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* Copyright (C) 2013 The FindStatCrew <info@findstat.org> *
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* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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------------------------------------------------------------------------
Map identifier: Mp00308
------------------------------------------------------------------------
Map name: Bulgarian solitaire
------------------------------------------------------------------------
Domain: Integer partitions
------------------------------------------------------------------------
Codomain: Integer partitions
------------------------------------------------------------------------
Description: A move in Bulgarian solitaire.
Remove the first column of the Ferrers diagram and insert it as a new row.
If the partition is empty, return the empty partition.
------------------------------------------------------------------------
References: [1] Harris, A. J., Nguyen, S. Bulgarian Solitaire: A new representation for depth generating functions [[arXiv:2308.05321]]
------------------------------------------------------------------------
Code:
def mapping(la):
return Partition(sorted([p-1 for p in la] + [len(la)], reverse=True))
------------------------------------------------------------------------
Map images:
[1] => [1]
[2] => [1,1]
[1,1] => [2]
[3] => [2,1]
[2,1] => [2,1]
[1,1,1] => [3]
[4] => [3,1]
[3,1] => [2,2]
[2,2] => [2,1,1]
[2,1,1] => [3,1]
[1,1,1,1] => [4]
[5] => [4,1]
[4,1] => [3,2]
[3,2] => [2,2,1]
[3,1,1] => [3,2]
[2,2,1] => [3,1,1]
[2,1,1,1] => [4,1]
[1,1,1,1,1] => [5]
[6] => [5,1]
[5,1] => [4,2]
[4,2] => [3,2,1]
[4,1,1] => [3,3]
[3,3] => [2,2,2]
[3,2,1] => [3,2,1]
[3,1,1,1] => [4,2]
[2,2,2] => [3,1,1,1]
[2,2,1,1] => [4,1,1]
[2,1,1,1,1] => [5,1]
[1,1,1,1,1,1] => [6]
[7] => [6,1]
[6,1] => [5,2]
[5,2] => [4,2,1]
[5,1,1] => [4,3]
[4,3] => [3,2,2]
[4,2,1] => [3,3,1]
[4,1,1,1] => [4,3]
[3,3,1] => [3,2,2]
[3,2,2] => [3,2,1,1]
[3,2,1,1] => [4,2,1]
[3,1,1,1,1] => [5,2]
[2,2,2,1] => [4,1,1,1]
[2,2,1,1,1] => [5,1,1]
[2,1,1,1,1,1] => [6,1]
[1,1,1,1,1,1,1] => [7]
[8] => [7,1]
[7,1] => [6,2]
[6,2] => [5,2,1]
[6,1,1] => [5,3]
[5,3] => [4,2,2]
[5,2,1] => [4,3,1]
[5,1,1,1] => [4,4]
[4,4] => [3,3,2]
[4,3,1] => [3,3,2]
[4,2,2] => [3,3,1,1]
[4,2,1,1] => [4,3,1]
[4,1,1,1,1] => [5,3]
[3,3,2] => [3,2,2,1]
[3,3,1,1] => [4,2,2]
[3,2,2,1] => [4,2,1,1]
[3,2,1,1,1] => [5,2,1]
[3,1,1,1,1,1] => [6,2]
[2,2,2,2] => [4,1,1,1,1]
[2,2,2,1,1] => [5,1,1,1]
[2,2,1,1,1,1] => [6,1,1]
[2,1,1,1,1,1,1] => [7,1]
[1,1,1,1,1,1,1,1] => [8]
[9] => [8,1]
[8,1] => [7,2]
[7,2] => [6,2,1]
[7,1,1] => [6,3]
[6,3] => [5,2,2]
[6,2,1] => [5,3,1]
[6,1,1,1] => [5,4]
[5,4] => [4,3,2]
[5,3,1] => [4,3,2]
[5,2,2] => [4,3,1,1]
[5,2,1,1] => [4,4,1]
[5,1,1,1,1] => [5,4]
[4,4,1] => [3,3,3]
[4,3,2] => [3,3,2,1]
[4,3,1,1] => [4,3,2]
[4,2,2,1] => [4,3,1,1]
[4,2,1,1,1] => [5,3,1]
[4,1,1,1,1,1] => [6,3]
[3,3,3] => [3,2,2,2]
[3,3,2,1] => [4,2,2,1]
[3,3,1,1,1] => [5,2,2]
[3,2,2,2] => [4,2,1,1,1]
[3,2,2,1,1] => [5,2,1,1]
[3,2,1,1,1,1] => [6,2,1]
[3,1,1,1,1,1,1] => [7,2]
[2,2,2,2,1] => [5,1,1,1,1]
[2,2,2,1,1,1] => [6,1,1,1]
[2,2,1,1,1,1,1] => [7,1,1]
[2,1,1,1,1,1,1,1] => [8,1]
[1,1,1,1,1,1,1,1,1] => [9]
[10] => [9,1]
[9,1] => [8,2]
[8,2] => [7,2,1]
[8,1,1] => [7,3]
[7,3] => [6,2,2]
[7,2,1] => [6,3,1]
[7,1,1,1] => [6,4]
[6,4] => [5,3,2]
[6,3,1] => [5,3,2]
[6,2,2] => [5,3,1,1]
[6,2,1,1] => [5,4,1]
[6,1,1,1,1] => [5,5]
[5,5] => [4,4,2]
[5,4,1] => [4,3,3]
[5,3,2] => [4,3,2,1]
[5,3,1,1] => [4,4,2]
[5,2,2,1] => [4,4,1,1]
[5,2,1,1,1] => [5,4,1]
[5,1,1,1,1,1] => [6,4]
[4,4,2] => [3,3,3,1]
[4,4,1,1] => [4,3,3]
[4,3,3] => [3,3,2,2]
[4,3,2,1] => [4,3,2,1]
[4,3,1,1,1] => [5,3,2]
[4,2,2,2] => [4,3,1,1,1]
[4,2,2,1,1] => [5,3,1,1]
[4,2,1,1,1,1] => [6,3,1]
[4,1,1,1,1,1,1] => [7,3]
[3,3,3,1] => [4,2,2,2]
[3,3,2,2] => [4,2,2,1,1]
[3,3,2,1,1] => [5,2,2,1]
[3,3,1,1,1,1] => [6,2,2]
[3,2,2,2,1] => [5,2,1,1,1]
[3,2,2,1,1,1] => [6,2,1,1]
[3,2,1,1,1,1,1] => [7,2,1]
[3,1,1,1,1,1,1,1] => [8,2]
[2,2,2,2,2] => [5,1,1,1,1,1]
[2,2,2,2,1,1] => [6,1,1,1,1]
[2,2,2,1,1,1,1] => [7,1,1,1]
[2,2,1,1,1,1,1,1] => [8,1,1]
[2,1,1,1,1,1,1,1,1] => [9,1]
[1,1,1,1,1,1,1,1,1,1] => [10]
[11] => [10,1]
[10,1] => [9,2]
[9,2] => [8,2,1]
[9,1,1] => [8,3]
[8,3] => [7,2,2]
[8,2,1] => [7,3,1]
[8,1,1,1] => [7,4]
[7,4] => [6,3,2]
[7,3,1] => [6,3,2]
[7,2,2] => [6,3,1,1]
[7,2,1,1] => [6,4,1]
[7,1,1,1,1] => [6,5]
[6,5] => [5,4,2]
[6,4,1] => [5,3,3]
[6,3,2] => [5,3,2,1]
[6,3,1,1] => [5,4,2]
[6,2,2,1] => [5,4,1,1]
[6,2,1,1,1] => [5,5,1]
[6,1,1,1,1,1] => [6,5]
[5,5,1] => [4,4,3]
[5,4,2] => [4,3,3,1]
[5,4,1,1] => [4,4,3]
[5,3,3] => [4,3,2,2]
[5,3,2,1] => [4,4,2,1]
[5,3,1,1,1] => [5,4,2]
[5,2,2,2] => [4,4,1,1,1]
[5,2,2,1,1] => [5,4,1,1]
[5,2,1,1,1,1] => [6,4,1]
[5,1,1,1,1,1,1] => [7,4]
[4,4,3] => [3,3,3,2]
[4,4,2,1] => [4,3,3,1]
[4,4,1,1,1] => [5,3,3]
[4,3,3,1] => [4,3,2,2]
[4,3,2,2] => [4,3,2,1,1]
[4,3,2,1,1] => [5,3,2,1]
[4,3,1,1,1,1] => [6,3,2]
[4,2,2,2,1] => [5,3,1,1,1]
[4,2,2,1,1,1] => [6,3,1,1]
[4,2,1,1,1,1,1] => [7,3,1]
[4,1,1,1,1,1,1,1] => [8,3]
[3,3,3,2] => [4,2,2,2,1]
[3,3,3,1,1] => [5,2,2,2]
[3,3,2,2,1] => [5,2,2,1,1]
[3,3,2,1,1,1] => [6,2,2,1]
[3,3,1,1,1,1,1] => [7,2,2]
[3,2,2,2,2] => [5,2,1,1,1,1]
[3,2,2,2,1,1] => [6,2,1,1,1]
[3,2,2,1,1,1,1] => [7,2,1,1]
[3,2,1,1,1,1,1,1] => [8,2,1]
[3,1,1,1,1,1,1,1,1] => [9,2]
[2,2,2,2,2,1] => [6,1,1,1,1,1]
[2,2,2,2,1,1,1] => [7,1,1,1,1]
[2,2,2,1,1,1,1,1] => [8,1,1,1]
[2,2,1,1,1,1,1,1,1] => [9,1,1]
[2,1,1,1,1,1,1,1,1,1] => [10,1]
[1,1,1,1,1,1,1,1,1,1,1] => [11]
[12] => [11,1]
[11,1] => [10,2]
[10,2] => [9,2,1]
[10,1,1] => [9,3]
[9,3] => [8,2,2]
[9,2,1] => [8,3,1]
[9,1,1,1] => [8,4]
[8,4] => [7,3,2]
[8,3,1] => [7,3,2]
[8,2,2] => [7,3,1,1]
[8,2,1,1] => [7,4,1]
[8,1,1,1,1] => [7,5]
[7,5] => [6,4,2]
[7,4,1] => [6,3,3]
[7,3,2] => [6,3,2,1]
[7,3,1,1] => [6,4,2]
[7,2,2,1] => [6,4,1,1]
[7,2,1,1,1] => [6,5,1]
[7,1,1,1,1,1] => [6,6]
[6,6] => [5,5,2]
[6,5,1] => [5,4,3]
[6,4,2] => [5,3,3,1]
[6,4,1,1] => [5,4,3]
[6,3,3] => [5,3,2,2]
[6,3,2,1] => [5,4,2,1]
[6,3,1,1,1] => [5,5,2]
[6,2,2,2] => [5,4,1,1,1]
[6,2,2,1,1] => [5,5,1,1]
[6,2,1,1,1,1] => [6,5,1]
[6,1,1,1,1,1,1] => [7,5]
[5,5,2] => [4,4,3,1]
[5,5,1,1] => [4,4,4]
[5,4,3] => [4,3,3,2]
[5,4,2,1] => [4,4,3,1]
[5,4,1,1,1] => [5,4,3]
[5,3,3,1] => [4,4,2,2]
[5,3,2,2] => [4,4,2,1,1]
[5,3,2,1,1] => [5,4,2,1]
[5,3,1,1,1,1] => [6,4,2]
[5,2,2,2,1] => [5,4,1,1,1]
[5,2,2,1,1,1] => [6,4,1,1]
[5,2,1,1,1,1,1] => [7,4,1]
[5,1,1,1,1,1,1,1] => [8,4]
[4,4,4] => [3,3,3,3]
[4,4,3,1] => [4,3,3,2]
[4,4,2,2] => [4,3,3,1,1]
[4,4,2,1,1] => [5,3,3,1]
[4,4,1,1,1,1] => [6,3,3]
[4,3,3,2] => [4,3,2,2,1]
[4,3,3,1,1] => [5,3,2,2]
[4,3,2,2,1] => [5,3,2,1,1]
[4,3,2,1,1,1] => [6,3,2,1]
[4,3,1,1,1,1,1] => [7,3,2]
[4,2,2,2,2] => [5,3,1,1,1,1]
[4,2,2,2,1,1] => [6,3,1,1,1]
[4,2,2,1,1,1,1] => [7,3,1,1]
[4,2,1,1,1,1,1,1] => [8,3,1]
[4,1,1,1,1,1,1,1,1] => [9,3]
[3,3,3,3] => [4,2,2,2,2]
[3,3,3,2,1] => [5,2,2,2,1]
[3,3,3,1,1,1] => [6,2,2,2]
[3,3,2,2,2] => [5,2,2,1,1,1]
[3,3,2,2,1,1] => [6,2,2,1,1]
[3,3,2,1,1,1,1] => [7,2,2,1]
[3,3,1,1,1,1,1,1] => [8,2,2]
[3,2,2,2,2,1] => [6,2,1,1,1,1]
[3,2,2,2,1,1,1] => [7,2,1,1,1]
[3,2,2,1,1,1,1,1] => [8,2,1,1]
[3,2,1,1,1,1,1,1,1] => [9,2,1]
[3,1,1,1,1,1,1,1,1,1] => [10,2]
[2,2,2,2,2,2] => [6,1,1,1,1,1,1]
[2,2,2,2,2,1,1] => [7,1,1,1,1,1]
[2,2,2,2,1,1,1,1] => [8,1,1,1,1]
[2,2,2,1,1,1,1,1,1] => [9,1,1,1]
[2,2,1,1,1,1,1,1,1,1] => [10,1,1]
[2,1,1,1,1,1,1,1,1,1,1] => [11,1]
[1,1,1,1,1,1,1,1,1,1,1,1] => [12]
[13] => [12,1]
[12,1] => [11,2]
[11,2] => [10,2,1]
[11,1,1] => [10,3]
[10,3] => [9,2,2]
[10,2,1] => [9,3,1]
[10,1,1,1] => [9,4]
[9,4] => [8,3,2]
[9,3,1] => [8,3,2]
[9,2,2] => [8,3,1,1]
[9,2,1,1] => [8,4,1]
[9,1,1,1,1] => [8,5]
[8,5] => [7,4,2]
[8,4,1] => [7,3,3]
[8,3,2] => [7,3,2,1]
[8,3,1,1] => [7,4,2]
[8,2,2,1] => [7,4,1,1]
[8,2,1,1,1] => [7,5,1]
[8,1,1,1,1,1] => [7,6]
[7,6] => [6,5,2]
[7,5,1] => [6,4,3]
[7,4,2] => [6,3,3,1]
[7,4,1,1] => [6,4,3]
[7,3,3] => [6,3,2,2]
[7,3,2,1] => [6,4,2,1]
[7,3,1,1,1] => [6,5,2]
[7,2,2,2] => [6,4,1,1,1]
[7,2,2,1,1] => [6,5,1,1]
[7,2,1,1,1,1] => [6,6,1]
[7,1,1,1,1,1,1] => [7,6]
[6,6,1] => [5,5,3]
[6,5,2] => [5,4,3,1]
[6,5,1,1] => [5,4,4]
[6,4,3] => [5,3,3,2]
[6,4,2,1] => [5,4,3,1]
[6,4,1,1,1] => [5,5,3]
[6,3,3,1] => [5,4,2,2]
[6,3,2,2] => [5,4,2,1,1]
[6,3,2,1,1] => [5,5,2,1]
[6,3,1,1,1,1] => [6,5,2]
[6,2,2,2,1] => [5,5,1,1,1]
[6,2,2,1,1,1] => [6,5,1,1]
[6,2,1,1,1,1,1] => [7,5,1]
[6,1,1,1,1,1,1,1] => [8,5]
[5,5,3] => [4,4,3,2]
[5,5,2,1] => [4,4,4,1]
[5,5,1,1,1] => [5,4,4]
[5,4,4] => [4,3,3,3]
[5,4,3,1] => [4,4,3,2]
[5,4,2,2] => [4,4,3,1,1]
[5,4,2,1,1] => [5,4,3,1]
[5,4,1,1,1,1] => [6,4,3]
[5,3,3,2] => [4,4,2,2,1]
[5,3,3,1,1] => [5,4,2,2]
[5,3,2,2,1] => [5,4,2,1,1]
[5,3,2,1,1,1] => [6,4,2,1]
[5,3,1,1,1,1,1] => [7,4,2]
[5,2,2,2,2] => [5,4,1,1,1,1]
[5,2,2,2,1,1] => [6,4,1,1,1]
[5,2,2,1,1,1,1] => [7,4,1,1]
[5,2,1,1,1,1,1,1] => [8,4,1]
[5,1,1,1,1,1,1,1,1] => [9,4]
[4,4,4,1] => [4,3,3,3]
[4,4,3,2] => [4,3,3,2,1]
[4,4,3,1,1] => [5,3,3,2]
[4,4,2,2,1] => [5,3,3,1,1]
[4,4,2,1,1,1] => [6,3,3,1]
[4,4,1,1,1,1,1] => [7,3,3]
[4,3,3,3] => [4,3,2,2,2]
[4,3,3,2,1] => [5,3,2,2,1]
[4,3,3,1,1,1] => [6,3,2,2]
[4,3,2,2,2] => [5,3,2,1,1,1]
[4,3,2,2,1,1] => [6,3,2,1,1]
[4,3,2,1,1,1,1] => [7,3,2,1]
[4,3,1,1,1,1,1,1] => [8,3,2]
[4,2,2,2,2,1] => [6,3,1,1,1,1]
[4,2,2,2,1,1,1] => [7,3,1,1,1]
[4,2,2,1,1,1,1,1] => [8,3,1,1]
[4,2,1,1,1,1,1,1,1] => [9,3,1]
[4,1,1,1,1,1,1,1,1,1] => [10,3]
[3,3,3,3,1] => [5,2,2,2,2]
[3,3,3,2,2] => [5,2,2,2,1,1]
[3,3,3,2,1,1] => [6,2,2,2,1]
[3,3,3,1,1,1,1] => [7,2,2,2]
[3,3,2,2,2,1] => [6,2,2,1,1,1]
[3,3,2,2,1,1,1] => [7,2,2,1,1]
[3,3,2,1,1,1,1,1] => [8,2,2,1]
[3,3,1,1,1,1,1,1,1] => [9,2,2]
[3,2,2,2,2,2] => [6,2,1,1,1,1,1]
[3,2,2,2,2,1,1] => [7,2,1,1,1,1]
[3,2,2,2,1,1,1,1] => [8,2,1,1,1]
[3,2,2,1,1,1,1,1,1] => [9,2,1,1]
[3,2,1,1,1,1,1,1,1,1] => [10,2,1]
[3,1,1,1,1,1,1,1,1,1,1] => [11,2]
[2,2,2,2,2,2,1] => [7,1,1,1,1,1,1]
[2,2,2,2,2,1,1,1] => [8,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1] => [9,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1] => [10,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1] => [11,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [13]
[14] => [13,1]
[13,1] => [12,2]
[12,2] => [11,2,1]
[12,1,1] => [11,3]
[11,3] => [10,2,2]
[11,2,1] => [10,3,1]
[11,1,1,1] => [10,4]
[10,4] => [9,3,2]
[10,3,1] => [9,3,2]
[10,2,2] => [9,3,1,1]
[10,2,1,1] => [9,4,1]
[10,1,1,1,1] => [9,5]
[9,5] => [8,4,2]
[9,4,1] => [8,3,3]
[9,3,2] => [8,3,2,1]
[9,3,1,1] => [8,4,2]
[9,2,2,1] => [8,4,1,1]
[9,2,1,1,1] => [8,5,1]
[9,1,1,1,1,1] => [8,6]
[8,6] => [7,5,2]
[8,5,1] => [7,4,3]
[8,4,2] => [7,3,3,1]
[8,4,1,1] => [7,4,3]
[8,3,3] => [7,3,2,2]
[8,3,2,1] => [7,4,2,1]
[8,3,1,1,1] => [7,5,2]
[8,2,2,2] => [7,4,1,1,1]
[8,2,2,1,1] => [7,5,1,1]
[8,2,1,1,1,1] => [7,6,1]
[8,1,1,1,1,1,1] => [7,7]
[7,7] => [6,6,2]
[7,6,1] => [6,5,3]
[7,5,2] => [6,4,3,1]
[7,5,1,1] => [6,4,4]
[7,4,3] => [6,3,3,2]
[7,4,2,1] => [6,4,3,1]
[7,4,1,1,1] => [6,5,3]
[7,3,3,1] => [6,4,2,2]
[7,3,2,2] => [6,4,2,1,1]
[7,3,2,1,1] => [6,5,2,1]
[7,3,1,1,1,1] => [6,6,2]
[7,2,2,2,1] => [6,5,1,1,1]
[7,2,2,1,1,1] => [6,6,1,1]
[7,2,1,1,1,1,1] => [7,6,1]
[7,1,1,1,1,1,1,1] => [8,6]
[6,6,2] => [5,5,3,1]
[6,6,1,1] => [5,5,4]
[6,5,3] => [5,4,3,2]
[6,5,2,1] => [5,4,4,1]
[6,5,1,1,1] => [5,5,4]
[6,4,4] => [5,3,3,3]
[6,4,3,1] => [5,4,3,2]
[6,4,2,2] => [5,4,3,1,1]
[6,4,2,1,1] => [5,5,3,1]
[6,4,1,1,1,1] => [6,5,3]
[6,3,3,2] => [5,4,2,2,1]
[6,3,3,1,1] => [5,5,2,2]
[6,3,2,2,1] => [5,5,2,1,1]
[6,3,2,1,1,1] => [6,5,2,1]
[6,3,1,1,1,1,1] => [7,5,2]
[6,2,2,2,2] => [5,5,1,1,1,1]
[6,2,2,2,1,1] => [6,5,1,1,1]
[6,2,2,1,1,1,1] => [7,5,1,1]
[6,2,1,1,1,1,1,1] => [8,5,1]
[6,1,1,1,1,1,1,1,1] => [9,5]
[5,5,4] => [4,4,3,3]
[5,5,3,1] => [4,4,4,2]
[5,5,2,2] => [4,4,4,1,1]
[5,5,2,1,1] => [5,4,4,1]
[5,5,1,1,1,1] => [6,4,4]
[5,4,4,1] => [4,4,3,3]
[5,4,3,2] => [4,4,3,2,1]
[5,4,3,1,1] => [5,4,3,2]
[5,4,2,2,1] => [5,4,3,1,1]
[5,4,2,1,1,1] => [6,4,3,1]
[5,4,1,1,1,1,1] => [7,4,3]
[5,3,3,3] => [4,4,2,2,2]
[5,3,3,2,1] => [5,4,2,2,1]
[5,3,3,1,1,1] => [6,4,2,2]
[5,3,2,2,2] => [5,4,2,1,1,1]
[5,3,2,2,1,1] => [6,4,2,1,1]
[5,3,2,1,1,1,1] => [7,4,2,1]
[5,3,1,1,1,1,1,1] => [8,4,2]
[5,2,2,2,2,1] => [6,4,1,1,1,1]
[5,2,2,2,1,1,1] => [7,4,1,1,1]
[5,2,2,1,1,1,1,1] => [8,4,1,1]
[5,2,1,1,1,1,1,1,1] => [9,4,1]
[5,1,1,1,1,1,1,1,1,1] => [10,4]
[4,4,4,2] => [4,3,3,3,1]
[4,4,4,1,1] => [5,3,3,3]
[4,4,3,3] => [4,3,3,2,2]
[4,4,3,2,1] => [5,3,3,2,1]
[4,4,3,1,1,1] => [6,3,3,2]
[4,4,2,2,2] => [5,3,3,1,1,1]
[4,4,2,2,1,1] => [6,3,3,1,1]
[4,4,2,1,1,1,1] => [7,3,3,1]
[4,4,1,1,1,1,1,1] => [8,3,3]
[4,3,3,3,1] => [5,3,2,2,2]
[4,3,3,2,2] => [5,3,2,2,1,1]
[4,3,3,2,1,1] => [6,3,2,2,1]
[4,3,3,1,1,1,1] => [7,3,2,2]
[4,3,2,2,2,1] => [6,3,2,1,1,1]
[4,3,2,2,1,1,1] => [7,3,2,1,1]
[4,3,2,1,1,1,1,1] => [8,3,2,1]
[4,3,1,1,1,1,1,1,1] => [9,3,2]
[4,2,2,2,2,2] => [6,3,1,1,1,1,1]
[4,2,2,2,2,1,1] => [7,3,1,1,1,1]
[4,2,2,2,1,1,1,1] => [8,3,1,1,1]
[4,2,2,1,1,1,1,1,1] => [9,3,1,1]
[4,2,1,1,1,1,1,1,1,1] => [10,3,1]
[4,1,1,1,1,1,1,1,1,1,1] => [11,3]
[3,3,3,3,2] => [5,2,2,2,2,1]
[3,3,3,3,1,1] => [6,2,2,2,2]
[3,3,3,2,2,1] => [6,2,2,2,1,1]
[3,3,3,2,1,1,1] => [7,2,2,2,1]
[3,3,3,1,1,1,1,1] => [8,2,2,2]
[3,3,2,2,2,2] => [6,2,2,1,1,1,1]
[3,3,2,2,2,1,1] => [7,2,2,1,1,1]
[3,3,2,2,1,1,1,1] => [8,2,2,1,1]
[3,3,2,1,1,1,1,1,1] => [9,2,2,1]
[3,3,1,1,1,1,1,1,1,1] => [10,2,2]
[3,2,2,2,2,2,1] => [7,2,1,1,1,1,1]
[3,2,2,2,2,1,1,1] => [8,2,1,1,1,1]
[3,2,2,2,1,1,1,1,1] => [9,2,1,1,1]
[3,2,2,1,1,1,1,1,1,1] => [10,2,1,1]
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1]
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,2]
[2,2,2,2,2,2,2] => [7,1,1,1,1,1,1,1]
[2,2,2,2,2,2,1,1] => [8,1,1,1,1,1,1]
[2,2,2,2,2,1,1,1,1] => [9,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1] => [10,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1] => [11,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14]
[15] => [14,1]
[14,1] => [13,2]
[13,2] => [12,2,1]
[13,1,1] => [12,3]
[12,3] => [11,2,2]
[12,2,1] => [11,3,1]
[12,1,1,1] => [11,4]
[11,4] => [10,3,2]
[11,3,1] => [10,3,2]
[11,2,2] => [10,3,1,1]
[11,2,1,1] => [10,4,1]
[11,1,1,1,1] => [10,5]
[10,5] => [9,4,2]
[10,4,1] => [9,3,3]
[10,3,2] => [9,3,2,1]
[10,3,1,1] => [9,4,2]
[10,2,2,1] => [9,4,1,1]
[10,2,1,1,1] => [9,5,1]
[10,1,1,1,1,1] => [9,6]
[9,6] => [8,5,2]
[9,5,1] => [8,4,3]
[9,4,2] => [8,3,3,1]
[9,4,1,1] => [8,4,3]
[9,3,3] => [8,3,2,2]
[9,3,2,1] => [8,4,2,1]
[9,3,1,1,1] => [8,5,2]
[9,2,2,2] => [8,4,1,1,1]
[9,2,2,1,1] => [8,5,1,1]
[9,2,1,1,1,1] => [8,6,1]
[9,1,1,1,1,1,1] => [8,7]
[8,7] => [7,6,2]
[8,6,1] => [7,5,3]
[8,5,2] => [7,4,3,1]
[8,5,1,1] => [7,4,4]
[8,4,3] => [7,3,3,2]
[8,4,2,1] => [7,4,3,1]
[8,4,1,1,1] => [7,5,3]
[8,3,3,1] => [7,4,2,2]
[8,3,2,2] => [7,4,2,1,1]
[8,3,2,1,1] => [7,5,2,1]
[8,3,1,1,1,1] => [7,6,2]
[8,2,2,2,1] => [7,5,1,1,1]
[8,2,2,1,1,1] => [7,6,1,1]
[8,2,1,1,1,1,1] => [7,7,1]
[8,1,1,1,1,1,1,1] => [8,7]
[7,7,1] => [6,6,3]
[7,6,2] => [6,5,3,1]
[7,6,1,1] => [6,5,4]
[7,5,3] => [6,4,3,2]
[7,5,2,1] => [6,4,4,1]
[7,5,1,1,1] => [6,5,4]
[7,4,4] => [6,3,3,3]
[7,4,3,1] => [6,4,3,2]
[7,4,2,2] => [6,4,3,1,1]
[7,4,2,1,1] => [6,5,3,1]
[7,4,1,1,1,1] => [6,6,3]
[7,3,3,2] => [6,4,2,2,1]
[7,3,3,1,1] => [6,5,2,2]
[7,3,2,2,1] => [6,5,2,1,1]
[7,3,2,1,1,1] => [6,6,2,1]
[7,3,1,1,1,1,1] => [7,6,2]
[7,2,2,2,2] => [6,5,1,1,1,1]
[7,2,2,2,1,1] => [6,6,1,1,1]
[7,2,2,1,1,1,1] => [7,6,1,1]
[7,2,1,1,1,1,1,1] => [8,6,1]
[7,1,1,1,1,1,1,1,1] => [9,6]
[6,6,3] => [5,5,3,2]
[6,6,2,1] => [5,5,4,1]
[6,6,1,1,1] => [5,5,5]
[6,5,4] => [5,4,3,3]
[6,5,3,1] => [5,4,4,2]
[6,5,2,2] => [5,4,4,1,1]
[6,5,2,1,1] => [5,5,4,1]
[6,5,1,1,1,1] => [6,5,4]
[6,4,4,1] => [5,4,3,3]
[6,4,3,2] => [5,4,3,2,1]
[6,4,3,1,1] => [5,5,3,2]
[6,4,2,2,1] => [5,5,3,1,1]
[6,4,2,1,1,1] => [6,5,3,1]
[6,4,1,1,1,1,1] => [7,5,3]
[6,3,3,3] => [5,4,2,2,2]
[6,3,3,2,1] => [5,5,2,2,1]
[6,3,3,1,1,1] => [6,5,2,2]
[6,3,2,2,2] => [5,5,2,1,1,1]
[6,3,2,2,1,1] => [6,5,2,1,1]
[6,3,2,1,1,1,1] => [7,5,2,1]
[6,3,1,1,1,1,1,1] => [8,5,2]
[6,2,2,2,2,1] => [6,5,1,1,1,1]
[6,2,2,2,1,1,1] => [7,5,1,1,1]
[6,2,2,1,1,1,1,1] => [8,5,1,1]
[6,2,1,1,1,1,1,1,1] => [9,5,1]
[6,1,1,1,1,1,1,1,1,1] => [10,5]
[5,5,5] => [4,4,4,3]
[5,5,4,1] => [4,4,4,3]
[5,5,3,2] => [4,4,4,2,1]
[5,5,3,1,1] => [5,4,4,2]
[5,5,2,2,1] => [5,4,4,1,1]
[5,5,2,1,1,1] => [6,4,4,1]
[5,5,1,1,1,1,1] => [7,4,4]
[5,4,4,2] => [4,4,3,3,1]
[5,4,4,1,1] => [5,4,3,3]
[5,4,3,3] => [4,4,3,2,2]
[5,4,3,2,1] => [5,4,3,2,1]
[5,4,3,1,1,1] => [6,4,3,2]
[5,4,2,2,2] => [5,4,3,1,1,1]
[5,4,2,2,1,1] => [6,4,3,1,1]
[5,4,2,1,1,1,1] => [7,4,3,1]
[5,4,1,1,1,1,1,1] => [8,4,3]
[5,3,3,3,1] => [5,4,2,2,2]
[5,3,3,2,2] => [5,4,2,2,1,1]
[5,3,3,2,1,1] => [6,4,2,2,1]
[5,3,3,1,1,1,1] => [7,4,2,2]
[5,3,2,2,2,1] => [6,4,2,1,1,1]
[5,3,2,2,1,1,1] => [7,4,2,1,1]
[5,3,2,1,1,1,1,1] => [8,4,2,1]
[5,3,1,1,1,1,1,1,1] => [9,4,2]
[5,2,2,2,2,2] => [6,4,1,1,1,1,1]
[5,2,2,2,2,1,1] => [7,4,1,1,1,1]
[5,2,2,2,1,1,1,1] => [8,4,1,1,1]
[5,2,2,1,1,1,1,1,1] => [9,4,1,1]
[5,2,1,1,1,1,1,1,1,1] => [10,4,1]
[5,1,1,1,1,1,1,1,1,1,1] => [11,4]
[4,4,4,3] => [4,3,3,3,2]
[4,4,4,2,1] => [5,3,3,3,1]
[4,4,4,1,1,1] => [6,3,3,3]
[4,4,3,3,1] => [5,3,3,2,2]
[4,4,3,2,2] => [5,3,3,2,1,1]
[4,4,3,2,1,1] => [6,3,3,2,1]
[4,4,3,1,1,1,1] => [7,3,3,2]
[4,4,2,2,2,1] => [6,3,3,1,1,1]
[4,4,2,2,1,1,1] => [7,3,3,1,1]
[4,4,2,1,1,1,1,1] => [8,3,3,1]
[4,4,1,1,1,1,1,1,1] => [9,3,3]
[4,3,3,3,2] => [5,3,2,2,2,1]
[4,3,3,3,1,1] => [6,3,2,2,2]
[4,3,3,2,2,1] => [6,3,2,2,1,1]
[4,3,3,2,1,1,1] => [7,3,2,2,1]
[4,3,3,1,1,1,1,1] => [8,3,2,2]
[4,3,2,2,2,2] => [6,3,2,1,1,1,1]
[4,3,2,2,2,1,1] => [7,3,2,1,1,1]
[4,3,2,2,1,1,1,1] => [8,3,2,1,1]
[4,3,2,1,1,1,1,1,1] => [9,3,2,1]
[4,3,1,1,1,1,1,1,1,1] => [10,3,2]
[4,2,2,2,2,2,1] => [7,3,1,1,1,1,1]
[4,2,2,2,2,1,1,1] => [8,3,1,1,1,1]
[4,2,2,2,1,1,1,1,1] => [9,3,1,1,1]
[4,2,2,1,1,1,1,1,1,1] => [10,3,1,1]
[4,2,1,1,1,1,1,1,1,1,1] => [11,3,1]
[4,1,1,1,1,1,1,1,1,1,1,1] => [12,3]
[3,3,3,3,3] => [5,2,2,2,2,2]
[3,3,3,3,2,1] => [6,2,2,2,2,1]
[3,3,3,3,1,1,1] => [7,2,2,2,2]
[3,3,3,2,2,2] => [6,2,2,2,1,1,1]
[3,3,3,2,2,1,1] => [7,2,2,2,1,1]
[3,3,3,2,1,1,1,1] => [8,2,2,2,1]
[3,3,3,1,1,1,1,1,1] => [9,2,2,2]
[3,3,2,2,2,2,1] => [7,2,2,1,1,1,1]
[3,3,2,2,2,1,1,1] => [8,2,2,1,1,1]
[3,3,2,2,1,1,1,1,1] => [9,2,2,1,1]
[3,3,2,1,1,1,1,1,1,1] => [10,2,2,1]
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2]
[3,2,2,2,2,2,2] => [7,2,1,1,1,1,1,1]
[3,2,2,2,2,2,1,1] => [8,2,1,1,1,1,1]
[3,2,2,2,2,1,1,1,1] => [9,2,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1] => [10,2,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1] => [11,2,1,1]
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,2]
[2,2,2,2,2,2,2,1] => [8,1,1,1,1,1,1,1]
[2,2,2,2,2,2,1,1,1] => [9,1,1,1,1,1,1]
[2,2,2,2,2,1,1,1,1,1] => [10,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1,1] => [11,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15]
[16] => [15,1]
[15,1] => [14,2]
[14,2] => [13,2,1]
[14,1,1] => [13,3]
[13,3] => [12,2,2]
[13,2,1] => [12,3,1]
[13,1,1,1] => [12,4]
[12,4] => [11,3,2]
[12,3,1] => [11,3,2]
[12,2,2] => [11,3,1,1]
[12,2,1,1] => [11,4,1]
[12,1,1,1,1] => [11,5]
[11,5] => [10,4,2]
[11,4,1] => [10,3,3]
[11,3,2] => [10,3,2,1]
[11,3,1,1] => [10,4,2]
[11,2,2,1] => [10,4,1,1]
[11,2,1,1,1] => [10,5,1]
[11,1,1,1,1,1] => [10,6]
[10,6] => [9,5,2]
[10,5,1] => [9,4,3]
[10,4,2] => [9,3,3,1]
[10,4,1,1] => [9,4,3]
[10,3,3] => [9,3,2,2]
[10,3,2,1] => [9,4,2,1]
[10,3,1,1,1] => [9,5,2]
[10,2,2,2] => [9,4,1,1,1]
[10,2,2,1,1] => [9,5,1,1]
[10,2,1,1,1,1] => [9,6,1]
[10,1,1,1,1,1,1] => [9,7]
[9,7] => [8,6,2]
[9,6,1] => [8,5,3]
[9,5,2] => [8,4,3,1]
[9,5,1,1] => [8,4,4]
[9,4,3] => [8,3,3,2]
[9,4,2,1] => [8,4,3,1]
[9,4,1,1,1] => [8,5,3]
[9,3,3,1] => [8,4,2,2]
[9,3,2,2] => [8,4,2,1,1]
[9,3,2,1,1] => [8,5,2,1]
[9,3,1,1,1,1] => [8,6,2]
[9,2,2,2,1] => [8,5,1,1,1]
[9,2,2,1,1,1] => [8,6,1,1]
[9,2,1,1,1,1,1] => [8,7,1]
[9,1,1,1,1,1,1,1] => [8,8]
[8,8] => [7,7,2]
[8,7,1] => [7,6,3]
[8,6,2] => [7,5,3,1]
[8,6,1,1] => [7,5,4]
[8,5,3] => [7,4,3,2]
[8,5,2,1] => [7,4,4,1]
[8,5,1,1,1] => [7,5,4]
[8,4,4] => [7,3,3,3]
[8,4,3,1] => [7,4,3,2]
[8,4,2,2] => [7,4,3,1,1]
[8,4,2,1,1] => [7,5,3,1]
[8,4,1,1,1,1] => [7,6,3]
[8,3,3,2] => [7,4,2,2,1]
[8,3,3,1,1] => [7,5,2,2]
[8,3,2,2,1] => [7,5,2,1,1]
[8,3,2,1,1,1] => [7,6,2,1]
[8,3,1,1,1,1,1] => [7,7,2]
[8,2,2,2,2] => [7,5,1,1,1,1]
[8,2,2,2,1,1] => [7,6,1,1,1]
[8,2,2,1,1,1,1] => [7,7,1,1]
[8,2,1,1,1,1,1,1] => [8,7,1]
[8,1,1,1,1,1,1,1,1] => [9,7]
[7,7,2] => [6,6,3,1]
[7,7,1,1] => [6,6,4]
[7,6,3] => [6,5,3,2]
[7,6,2,1] => [6,5,4,1]
[7,6,1,1,1] => [6,5,5]
[7,5,4] => [6,4,3,3]
[7,5,3,1] => [6,4,4,2]
[7,5,2,2] => [6,4,4,1,1]
[7,5,2,1,1] => [6,5,4,1]
[7,5,1,1,1,1] => [6,6,4]
[7,4,4,1] => [6,4,3,3]
[7,4,3,2] => [6,4,3,2,1]
[7,4,3,1,1] => [6,5,3,2]
[7,4,2,2,1] => [6,5,3,1,1]
[7,4,2,1,1,1] => [6,6,3,1]
[7,4,1,1,1,1,1] => [7,6,3]
[7,3,3,3] => [6,4,2,2,2]
[7,3,3,2,1] => [6,5,2,2,1]
[7,3,3,1,1,1] => [6,6,2,2]
[7,3,2,2,2] => [6,5,2,1,1,1]
[7,3,2,2,1,1] => [6,6,2,1,1]
[7,3,2,1,1,1,1] => [7,6,2,1]
[7,3,1,1,1,1,1,1] => [8,6,2]
[7,2,2,2,2,1] => [6,6,1,1,1,1]
[7,2,2,2,1,1,1] => [7,6,1,1,1]
[7,2,2,1,1,1,1,1] => [8,6,1,1]
[7,2,1,1,1,1,1,1,1] => [9,6,1]
[7,1,1,1,1,1,1,1,1,1] => [10,6]
[6,6,4] => [5,5,3,3]
[6,6,3,1] => [5,5,4,2]
[6,6,2,2] => [5,5,4,1,1]
[6,6,2,1,1] => [5,5,5,1]
[6,6,1,1,1,1] => [6,5,5]
[6,5,5] => [5,4,4,3]
[6,5,4,1] => [5,4,4,3]
[6,5,3,2] => [5,4,4,2,1]
[6,5,3,1,1] => [5,5,4,2]
[6,5,2,2,1] => [5,5,4,1,1]
[6,5,2,1,1,1] => [6,5,4,1]
[6,5,1,1,1,1,1] => [7,5,4]
[6,4,4,2] => [5,4,3,3,1]
[6,4,4,1,1] => [5,5,3,3]
[6,4,3,3] => [5,4,3,2,2]
[6,4,3,2,1] => [5,5,3,2,1]
[6,4,3,1,1,1] => [6,5,3,2]
[6,4,2,2,2] => [5,5,3,1,1,1]
[6,4,2,2,1,1] => [6,5,3,1,1]
[6,4,2,1,1,1,1] => [7,5,3,1]
[6,4,1,1,1,1,1,1] => [8,5,3]
[6,3,3,3,1] => [5,5,2,2,2]
[6,3,3,2,2] => [5,5,2,2,1,1]
[6,3,3,2,1,1] => [6,5,2,2,1]
[6,3,3,1,1,1,1] => [7,5,2,2]
[6,3,2,2,2,1] => [6,5,2,1,1,1]
[6,3,2,2,1,1,1] => [7,5,2,1,1]
[6,3,2,1,1,1,1,1] => [8,5,2,1]
[6,3,1,1,1,1,1,1,1] => [9,5,2]
[6,2,2,2,2,2] => [6,5,1,1,1,1,1]
[6,2,2,2,2,1,1] => [7,5,1,1,1,1]
[6,2,2,2,1,1,1,1] => [8,5,1,1,1]
[6,2,2,1,1,1,1,1,1] => [9,5,1,1]
[6,2,1,1,1,1,1,1,1,1] => [10,5,1]
[6,1,1,1,1,1,1,1,1,1,1] => [11,5]
[5,5,5,1] => [4,4,4,4]
[5,5,4,2] => [4,4,4,3,1]
[5,5,4,1,1] => [5,4,4,3]
[5,5,3,3] => [4,4,4,2,2]
[5,5,3,2,1] => [5,4,4,2,1]
[5,5,3,1,1,1] => [6,4,4,2]
[5,5,2,2,2] => [5,4,4,1,1,1]
[5,5,2,2,1,1] => [6,4,4,1,1]
[5,5,2,1,1,1,1] => [7,4,4,1]
[5,5,1,1,1,1,1,1] => [8,4,4]
[5,4,4,3] => [4,4,3,3,2]
[5,4,4,2,1] => [5,4,3,3,1]
[5,4,4,1,1,1] => [6,4,3,3]
[5,4,3,3,1] => [5,4,3,2,2]
[5,4,3,2,2] => [5,4,3,2,1,1]
[5,4,3,2,1,1] => [6,4,3,2,1]
[5,4,3,1,1,1,1] => [7,4,3,2]
[5,4,2,2,2,1] => [6,4,3,1,1,1]
[5,4,2,2,1,1,1] => [7,4,3,1,1]
[5,4,2,1,1,1,1,1] => [8,4,3,1]
[5,4,1,1,1,1,1,1,1] => [9,4,3]
[5,3,3,3,2] => [5,4,2,2,2,1]
[5,3,3,3,1,1] => [6,4,2,2,2]
[5,3,3,2,2,1] => [6,4,2,2,1,1]
[5,3,3,2,1,1,1] => [7,4,2,2,1]
[5,3,3,1,1,1,1,1] => [8,4,2,2]
[5,3,2,2,2,2] => [6,4,2,1,1,1,1]
[5,3,2,2,2,1,1] => [7,4,2,1,1,1]
[5,3,2,2,1,1,1,1] => [8,4,2,1,1]
[5,3,2,1,1,1,1,1,1] => [9,4,2,1]
[5,3,1,1,1,1,1,1,1,1] => [10,4,2]
[5,2,2,2,2,2,1] => [7,4,1,1,1,1,1]
[5,2,2,2,2,1,1,1] => [8,4,1,1,1,1]
[5,2,2,2,1,1,1,1,1] => [9,4,1,1,1]
[5,2,2,1,1,1,1,1,1,1] => [10,4,1,1]
[5,2,1,1,1,1,1,1,1,1,1] => [11,4,1]
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,4]
[4,4,4,4] => [4,3,3,3,3]
[4,4,4,3,1] => [5,3,3,3,2]
[4,4,4,2,2] => [5,3,3,3,1,1]
[4,4,4,2,1,1] => [6,3,3,3,1]
[4,4,4,1,1,1,1] => [7,3,3,3]
[4,4,3,3,2] => [5,3,3,2,2,1]
[4,4,3,3,1,1] => [6,3,3,2,2]
[4,4,3,2,2,1] => [6,3,3,2,1,1]
[4,4,3,2,1,1,1] => [7,3,3,2,1]
[4,4,3,1,1,1,1,1] => [8,3,3,2]
[4,4,2,2,2,2] => [6,3,3,1,1,1,1]
[4,4,2,2,2,1,1] => [7,3,3,1,1,1]
[4,4,2,2,1,1,1,1] => [8,3,3,1,1]
[4,4,2,1,1,1,1,1,1] => [9,3,3,1]
[4,4,1,1,1,1,1,1,1,1] => [10,3,3]
[4,3,3,3,3] => [5,3,2,2,2,2]
[4,3,3,3,2,1] => [6,3,2,2,2,1]
[4,3,3,3,1,1,1] => [7,3,2,2,2]
[4,3,3,2,2,2] => [6,3,2,2,1,1,1]
[4,3,3,2,2,1,1] => [7,3,2,2,1,1]
[4,3,3,2,1,1,1,1] => [8,3,2,2,1]
[4,3,3,1,1,1,1,1,1] => [9,3,2,2]
[4,3,2,2,2,2,1] => [7,3,2,1,1,1,1]
[4,3,2,2,2,1,1,1] => [8,3,2,1,1,1]
[4,3,2,2,1,1,1,1,1] => [9,3,2,1,1]
[4,3,2,1,1,1,1,1,1,1] => [10,3,2,1]
[4,3,1,1,1,1,1,1,1,1,1] => [11,3,2]
[4,2,2,2,2,2,2] => [7,3,1,1,1,1,1,1]
[4,2,2,2,2,2,1,1] => [8,3,1,1,1,1,1]
[4,2,2,2,2,1,1,1,1] => [9,3,1,1,1,1]
[4,2,2,2,1,1,1,1,1,1] => [10,3,1,1,1]
[4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1] => [12,3,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,3]
[3,3,3,3,3,1] => [6,2,2,2,2,2]
[3,3,3,3,2,2] => [6,2,2,2,2,1,1]
[3,3,3,3,2,1,1] => [7,2,2,2,2,1]
[3,3,3,3,1,1,1,1] => [8,2,2,2,2]
[3,3,3,2,2,2,1] => [7,2,2,2,1,1,1]
[3,3,3,2,2,1,1,1] => [8,2,2,2,1,1]
[3,3,3,2,1,1,1,1,1] => [9,2,2,2,1]
[3,3,3,1,1,1,1,1,1,1] => [10,2,2,2]
[3,3,2,2,2,2,2] => [7,2,2,1,1,1,1,1]
[3,3,2,2,2,2,1,1] => [8,2,2,1,1,1,1]
[3,3,2,2,2,1,1,1,1] => [9,2,2,1,1,1]
[3,3,2,2,1,1,1,1,1,1] => [10,2,2,1,1]
[3,3,2,1,1,1,1,1,1,1,1] => [11,2,2,1]
[3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2]
[3,2,2,2,2,2,2,1] => [8,2,1,1,1,1,1,1]
[3,2,2,2,2,2,1,1,1] => [9,2,1,1,1,1,1]
[3,2,2,2,2,1,1,1,1,1] => [10,2,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1,1] => [11,2,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1,1] => [12,2,1,1]
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2]
[2,2,2,2,2,2,2,2] => [8,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2,1,1] => [9,1,1,1,1,1,1,1]
[2,2,2,2,2,2,1,1,1,1] => [10,1,1,1,1,1,1]
[2,2,2,2,2,1,1,1,1,1,1] => [11,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16]
[17] => [16,1]
[16,1] => [15,2]
[15,2] => [14,2,1]
[15,1,1] => [14,3]
[14,3] => [13,2,2]
[14,2,1] => [13,3,1]
[14,1,1,1] => [13,4]
[13,4] => [12,3,2]
[13,3,1] => [12,3,2]
[13,2,2] => [12,3,1,1]
[13,2,1,1] => [12,4,1]
[13,1,1,1,1] => [12,5]
[12,5] => [11,4,2]
[12,4,1] => [11,3,3]
[12,3,2] => [11,3,2,1]
[12,3,1,1] => [11,4,2]
[12,2,2,1] => [11,4,1,1]
[12,2,1,1,1] => [11,5,1]
[12,1,1,1,1,1] => [11,6]
[11,6] => [10,5,2]
[11,5,1] => [10,4,3]
[11,4,2] => [10,3,3,1]
[11,4,1,1] => [10,4,3]
[11,3,3] => [10,3,2,2]
[11,3,2,1] => [10,4,2,1]
[11,3,1,1,1] => [10,5,2]
[11,2,2,2] => [10,4,1,1,1]
[11,2,2,1,1] => [10,5,1,1]
[11,2,1,1,1,1] => [10,6,1]
[11,1,1,1,1,1,1] => [10,7]
[10,7] => [9,6,2]
[10,6,1] => [9,5,3]
[10,5,2] => [9,4,3,1]
[10,5,1,1] => [9,4,4]
[10,4,3] => [9,3,3,2]
[10,4,2,1] => [9,4,3,1]
[10,4,1,1,1] => [9,5,3]
[10,3,3,1] => [9,4,2,2]
[10,3,2,2] => [9,4,2,1,1]
[10,3,2,1,1] => [9,5,2,1]
[10,3,1,1,1,1] => [9,6,2]
[10,2,2,2,1] => [9,5,1,1,1]
[10,2,2,1,1,1] => [9,6,1,1]
[10,2,1,1,1,1,1] => [9,7,1]
[10,1,1,1,1,1,1,1] => [9,8]
[9,8] => [8,7,2]
[9,7,1] => [8,6,3]
[9,6,2] => [8,5,3,1]
[9,6,1,1] => [8,5,4]
[9,5,3] => [8,4,3,2]
[9,5,2,1] => [8,4,4,1]
[9,5,1,1,1] => [8,5,4]
[9,4,4] => [8,3,3,3]
[9,4,3,1] => [8,4,3,2]
[9,4,2,2] => [8,4,3,1,1]
[9,4,2,1,1] => [8,5,3,1]
[9,4,1,1,1,1] => [8,6,3]
[9,3,3,2] => [8,4,2,2,1]
[9,3,3,1,1] => [8,5,2,2]
[9,3,2,2,1] => [8,5,2,1,1]
[9,3,2,1,1,1] => [8,6,2,1]
[9,3,1,1,1,1,1] => [8,7,2]
[9,2,2,2,2] => [8,5,1,1,1,1]
[9,2,2,2,1,1] => [8,6,1,1,1]
[9,2,2,1,1,1,1] => [8,7,1,1]
[9,2,1,1,1,1,1,1] => [8,8,1]
[9,1,1,1,1,1,1,1,1] => [9,8]
[8,8,1] => [7,7,3]
[8,7,2] => [7,6,3,1]
[8,7,1,1] => [7,6,4]
[8,6,3] => [7,5,3,2]
[8,6,2,1] => [7,5,4,1]
[8,6,1,1,1] => [7,5,5]
[8,5,4] => [7,4,3,3]
[8,5,3,1] => [7,4,4,2]
[8,5,2,2] => [7,4,4,1,1]
[8,5,2,1,1] => [7,5,4,1]
[8,5,1,1,1,1] => [7,6,4]
[8,4,4,1] => [7,4,3,3]
[8,4,3,2] => [7,4,3,2,1]
[8,4,3,1,1] => [7,5,3,2]
[8,4,2,2,1] => [7,5,3,1,1]
[8,4,2,1,1,1] => [7,6,3,1]
[8,4,1,1,1,1,1] => [7,7,3]
[8,3,3,3] => [7,4,2,2,2]
[8,3,3,2,1] => [7,5,2,2,1]
[8,3,3,1,1,1] => [7,6,2,2]
[8,3,2,2,2] => [7,5,2,1,1,1]
[8,3,2,2,1,1] => [7,6,2,1,1]
[8,3,2,1,1,1,1] => [7,7,2,1]
[8,3,1,1,1,1,1,1] => [8,7,2]
[8,2,2,2,2,1] => [7,6,1,1,1,1]
[8,2,2,2,1,1,1] => [7,7,1,1,1]
[8,2,2,1,1,1,1,1] => [8,7,1,1]
[8,2,1,1,1,1,1,1,1] => [9,7,1]
[8,1,1,1,1,1,1,1,1,1] => [10,7]
[7,7,3] => [6,6,3,2]
[7,7,2,1] => [6,6,4,1]
[7,7,1,1,1] => [6,6,5]
[7,6,4] => [6,5,3,3]
[7,6,3,1] => [6,5,4,2]
[7,6,2,2] => [6,5,4,1,1]
[7,6,2,1,1] => [6,5,5,1]
[7,6,1,1,1,1] => [6,6,5]
[7,5,5] => [6,4,4,3]
[7,5,4,1] => [6,4,4,3]
[7,5,3,2] => [6,4,4,2,1]
[7,5,3,1,1] => [6,5,4,2]
[7,5,2,2,1] => [6,5,4,1,1]
[7,5,2,1,1,1] => [6,6,4,1]
[7,5,1,1,1,1,1] => [7,6,4]
[7,4,4,2] => [6,4,3,3,1]
[7,4,4,1,1] => [6,5,3,3]
[7,4,3,3] => [6,4,3,2,2]
[7,4,3,2,1] => [6,5,3,2,1]
[7,4,3,1,1,1] => [6,6,3,2]
[7,4,2,2,2] => [6,5,3,1,1,1]
[7,4,2,2,1,1] => [6,6,3,1,1]
[7,4,2,1,1,1,1] => [7,6,3,1]
[7,4,1,1,1,1,1,1] => [8,6,3]
[7,3,3,3,1] => [6,5,2,2,2]
[7,3,3,2,2] => [6,5,2,2,1,1]
[7,3,3,2,1,1] => [6,6,2,2,1]
[7,3,3,1,1,1,1] => [7,6,2,2]
[7,3,2,2,2,1] => [6,6,2,1,1,1]
[7,3,2,2,1,1,1] => [7,6,2,1,1]
[7,3,2,1,1,1,1,1] => [8,6,2,1]
[7,3,1,1,1,1,1,1,1] => [9,6,2]
[7,2,2,2,2,2] => [6,6,1,1,1,1,1]
[7,2,2,2,2,1,1] => [7,6,1,1,1,1]
[7,2,2,2,1,1,1,1] => [8,6,1,1,1]
[7,2,2,1,1,1,1,1,1] => [9,6,1,1]
[7,2,1,1,1,1,1,1,1,1] => [10,6,1]
[7,1,1,1,1,1,1,1,1,1,1] => [11,6]
[6,6,5] => [5,5,4,3]
[6,6,4,1] => [5,5,4,3]
[6,6,3,2] => [5,5,4,2,1]
[6,6,3,1,1] => [5,5,5,2]
[6,6,2,2,1] => [5,5,5,1,1]
[6,6,2,1,1,1] => [6,5,5,1]
[6,6,1,1,1,1,1] => [7,5,5]
[6,5,5,1] => [5,4,4,4]
[6,5,4,2] => [5,4,4,3,1]
[6,5,4,1,1] => [5,5,4,3]
[6,5,3,3] => [5,4,4,2,2]
[6,5,3,2,1] => [5,5,4,2,1]
[6,5,3,1,1,1] => [6,5,4,2]
[6,5,2,2,2] => [5,5,4,1,1,1]
[6,5,2,2,1,1] => [6,5,4,1,1]
[6,5,2,1,1,1,1] => [7,5,4,1]
[6,5,1,1,1,1,1,1] => [8,5,4]
[6,4,4,3] => [5,4,3,3,2]
[6,4,4,2,1] => [5,5,3,3,1]
[6,4,4,1,1,1] => [6,5,3,3]
[6,4,3,3,1] => [5,5,3,2,2]
[6,4,3,2,2] => [5,5,3,2,1,1]
[6,4,3,2,1,1] => [6,5,3,2,1]
[6,4,3,1,1,1,1] => [7,5,3,2]
[6,4,2,2,2,1] => [6,5,3,1,1,1]
[6,4,2,2,1,1,1] => [7,5,3,1,1]
[6,4,2,1,1,1,1,1] => [8,5,3,1]
[6,4,1,1,1,1,1,1,1] => [9,5,3]
[6,3,3,3,2] => [5,5,2,2,2,1]
[6,3,3,3,1,1] => [6,5,2,2,2]
[6,3,3,2,2,1] => [6,5,2,2,1,1]
[6,3,3,2,1,1,1] => [7,5,2,2,1]
[6,3,3,1,1,1,1,1] => [8,5,2,2]
[6,3,2,2,2,2] => [6,5,2,1,1,1,1]
[6,3,2,2,2,1,1] => [7,5,2,1,1,1]
[6,3,2,2,1,1,1,1] => [8,5,2,1,1]
[6,3,2,1,1,1,1,1,1] => [9,5,2,1]
[6,3,1,1,1,1,1,1,1,1] => [10,5,2]
[6,2,2,2,2,2,1] => [7,5,1,1,1,1,1]
[6,2,2,2,2,1,1,1] => [8,5,1,1,1,1]
[6,2,2,2,1,1,1,1,1] => [9,5,1,1,1]
[6,2,2,1,1,1,1,1,1,1] => [10,5,1,1]
[6,2,1,1,1,1,1,1,1,1,1] => [11,5,1]
[6,1,1,1,1,1,1,1,1,1,1,1] => [12,5]
[5,5,5,2] => [4,4,4,4,1]
[5,5,5,1,1] => [5,4,4,4]
[5,5,4,3] => [4,4,4,3,2]
[5,5,4,2,1] => [5,4,4,3,1]
[5,5,4,1,1,1] => [6,4,4,3]
[5,5,3,3,1] => [5,4,4,2,2]
[5,5,3,2,2] => [5,4,4,2,1,1]
[5,5,3,2,1,1] => [6,4,4,2,1]
[5,5,3,1,1,1,1] => [7,4,4,2]
[5,5,2,2,2,1] => [6,4,4,1,1,1]
[5,5,2,2,1,1,1] => [7,4,4,1,1]
[5,5,2,1,1,1,1,1] => [8,4,4,1]
[5,5,1,1,1,1,1,1,1] => [9,4,4]
[5,4,4,4] => [4,4,3,3,3]
[5,4,4,3,1] => [5,4,3,3,2]
[5,4,4,2,2] => [5,4,3,3,1,1]
[5,4,4,2,1,1] => [6,4,3,3,1]
[5,4,4,1,1,1,1] => [7,4,3,3]
[5,4,3,3,2] => [5,4,3,2,2,1]
[5,4,3,3,1,1] => [6,4,3,2,2]
[5,4,3,2,2,1] => [6,4,3,2,1,1]
[5,4,3,2,1,1,1] => [7,4,3,2,1]
[5,4,3,1,1,1,1,1] => [8,4,3,2]
[5,4,2,2,2,2] => [6,4,3,1,1,1,1]
[5,4,2,2,2,1,1] => [7,4,3,1,1,1]
[5,4,2,2,1,1,1,1] => [8,4,3,1,1]
[5,4,2,1,1,1,1,1,1] => [9,4,3,1]
[5,4,1,1,1,1,1,1,1,1] => [10,4,3]
[5,3,3,3,3] => [5,4,2,2,2,2]
[5,3,3,3,2,1] => [6,4,2,2,2,1]
[5,3,3,3,1,1,1] => [7,4,2,2,2]
[5,3,3,2,2,2] => [6,4,2,2,1,1,1]
[5,3,3,2,2,1,1] => [7,4,2,2,1,1]
[5,3,3,2,1,1,1,1] => [8,4,2,2,1]
[5,3,3,1,1,1,1,1,1] => [9,4,2,2]
[5,3,2,2,2,2,1] => [7,4,2,1,1,1,1]
[5,3,2,2,2,1,1,1] => [8,4,2,1,1,1]
[5,3,2,2,1,1,1,1,1] => [9,4,2,1,1]
[5,3,2,1,1,1,1,1,1,1] => [10,4,2,1]
[5,3,1,1,1,1,1,1,1,1,1] => [11,4,2]
[5,2,2,2,2,2,2] => [7,4,1,1,1,1,1,1]
[5,2,2,2,2,2,1,1] => [8,4,1,1,1,1,1]
[5,2,2,2,2,1,1,1,1] => [9,4,1,1,1,1]
[5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1]
[5,2,2,1,1,1,1,1,1,1,1] => [11,4,1,1]
[5,2,1,1,1,1,1,1,1,1,1,1] => [12,4,1]
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,4]
[4,4,4,4,1] => [5,3,3,3,3]
[4,4,4,3,2] => [5,3,3,3,2,1]
[4,4,4,3,1,1] => [6,3,3,3,2]
[4,4,4,2,2,1] => [6,3,3,3,1,1]
[4,4,4,2,1,1,1] => [7,3,3,3,1]
[4,4,4,1,1,1,1,1] => [8,3,3,3]
[4,4,3,3,3] => [5,3,3,2,2,2]
[4,4,3,3,2,1] => [6,3,3,2,2,1]
[4,4,3,3,1,1,1] => [7,3,3,2,2]
[4,4,3,2,2,2] => [6,3,3,2,1,1,1]
[4,4,3,2,2,1,1] => [7,3,3,2,1,1]
[4,4,3,2,1,1,1,1] => [8,3,3,2,1]
[4,4,3,1,1,1,1,1,1] => [9,3,3,2]
[4,4,2,2,2,2,1] => [7,3,3,1,1,1,1]
[4,4,2,2,2,1,1,1] => [8,3,3,1,1,1]
[4,4,2,2,1,1,1,1,1] => [9,3,3,1,1]
[4,4,2,1,1,1,1,1,1,1] => [10,3,3,1]
[4,4,1,1,1,1,1,1,1,1,1] => [11,3,3]
[4,3,3,3,3,1] => [6,3,2,2,2,2]
[4,3,3,3,2,2] => [6,3,2,2,2,1,1]
[4,3,3,3,2,1,1] => [7,3,2,2,2,1]
[4,3,3,3,1,1,1,1] => [8,3,2,2,2]
[4,3,3,2,2,2,1] => [7,3,2,2,1,1,1]
[4,3,3,2,2,1,1,1] => [8,3,2,2,1,1]
[4,3,3,2,1,1,1,1,1] => [9,3,2,2,1]
[4,3,3,1,1,1,1,1,1,1] => [10,3,2,2]
[4,3,2,2,2,2,2] => [7,3,2,1,1,1,1,1]
[4,3,2,2,2,2,1,1] => [8,3,2,1,1,1,1]
[4,3,2,2,2,1,1,1,1] => [9,3,2,1,1,1]
[4,3,2,2,1,1,1,1,1,1] => [10,3,2,1,1]
[4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1]
[4,3,1,1,1,1,1,1,1,1,1,1] => [12,3,2]
[4,2,2,2,2,2,2,1] => [8,3,1,1,1,1,1,1]
[4,2,2,2,2,2,1,1,1] => [9,3,1,1,1,1,1]
[4,2,2,2,2,1,1,1,1,1] => [10,3,1,1,1,1]
[4,2,2,2,1,1,1,1,1,1,1] => [11,3,1,1,1]
[4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,3,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,3]
[3,3,3,3,3,2] => [6,2,2,2,2,2,1]
[3,3,3,3,3,1,1] => [7,2,2,2,2,2]
[3,3,3,3,2,2,1] => [7,2,2,2,2,1,1]
[3,3,3,3,2,1,1,1] => [8,2,2,2,2,1]
[3,3,3,3,1,1,1,1,1] => [9,2,2,2,2]
[3,3,3,2,2,2,2] => [7,2,2,2,1,1,1,1]
[3,3,3,2,2,2,1,1] => [8,2,2,2,1,1,1]
[3,3,3,2,2,1,1,1,1] => [9,2,2,2,1,1]
[3,3,3,2,1,1,1,1,1,1] => [10,2,2,2,1]
[3,3,3,1,1,1,1,1,1,1,1] => [11,2,2,2]
[3,3,2,2,2,2,2,1] => [8,2,2,1,1,1,1,1]
[3,3,2,2,2,2,1,1,1] => [9,2,2,1,1,1,1]
[3,3,2,2,2,1,1,1,1,1] => [10,2,2,1,1,1]
[3,3,2,2,1,1,1,1,1,1,1] => [11,2,2,1,1]
[3,3,2,1,1,1,1,1,1,1,1,1] => [12,2,2,1]
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2]
[3,2,2,2,2,2,2,2] => [8,2,1,1,1,1,1,1,1]
[3,2,2,2,2,2,2,1,1] => [9,2,1,1,1,1,1,1]
[3,2,2,2,2,2,1,1,1,1] => [10,2,1,1,1,1,1]
[3,2,2,2,2,1,1,1,1,1,1] => [11,2,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1,1,1] => [12,2,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1]
-----------------------------------------------------------------------------
Created: Aug 11, 2023 at 10:30 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Aug 13, 2023 at 22:07 by Martin Rubey