,2,2,1,1,1]
[4,1,3,1,1,2,1] => [4,3,2,1,1,1,1]
[2,4,2,1,1,2,1] => [4,2,2,2,1,1,1]
[3,3,2,1,1,2,1] => [3,3,2,2,1,1,1]
[4,2,2,1,1,2,1] => [4,2,2,2,1,1,1]
[5,1,2,1,1,2,1] => [5,2,2,1,1,1,1]
[2,5,1,1,1,2,1] => [5,2,2,1,1,1,1]
[3,4,1,1,1,2,1] => [4,3,2,1,1,1,1]
[4,3,1,1,1,2,1] => [4,3,2,1,1,1,1]
[5,2,1,1,1,2,1] => [5,2,2,1,1,1,1]
[6,1,1,1,1,2,1] => [6,2,1,1,1,1,1]
[2,2,2,2,3,1,1] => [3,2,2,2,2,1,1]
[3,1,2,2,3,1,1] => [3,3,2,2,1,1,1]
[2,3,1,2,3,1,1] => [3,3,2,2,1,1,1]
[3,2,1,2,3,1,1] => [3,3,2,2,1,1,1]
[4,1,1,2,3,1,1] => [4,3,2,1,1,1,1]
[2,2,3,1,3,1,1] => [3,3,2,2,1,1,1]
[3,1,3,1,3,1,1] => [3,3,3,1,1,1,1]
[2,3,2,1,3,1,1] => [3,3,2,2,1,1,1]
[3,2,2,1,3,1,1] => [3,3,2,2,1,1,1]
[4,1,2,1,3,1,1] => [4,3,2,1,1,1,1]
[2,4,1,1,3,1,1] => [4,3,2,1,1,1,1]
[3,3,1,1,3,1,1] => [3,3,3,1,1,1,1]
[4,2,1,1,3,1,1] => [4,3,2,1,1,1,1]
[5,1,1,1,3,1,1] => [5,3,1,1,1,1,1]
[2,2,2,3,2,1,1] => [3,2,2,2,2,1,1]
[3,1,2,3,2,1,1] => [3,3,2,2,1,1,1]
[2,3,1,3,2,1,1] => [3,3,2,2,1,1,1]
[3,2,1,3,2,1,1] => [3,3,2,2,1,1,1]
[4,1,1,3,2,1,1] => [4,3,2,1,1,1,1]
[2,2,3,2,2,1,1] => [3,2,2,2,2,1,1]
[3,1,3,2,2,1,1] => [3,3,2,2,1,1,1]
[2,3,2,2,2,1,1] => [3,2,2,2,2,1,1]
[3,2,2,2,2,1,1] => [3,2,2,2,2,1,1]
[4,1,2,2,2,1,1] => [4,2,2,2,1,1,1]
[2,4,1,2,2,1,1] => [4,2,2,2,1,1,1]
[3,3,1,2,2,1,1] => [3,3,2,2,1,1,1]
[4,2,1,2,2,1,1] => [4,2,2,2,1,1,1]
[5,1,1,2,2,1,1] => [5,2,2,1,1,1,1]
[2,2,4,1,2,1,1] => [4,2,2,2,1,1,1]
[3,1,4,1,2,1,1] => [4,3,2,1,1,1,1]
[2,3,3,1,2,1,1] => [3,3,2,2,1,1,1]
[3,2,3,1,2,1,1] => [3,3,2,2,1,1,1]
[4,1,3,1,2,1,1] => [4,3,2,1,1,1,1]
[2,4,2,1,2,1,1] => [4,2,2,2,1,1,1]
[3,3,2,1,2,1,1] => [3,3,2,2,1,1,1]
[4,2,2,1,2,1,1] => [4,2,2,2,1,1,1]
[5,1,2,1,2,1,1] => [5,2,2,1,1,1,1]
[2,5,1,1,2,1,1] => [5,2,2,1,1,1,1]
[3,4,1,1,2,1,1] => [4,3,2,1,1,1,1]
[4,3,1,1,2,1,1] => [4,3,2,1,1,1,1]
[5,2,1,1,2,1,1] => [5,2,2,1,1,1,1]
[6,1,1,1,2,1,1] => [6,2,1,1,1,1,1]
[2,2,2,4,1,1,1] => [4,2,2,2,1,1,1]
[3,1,2,4,1,1,1] => [4,3,2,1,1,1,1]
[2,3,1,4,1,1,1] => [4,3,2,1,1,1,1]
[3,2,1,4,1,1,1] => [4,3,2,1,1,1,1]
[4,1,1,4,1,1,1] => [4,4,1,1,1,1,1]
[2,2,3,3,1,1,1] => [3,3,2,2,1,1,1]
[3,1,3,3,1,1,1] => [3,3,3,1,1,1,1]
[2,3,2,3,1,1,1] => [3,3,2,2,1,1,1]
[3,2,2,3,1,1,1] => [3,3,2,2,1,1,1]
[4,1,2,3,1,1,1] => [4,3,2,1,1,1,1]
[2,4,1,3,1,1,1] => [4,3,2,1,1,1,1]
[3,3,1,3,1,1,1] => [3,3,3,1,1,1,1]
[4,2,1,3,1,1,1] => [4,3,2,1,1,1,1]
[5,1,1,3,1,1,1] => [5,3,1,1,1,1,1]
[2,2,4,2,1,1,1] => [4,2,2,2,1,1,1]
[3,1,4,2,1,1,1] => [4,3,2,1,1,1,1]
[2,3,3,2,1,1,1] => [3,3,2,2,1,1,1]
[3,2,3,2,1,1,1] => [3,3,2,2,1,1,1]
[4,1,3,2,1,1,1] => [4,3,2,1,1,1,1]
[2,4,2,2,1,1,1] => [4,2,2,2,1,1,1]
[3,3,2,2,1,1,1] => [3,3,2,2,1,1,1]
[4,2,2,2,1,1,1] => [4,2,2,2,1,1,1]
[5,1,2,2,1,1,1] => [5,2,2,1,1,1,1]
[2,5,1,2,1,1,1] => [5,2,2,1,1,1,1]
[3,4,1,2,1,1,1] => [4,3,2,1,1,1,1]
[4,3,1,2,1,1,1] => [4,3,2,1,1,1,1]
[5,2,1,2,1,1,1] => [5,2,2,1,1,1,1]
[6,1,1,2,1,1,1] => [6,2,1,1,1,1,1]
[2,2,5,1,1,1,1] => [5,2,2,1,1,1,1]
[3,1,5,1,1,1,1] => [5,3,1,1,1,1,1]
[2,3,4,1,1,1,1] => [4,3,2,1,1,1,1]
[3,2,4,1,1,1,1] => [4,3,2,1,1,1,1]
[4,1,4,1,1,1,1] => [4,4,1,1,1,1,1]
[2,4,3,1,1,1,1] => [4,3,2,1,1,1,1]
[3,3,3,1,1,1,1] => [3,3,3,1,1,1,1]
[4,2,3,1,1,1,1] => [4,3,2,1,1,1,1]
[5,1,3,1,1,1,1] => [5,3,1,1,1,1,1]
[2,5,2,1,1,1,1] => [5,2,2,1,1,1,1]
[3,4,2,1,1,1,1] => [4,3,2,1,1,1,1]
[4,3,2,1,1,1,1] => [4,3,2,1,1,1,1]
[5,2,2,1,1,1,1] => [5,2,2,1,1,1,1]
[6,1,2,1,1,1,1] => [6,2,1,1,1,1,1]
[2,6,1,1,1,1,1] => [6,2,1,1,1,1,1]
[3,5,1,1,1,1,1] => [5,3,1,1,1,1,1]
[4,4,1,1,1,1,1] => [4,4,1,1,1,1,1]
[5,3,1,1,1,1,1] => [5,3,1,1,1,1,1]
[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]
[1,3,1,3,1,3,1] => [3,3,3,1,1,1,1]
[1,3,1,2,3,2,1] => [3,3,2,2,1,1,1]
[1,3,1,2,1,4,1] => [4,3,2,1,1,1,1]
[1,3,1,1,1,5,1] => [5,3,1,1,1,1,1]
[1,2,3,2,1,3,1] => [3,3,2,2,1,1,1]
[1,2,3,1,3,2,1] => [3,3,2,2,1,1,1]
[1,2,3,1,1,4,1] => [4,3,2,1,1,1,1]
[1,2,2,3,2,2,1] => [3,2,2,2,2,1,1]
[1,2,2,1,4,2,1] => [4,2,2,2,1,1,1]
[1,2,2,1,2,4,1] => [4,2,2,2,1,1,1]
[1,2,1,4,1,3,1] => [4,3,2,1,1,1,1]
[1,2,1,3,3,2,1] => [3,3,2,2,1,1,1]
[1,2,1,3,1,4,1] => [4,3,2,1,1,1,1]
[1,2,1,2,1,5,1] => [5,2,2,1,1,1,1]
[1,2,1,1,5,2,1] => [5,2,2,1,1,1,1]
[1,2,1,1,3,4,1] => [4,3,2,1,1,1,1]
[1,2,1,1,1,6,1] => [6,2,1,1,1,1,1]
[1,1,1,5,1,3,1] => [5,3,1,1,1,1,1]
[1,1,1,4,3,2,1] => [4,3,2,1,1,1,1]
[1,1,1,4,1,4,1] => [4,4,1,1,1,1,1]
[1,1,1,3,1,5,1] => [5,3,1,1,1,1,1]
[1,1,1,2,5,2,1] => [5,2,2,1,1,1,1]
[1,1,1,2,3,4,1] => [4,3,2,1,1,1,1]
[1,1,1,2,1,6,1] => [6,2,1,1,1,1,1]
[1,1,1,1,1,7,1] => [7,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,5,1] => [5,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,3,1,3,1] => [3,3,1,1,1,1,1,1,1]
[1,1,1,1,1,5,1,1,1] => [5,1,1,1,1,1,1,1,1]
[1,1,1,1,1,4,1,2,1] => [4,2,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,4,1] => [4,2,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,3,2,1] => [3,2,2,1,1,1,1,1,1]
[1,1,1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1]
[1,1,1,3,1,1,1,3,1] => [3,3,1,1,1,1,1,1,1]
[1,1,1,3,1,3,1,1,1] => [3,3,1,1,1,1,1,1,1]
[1,1,1,3,1,2,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,1,1,5,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1]
[1,1,1,7,1,1,1] => [7,1,1,1,1,1,1]
[1,1,1,9,1] => [9,1,1,1,1]
[1,1,1,6,1,2,1] => [6,2,1,1,1,1,1]
[1,1,1,4,1,2,1,1,1] => [4,2,1,1,1,1,1,1,1]
[1,1,1,4,1,1,1,2,1] => [4,2,1,1,1,1,1,1,1]
[1,1,1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,1,1,2,1,2,1,3,1] => [3,2,2,1,1,1,1,1,1]
[1,1,1,2,1,4,1,1,1] => [4,2,1,1,1,1,1,1,1]
[1,1,1,2,1,3,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,1,1,2,1,1,1,4,1] => [4,2,1,1,1,1,1,1,1]
[1,1,1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,1,1,2,1,1,3,2,1] => [3,2,2,1,1,1,1,1,1]
[1,1,1,2,3,2,1,1,1] => [3,2,2,1,1,1,1,1,1]
[1,1,1,2,3,1,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1,1]
[1,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1]
[1,3,1,1,1,1,1,3,1] => [3,3,1,1,1,1,1,1,1]
[1,3,1,1,1,3,1,1,1] => [3,3,1,1,1,1,1,1,1]
[1,3,1,1,1,2,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,3,1,3,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1]
[1,3,1,5,1,1,1] => [5,3,1,1,1,1,1]
[1,3,1,7,1] => [7,3,1,1,1]
[1,3,1,4,1,2,1] => [4,3,2,1,1,1,1]
[1,3,1,2,1,2,1,1,1] => [3,2,2,1,1,1,1,1,1]
[1,3,1,2,1,1,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1]
[1,5,1,1,1,3,1] => [5,3,1,1,1,1,1]
[1,5,1,3,1,1,1] => [5,3,1,1,1,1,1]
[1,5,1,5,1] => [5,5,1,1,1]
[1,5,1,2,1,2,1] => [5,2,2,1,1,1,1]
[1,7,1,1,1,1,1] => [7,1,1,1,1,1,1]
[1,7,1,3,1] => [7,3,1,1,1]
[1,9,1,1,1] => [9,1,1,1,1]
[1,11,1] => [11,1,1]
[1,8,1,2,1] => [8,2,1,1,1]
[1,6,1,2,1,1,1] => [6,2,1,1,1,1,1]
[1,6,1,4,1] => [6,4,1,1,1]
[1,6,1,1,1,2,1] => [6,2,1,1,1,1,1]
[1,6,3,2,1] => [6,3,2,1,1]
[1,4,1,2,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1]
[1,4,1,2,1,3,1] => [4,3,2,1,1,1,1]
[1,4,1,4,1,1,1] => [4,4,1,1,1,1,1]
[1,4,1,6,1] => [6,4,1,1,1]
[1,4,1,3,1,2,1] => [4,3,2,1,1,1,1]
[1,4,1,1,1,2,1,1,1] => [4,2,1,1,1,1,1,1,1]
[1,4,1,1,1,4,1] => [4,4,1,1,1,1,1]
[1,4,1,1,1,1,1,2,1] => [4,2,1,1,1,1,1,1,1]
[1,4,1,1,3,2,1] => [4,3,2,1,1,1,1]
[1,4,3,2,1,1,1] => [4,3,2,1,1,1,1]
[1,4,3,4,1] => [4,4,3,1,1]
[1,4,3,1,1,2,1] => [4,3,2,1,1,1,1]
[1,4,5,2,1] => [5,4,2,1,1]
[1,4,2,1,2,2,1] => [4,2,2,2,1,1,1]
[1,2,1,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,2,1,2,1,1,1,3,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,2,1,3,1,1,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1,1]
[1,2,1,4,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1]
[1,2,1,6,1,1,1] => [6,2,1,1,1,1,1]
[1,2,1,8,1] => [8,2,1,1,1]
[1,2,1,5,1,2,1] => [5,2,2,1,1,1,1]
[1,2,1,3,1,2,1,1,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,3,1,1,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,1,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,2,1,1,1,2,1,3,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,1,1,4,1,1,1] => [4,2,1,1,1,1,1,1,1]
[1,2,1,1,1,3,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1]
[1,2,1,1,1,1,3,2,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,1,3,2,1,1,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,1,3,1,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1,1]
[1,2,3,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1]
[1,2,3,4,1,1,1] => [4,3,2,1,1,1,1]
[1,2,3,6,1] => [6,3,2,1,1]
[1,2,3,3,1,2,1] => [3,3,2,2,1,1,1]
[1,2,3,1,1,2,1,1,1] => [3,2,2,1,1,1,1,1,1]
[1,2,3,1,1,1,1,2,1] => [3,2,2,1,1,1,1,1,1]
[1,2,5,2,1,1,1] => [5,2,2,1,1,1,1]
[1,2,5,4,1] => [5,4,2,1,1]
[1,2,5,1,1,2,1] => [5,2,2,1,1,1,1]
[1,2,7,2,1] => [7,2,2,1,1]
[1,2,4,1,2,2,1] => [4,2,2,2,1,1,1]
[1,2,2,1,2,2,1,1,1] => [2,2,2,2,1,1,1,1,1]
[1,2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1,1]
[1,2,2,1,1,1,2,2,1] => [2,2,2,2,1,1,1,1,1]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Sends a composition to the partition obtained by sorting the entries.
Properties
surjective, graded
Sage code
def mapping(elt):
    return Partition(sorted(elt, reverse=True))
Weight
26
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey