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------------------------------------------------------------------------
Map identifier: Mp00180
------------------------------------------------------------------------
Map name: to ribbon
------------------------------------------------------------------------
Domain: Integer compositions
------------------------------------------------------------------------
Codomain: Skew partitions
------------------------------------------------------------------------
Description: The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(a):
return a.to_skew_partition()
------------------------------------------------------------------------
Map images:
[1] => [[1],[]]
[1,1] => [[1,1],[]]
[2] => [[2],[]]
[1,1,1] => [[1,1,1],[]]
[1,2] => [[2,1],[]]
[2,1] => [[2,2],[1]]
[3] => [[3],[]]
[1,1,1,1] => [[1,1,1,1],[]]
[1,1,2] => [[2,1,1],[]]
[1,2,1] => [[2,2,1],[1]]
[1,3] => [[3,1],[]]
[2,1,1] => [[2,2,2],[1,1]]
[2,2] => [[3,2],[1]]
[3,1] => [[3,3],[2]]
[4] => [[4],[]]
[1,1,1,1,1] => [[1,1,1,1,1],[]]
[1,1,1,2] => [[2,1,1,1],[]]
[1,1,2,1] => [[2,2,1,1],[1]]
[1,1,3] => [[3,1,1],[]]
[1,2,1,1] => [[2,2,2,1],[1,1]]
[1,2,2] => [[3,2,1],[1]]
[1,3,1] => [[3,3,1],[2]]
[1,4] => [[4,1],[]]
[2,1,1,1] => [[2,2,2,2],[1,1,1]]
[2,1,2] => [[3,2,2],[1,1]]
[2,2,1] => [[3,3,2],[2,1]]
[2,3] => [[4,2],[1]]
[3,1,1] => [[3,3,3],[2,2]]
[3,2] => [[4,3],[2]]
[4,1] => [[4,4],[3]]
[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] => [[2,2,1,1,1],[1]]
[1,1,1,3] => [[3,1,1,1],[]]
[1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
[1,1,2,2] => [[3,2,1,1],[1]]
[1,1,3,1] => [[3,3,1,1],[2]]
[1,1,4] => [[4,1,1],[]]
[1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]]
[1,2,1,2] => [[3,2,2,1],[1,1]]
[1,2,2,1] => [[3,3,2,1],[2,1]]
[1,2,3] => [[4,2,1],[1]]
[1,3,1,1] => [[3,3,3,1],[2,2]]
[1,3,2] => [[4,3,1],[2]]
[1,4,1] => [[4,4,1],[3]]
[1,5] => [[5,1],[]]
[2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
[2,1,1,2] => [[3,2,2,2],[1,1,1]]
[2,1,2,1] => [[3,3,2,2],[2,1,1]]
[2,1,3] => [[4,2,2],[1,1]]
[2,2,1,1] => [[3,3,3,2],[2,2,1]]
[2,2,2] => [[4,3,2],[2,1]]
[2,3,1] => [[4,4,2],[3,1]]
[2,4] => [[5,2],[1]]
[3,1,1,1] => [[3,3,3,3],[2,2,2]]
[3,1,2] => [[4,3,3],[2,2]]
[3,2,1] => [[4,4,3],[3,2]]
[3,3] => [[5,3],[2]]
[4,1,1] => [[4,4,4],[3,3]]
[4,2] => [[5,4],[3]]
[5,1] => [[5,5],[4]]
[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] => [[2,2,1,1,1,1],[1]]
[1,1,1,1,3] => [[3,1,1,1,1],[]]
[1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]]
[1,1,1,2,2] => [[3,2,1,1,1],[1]]
[1,1,1,3,1] => [[3,3,1,1,1],[2]]
[1,1,1,4] => [[4,1,1,1],[]]
[1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]]
[1,1,2,1,2] => [[3,2,2,1,1],[1,1]]
[1,1,2,2,1] => [[3,3,2,1,1],[2,1]]
[1,1,2,3] => [[4,2,1,1],[1]]
[1,1,3,1,1] => [[3,3,3,1,1],[2,2]]
[1,1,3,2] => [[4,3,1,1],[2]]
[1,1,4,1] => [[4,4,1,1],[3]]
[1,1,5] => [[5,1,1],[]]
[1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]]
[1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]]
[1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]]
[1,2,1,3] => [[4,2,2,1],[1,1]]
[1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]]
[1,2,2,2] => [[4,3,2,1],[2,1]]
[1,2,3,1] => [[4,4,2,1],[3,1]]
[1,2,4] => [[5,2,1],[1]]
[1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]]
[1,3,1,2] => [[4,3,3,1],[2,2]]
[1,3,2,1] => [[4,4,3,1],[3,2]]
[1,3,3] => [[5,3,1],[2]]
[1,4,1,1] => [[4,4,4,1],[3,3]]
[1,4,2] => [[5,4,1],[3]]
[1,5,1] => [[5,5,1],[4]]
[1,6] => [[6,1],[]]
[2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]]
[2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]]
[2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]]
[2,1,1,3] => [[4,2,2,2],[1,1,1]]
[2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]]
[2,1,2,2] => [[4,3,2,2],[2,1,1]]
[2,1,3,1] => [[4,4,2,2],[3,1,1]]
[2,1,4] => [[5,2,2],[1,1]]
[2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]]
[2,2,1,2] => [[4,3,3,2],[2,2,1]]
[2,2,2,1] => [[4,4,3,2],[3,2,1]]
[2,2,3] => [[5,3,2],[2,1]]
[2,3,1,1] => [[4,4,4,2],[3,3,1]]
[2,3,2] => [[5,4,2],[3,1]]
[2,4,1] => [[5,5,2],[4,1]]
[2,5] => [[6,2],[1]]
[3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]]
[3,1,1,2] => [[4,3,3,3],[2,2,2]]
[3,1,2,1] => [[4,4,3,3],[3,2,2]]
[3,1,3] => [[5,3,3],[2,2]]
[3,2,1,1] => [[4,4,4,3],[3,3,2]]
[3,2,2] => [[5,4,3],[3,2]]
[3,3,1] => [[5,5,3],[4,2]]
[3,4] => [[6,3],[2]]
[4,1,1,1] => [[4,4,4,4],[3,3,3]]
[4,1,2] => [[5,4,4],[3,3]]
[4,2,1] => [[5,5,4],[4,3]]
[4,3] => [[6,4],[3]]
[5,1,1] => [[5,5,5],[4,4]]
[5,2] => [[6,5],[4]]
[6,1] => [[6,6],[5]]
[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] => [[2,2,1,1,1,1,1],[1]]
[1,1,1,1,1,3] => [[3,1,1,1,1,1],[]]
[1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]]
[1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]]
[1,1,1,1,3,1] => [[3,3,1,1,1,1],[2]]
[1,1,1,1,4] => [[4,1,1,1,1],[]]
[1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]]
[1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]]
[1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]]
[1,1,1,2,3] => [[4,2,1,1,1],[1]]
[1,1,1,3,1,1] => [[3,3,3,1,1,1],[2,2]]
[1,1,1,3,2] => [[4,3,1,1,1],[2]]
[1,1,1,4,1] => [[4,4,1,1,1],[3]]
[1,1,1,5] => [[5,1,1,1],[]]
[1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]]
[1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]]
[1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
[1,1,2,1,3] => [[4,2,2,1,1],[1,1]]
[1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]]
[1,1,2,2,2] => [[4,3,2,1,1],[2,1]]
[1,1,2,3,1] => [[4,4,2,1,1],[3,1]]
[1,1,2,4] => [[5,2,1,1],[1]]
[1,1,3,1,1,1] => [[3,3,3,3,1,1],[2,2,2]]
[1,1,3,1,2] => [[4,3,3,1,1],[2,2]]
[1,1,3,2,1] => [[4,4,3,1,1],[3,2]]
[1,1,3,3] => [[5,3,1,1],[2]]
[1,1,4,1,1] => [[4,4,4,1,1],[3,3]]
[1,1,4,2] => [[5,4,1,1],[3]]
[1,1,5,1] => [[5,5,1,1],[4]]
[1,1,6] => [[6,1,1],[]]
[1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]]
[1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]]
[1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]]
[1,2,1,1,3] => [[4,2,2,2,1],[1,1,1]]
[1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]]
[1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]]
[1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]]
[1,2,1,4] => [[5,2,2,1],[1,1]]
[1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]]
[1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]]
[1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]]
[1,2,2,3] => [[5,3,2,1],[2,1]]
[1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]]
[1,2,3,2] => [[5,4,2,1],[3,1]]
[1,2,4,1] => [[5,5,2,1],[4,1]]
[1,2,5] => [[6,2,1],[1]]
[1,3,1,1,1,1] => [[3,3,3,3,3,1],[2,2,2,2]]
[1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]]
[1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]]
[1,3,1,3] => [[5,3,3,1],[2,2]]
[1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]]
[1,3,2,2] => [[5,4,3,1],[3,2]]
[1,3,3,1] => [[5,5,3,1],[4,2]]
[1,3,4] => [[6,3,1],[2]]
[1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]]
[1,4,1,2] => [[5,4,4,1],[3,3]]
[1,4,2,1] => [[5,5,4,1],[4,3]]
[1,4,3] => [[6,4,1],[3]]
[1,5,1,1] => [[5,5,5,1],[4,4]]
[1,5,2] => [[6,5,1],[4]]
[1,6,1] => [[6,6,1],[5]]
[1,7] => [[7,1],[]]
[2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]]
[2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]]
[2,1,1,1,3] => [[4,2,2,2,2],[1,1,1,1]]
[2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]]
[2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]]
[2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]]
[2,1,1,4] => [[5,2,2,2],[1,1,1]]
[2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]]
[2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]]
[2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]]
[2,1,2,3] => [[5,3,2,2],[2,1,1]]
[2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]]
[2,1,3,2] => [[5,4,2,2],[3,1,1]]
[2,1,4,1] => [[5,5,2,2],[4,1,1]]
[2,1,5] => [[6,2,2],[1,1]]
[2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]]
[2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]]
[2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]]
[2,2,1,3] => [[5,3,3,2],[2,2,1]]
[2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]]
[2,2,2,2] => [[5,4,3,2],[3,2,1]]
[2,2,3,1] => [[5,5,3,2],[4,2,1]]
[2,2,4] => [[6,3,2],[2,1]]
[2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]]
[2,3,1,2] => [[5,4,4,2],[3,3,1]]
[2,3,2,1] => [[5,5,4,2],[4,3,1]]
[2,3,3] => [[6,4,2],[3,1]]
[2,4,1,1] => [[5,5,5,2],[4,4,1]]
[2,4,2] => [[6,5,2],[4,1]]
[2,5,1] => [[6,6,2],[5,1]]
[2,6] => [[7,2],[1]]
[3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]]
[3,1,1,1,2] => [[4,3,3,3,3],[2,2,2,2]]
[3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]]
[3,1,1,3] => [[5,3,3,3],[2,2,2]]
[3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]]
[3,1,2,2] => [[5,4,3,3],[3,2,2]]
[3,1,3,1] => [[5,5,3,3],[4,2,2]]
[3,1,4] => [[6,3,3],[2,2]]
[3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]]
[3,2,1,2] => [[5,4,4,3],[3,3,2]]
[3,2,2,1] => [[5,5,4,3],[4,3,2]]
[3,2,3] => [[6,4,3],[3,2]]
[3,3,1,1] => [[5,5,5,3],[4,4,2]]
[3,3,2] => [[6,5,3],[4,2]]
[3,4,1] => [[6,6,3],[5,2]]
[3,5] => [[7,3],[2]]
[4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]]
[4,1,1,2] => [[5,4,4,4],[3,3,3]]
[4,1,2,1] => [[5,5,4,4],[4,3,3]]
[4,1,3] => [[6,4,4],[3,3]]
[4,2,1,1] => [[5,5,5,4],[4,4,3]]
[4,2,2] => [[6,5,4],[4,3]]
[4,3,1] => [[6,6,4],[5,3]]
[4,4] => [[7,4],[3]]
[5,1,1,1] => [[5,5,5,5],[4,4,4]]
[5,1,2] => [[6,5,5],[4,4]]
[5,2,1] => [[6,6,5],[5,4]]
[5,3] => [[7,5],[4]]
[6,1,1] => [[6,6,6],[5,5]]
[6,2] => [[7,6],[5]]
[7,1] => [[7,7],[6]]
[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] => [[2,2,1,1,1,1,1,1],[1]]
[1,1,1,1,1,1,3] => [[3,1,1,1,1,1,1],[]]
[1,1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1,1],[1,1]]
[1,1,1,1,1,2,2] => [[3,2,1,1,1,1,1],[1]]
[1,1,1,1,1,3,1] => [[3,3,1,1,1,1,1],[2]]
[1,1,1,1,1,4] => [[4,1,1,1,1,1],[]]
[1,1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1,1],[1,1,1]]
[1,1,1,1,2,1,2] => [[3,2,2,1,1,1,1],[1,1]]
[1,1,1,1,2,2,1] => [[3,3,2,1,1,1,1],[2,1]]
[1,1,1,1,2,3] => [[4,2,1,1,1,1],[1]]
[1,1,1,1,3,1,1] => [[3,3,3,1,1,1,1],[2,2]]
[1,1,1,1,3,2] => [[4,3,1,1,1,1],[2]]
[1,1,1,1,4,1] => [[4,4,1,1,1,1],[3]]
[1,1,1,1,5] => [[5,1,1,1,1],[]]
[1,1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1,1],[1,1,1,1]]
[1,1,1,2,1,1,2] => [[3,2,2,2,1,1,1],[1,1,1]]
[1,1,1,2,1,2,1] => [[3,3,2,2,1,1,1],[2,1,1]]
[1,1,1,2,1,3] => [[4,2,2,1,1,1],[1,1]]
[1,1,1,2,2,1,1] => [[3,3,3,2,1,1,1],[2,2,1]]
[1,1,1,2,2,2] => [[4,3,2,1,1,1],[2,1]]
[1,1,1,2,3,1] => [[4,4,2,1,1,1],[3,1]]
[1,1,1,2,4] => [[5,2,1,1,1],[1]]
[1,1,1,3,1,1,1] => [[3,3,3,3,1,1,1],[2,2,2]]
[1,1,1,3,1,2] => [[4,3,3,1,1,1],[2,2]]
[1,1,1,3,2,1] => [[4,4,3,1,1,1],[3,2]]
[1,1,1,3,3] => [[5,3,1,1,1],[2]]
[1,1,1,4,1,1] => [[4,4,4,1,1,1],[3,3]]
[1,1,1,4,2] => [[5,4,1,1,1],[3]]
[1,1,1,5,1] => [[5,5,1,1,1],[4]]
[1,1,1,6] => [[6,1,1,1],[]]
[1,1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1,1],[1,1,1,1,1]]
[1,1,2,1,1,1,2] => [[3,2,2,2,2,1,1],[1,1,1,1]]
[1,1,2,1,1,2,1] => [[3,3,2,2,2,1,1],[2,1,1,1]]
[1,1,2,1,1,3] => [[4,2,2,2,1,1],[1,1,1]]
[1,1,2,1,2,1,1] => [[3,3,3,2,2,1,1],[2,2,1,1]]
[1,1,2,1,2,2] => [[4,3,2,2,1,1],[2,1,1]]
[1,1,2,1,3,1] => [[4,4,2,2,1,1],[3,1,1]]
[1,1,2,1,4] => [[5,2,2,1,1],[1,1]]
[1,1,2,2,1,1,1] => [[3,3,3,3,2,1,1],[2,2,2,1]]
[1,1,2,2,1,2] => [[4,3,3,2,1,1],[2,2,1]]
[1,1,2,2,2,1] => [[4,4,3,2,1,1],[3,2,1]]
[1,1,2,2,3] => [[5,3,2,1,1],[2,1]]
[1,1,2,3,1,1] => [[4,4,4,2,1,1],[3,3,1]]
[1,1,2,3,2] => [[5,4,2,1,1],[3,1]]
[1,1,2,4,1] => [[5,5,2,1,1],[4,1]]
[1,1,2,5] => [[6,2,1,1],[1]]
[1,1,3,1,1,1,1] => [[3,3,3,3,3,1,1],[2,2,2,2]]
[1,1,3,1,1,2] => [[4,3,3,3,1,1],[2,2,2]]
[1,1,3,1,2,1] => [[4,4,3,3,1,1],[3,2,2]]
[1,1,3,1,3] => [[5,3,3,1,1],[2,2]]
[1,1,3,2,1,1] => [[4,4,4,3,1,1],[3,3,2]]
[1,1,3,2,2] => [[5,4,3,1,1],[3,2]]
[1,1,3,3,1] => [[5,5,3,1,1],[4,2]]
[1,1,3,4] => [[6,3,1,1],[2]]
[1,1,4,1,1,1] => [[4,4,4,4,1,1],[3,3,3]]
[1,1,4,1,2] => [[5,4,4,1,1],[3,3]]
[1,1,4,2,1] => [[5,5,4,1,1],[4,3]]
[1,1,4,3] => [[6,4,1,1],[3]]
[1,1,5,1,1] => [[5,5,5,1,1],[4,4]]
[1,1,5,2] => [[6,5,1,1],[4]]
[1,1,6,1] => [[6,6,1,1],[5]]
[1,1,7] => [[7,1,1],[]]
[1,2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,1],[1,1,1,1,1,1]]
[1,2,1,1,1,1,2] => [[3,2,2,2,2,2,1],[1,1,1,1,1]]
[1,2,1,1,1,2,1] => [[3,3,2,2,2,2,1],[2,1,1,1,1]]
[1,2,1,1,1,3] => [[4,2,2,2,2,1],[1,1,1,1]]
[1,2,1,1,2,1,1] => [[3,3,3,2,2,2,1],[2,2,1,1,1]]
[1,2,1,1,2,2] => [[4,3,2,2,2,1],[2,1,1,1]]
[1,2,1,1,3,1] => [[4,4,2,2,2,1],[3,1,1,1]]
[1,2,1,1,4] => [[5,2,2,2,1],[1,1,1]]
[1,2,1,2,1,1,1] => [[3,3,3,3,2,2,1],[2,2,2,1,1]]
[1,2,1,2,1,2] => [[4,3,3,2,2,1],[2,2,1,1]]
[1,2,1,2,2,1] => [[4,4,3,2,2,1],[3,2,1,1]]
[1,2,1,2,3] => [[5,3,2,2,1],[2,1,1]]
[1,2,1,3,1,1] => [[4,4,4,2,2,1],[3,3,1,1]]
[1,2,1,3,2] => [[5,4,2,2,1],[3,1,1]]
[1,2,1,4,1] => [[5,5,2,2,1],[4,1,1]]
[1,2,1,5] => [[6,2,2,1],[1,1]]
[1,2,2,1,1,1,1] => [[3,3,3,3,3,2,1],[2,2,2,2,1]]
[1,2,2,1,1,2] => [[4,3,3,3,2,1],[2,2,2,1]]
[1,2,2,1,2,1] => [[4,4,3,3,2,1],[3,2,2,1]]
[1,2,2,1,3] => [[5,3,3,2,1],[2,2,1]]
[1,2,2,2,1,1] => [[4,4,4,3,2,1],[3,3,2,1]]
[1,2,2,2,2] => [[5,4,3,2,1],[3,2,1]]
[1,2,2,3,1] => [[5,5,3,2,1],[4,2,1]]
[1,2,2,4] => [[6,3,2,1],[2,1]]
[1,2,3,1,1,1] => [[4,4,4,4,2,1],[3,3,3,1]]
[1,2,3,1,2] => [[5,4,4,2,1],[3,3,1]]
[1,2,3,2,1] => [[5,5,4,2,1],[4,3,1]]
[1,2,3,3] => [[6,4,2,1],[3,1]]
[1,2,4,1,1] => [[5,5,5,2,1],[4,4,1]]
[1,2,4,2] => [[6,5,2,1],[4,1]]
[1,2,5,1] => [[6,6,2,1],[5,1]]
[1,2,6] => [[7,2,1],[1]]
[1,3,1,1,1,1,1] => [[3,3,3,3,3,3,1],[2,2,2,2,2]]
[1,3,1,1,1,2] => [[4,3,3,3,3,1],[2,2,2,2]]
[1,3,1,1,2,1] => [[4,4,3,3,3,1],[3,2,2,2]]
[1,3,1,1,3] => [[5,3,3,3,1],[2,2,2]]
[1,3,1,2,1,1] => [[4,4,4,3,3,1],[3,3,2,2]]
[1,3,1,2,2] => [[5,4,3,3,1],[3,2,2]]
[1,3,1,3,1] => [[5,5,3,3,1],[4,2,2]]
[1,3,1,4] => [[6,3,3,1],[2,2]]
[1,3,2,1,1,1] => [[4,4,4,4,3,1],[3,3,3,2]]
[1,3,2,1,2] => [[5,4,4,3,1],[3,3,2]]
[1,3,2,2,1] => [[5,5,4,3,1],[4,3,2]]
[1,3,2,3] => [[6,4,3,1],[3,2]]
[1,3,3,1,1] => [[5,5,5,3,1],[4,4,2]]
[1,3,3,2] => [[6,5,3,1],[4,2]]
[1,3,4,1] => [[6,6,3,1],[5,2]]
[1,3,5] => [[7,3,1],[2]]
[1,4,1,1,1,1] => [[4,4,4,4,4,1],[3,3,3,3]]
[1,4,1,1,2] => [[5,4,4,4,1],[3,3,3]]
[1,4,1,2,1] => [[5,5,4,4,1],[4,3,3]]
[1,4,1,3] => [[6,4,4,1],[3,3]]
[1,4,2,1,1] => [[5,5,5,4,1],[4,4,3]]
[1,4,2,2] => [[6,5,4,1],[4,3]]
[1,4,3,1] => [[6,6,4,1],[5,3]]
[1,4,4] => [[7,4,1],[3]]
[1,5,1,1,1] => [[5,5,5,5,1],[4,4,4]]
[1,5,1,2] => [[6,5,5,1],[4,4]]
[1,5,2,1] => [[6,6,5,1],[5,4]]
[1,5,3] => [[7,5,1],[4]]
[1,6,1,1] => [[6,6,6,1],[5,5]]
[1,6,2] => [[7,6,1],[5]]
[1,7,1] => [[7,7,1],[6]]
[1,8] => [[8,1],[]]
[2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[2,1,1,1,1,1,2] => [[3,2,2,2,2,2,2],[1,1,1,1,1,1]]
[2,1,1,1,1,2,1] => [[3,3,2,2,2,2,2],[2,1,1,1,1,1]]
[2,1,1,1,1,3] => [[4,2,2,2,2,2],[1,1,1,1,1]]
[2,1,1,1,2,1,1] => [[3,3,3,2,2,2,2],[2,2,1,1,1,1]]
[2,1,1,1,2,2] => [[4,3,2,2,2,2],[2,1,1,1,1]]
[2,1,1,1,3,1] => [[4,4,2,2,2,2],[3,1,1,1,1]]
[2,1,1,1,4] => [[5,2,2,2,2],[1,1,1,1]]
[2,1,1,2,1,1,1] => [[3,3,3,3,2,2,2],[2,2,2,1,1,1]]
[2,1,1,2,1,2] => [[4,3,3,2,2,2],[2,2,1,1,1]]
[2,1,1,2,2,1] => [[4,4,3,2,2,2],[3,2,1,1,1]]
[2,1,1,2,3] => [[5,3,2,2,2],[2,1,1,1]]
[2,1,1,3,1,1] => [[4,4,4,2,2,2],[3,3,1,1,1]]
[2,1,1,3,2] => [[5,4,2,2,2],[3,1,1,1]]
[2,1,1,4,1] => [[5,5,2,2,2],[4,1,1,1]]
[2,1,1,5] => [[6,2,2,2],[1,1,1]]
[2,1,2,1,1,1,1] => [[3,3,3,3,3,2,2],[2,2,2,2,1,1]]
[2,1,2,1,1,2] => [[4,3,3,3,2,2],[2,2,2,1,1]]
[2,1,2,1,2,1] => [[4,4,3,3,2,2],[3,2,2,1,1]]
[2,1,2,1,3] => [[5,3,3,2,2],[2,2,1,1]]
[2,1,2,2,1,1] => [[4,4,4,3,2,2],[3,3,2,1,1]]
[2,1,2,2,2] => [[5,4,3,2,2],[3,2,1,1]]
[2,1,2,3,1] => [[5,5,3,2,2],[4,2,1,1]]
[2,1,2,4] => [[6,3,2,2],[2,1,1]]
[2,1,3,1,1,1] => [[4,4,4,4,2,2],[3,3,3,1,1]]
[2,1,3,1,2] => [[5,4,4,2,2],[3,3,1,1]]
[2,1,3,2,1] => [[5,5,4,2,2],[4,3,1,1]]
[2,1,3,3] => [[6,4,2,2],[3,1,1]]
[2,1,4,1,1] => [[5,5,5,2,2],[4,4,1,1]]
[2,1,4,2] => [[6,5,2,2],[4,1,1]]
[2,1,5,1] => [[6,6,2,2],[5,1,1]]
[2,1,6] => [[7,2,2],[1,1]]
[2,2,1,1,1,1,1] => [[3,3,3,3,3,3,2],[2,2,2,2,2,1]]
[2,2,1,1,1,2] => [[4,3,3,3,3,2],[2,2,2,2,1]]
[2,2,1,1,2,1] => [[4,4,3,3,3,2],[3,2,2,2,1]]
[2,2,1,1,3] => [[5,3,3,3,2],[2,2,2,1]]
[2,2,1,2,1,1] => [[4,4,4,3,3,2],[3,3,2,2,1]]
[2,2,1,2,2] => [[5,4,3,3,2],[3,2,2,1]]
[2,2,1,3,1] => [[5,5,3,3,2],[4,2,2,1]]
[2,2,1,4] => [[6,3,3,2],[2,2,1]]
[2,2,2,1,1,1] => [[4,4,4,4,3,2],[3,3,3,2,1]]
[2,2,2,1,2] => [[5,4,4,3,2],[3,3,2,1]]
[2,2,2,2,1] => [[5,5,4,3,2],[4,3,2,1]]
[2,2,2,3] => [[6,4,3,2],[3,2,1]]
[2,2,3,1,1] => [[5,5,5,3,2],[4,4,2,1]]
[2,2,3,2] => [[6,5,3,2],[4,2,1]]
[2,2,4,1] => [[6,6,3,2],[5,2,1]]
[2,2,5] => [[7,3,2],[2,1]]
[2,3,1,1,1,1] => [[4,4,4,4,4,2],[3,3,3,3,1]]
[2,3,1,1,2] => [[5,4,4,4,2],[3,3,3,1]]
[2,3,1,2,1] => [[5,5,4,4,2],[4,3,3,1]]
[2,3,1,3] => [[6,4,4,2],[3,3,1]]
[2,3,2,1,1] => [[5,5,5,4,2],[4,4,3,1]]
[2,3,2,2] => [[6,5,4,2],[4,3,1]]
[2,3,3,1] => [[6,6,4,2],[5,3,1]]
[2,3,4] => [[7,4,2],[3,1]]
[2,4,1,1,1] => [[5,5,5,5,2],[4,4,4,1]]
[2,4,1,2] => [[6,5,5,2],[4,4,1]]
[2,4,2,1] => [[6,6,5,2],[5,4,1]]
[2,4,3] => [[7,5,2],[4,1]]
[2,5,1,1] => [[6,6,6,2],[5,5,1]]
[2,5,2] => [[7,6,2],[5,1]]
[2,6,1] => [[7,7,2],[6,1]]
[2,7] => [[8,2],[1]]
[3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]]
[3,1,1,1,1,2] => [[4,3,3,3,3,3],[2,2,2,2,2]]
[3,1,1,1,2,1] => [[4,4,3,3,3,3],[3,2,2,2,2]]
[3,1,1,1,3] => [[5,3,3,3,3],[2,2,2,2]]
[3,1,1,2,1,1] => [[4,4,4,3,3,3],[3,3,2,2,2]]
[3,1,1,2,2] => [[5,4,3,3,3],[3,2,2,2]]
[3,1,1,3,1] => [[5,5,3,3,3],[4,2,2,2]]
[3,1,1,4] => [[6,3,3,3],[2,2,2]]
[3,1,2,1,1,1] => [[4,4,4,4,3,3],[3,3,3,2,2]]
[3,1,2,1,2] => [[5,4,4,3,3],[3,3,2,2]]
[3,1,2,2,1] => [[5,5,4,3,3],[4,3,2,2]]
[3,1,2,3] => [[6,4,3,3],[3,2,2]]
[3,1,3,1,1] => [[5,5,5,3,3],[4,4,2,2]]
[3,1,3,2] => [[6,5,3,3],[4,2,2]]
[3,1,4,1] => [[6,6,3,3],[5,2,2]]
[3,1,5] => [[7,3,3],[2,2]]
[3,2,1,1,1,1] => [[4,4,4,4,4,3],[3,3,3,3,2]]
[3,2,1,1,2] => [[5,4,4,4,3],[3,3,3,2]]
[3,2,1,2,1] => [[5,5,4,4,3],[4,3,3,2]]
[3,2,1,3] => [[6,4,4,3],[3,3,2]]
[3,2,2,1,1] => [[5,5,5,4,3],[4,4,3,2]]
[3,2,2,2] => [[6,5,4,3],[4,3,2]]
[3,2,3,1] => [[6,6,4,3],[5,3,2]]
[3,2,4] => [[7,4,3],[3,2]]
[3,3,1,1,1] => [[5,5,5,5,3],[4,4,4,2]]
[3,3,1,2] => [[6,5,5,3],[4,4,2]]
[3,3,2,1] => [[6,6,5,3],[5,4,2]]
[3,3,3] => [[7,5,3],[4,2]]
[3,4,1,1] => [[6,6,6,3],[5,5,2]]
[3,4,2] => [[7,6,3],[5,2]]
[3,5,1] => [[7,7,3],[6,2]]
[3,6] => [[8,3],[2]]
[4,1,1,1,1,1] => [[4,4,4,4,4,4],[3,3,3,3,3]]
[4,1,1,1,2] => [[5,4,4,4,4],[3,3,3,3]]
[4,1,1,2,1] => [[5,5,4,4,4],[4,3,3,3]]
[4,1,1,3] => [[6,4,4,4],[3,3,3]]
[4,1,2,1,1] => [[5,5,5,4,4],[4,4,3,3]]
[4,1,2,2] => [[6,5,4,4],[4,3,3]]
[4,1,3,1] => [[6,6,4,4],[5,3,3]]
[4,1,4] => [[7,4,4],[3,3]]
[4,2,1,1,1] => [[5,5,5,5,4],[4,4,4,3]]
[4,2,1,2] => [[6,5,5,4],[4,4,3]]
[4,2,2,1] => [[6,6,5,4],[5,4,3]]
[4,2,3] => [[7,5,4],[4,3]]
[4,3,1,1] => [[6,6,6,4],[5,5,3]]
[4,3,2] => [[7,6,4],[5,3]]
[4,4,1] => [[7,7,4],[6,3]]
[4,5] => [[8,4],[3]]
[5,1,1,1,1] => [[5,5,5,5,5],[4,4,4,4]]
[5,1,1,2] => [[6,5,5,5],[4,4,4]]
[5,1,2,1] => [[6,6,5,5],[5,4,4]]
[5,1,3] => [[7,5,5],[4,4]]
[5,2,1,1] => [[6,6,6,5],[5,5,4]]
[5,2,2] => [[7,6,5],[5,4]]
[5,3,1] => [[7,7,5],[6,4]]
[5,4] => [[8,5],[4]]
[6,1,1,1] => [[6,6,6,6],[5,5,5]]
[6,1,2] => [[7,6,6],[5,5]]
[6,2,1] => [[7,7,6],[6,5]]
[6,3] => [[8,6],[5]]
[7,1,1] => [[7,7,7],[6,6]]
[7,2] => [[8,7],[6]]
[8,1] => [[8,8],[7]]
[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] => [[2,2,1,1,1,1,1,1,1],[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] => [[2,2,2,1,1,1,1,1,1],[1,1]]
[1,1,1,1,1,1,2,2] => [[3,2,1,1,1,1,1,1],[1]]
[1,1,1,1,1,1,3,1] => [[3,3,1,1,1,1,1,1],[2]]
[1,1,1,1,1,1,4] => [[4,1,1,1,1,1,1],[]]
[1,1,1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1,1,1],[1,1,1]]
[1,1,1,1,1,2,1,2] => [[3,2,2,1,1,1,1,1],[1,1]]
[1,1,1,1,1,2,2,1] => [[3,3,2,1,1,1,1,1],[2,1]]
[1,1,1,1,1,2,3] => [[4,2,1,1,1,1,1],[1]]
[1,1,1,1,1,3,1,1] => [[3,3,3,1,1,1,1,1],[2,2]]
[1,1,1,1,1,3,2] => [[4,3,1,1,1,1,1],[2]]
[1,1,1,1,1,4,1] => [[4,4,1,1,1,1,1],[3]]
[1,1,1,1,1,5] => [[5,1,1,1,1,1],[]]
[1,1,1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1,1,1],[1,1,1,1]]
[1,1,1,1,2,1,1,2] => [[3,2,2,2,1,1,1,1],[1,1,1]]
[1,1,1,1,2,1,2,1] => [[3,3,2,2,1,1,1,1],[2,1,1]]
[1,1,1,1,2,1,3] => [[4,2,2,1,1,1,1],[1,1]]
[1,1,1,1,2,2,1,1] => [[3,3,3,2,1,1,1,1],[2,2,1]]
[1,1,1,1,2,2,2] => [[4,3,2,1,1,1,1],[2,1]]
[1,1,1,1,2,3,1] => [[4,4,2,1,1,1,1],[3,1]]
[1,1,1,1,2,4] => [[5,2,1,1,1,1],[1]]
[1,1,1,1,3,1,1,1] => [[3,3,3,3,1,1,1,1],[2,2,2]]
[1,1,1,1,3,1,2] => [[4,3,3,1,1,1,1],[2,2]]
[1,1,1,1,3,2,1] => [[4,4,3,1,1,1,1],[3,2]]
[1,1,1,1,3,3] => [[5,3,1,1,1,1],[2]]
[1,1,1,1,4,1,1] => [[4,4,4,1,1,1,1],[3,3]]
[1,1,1,1,4,2] => [[5,4,1,1,1,1],[3]]
[1,1,1,1,5,1] => [[5,5,1,1,1,1],[4]]
[1,1,1,1,6] => [[6,1,1,1,1],[]]
[1,1,1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1,1,1],[1,1,1,1,1]]
[1,1,1,2,1,1,1,2] => [[3,2,2,2,2,1,1,1],[1,1,1,1]]
[1,1,1,2,1,1,2,1] => [[3,3,2,2,2,1,1,1],[2,1,1,1]]
[1,1,1,2,1,1,3] => [[4,2,2,2,1,1,1],[1,1,1]]
[1,1,1,2,1,2,1,1] => [[3,3,3,2,2,1,1,1],[2,2,1,1]]
[1,1,1,2,1,2,2] => [[4,3,2,2,1,1,1],[2,1,1]]
[1,1,1,2,1,3,1] => [[4,4,2,2,1,1,1],[3,1,1]]
[1,1,1,2,1,4] => [[5,2,2,1,1,1],[1,1]]
[1,1,1,2,2,1,1,1] => [[3,3,3,3,2,1,1,1],[2,2,2,1]]
[1,1,1,2,2,1,2] => [[4,3,3,2,1,1,1],[2,2,1]]
[1,1,1,2,2,2,1] => [[4,4,3,2,1,1,1],[3,2,1]]
[1,1,1,2,2,3] => [[5,3,2,1,1,1],[2,1]]
[1,1,1,2,3,1,1] => [[4,4,4,2,1,1,1],[3,3,1]]
[1,1,1,2,3,2] => [[5,4,2,1,1,1],[3,1]]
[1,1,1,2,4,1] => [[5,5,2,1,1,1],[4,1]]
[1,1,1,2,5] => [[6,2,1,1,1],[1]]
[1,1,1,3,1,1,1,1] => [[3,3,3,3,3,1,1,1],[2,2,2,2]]
[1,1,1,3,1,1,2] => [[4,3,3,3,1,1,1],[2,2,2]]
[1,1,1,3,1,2,1] => [[4,4,3,3,1,1,1],[3,2,2]]
[1,1,1,3,1,3] => [[5,3,3,1,1,1],[2,2]]
[1,1,1,3,2,1,1] => [[4,4,4,3,1,1,1],[3,3,2]]
[1,1,1,3,2,2] => [[5,4,3,1,1,1],[3,2]]
[1,1,1,3,3,1] => [[5,5,3,1,1,1],[4,2]]
[1,1,1,3,4] => [[6,3,1,1,1],[2]]
[1,1,1,4,1,1,1] => [[4,4,4,4,1,1,1],[3,3,3]]
[1,1,1,4,1,2] => [[5,4,4,1,1,1],[3,3]]
[1,1,1,4,2,1] => [[5,5,4,1,1,1],[4,3]]
[1,1,1,4,3] => [[6,4,1,1,1],[3]]
[1,1,1,5,1,1] => [[5,5,5,1,1,1],[4,4]]
[1,1,1,5,2] => [[6,5,1,1,1],[4]]
[1,1,1,6,1] => [[6,6,1,1,1],[5]]
[1,1,1,7] => [[7,1,1,1],[]]
[1,1,2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,1,1],[1,1,1,1,1,1]]
[1,1,2,1,1,1,1,2] => [[3,2,2,2,2,2,1,1],[1,1,1,1,1]]
[1,1,2,1,1,1,2,1] => [[3,3,2,2,2,2,1,1],[2,1,1,1,1]]
[1,1,2,1,1,1,3] => [[4,2,2,2,2,1,1],[1,1,1,1]]
[1,1,2,1,1,2,1,1] => [[3,3,3,2,2,2,1,1],[2,2,1,1,1]]
[1,1,2,1,1,2,2] => [[4,3,2,2,2,1,1],[2,1,1,1]]
[1,1,2,1,1,3,1] => [[4,4,2,2,2,1,1],[3,1,1,1]]
[1,1,2,1,1,4] => [[5,2,2,2,1,1],[1,1,1]]
[1,1,2,1,2,1,1,1] => [[3,3,3,3,2,2,1,1],[2,2,2,1,1]]
[1,1,2,1,2,1,2] => [[4,3,3,2,2,1,1],[2,2,1,1]]
[1,1,2,1,2,2,1] => [[4,4,3,2,2,1,1],[3,2,1,1]]
[1,1,2,1,2,3] => [[5,3,2,2,1,1],[2,1,1]]
[1,1,2,1,3,1,1] => [[4,4,4,2,2,1,1],[3,3,1,1]]
[1,1,2,1,3,2] => [[5,4,2,2,1,1],[3,1,1]]
[1,1,2,1,4,1] => [[5,5,2,2,1,1],[4,1,1]]
[1,1,2,1,5] => [[6,2,2,1,1],[1,1]]
[1,1,2,2,1,1,1,1] => [[3,3,3,3,3,2,1,1],[2,2,2,2,1]]
[1,1,2,2,1,1,2] => [[4,3,3,3,2,1,1],[2,2,2,1]]
[1,1,2,2,1,2,1] => [[4,4,3,3,2,1,1],[3,2,2,1]]
[1,1,2,2,1,3] => [[5,3,3,2,1,1],[2,2,1]]
[1,1,2,2,2,1,1] => [[4,4,4,3,2,1,1],[3,3,2,1]]
[1,1,2,2,2,2] => [[5,4,3,2,1,1],[3,2,1]]
[1,1,2,2,3,1] => [[5,5,3,2,1,1],[4,2,1]]
[1,1,2,2,4] => [[6,3,2,1,1],[2,1]]
[1,1,2,3,1,1,1] => [[4,4,4,4,2,1,1],[3,3,3,1]]
[1,1,2,3,1,2] => [[5,4,4,2,1,1],[3,3,1]]
[1,1,2,3,2,1] => [[5,5,4,2,1,1],[4,3,1]]
[1,1,2,3,3] => [[6,4,2,1,1],[3,1]]
[1,1,2,4,1,1] => [[5,5,5,2,1,1],[4,4,1]]
[1,1,2,4,2] => [[6,5,2,1,1],[4,1]]
[1,1,2,5,1] => [[6,6,2,1,1],[5,1]]
[1,1,2,6] => [[7,2,1,1],[1]]
[1,1,3,1,1,1,1,1] => [[3,3,3,3,3,3,1,1],[2,2,2,2,2]]
[1,1,3,1,1,1,2] => [[4,3,3,3,3,1,1],[2,2,2,2]]
[1,1,3,1,1,2,1] => [[4,4,3,3,3,1,1],[3,2,2,2]]
[1,1,3,1,1,3] => [[5,3,3,3,1,1],[2,2,2]]
[1,1,3,1,2,1,1] => [[4,4,4,3,3,1,1],[3,3,2,2]]
[1,1,3,1,2,2] => [[5,4,3,3,1,1],[3,2,2]]
[1,1,3,1,3,1] => [[5,5,3,3,1,1],[4,2,2]]
[1,1,3,1,4] => [[6,3,3,1,1],[2,2]]
[1,1,3,2,1,1,1] => [[4,4,4,4,3,1,1],[3,3,3,2]]
[1,1,3,2,1,2] => [[5,4,4,3,1,1],[3,3,2]]
[1,1,3,2,2,1] => [[5,5,4,3,1,1],[4,3,2]]
[1,1,3,2,3] => [[6,4,3,1,1],[3,2]]
[1,1,3,3,1,1] => [[5,5,5,3,1,1],[4,4,2]]
[1,1,3,3,2] => [[6,5,3,1,1],[4,2]]
[1,1,3,4,1] => [[6,6,3,1,1],[5,2]]
[1,1,3,5] => [[7,3,1,1],[2]]
[1,1,4,1,1,1,1] => [[4,4,4,4,4,1,1],[3,3,3,3]]
[1,1,4,1,1,2] => [[5,4,4,4,1,1],[3,3,3]]
[1,1,4,1,2,1] => [[5,5,4,4,1,1],[4,3,3]]
[1,1,4,1,3] => [[6,4,4,1,1],[3,3]]
[1,1,4,2,1,1] => [[5,5,5,4,1,1],[4,4,3]]
[1,1,4,2,2] => [[6,5,4,1,1],[4,3]]
[1,1,4,3,1] => [[6,6,4,1,1],[5,3]]
[1,1,4,4] => [[7,4,1,1],[3]]
[1,1,5,1,1,1] => [[5,5,5,5,1,1],[4,4,4]]
[1,1,5,1,2] => [[6,5,5,1,1],[4,4]]
[1,1,5,2,1] => [[6,6,5,1,1],[5,4]]
[1,1,5,3] => [[7,5,1,1],[4]]
[1,1,6,1,1] => [[6,6,6,1,1],[5,5]]
[1,1,6,2] => [[7,6,1,1],[5]]
[1,1,7,1] => [[7,7,1,1],[6]]
[1,1,8] => [[8,1,1],[]]
[1,2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,1],[1,1,1,1,1,1,1]]
[1,2,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,1],[1,1,1,1,1,1]]
[1,2,1,1,1,1,2,1] => [[3,3,2,2,2,2,2,1],[2,1,1,1,1,1]]
[1,2,1,1,1,1,3] => [[4,2,2,2,2,2,1],[1,1,1,1,1]]
[1,2,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,1],[2,2,1,1,1,1]]
[1,2,1,1,1,2,2] => [[4,3,2,2,2,2,1],[2,1,1,1,1]]
[1,2,1,1,1,3,1] => [[4,4,2,2,2,2,1],[3,1,1,1,1]]
[1,2,1,1,1,4] => [[5,2,2,2,2,1],[1,1,1,1]]
[1,2,1,1,2,1,1,1] => [[3,3,3,3,2,2,2,1],[2,2,2,1,1,1]]
[1,2,1,1,2,1,2] => [[4,3,3,2,2,2,1],[2,2,1,1,1]]
[1,2,1,1,2,2,1] => [[4,4,3,2,2,2,1],[3,2,1,1,1]]
[1,2,1,1,2,3] => [[5,3,2,2,2,1],[2,1,1,1]]
[1,2,1,1,3,1,1] => [[4,4,4,2,2,2,1],[3,3,1,1,1]]
[1,2,1,1,3,2] => [[5,4,2,2,2,1],[3,1,1,1]]
[1,2,1,1,4,1] => [[5,5,2,2,2,1],[4,1,1,1]]
[1,2,1,1,5] => [[6,2,2,2,1],[1,1,1]]
[1,2,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,1],[2,2,2,2,1,1]]
[1,2,1,2,1,1,2] => [[4,3,3,3,2,2,1],[2,2,2,1,1]]
[1,2,1,2,1,2,1] => [[4,4,3,3,2,2,1],[3,2,2,1,1]]
[1,2,1,2,1,3] => [[5,3,3,2,2,1],[2,2,1,1]]
[1,2,1,2,2,1,1] => [[4,4,4,3,2,2,1],[3,3,2,1,1]]
[1,2,1,2,2,2] => [[5,4,3,2,2,1],[3,2,1,1]]
[1,2,1,2,3,1] => [[5,5,3,2,2,1],[4,2,1,1]]
[1,2,1,2,4] => [[6,3,2,2,1],[2,1,1]]
[1,2,1,3,1,1,1] => [[4,4,4,4,2,2,1],[3,3,3,1,1]]
[1,2,1,3,1,2] => [[5,4,4,2,2,1],[3,3,1,1]]
[1,2,1,3,2,1] => [[5,5,4,2,2,1],[4,3,1,1]]
[1,2,1,3,3] => [[6,4,2,2,1],[3,1,1]]
[1,2,1,4,1,1] => [[5,5,5,2,2,1],[4,4,1,1]]
[1,2,1,4,2] => [[6,5,2,2,1],[4,1,1]]
[1,2,1,5,1] => [[6,6,2,2,1],[5,1,1]]
[1,2,1,6] => [[7,2,2,1],[1,1]]
[1,2,2,1,1,1,1,1] => [[3,3,3,3,3,3,2,1],[2,2,2,2,2,1]]
[1,2,2,1,1,1,2] => [[4,3,3,3,3,2,1],[2,2,2,2,1]]
[1,2,2,1,1,2,1] => [[4,4,3,3,3,2,1],[3,2,2,2,1]]
[1,2,2,1,1,3] => [[5,3,3,3,2,1],[2,2,2,1]]
[1,2,2,1,2,1,1] => [[4,4,4,3,3,2,1],[3,3,2,2,1]]
[1,2,2,1,2,2] => [[5,4,3,3,2,1],[3,2,2,1]]
[1,2,2,1,3,1] => [[5,5,3,3,2,1],[4,2,2,1]]
[1,2,2,1,4] => [[6,3,3,2,1],[2,2,1]]
[1,2,2,2,1,1,1] => [[4,4,4,4,3,2,1],[3,3,3,2,1]]
[1,2,2,2,1,2] => [[5,4,4,3,2,1],[3,3,2,1]]
[1,2,2,2,2,1] => [[5,5,4,3,2,1],[4,3,2,1]]
[1,2,2,2,3] => [[6,4,3,2,1],[3,2,1]]
[1,2,2,3,1,1] => [[5,5,5,3,2,1],[4,4,2,1]]
[1,2,2,3,2] => [[6,5,3,2,1],[4,2,1]]
[1,2,2,4,1] => [[6,6,3,2,1],[5,2,1]]
[1,2,2,5] => [[7,3,2,1],[2,1]]
[1,2,3,1,1,1,1] => [[4,4,4,4,4,2,1],[3,3,3,3,1]]
[1,2,3,1,1,2] => [[5,4,4,4,2,1],[3,3,3,1]]
[1,2,3,1,2,1] => [[5,5,4,4,2,1],[4,3,3,1]]
[1,2,3,1,3] => [[6,4,4,2,1],[3,3,1]]
[1,2,3,2,1,1] => [[5,5,5,4,2,1],[4,4,3,1]]
[1,2,3,2,2] => [[6,5,4,2,1],[4,3,1]]
[1,2,3,3,1] => [[6,6,4,2,1],[5,3,1]]
[1,2,3,4] => [[7,4,2,1],[3,1]]
[1,2,4,1,1,1] => [[5,5,5,5,2,1],[4,4,4,1]]
[1,2,4,1,2] => [[6,5,5,2,1],[4,4,1]]
[1,2,4,2,1] => [[6,6,5,2,1],[5,4,1]]
[1,2,4,3] => [[7,5,2,1],[4,1]]
[1,2,5,1,1] => [[6,6,6,2,1],[5,5,1]]
[1,2,5,2] => [[7,6,2,1],[5,1]]
[1,2,6,1] => [[7,7,2,1],[6,1]]
[1,2,7] => [[8,2,1],[1]]
[1,3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,1],[2,2,2,2,2,2]]
[1,3,1,1,1,1,2] => [[4,3,3,3,3,3,1],[2,2,2,2,2]]
[1,3,1,1,1,2,1] => [[4,4,3,3,3,3,1],[3,2,2,2,2]]
[1,3,1,1,1,3] => [[5,3,3,3,3,1],[2,2,2,2]]
[1,3,1,1,2,1,1] => [[4,4,4,3,3,3,1],[3,3,2,2,2]]
[1,3,1,1,2,2] => [[5,4,3,3,3,1],[3,2,2,2]]
[1,3,1,1,3,1] => [[5,5,3,3,3,1],[4,2,2,2]]
[1,3,1,1,4] => [[6,3,3,3,1],[2,2,2]]
[1,3,1,2,1,1,1] => [[4,4,4,4,3,3,1],[3,3,3,2,2]]
[1,3,1,2,1,2] => [[5,4,4,3,3,1],[3,3,2,2]]
[1,3,1,2,2,1] => [[5,5,4,3,3,1],[4,3,2,2]]
[1,3,1,2,3] => [[6,4,3,3,1],[3,2,2]]
[1,3,1,3,1,1] => [[5,5,5,3,3,1],[4,4,2,2]]
[1,3,1,3,2] => [[6,5,3,3,1],[4,2,2]]
[1,3,1,4,1] => [[6,6,3,3,1],[5,2,2]]
[1,3,1,5] => [[7,3,3,1],[2,2]]
[1,3,2,1,1,1,1] => [[4,4,4,4,4,3,1],[3,3,3,3,2]]
[1,3,2,1,1,2] => [[5,4,4,4,3,1],[3,3,3,2]]
[1,3,2,1,2,1] => [[5,5,4,4,3,1],[4,3,3,2]]
[1,3,2,1,3] => [[6,4,4,3,1],[3,3,2]]
[1,3,2,2,1,1] => [[5,5,5,4,3,1],[4,4,3,2]]
[1,3,2,2,2] => [[6,5,4,3,1],[4,3,2]]
[1,3,2,3,1] => [[6,6,4,3,1],[5,3,2]]
[1,3,2,4] => [[7,4,3,1],[3,2]]
[1,3,3,1,1,1] => [[5,5,5,5,3,1],[4,4,4,2]]
[1,3,3,1,2] => [[6,5,5,3,1],[4,4,2]]
[1,3,3,2,1] => [[6,6,5,3,1],[5,4,2]]
[1,3,3,3] => [[7,5,3,1],[4,2]]
[1,3,4,1,1] => [[6,6,6,3,1],[5,5,2]]
[1,3,4,2] => [[7,6,3,1],[5,2]]
[1,3,5,1] => [[7,7,3,1],[6,2]]
[1,3,6] => [[8,3,1],[2]]
[1,4,1,1,1,1,1] => [[4,4,4,4,4,4,1],[3,3,3,3,3]]
[1,4,1,1,1,2] => [[5,4,4,4,4,1],[3,3,3,3]]
[1,4,1,1,2,1] => [[5,5,4,4,4,1],[4,3,3,3]]
[1,4,1,1,3] => [[6,4,4,4,1],[3,3,3]]
[1,4,1,2,1,1] => [[5,5,5,4,4,1],[4,4,3,3]]
[1,4,1,2,2] => [[6,5,4,4,1],[4,3,3]]
[1,4,1,3,1] => [[6,6,4,4,1],[5,3,3]]
[1,4,1,4] => [[7,4,4,1],[3,3]]
[1,4,2,1,1,1] => [[5,5,5,5,4,1],[4,4,4,3]]
[1,4,2,1,2] => [[6,5,5,4,1],[4,4,3]]
[1,4,2,2,1] => [[6,6,5,4,1],[5,4,3]]
[1,4,2,3] => [[7,5,4,1],[4,3]]
[1,4,3,1,1] => [[6,6,6,4,1],[5,5,3]]
[1,4,3,2] => [[7,6,4,1],[5,3]]
[1,4,4,1] => [[7,7,4,1],[6,3]]
[1,4,5] => [[8,4,1],[3]]
[1,5,1,1,1,1] => [[5,5,5,5,5,1],[4,4,4,4]]
[1,5,1,1,2] => [[6,5,5,5,1],[4,4,4]]
[1,5,1,2,1] => [[6,6,5,5,1],[5,4,4]]
[1,5,1,3] => [[7,5,5,1],[4,4]]
[1,5,2,1,1] => [[6,6,6,5,1],[5,5,4]]
[1,5,2,2] => [[7,6,5,1],[5,4]]
[1,5,3,1] => [[7,7,5,1],[6,4]]
[1,5,4] => [[8,5,1],[4]]
[1,6,1,1,1] => [[6,6,6,6,1],[5,5,5]]
[1,6,1,2] => [[7,6,6,1],[5,5]]
[1,6,2,1] => [[7,7,6,1],[6,5]]
[1,6,3] => [[8,6,1],[5]]
[1,7,1,1] => [[7,7,7,1],[6,6]]
[1,7,2] => [[8,7,1],[6]]
[1,8,1] => [[8,8,1],[7]]
[1,9] => [[9,1],[]]
[2,1,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]
[2,1,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[2,1,1,1,1,1,2,1] => [[3,3,2,2,2,2,2,2],[2,1,1,1,1,1,1]]
[2,1,1,1,1,1,3] => [[4,2,2,2,2,2,2],[1,1,1,1,1,1]]
[2,1,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,2],[2,2,1,1,1,1,1]]
[2,1,1,1,1,2,2] => [[4,3,2,2,2,2,2],[2,1,1,1,1,1]]
[2,1,1,1,1,3,1] => [[4,4,2,2,2,2,2],[3,1,1,1,1,1]]
[2,1,1,1,1,4] => [[5,2,2,2,2,2],[1,1,1,1,1]]
[2,1,1,1,2,1,1,1] => [[3,3,3,3,2,2,2,2],[2,2,2,1,1,1,1]]
[2,1,1,1,2,1,2] => [[4,3,3,2,2,2,2],[2,2,1,1,1,1]]
[2,1,1,1,2,2,1] => [[4,4,3,2,2,2,2],[3,2,1,1,1,1]]
[2,1,1,1,2,3] => [[5,3,2,2,2,2],[2,1,1,1,1]]
[2,1,1,1,3,1,1] => [[4,4,4,2,2,2,2],[3,3,1,1,1,1]]
[2,1,1,1,3,2] => [[5,4,2,2,2,2],[3,1,1,1,1]]
[2,1,1,1,4,1] => [[5,5,2,2,2,2],[4,1,1,1,1]]
[2,1,1,1,5] => [[6,2,2,2,2],[1,1,1,1]]
[2,1,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,2],[2,2,2,2,1,1,1]]
[2,1,1,2,1,1,2] => [[4,3,3,3,2,2,2],[2,2,2,1,1,1]]
[2,1,1,2,1,2,1] => [[4,4,3,3,2,2,2],[3,2,2,1,1,1]]
[2,1,1,2,1,3] => [[5,3,3,2,2,2],[2,2,1,1,1]]
[2,1,1,2,2,1,1] => [[4,4,4,3,2,2,2],[3,3,2,1,1,1]]
[2,1,1,2,2,2] => [[5,4,3,2,2,2],[3,2,1,1,1]]
[2,1,1,2,3,1] => [[5,5,3,2,2,2],[4,2,1,1,1]]
[2,1,1,2,4] => [[6,3,2,2,2],[2,1,1,1]]
[2,1,1,3,1,1,1] => [[4,4,4,4,2,2,2],[3,3,3,1,1,1]]
[2,1,1,3,1,2] => [[5,4,4,2,2,2],[3,3,1,1,1]]
[2,1,1,3,2,1] => [[5,5,4,2,2,2],[4,3,1,1,1]]
[2,1,1,3,3] => [[6,4,2,2,2],[3,1,1,1]]
[2,1,1,4,1,1] => [[5,5,5,2,2,2],[4,4,1,1,1]]
[2,1,1,4,2] => [[6,5,2,2,2],[4,1,1,1]]
[2,1,1,5,1] => [[6,6,2,2,2],[5,1,1,1]]
[2,1,1,6] => [[7,2,2,2],[1,1,1]]
[2,1,2,1,1,1,1,1] => [[3,3,3,3,3,3,2,2],[2,2,2,2,2,1,1]]
[2,1,2,1,1,1,2] => [[4,3,3,3,3,2,2],[2,2,2,2,1,1]]
[2,1,2,1,1,2,1] => [[4,4,3,3,3,2,2],[3,2,2,2,1,1]]
[2,1,2,1,1,3] => [[5,3,3,3,2,2],[2,2,2,1,1]]
[2,1,2,1,2,1,1] => [[4,4,4,3,3,2,2],[3,3,2,2,1,1]]
[2,1,2,1,2,2] => [[5,4,3,3,2,2],[3,2,2,1,1]]
[2,1,2,1,3,1] => [[5,5,3,3,2,2],[4,2,2,1,1]]
[2,1,2,1,4] => [[6,3,3,2,2],[2,2,1,1]]
[2,1,2,2,1,1,1] => [[4,4,4,4,3,2,2],[3,3,3,2,1,1]]
[2,1,2,2,1,2] => [[5,4,4,3,2,2],[3,3,2,1,1]]
[2,1,2,2,2,1] => [[5,5,4,3,2,2],[4,3,2,1,1]]
[2,1,2,2,3] => [[6,4,3,2,2],[3,2,1,1]]
[2,1,2,3,1,1] => [[5,5,5,3,2,2],[4,4,2,1,1]]
[2,1,2,3,2] => [[6,5,3,2,2],[4,2,1,1]]
[2,1,2,4,1] => [[6,6,3,2,2],[5,2,1,1]]
[2,1,2,5] => [[7,3,2,2],[2,1,1]]
[2,1,3,1,1,1,1] => [[4,4,4,4,4,2,2],[3,3,3,3,1,1]]
[2,1,3,1,1,2] => [[5,4,4,4,2,2],[3,3,3,1,1]]
[2,1,3,1,2,1] => [[5,5,4,4,2,2],[4,3,3,1,1]]
[2,1,3,1,3] => [[6,4,4,2,2],[3,3,1,1]]
[2,1,3,2,1,1] => [[5,5,5,4,2,2],[4,4,3,1,1]]
[2,1,3,2,2] => [[6,5,4,2,2],[4,3,1,1]]
[2,1,3,3,1] => [[6,6,4,2,2],[5,3,1,1]]
[2,1,3,4] => [[7,4,2,2],[3,1,1]]
[2,1,4,1,1,1] => [[5,5,5,5,2,2],[4,4,4,1,1]]
[2,1,4,1,2] => [[6,5,5,2,2],[4,4,1,1]]
[2,1,4,2,1] => [[6,6,5,2,2],[5,4,1,1]]
[2,1,4,3] => [[7,5,2,2],[4,1,1]]
[2,1,5,1,1] => [[6,6,6,2,2],[5,5,1,1]]
[2,1,5,2] => [[7,6,2,2],[5,1,1]]
[2,1,6,1] => [[7,7,2,2],[6,1,1]]
[2,1,7] => [[8,2,2],[1,1]]
[2,2,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,2],[2,2,2,2,2,2,1]]
[2,2,1,1,1,1,2] => [[4,3,3,3,3,3,2],[2,2,2,2,2,1]]
[2,2,1,1,1,2,1] => [[4,4,3,3,3,3,2],[3,2,2,2,2,1]]
[2,2,1,1,1,3] => [[5,3,3,3,3,2],[2,2,2,2,1]]
[2,2,1,1,2,1,1] => [[4,4,4,3,3,3,2],[3,3,2,2,2,1]]
[2,2,1,1,2,2] => [[5,4,3,3,3,2],[3,2,2,2,1]]
[2,2,1,1,3,1] => [[5,5,3,3,3,2],[4,2,2,2,1]]
[2,2,1,1,4] => [[6,3,3,3,2],[2,2,2,1]]
[2,2,1,2,1,1,1] => [[4,4,4,4,3,3,2],[3,3,3,2,2,1]]
[2,2,1,2,1,2] => [[5,4,4,3,3,2],[3,3,2,2,1]]
[2,2,1,2,2,1] => [[5,5,4,3,3,2],[4,3,2,2,1]]
[2,2,1,2,3] => [[6,4,3,3,2],[3,2,2,1]]
[2,2,1,3,1,1] => [[5,5,5,3,3,2],[4,4,2,2,1]]
[2,2,1,3,2] => [[6,5,3,3,2],[4,2,2,1]]
[2,2,1,4,1] => [[6,6,3,3,2],[5,2,2,1]]
[2,2,1,5] => [[7,3,3,2],[2,2,1]]
[2,2,2,1,1,1,1] => [[4,4,4,4,4,3,2],[3,3,3,3,2,1]]
[2,2,2,1,1,2] => [[5,4,4,4,3,2],[3,3,3,2,1]]
[2,2,2,1,2,1] => [[5,5,4,4,3,2],[4,3,3,2,1]]
[2,2,2,1,3] => [[6,4,4,3,2],[3,3,2,1]]
[2,2,2,2,1,1] => [[5,5,5,4,3,2],[4,4,3,2,1]]
[2,2,2,2,2] => [[6,5,4,3,2],[4,3,2,1]]
[2,2,2,3,1] => [[6,6,4,3,2],[5,3,2,1]]
[2,2,2,4] => [[7,4,3,2],[3,2,1]]
[2,2,3,1,1,1] => [[5,5,5,5,3,2],[4,4,4,2,1]]
[2,2,3,1,2] => [[6,5,5,3,2],[4,4,2,1]]
[2,2,3,2,1] => [[6,6,5,3,2],[5,4,2,1]]
[2,2,3,3] => [[7,5,3,2],[4,2,1]]
[2,2,4,1,1] => [[6,6,6,3,2],[5,5,2,1]]
[2,2,4,2] => [[7,6,3,2],[5,2,1]]
[2,2,5,1] => [[7,7,3,2],[6,2,1]]
[2,2,6] => [[8,3,2],[2,1]]
[2,3,1,1,1,1,1] => [[4,4,4,4,4,4,2],[3,3,3,3,3,1]]
[2,3,1,1,1,2] => [[5,4,4,4,4,2],[3,3,3,3,1]]
[2,3,1,1,2,1] => [[5,5,4,4,4,2],[4,3,3,3,1]]
[2,3,1,1,3] => [[6,4,4,4,2],[3,3,3,1]]
[2,3,1,2,1,1] => [[5,5,5,4,4,2],[4,4,3,3,1]]
[2,3,1,2,2] => [[6,5,4,4,2],[4,3,3,1]]
[2,3,1,3,1] => [[6,6,4,4,2],[5,3,3,1]]
[2,3,1,4] => [[7,4,4,2],[3,3,1]]
[2,3,2,1,1,1] => [[5,5,5,5,4,2],[4,4,4,3,1]]
[2,3,2,1,2] => [[6,5,5,4,2],[4,4,3,1]]
[2,3,2,2,1] => [[6,6,5,4,2],[5,4,3,1]]
[2,3,2,3] => [[7,5,4,2],[4,3,1]]
[2,3,3,1,1] => [[6,6,6,4,2],[5,5,3,1]]
[2,3,3,2] => [[7,6,4,2],[5,3,1]]
[2,3,4,1] => [[7,7,4,2],[6,3,1]]
[2,3,5] => [[8,4,2],[3,1]]
[2,4,1,1,1,1] => [[5,5,5,5,5,2],[4,4,4,4,1]]
[2,4,1,1,2] => [[6,5,5,5,2],[4,4,4,1]]
[2,4,1,2,1] => [[6,6,5,5,2],[5,4,4,1]]
[2,4,1,3] => [[7,5,5,2],[4,4,1]]
[2,4,2,1,1] => [[6,6,6,5,2],[5,5,4,1]]
[2,4,2,2] => [[7,6,5,2],[5,4,1]]
[2,4,3,1] => [[7,7,5,2],[6,4,1]]
[2,4,4] => [[8,5,2],[4,1]]
[2,5,1,1,1] => [[6,6,6,6,2],[5,5,5,1]]
[2,5,1,2] => [[7,6,6,2],[5,5,1]]
[2,5,2,1] => [[7,7,6,2],[6,5,1]]
[2,5,3] => [[8,6,2],[5,1]]
[2,6,1,1] => [[7,7,7,2],[6,6,1]]
[2,6,2] => [[8,7,2],[6,1]]
[2,7,1] => [[8,8,2],[7,1]]
[2,8] => [[9,2],[1]]
[3,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]]
[3,1,1,1,1,1,2] => [[4,3,3,3,3,3,3],[2,2,2,2,2,2]]
[3,1,1,1,1,2,1] => [[4,4,3,3,3,3,3],[3,2,2,2,2,2]]
[3,1,1,1,1,3] => [[5,3,3,3,3,3],[2,2,2,2,2]]
[3,1,1,1,2,1,1] => [[4,4,4,3,3,3,3],[3,3,2,2,2,2]]
[3,1,1,1,2,2] => [[5,4,3,3,3,3],[3,2,2,2,2]]
[3,1,1,1,3,1] => [[5,5,3,3,3,3],[4,2,2,2,2]]
[3,1,1,1,4] => [[6,3,3,3,3],[2,2,2,2]]
[3,1,1,2,1,1,1] => [[4,4,4,4,3,3,3],[3,3,3,2,2,2]]
[3,1,1,2,1,2] => [[5,4,4,3,3,3],[3,3,2,2,2]]
[3,1,1,2,2,1] => [[5,5,4,3,3,3],[4,3,2,2,2]]
[3,1,1,2,3] => [[6,4,3,3,3],[3,2,2,2]]
[3,1,1,3,1,1] => [[5,5,5,3,3,3],[4,4,2,2,2]]
[3,1,1,3,2] => [[6,5,3,3,3],[4,2,2,2]]
[3,1,1,4,1] => [[6,6,3,3,3],[5,2,2,2]]
[3,1,1,5] => [[7,3,3,3],[2,2,2]]
[3,1,2,1,1,1,1] => [[4,4,4,4,4,3,3],[3,3,3,3,2,2]]
[3,1,2,1,1,2] => [[5,4,4,4,3,3],[3,3,3,2,2]]
[3,1,2,1,2,1] => [[5,5,4,4,3,3],[4,3,3,2,2]]
[3,1,2,1,3] => [[6,4,4,3,3],[3,3,2,2]]
[3,1,2,2,1,1] => [[5,5,5,4,3,3],[4,4,3,2,2]]
[3,1,2,2,2] => [[6,5,4,3,3],[4,3,2,2]]
[3,1,2,3,1] => [[6,6,4,3,3],[5,3,2,2]]
[3,1,2,4] => [[7,4,3,3],[3,2,2]]
[3,1,3,1,1,1] => [[5,5,5,5,3,3],[4,4,4,2,2]]
[3,1,3,1,2] => [[6,5,5,3,3],[4,4,2,2]]
[3,1,3,2,1] => [[6,6,5,3,3],[5,4,2,2]]
[3,1,3,3] => [[7,5,3,3],[4,2,2]]
[3,1,4,1,1] => [[6,6,6,3,3],[5,5,2,2]]
[3,1,4,2] => [[7,6,3,3],[5,2,2]]
[3,1,5,1] => [[7,7,3,3],[6,2,2]]
[3,1,6] => [[8,3,3],[2,2]]
[3,2,1,1,1,1,1] => [[4,4,4,4,4,4,3],[3,3,3,3,3,2]]
[3,2,1,1,1,2] => [[5,4,4,4,4,3],[3,3,3,3,2]]
[3,2,1,1,2,1] => [[5,5,4,4,4,3],[4,3,3,3,2]]
[3,2,1,1,3] => [[6,4,4,4,3],[3,3,3,2]]
[3,2,1,2,1,1] => [[5,5,5,4,4,3],[4,4,3,3,2]]
[3,2,1,2,2] => [[6,5,4,4,3],[4,3,3,2]]
[3,2,1,3,1] => [[6,6,4,4,3],[5,3,3,2]]
[3,2,1,4] => [[7,4,4,3],[3,3,2]]
[3,2,2,1,1,1] => [[5,5,5,5,4,3],[4,4,4,3,2]]
[3,2,2,1,2] => [[6,5,5,4,3],[4,4,3,2]]
[3,2,2,2,1] => [[6,6,5,4,3],[5,4,3,2]]
[3,2,2,3] => [[7,5,4,3],[4,3,2]]
[3,2,3,1,1] => [[6,6,6,4,3],[5,5,3,2]]
[3,2,3,2] => [[7,6,4,3],[5,3,2]]
[3,2,4,1] => [[7,7,4,3],[6,3,2]]
[3,2,5] => [[8,4,3],[3,2]]
[3,3,1,1,1,1] => [[5,5,5,5,5,3],[4,4,4,4,2]]
[3,3,1,1,2] => [[6,5,5,5,3],[4,4,4,2]]
[3,3,1,2,1] => [[6,6,5,5,3],[5,4,4,2]]
[3,3,1,3] => [[7,5,5,3],[4,4,2]]
[3,3,2,1,1] => [[6,6,6,5,3],[5,5,4,2]]
[3,3,2,2] => [[7,6,5,3],[5,4,2]]
[3,3,3,1] => [[7,7,5,3],[6,4,2]]
[3,3,4] => [[8,5,3],[4,2]]
[3,4,1,1,1] => [[6,6,6,6,3],[5,5,5,2]]
[3,4,1,2] => [[7,6,6,3],[5,5,2]]
[3,4,2,1] => [[7,7,6,3],[6,5,2]]
[3,4,3] => [[8,6,3],[5,2]]
[3,5,1,1] => [[7,7,7,3],[6,6,2]]
[3,5,2] => [[8,7,3],[6,2]]
[3,6,1] => [[8,8,3],[7,2]]
[3,7] => [[9,3],[2]]
[4,1,1,1,1,1,1] => [[4,4,4,4,4,4,4],[3,3,3,3,3,3]]
[4,1,1,1,1,2] => [[5,4,4,4,4,4],[3,3,3,3,3]]
[4,1,1,1,2,1] => [[5,5,4,4,4,4],[4,3,3,3,3]]
[4,1,1,1,3] => [[6,4,4,4,4],[3,3,3,3]]
[4,1,1,2,1,1] => [[5,5,5,4,4,4],[4,4,3,3,3]]
[4,1,1,2,2] => [[6,5,4,4,4],[4,3,3,3]]
[4,1,1,3,1] => [[6,6,4,4,4],[5,3,3,3]]
[4,1,1,4] => [[7,4,4,4],[3,3,3]]
[4,1,2,1,1,1] => [[5,5,5,5,4,4],[4,4,4,3,3]]
[4,1,2,1,2] => [[6,5,5,4,4],[4,4,3,3]]
[4,1,2,2,1] => [[6,6,5,4,4],[5,4,3,3]]
[4,1,2,3] => [[7,5,4,4],[4,3,3]]
[4,1,3,1,1] => [[6,6,6,4,4],[5,5,3,3]]
[4,1,3,2] => [[7,6,4,4],[5,3,3]]
[4,1,4,1] => [[7,7,4,4],[6,3,3]]
[4,1,5] => [[8,4,4],[3,3]]
[4,2,1,1,1,1] => [[5,5,5,5,5,4],[4,4,4,4,3]]
[4,2,1,1,2] => [[6,5,5,5,4],[4,4,4,3]]
[4,2,1,2,1] => [[6,6,5,5,4],[5,4,4,3]]
[4,2,1,3] => [[7,5,5,4],[4,4,3]]
[4,2,2,1,1] => [[6,6,6,5,4],[5,5,4,3]]
[4,2,2,2] => [[7,6,5,4],[5,4,3]]
[4,2,3,1] => [[7,7,5,4],[6,4,3]]
[4,2,4] => [[8,5,4],[4,3]]
[4,3,1,1,1] => [[6,6,6,6,4],[5,5,5,3]]
[4,3,1,2] => [[7,6,6,4],[5,5,3]]
[4,3,2,1] => [[7,7,6,4],[6,5,3]]
[4,3,3] => [[8,6,4],[5,3]]
[4,4,1,1] => [[7,7,7,4],[6,6,3]]
[4,4,2] => [[8,7,4],[6,3]]
[4,5,1] => [[8,8,4],[7,3]]
[4,6] => [[9,4],[3]]
[5,1,1,1,1,1] => [[5,5,5,5,5,5],[4,4,4,4,4]]
[5,1,1,1,2] => [[6,5,5,5,5],[4,4,4,4]]
[5,1,1,2,1] => [[6,6,5,5,5],[5,4,4,4]]
[5,1,1,3] => [[7,5,5,5],[4,4,4]]
[5,1,2,1,1] => [[6,6,6,5,5],[5,5,4,4]]
[5,1,2,2] => [[7,6,5,5],[5,4,4]]
[5,1,3,1] => [[7,7,5,5],[6,4,4]]
[5,1,4] => [[8,5,5],[4,4]]
[5,2,1,1,1] => [[6,6,6,6,5],[5,5,5,4]]
[5,2,1,2] => [[7,6,6,5],[5,5,4]]
[5,2,2,1] => [[7,7,6,5],[6,5,4]]
[5,2,3] => [[8,6,5],[5,4]]
[5,3,1,1] => [[7,7,7,5],[6,6,4]]
[5,3,2] => [[8,7,5],[6,4]]
[5,4,1] => [[8,8,5],[7,4]]
[5,5] => [[9,5],[4]]
[6,1,1,1,1] => [[6,6,6,6,6],[5,5,5,5]]
[6,1,1,2] => [[7,6,6,6],[5,5,5]]
[6,1,2,1] => [[7,7,6,6],[6,5,5]]
[6,1,3] => [[8,6,6],[5,5]]
[6,2,1,1] => [[7,7,7,6],[6,6,5]]
[6,2,2] => [[8,7,6],[6,5]]
[6,3,1] => [[8,8,6],[7,5]]
[6,4] => [[9,6],[5]]
[7,1,1,1] => [[7,7,7,7],[6,6,6]]
[7,1,2] => [[8,7,7],[6,6]]
[7,2,1] => [[8,8,7],[7,6]]
[7,3] => [[9,7],[6]]
[8,1,1] => [[8,8,8],[7,7]]
[8,2] => [[9,8],[7]]
[9,1] => [[9,9],[8]]
[10] => [[10],[]]
[1,10] => [[10,1],[]]
[1,8,1,1] => [[8,8,8,1],[7,7]]
[1,7,2,1] => [[8,8,7,1],[7,6]]
[1,6,3,1] => [[8,8,6,1],[7,5]]
[1,5,4,1] => [[8,8,5,1],[7,4]]
[1,4,5,1] => [[8,8,4,1],[7,3]]
[1,3,6,1] => [[8,8,3,1],[7,2]]
[1,2,7,1] => [[8,8,2,1],[7,1]]
[1,1,8,1] => [[8,8,1,1],[7]]
[10,1] => [[10,10],[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],[]]
[1,1,1,1,1,1,1,1,2,2] => [[3,2,1,1,1,1,1,1,1,1],[1]]
[1,1,1,1,1,1,2,2,1,1] => [[3,3,3,2,1,1,1,1,1,1],[2,2,1]]
[1,1,1,1,1,1,2,1,1,2] => [[3,2,2,2,1,1,1,1,1,1],[1,1,1]]
[1,1,1,1,1,1,3,3] => [[5,3,1,1,1,1,1,1],[2]]
[1,1,1,1,2,2,1,1,1,1] => [[3,3,3,3,3,2,1,1,1,1],[2,2,2,2,1]]
[1,1,1,1,2,2,2,2] => [[5,4,3,2,1,1,1,1],[3,2,1]]
[1,1,1,1,2,1,1,2,1,1] => [[3,3,3,2,2,2,1,1,1,1],[2,2,1,1,1]]
[1,1,1,1,2,1,1,1,1,2] => [[3,2,2,2,2,2,1,1,1,1],[1,1,1,1,1]]
[1,1,1,1,2,1,2,3] => [[5,3,2,2,1,1,1,1],[2,1,1]]
[1,1,1,1,3,3,1,1] => [[5,5,5,3,1,1,1,1],[4,4,2]]
[1,1,1,1,3,2,1,2] => [[5,4,4,3,1,1,1,1],[3,3,2]]
[1,1,1,1,3,1,1,3] => [[5,3,3,3,1,1,1,1],[2,2,2]]
[1,1,1,1,4,4] => [[7,4,1,1,1,1],[3]]
[1,1,2,2,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,2,1,1],[2,2,2,2,2,2,1]]
[1,1,2,2,1,1,2,2] => [[5,4,3,3,3,2,1,1],[3,2,2,2,1]]
[1,1,2,2,2,2,1,1] => [[5,5,5,4,3,2,1,1],[4,4,3,2,1]]
[1,1,2,2,2,1,1,2] => [[5,4,4,4,3,2,1,1],[3,3,3,2,1]]
[1,1,2,2,3,3] => [[7,5,3,2,1,1],[4,2,1]]
[1,1,2,1,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,2,1,1],[2,2,2,2,1,1,1]]
[1,1,2,1,1,2,2,2] => [[5,4,3,2,2,2,1,1],[3,2,1,1,1]]
[1,1,2,1,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,2,1,1],[2,2,1,1,1,1,1]]
[1,1,2,1,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,2,1,1],[1,1,1,1,1,1,1]]
[1,1,2,1,1,1,2,3] => [[5,3,2,2,2,2,1,1],[2,1,1,1,1]]
[1,1,2,1,2,3,1,1] => [[5,5,5,3,2,2,1,1],[4,4,2,1,1]]
[1,1,2,1,2,2,1,2] => [[5,4,4,3,2,2,1,1],[3,3,2,1,1]]
[1,1,2,1,2,1,1,3] => [[5,3,3,3,2,2,1,1],[2,2,2,1,1]]
[1,1,2,1,3,4] => [[7,4,2,2,1,1],[3,1,1]]
[1,1,3,3,1,1,1,1] => [[5,5,5,5,5,3,1,1],[4,4,4,4,2]]
[1,1,3,3,2,2] => [[7,6,5,3,1,1],[5,4,2]]
[1,1,3,2,1,2,1,1] => [[5,5,5,4,4,3,1,1],[4,4,3,3,2]]
[1,1,3,2,1,1,1,2] => [[5,4,4,4,4,3,1,1],[3,3,3,3,2]]
[1,1,3,2,2,3] => [[7,5,4,3,1,1],[4,3,2]]
[1,1,3,1,1,3,1,1] => [[5,5,5,3,3,3,1,1],[4,4,2,2,2]]
[1,1,3,1,1,2,1,2] => [[5,4,4,3,3,3,1,1],[3,3,2,2,2]]
[1,1,3,1,1,1,1,3] => [[5,3,3,3,3,3,1,1],[2,2,2,2,2]]
[1,1,3,1,2,4] => [[7,4,3,3,1,1],[3,2,2]]
[1,1,4,4,1,1] => [[7,7,7,4,1,1],[6,6,3]]
[1,1,4,3,1,2] => [[7,6,6,4,1,1],[5,5,3]]
[1,1,4,2,1,3] => [[7,5,5,4,1,1],[4,4,3]]
[1,1,4,1,1,4] => [[7,4,4,4,1,1],[3,3,3]]
[1,1,5,5] => [[9,5,1,1],[4]]
[2,2,1,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3,3,2],[2,2,2,2,2,2,2,2,1]]
[2,2,1,1,1,1,2,2] => [[5,4,3,3,3,3,3,2],[3,2,2,2,2,2,1]]
[2,2,1,1,2,2,1,1] => [[5,5,5,4,3,3,3,2],[4,4,3,2,2,2,1]]
[2,2,1,1,2,1,1,2] => [[5,4,4,4,3,3,3,2],[3,3,3,2,2,2,1]]
[2,2,1,1,3,3] => [[7,5,3,3,3,2],[4,2,2,2,1]]
[2,2,2,2,1,1,1,1] => [[5,5,5,5,5,4,3,2],[4,4,4,4,3,2,1]]
[2,2,2,2,2,2] => [[7,6,5,4,3,2],[5,4,3,2,1]]
[2,2,2,1,1,2,1,1] => [[5,5,5,4,4,4,3,2],[4,4,3,3,3,2,1]]
[2,2,2,1,1,1,1,2] => [[5,4,4,4,4,4,3,2],[3,3,3,3,3,2,1]]
[2,2,2,1,2,3] => [[7,5,4,4,3,2],[4,3,3,2,1]]
[2,2,3,3,1,1] => [[7,7,7,5,3,2],[6,6,4,2,1]]
[2,2,3,2,1,2] => [[7,6,6,5,3,2],[5,5,4,2,1]]
[2,2,3,1,1,3] => [[7,5,5,5,3,2],[4,4,4,2,1]]
[2,2,4,4] => [[9,6,3,2],[5,2,1]]
[2,1,1,2,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,2,2,2],[2,2,2,2,2,2,1,1,1]]
[2,1,1,2,1,1,2,2] => [[5,4,3,3,3,2,2,2],[3,2,2,2,1,1,1]]
[2,1,1,2,2,2,1,1] => [[5,5,5,4,3,2,2,2],[4,4,3,2,1,1,1]]
[2,1,1,2,2,1,1,2] => [[5,4,4,4,3,2,2,2],[3,3,3,2,1,1,1]]
[2,1,1,2,3,3] => [[7,5,3,2,2,2],[4,2,1,1,1]]
[2,1,1,1,1,2,1,1,1,1] => [[3,3,3,3,3,2,2,2,2,2],[2,2,2,2,1,1,1,1,1]]
[2,1,1,1,1,2,2,2] => [[5,4,3,2,2,2,2,2],[3,2,1,1,1,1,1]]
[2,1,1,1,1,1,1,2,1,1] => [[3,3,3,2,2,2,2,2,2,2],[2,2,1,1,1,1,1,1,1]]
[2,1,1,1,1,1,1,1,1,2] => [[3,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1,1]]
[2,1,1,1,1,1,2,3] => [[5,3,2,2,2,2,2,2],[2,1,1,1,1,1,1]]
[2,1,1,1,2,3,1,1] => [[5,5,5,3,2,2,2,2],[4,4,2,1,1,1,1]]
[2,1,1,1,2,2,1,2] => [[5,4,4,3,2,2,2,2],[3,3,2,1,1,1,1]]
[2,1,1,1,2,1,1,3] => [[5,3,3,3,2,2,2,2],[2,2,2,1,1,1,1]]
[2,1,1,1,3,4] => [[7,4,2,2,2,2],[3,1,1,1,1]]
[2,1,2,3,1,1,1,1] => [[5,5,5,5,5,3,2,2],[4,4,4,4,2,1,1]]
[2,1,2,3,2,2] => [[7,6,5,3,2,2],[5,4,2,1,1]]
[2,1,2,2,1,2,1,1] => [[5,5,5,4,4,3,2,2],[4,4,3,3,2,1,1]]
[2,1,2,2,1,1,1,2] => [[5,4,4,4,4,3,2,2],[3,3,3,3,2,1,1]]
[2,1,2,2,2,3] => [[7,5,4,3,2,2],[4,3,2,1,1]]
[2,1,2,1,1,3,1,1] => [[5,5,5,3,3,3,2,2],[4,4,2,2,2,1,1]]
[2,1,2,1,1,2,1,2] => [[5,4,4,3,3,3,2,2],[3,3,2,2,2,1,1]]
[2,1,2,1,1,1,1,3] => [[5,3,3,3,3,3,2,2],[2,2,2,2,2,1,1]]
[2,1,2,1,2,4] => [[7,4,3,3,2,2],[3,2,2,1,1]]
[2,1,3,4,1,1] => [[7,7,7,4,2,2],[6,6,3,1,1]]
[2,1,3,3,1,2] => [[7,6,6,4,2,2],[5,5,3,1,1]]
[2,1,3,2,1,3] => [[7,5,5,4,2,2],[4,4,3,1,1]]
[2,1,3,1,1,4] => [[7,4,4,4,2,2],[3,3,3,1,1]]
[2,1,4,5] => [[9,5,2,2],[4,1,1]]
[3,3,1,1,1,1,1,1] => [[5,5,5,5,5,5,5,3],[4,4,4,4,4,4,2]]
[3,3,1,1,2,2] => [[7,6,5,5,5,3],[5,4,4,4,2]]
[3,3,2,2,1,1] => [[7,7,7,6,5,3],[6,6,5,4,2]]
[3,3,2,1,1,2] => [[7,6,6,6,5,3],[5,5,5,4,2]]
[3,3,3,3] => [[9,7,5,3],[6,4,2]]
[3,2,1,2,1,1,1,1] => [[5,5,5,5,5,4,4,3],[4,4,4,4,3,3,2]]
[3,2,1,2,2,2] => [[7,6,5,4,4,3],[5,4,3,3,2]]
[3,2,1,1,1,2,1,1] => [[5,5,5,4,4,4,4,3],[4,4,3,3,3,3,2]]
[3,2,1,1,1,1,1,2] => [[5,4,4,4,4,4,4,3],[3,3,3,3,3,3,2]]
[3,2,1,1,2,3] => [[7,5,4,4,4,3],[4,3,3,3,2]]
[3,2,2,3,1,1] => [[7,7,7,5,4,3],[6,6,4,3,2]]
[3,2,2,2,1,2] => [[7,6,6,5,4,3],[5,5,4,3,2]]
[3,2,2,1,1,3] => [[7,5,5,5,4,3],[4,4,4,3,2]]
[3,2,3,4] => [[9,6,4,3],[5,3,2]]
[3,1,1,3,1,1,1,1] => [[5,5,5,5,5,3,3,3],[4,4,4,4,2,2,2]]
[3,1,1,3,2,2] => [[7,6,5,3,3,3],[5,4,2,2,2]]
[3,1,1,2,1,2,1,1] => [[5,5,5,4,4,3,3,3],[4,4,3,3,2,2,2]]
[3,1,1,2,1,1,1,2] => [[5,4,4,4,4,3,3,3],[3,3,3,3,2,2,2]]
[3,1,1,2,2,3] => [[7,5,4,3,3,3],[4,3,2,2,2]]
[3,1,1,1,1,3,1,1] => [[5,5,5,3,3,3,3,3],[4,4,2,2,2,2,2]]
[3,1,1,1,1,2,1,2] => [[5,4,4,3,3,3,3,3],[3,3,2,2,2,2,2]]
[3,1,1,1,1,1,1,3] => [[5,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]]
[3,1,1,1,2,4] => [[7,4,3,3,3,3],[3,2,2,2,2]]
[3,1,2,4,1,1] => [[7,7,7,4,3,3],[6,6,3,2,2]]
[3,1,2,3,1,2] => [[7,6,6,4,3,3],[5,5,3,2,2]]
[3,1,2,2,1,3] => [[7,5,5,4,3,3],[4,4,3,2,2]]
[3,1,2,1,1,4] => [[7,4,4,4,3,3],[3,3,3,2,2]]
[3,1,3,5] => [[9,5,3,3],[4,2,2]]
[4,4,1,1,1,1] => [[7,7,7,7,7,4],[6,6,6,6,3]]
[4,4,2,2] => [[9,8,7,4],[7,6,3]]
[4,3,1,2,1,1] => [[7,7,7,6,6,4],[6,6,5,5,3]]
[4,3,1,1,1,2] => [[7,6,6,6,6,4],[5,5,5,5,3]]
[4,3,2,3] => [[9,7,6,4],[6,5,3]]
[4,2,1,3,1,1] => [[7,7,7,5,5,4],[6,6,4,4,3]]
[4,2,1,2,1,2] => [[7,6,6,5,5,4],[5,5,4,4,3]]
[4,2,1,1,1,3] => [[7,5,5,5,5,4],[4,4,4,4,3]]
[4,2,2,4] => [[9,6,5,4],[5,4,3]]
[4,1,1,4,1,1] => [[7,7,7,4,4,4],[6,6,3,3,3]]
[4,1,1,3,1,2] => [[7,6,6,4,4,4],[5,5,3,3,3]]
[4,1,1,2,1,3] => [[7,5,5,4,4,4],[4,4,3,3,3]]
[4,1,1,1,1,4] => [[7,4,4,4,4,4],[3,3,3,3,3]]
[4,1,2,5] => [[9,5,4,4],[4,3,3]]
[5,5,1,1] => [[9,9,9,5],[8,8,4]]
[5,4,1,2] => [[9,8,8,5],[7,7,4]]
[5,3,1,3] => [[9,7,7,5],[6,6,4]]
[5,2,1,4] => [[9,6,6,5],[5,5,4]]
[5,1,1,5] => [[9,5,5,5],[4,4,4]]
[6,6] => [[11,6],[5]]
[1,2,2,2,2,2,1] => [[6,6,5,4,3,2,1],[5,4,3,2,1]]
[1,2,2,2,3,2] => [[7,6,4,3,2,1],[5,3,2,1]]
[1,2,2,3,3,1] => [[7,7,5,3,2,1],[6,4,2,1]]
[1,2,2,3,2,2] => [[7,6,5,3,2,1],[5,4,2,1]]
[1,2,2,4,3] => [[8,6,3,2,1],[5,2,1]]
[1,2,3,3,2,1] => [[7,7,6,4,2,1],[6,5,3,1]]
[1,2,3,4,2] => [[8,7,4,2,1],[6,3,1]]
[1,2,3,2,3,1] => [[7,7,5,4,2,1],[6,4,3,1]]
[1,2,3,2,2,2] => [[7,6,5,4,2,1],[5,4,3,1]]
[1,2,3,3,3] => [[8,6,4,2,1],[5,3,1]]
[1,2,4,4,1] => [[8,8,5,2,1],[7,4,1]]
[1,2,4,3,2] => [[8,7,5,2,1],[6,4,1]]
[1,2,4,2,3] => [[8,6,5,2,1],[5,4,1]]
[1,2,5,4] => [[9,6,2,1],[5,1]]
[1,3,3,2,2,1] => [[7,7,6,5,3,1],[6,5,4,2]]
[1,3,3,3,2] => [[8,7,5,3,1],[6,4,2]]
[1,3,4,3,1] => [[8,8,6,3,1],[7,5,2]]
[1,3,4,2,2] => [[8,7,6,3,1],[6,5,2]]
[1,3,5,3] => [[9,7,3,1],[6,2]]
[1,3,2,3,2,1] => [[7,7,6,4,3,1],[6,5,3,2]]
[1,3,2,4,2] => [[8,7,4,3,1],[6,3,2]]
[1,3,2,2,3,1] => [[7,7,5,4,3,1],[6,4,3,2]]
[1,3,2,2,2,2] => [[7,6,5,4,3,1],[5,4,3,2]]
[1,3,2,3,3] => [[8,6,4,3,1],[5,3,2]]
[1,3,3,4,1] => [[8,8,5,3,1],[7,4,2]]
[1,3,3,2,3] => [[8,6,5,3,1],[5,4,2]]
[1,3,4,4] => [[9,6,3,1],[5,2]]
[1,4,4,2,1] => [[8,8,7,4,1],[7,6,3]]
[1,4,5,2] => [[9,8,4,1],[7,3]]
[1,4,3,3,1] => [[8,8,6,4,1],[7,5,3]]
[1,4,3,2,2] => [[8,7,6,4,1],[6,5,3]]
[1,4,4,3] => [[9,7,4,1],[6,3]]
[1,4,2,4,1] => [[8,8,5,4,1],[7,4,3]]
[1,4,2,3,2] => [[8,7,5,4,1],[6,4,3]]
[1,4,2,2,3] => [[8,6,5,4,1],[5,4,3]]
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Created: Sep 22, 2020 at 11:07 by Martin Rubey
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Last Updated: Sep 22, 2020 at 11:07 by Martin Rubey