************************************************************************
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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: Mp00315
------------------------------------------------------------------------
Map name: inverse Foata bijection
------------------------------------------------------------------------
Domain: Integer compositions
------------------------------------------------------------------------
Codomain: Integer compositions
------------------------------------------------------------------------
Description: The inverse of Foata's bijection.
See [[Mp00314]].
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(self):
"""
sage: all(mapping(foata(pi)) == pi for n in range(1, 9) for pi in Compositions(n))
True
"""
self = Words()(self)
s = self.standard_permutation()
ordered_alphabet = sorted(self.letters(),
key=self.parent().sortkey_letters)
eval_dict = self.evaluation_dict()
weight = [eval_dict[a] for a in ordered_alphabet]
return Composition((s.foata_bijection_inverse()).destandardize(weight, ordered_alphabet=ordered_alphabet))
------------------------------------------------------------------------
Map images:
[1] => [1]
[1,1] => [1,1]
[2] => [2]
[1,1,1] => [1,1,1]
[1,2] => [1,2]
[2,1] => [2,1]
[3] => [3]
[1,1,1,1] => [1,1,1,1]
[1,1,2] => [1,1,2]
[1,2,1] => [2,1,1]
[1,3] => [1,3]
[2,1,1] => [1,2,1]
[2,2] => [2,2]
[3,1] => [3,1]
[4] => [4]
[1,1,1,1,1] => [1,1,1,1,1]
[1,1,1,2] => [1,1,1,2]
[1,1,2,1] => [2,1,1,1]
[1,1,3] => [1,1,3]
[1,2,1,1] => [1,2,1,1]
[1,2,2] => [1,2,2]
[1,3,1] => [3,1,1]
[1,4] => [1,4]
[2,1,1,1] => [1,1,2,1]
[2,1,2] => [2,1,2]
[2,2,1] => [2,2,1]
[2,3] => [2,3]
[3,1,1] => [1,3,1]
[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] => [1,1,1,1,2]
[1,1,1,2,1] => [2,1,1,1,1]
[1,1,1,3] => [1,1,1,3]
[1,1,2,1,1] => [1,2,1,1,1]
[1,1,2,2] => [1,1,2,2]
[1,1,3,1] => [3,1,1,1]
[1,1,4] => [1,1,4]
[1,2,1,1,1] => [1,1,2,1,1]
[1,2,1,2] => [2,1,1,2]
[1,2,2,1] => [2,2,1,1]
[1,2,3] => [1,2,3]
[1,3,1,1] => [1,3,1,1]
[1,3,2] => [3,1,2]
[1,4,1] => [4,1,1]
[1,5] => [1,5]
[2,1,1,1,1] => [1,1,1,2,1]
[2,1,1,2] => [1,2,1,2]
[2,1,2,1] => [1,2,2,1]
[2,1,3] => [2,1,3]
[2,2,1,1] => [2,1,2,1]
[2,2,2] => [2,2,2]
[2,3,1] => [2,3,1]
[2,4] => [2,4]
[3,1,1,1] => [1,1,3,1]
[3,1,2] => [1,3,2]
[3,2,1] => [3,2,1]
[3,3] => [3,3]
[4,1,1] => [1,4,1]
[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] => [1,1,1,1,1,2]
[1,1,1,1,2,1] => [2,1,1,1,1,1]
[1,1,1,1,3] => [1,1,1,1,3]
[1,1,1,2,1,1] => [1,2,1,1,1,1]
[1,1,1,2,2] => [1,1,1,2,2]
[1,1,1,3,1] => [3,1,1,1,1]
[1,1,1,4] => [1,1,1,4]
[1,1,2,1,1,1] => [1,1,2,1,1,1]
[1,1,2,1,2] => [2,1,1,1,2]
[1,1,2,2,1] => [2,2,1,1,1]
[1,1,2,3] => [1,1,2,3]
[1,1,3,1,1] => [1,3,1,1,1]
[1,1,3,2] => [3,1,1,2]
[1,1,4,1] => [4,1,1,1]
[1,1,5] => [1,1,5]
[1,2,1,1,1,1] => [1,1,1,2,1,1]
[1,2,1,1,2] => [1,2,1,1,2]
[1,2,1,2,1] => [1,2,2,1,1]
[1,2,1,3] => [2,1,1,3]
[1,2,2,1,1] => [2,1,2,1,1]
[1,2,2,2] => [1,2,2,2]
[1,2,3,1] => [2,3,1,1]
[1,2,4] => [1,2,4]
[1,3,1,1,1] => [1,1,3,1,1]
[1,3,1,2] => [1,3,1,2]
[1,3,2,1] => [3,2,1,1]
[1,3,3] => [1,3,3]
[1,4,1,1] => [1,4,1,1]
[1,4,2] => [4,1,2]
[1,5,1] => [5,1,1]
[1,6] => [1,6]
[2,1,1,1,1,1] => [1,1,1,1,2,1]
[2,1,1,1,2] => [1,1,2,1,2]
[2,1,1,2,1] => [1,1,2,2,1]
[2,1,1,3] => [1,2,1,3]
[2,1,2,1,1] => [2,1,1,2,1]
[2,1,2,2] => [2,1,2,2]
[2,1,3,1] => [1,2,3,1]
[2,1,4] => [2,1,4]
[2,2,1,1,1] => [1,2,1,2,1]
[2,2,1,2] => [2,2,1,2]
[2,2,2,1] => [2,2,2,1]
[2,2,3] => [2,2,3]
[2,3,1,1] => [2,1,3,1]
[2,3,2] => [3,2,2]
[2,4,1] => [2,4,1]
[2,5] => [2,5]
[3,1,1,1,1] => [1,1,1,3,1]
[3,1,1,2] => [1,1,3,2]
[3,1,2,1] => [3,1,2,1]
[3,1,3] => [3,1,3]
[3,2,1,1] => [1,3,2,1]
[3,2,2] => [2,3,2]
[3,3,1] => [3,3,1]
[3,4] => [3,4]
[4,1,1,1] => [1,1,4,1]
[4,1,2] => [1,4,2]
[4,2,1] => [4,2,1]
[4,3] => [4,3]
[5,1,1] => [1,5,1]
[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] => [1,1,1,1,1,1,2]
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1]
[1,1,1,1,1,3] => [1,1,1,1,1,3]
[1,1,1,1,2,1,1] => [1,2,1,1,1,1,1]
[1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,1,1,1,3,1] => [3,1,1,1,1,1]
[1,1,1,1,4] => [1,1,1,1,4]
[1,1,1,2,1,1,1] => [1,1,2,1,1,1,1]
[1,1,1,2,1,2] => [2,1,1,1,1,2]
[1,1,1,2,2,1] => [2,2,1,1,1,1]
[1,1,1,2,3] => [1,1,1,2,3]
[1,1,1,3,1,1] => [1,3,1,1,1,1]
[1,1,1,3,2] => [3,1,1,1,2]
[1,1,1,4,1] => [4,1,1,1,1]
[1,1,1,5] => [1,1,1,5]
[1,1,2,1,1,1,1] => [1,1,1,2,1,1,1]
[1,1,2,1,1,2] => [1,2,1,1,1,2]
[1,1,2,1,2,1] => [1,2,2,1,1,1]
[1,1,2,1,3] => [2,1,1,1,3]
[1,1,2,2,1,1] => [2,1,2,1,1,1]
[1,1,2,2,2] => [1,1,2,2,2]
[1,1,2,3,1] => [2,3,1,1,1]
[1,1,2,4] => [1,1,2,4]
[1,1,3,1,1,1] => [1,1,3,1,1,1]
[1,1,3,1,2] => [1,3,1,1,2]
[1,1,3,2,1] => [3,2,1,1,1]
[1,1,3,3] => [1,1,3,3]
[1,1,4,1,1] => [1,4,1,1,1]
[1,1,4,2] => [4,1,1,2]
[1,1,5,1] => [5,1,1,1]
[1,1,6] => [1,1,6]
[1,2,1,1,1,1,1] => [1,1,1,1,2,1,1]
[1,2,1,1,1,2] => [1,1,2,1,1,2]
[1,2,1,1,2,1] => [1,1,2,2,1,1]
[1,2,1,1,3] => [1,2,1,1,3]
[1,2,1,2,1,1] => [2,1,1,2,1,1]
[1,2,1,2,2] => [2,1,1,2,2]
[1,2,1,3,1] => [1,2,3,1,1]
[1,2,1,4] => [2,1,1,4]
[1,2,2,1,1,1] => [1,2,1,2,1,1]
[1,2,2,1,2] => [2,2,1,1,2]
[1,2,2,2,1] => [2,2,2,1,1]
[1,2,2,3] => [1,2,2,3]
[1,2,3,1,1] => [2,1,3,1,1]
[1,2,3,2] => [3,1,2,2]
[1,2,4,1] => [2,4,1,1]
[1,2,5] => [1,2,5]
[1,3,1,1,1,1] => [1,1,1,3,1,1]
[1,3,1,1,2] => [1,1,3,1,2]
[1,3,1,2,1] => [3,1,2,1,1]
[1,3,1,3] => [3,1,1,3]
[1,3,2,1,1] => [1,3,2,1,1]
[1,3,2,2] => [1,3,2,2]
[1,3,3,1] => [3,3,1,1]
[1,3,4] => [1,3,4]
[1,4,1,1,1] => [1,1,4,1,1]
[1,4,1,2] => [1,4,1,2]
[1,4,2,1] => [4,2,1,1]
[1,4,3] => [4,1,3]
[1,5,1,1] => [1,5,1,1]
[1,5,2] => [5,1,2]
[1,6,1] => [6,1,1]
[1,7] => [1,7]
[2,1,1,1,1,1,1] => [1,1,1,1,1,2,1]
[2,1,1,1,1,2] => [1,1,1,2,1,2]
[2,1,1,1,2,1] => [1,1,1,2,2,1]
[2,1,1,1,3] => [1,1,2,1,3]
[2,1,1,2,1,1] => [2,1,1,1,2,1]
[2,1,1,2,2] => [1,2,1,2,2]
[2,1,1,3,1] => [1,1,2,3,1]
[2,1,1,4] => [1,2,1,4]
[2,1,2,1,1,1] => [1,2,1,1,2,1]
[2,1,2,1,2] => [1,2,2,1,2]
[2,1,2,2,1] => [1,2,2,2,1]
[2,1,2,3] => [2,1,2,3]
[2,1,3,1,1] => [2,1,1,3,1]
[2,1,3,2] => [2,3,1,2]
[2,1,4,1] => [1,2,4,1]
[2,1,5] => [2,1,5]
[2,2,1,1,1,1] => [1,1,2,1,2,1]
[2,2,1,1,2] => [2,1,2,1,2]
[2,2,1,2,1] => [2,1,2,2,1]
[2,2,1,3] => [2,2,1,3]
[2,2,2,1,1] => [2,2,1,2,1]
[2,2,2,2] => [2,2,2,2]
[2,2,3,1] => [2,2,3,1]
[2,2,4] => [2,2,4]
[2,3,1,1,1] => [1,2,1,3,1]
[2,3,1,2] => [3,2,1,2]
[2,3,2,1] => [3,2,2,1]
[2,3,3] => [2,3,3]
[2,4,1,1] => [2,1,4,1]
[2,4,2] => [4,2,2]
[2,5,1] => [2,5,1]
[2,6] => [2,6]
[3,1,1,1,1,1] => [1,1,1,1,3,1]
[3,1,1,1,2] => [1,1,1,3,2]
[3,1,1,2,1] => [3,1,1,2,1]
[3,1,1,3] => [1,3,1,3]
[3,1,2,1,1] => [1,3,1,2,1]
[3,1,2,2] => [1,2,3,2]
[3,1,3,1] => [1,3,3,1]
[3,1,4] => [3,1,4]
[3,2,1,1,1] => [1,1,3,2,1]
[3,2,1,2] => [2,1,3,2]
[3,2,2,1] => [2,3,2,1]
[3,2,3] => [3,2,3]
[3,3,1,1] => [3,1,3,1]
[3,3,2] => [3,3,2]
[3,4,1] => [3,4,1]
[3,5] => [3,5]
[4,1,1,1,1] => [1,1,1,4,1]
[4,1,1,2] => [1,1,4,2]
[4,1,2,1] => [4,1,2,1]
[4,1,3] => [1,4,3]
[4,2,1,1] => [1,4,2,1]
[4,2,2] => [2,4,2]
[4,3,1] => [4,3,1]
[4,4] => [4,4]
[5,1,1,1] => [1,1,5,1]
[5,1,2] => [1,5,2]
[5,2,1] => [5,2,1]
[5,3] => [5,3]
[6,1,1] => [1,6,1]
[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] => [1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,3] => [1,1,1,1,1,1,3]
[1,1,1,1,1,2,1,1] => [1,2,1,1,1,1,1,1]
[1,1,1,1,1,2,2] => [1,1,1,1,1,2,2]
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,4] => [1,1,1,1,1,4]
[1,1,1,1,2,1,1,1] => [1,1,2,1,1,1,1,1]
[1,1,1,1,2,1,2] => [2,1,1,1,1,1,2]
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1]
[1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,1,1,3,1,1] => [1,3,1,1,1,1,1]
[1,1,1,1,3,2] => [3,1,1,1,1,2]
[1,1,1,1,4,1] => [4,1,1,1,1,1]
[1,1,1,1,5] => [1,1,1,1,5]
[1,1,1,2,1,1,1,1] => [1,1,1,2,1,1,1,1]
[1,1,1,2,1,1,2] => [1,2,1,1,1,1,2]
[1,1,1,2,1,2,1] => [1,2,2,1,1,1,1]
[1,1,1,2,1,3] => [2,1,1,1,1,3]
[1,1,1,2,2,1,1] => [2,1,2,1,1,1,1]
[1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,1,1,2,3,1] => [2,3,1,1,1,1]
[1,1,1,2,4] => [1,1,1,2,4]
[1,1,1,3,1,1,1] => [1,1,3,1,1,1,1]
[1,1,1,3,1,2] => [1,3,1,1,1,2]
[1,1,1,3,2,1] => [3,2,1,1,1,1]
[1,1,1,3,3] => [1,1,1,3,3]
[1,1,1,4,1,1] => [1,4,1,1,1,1]
[1,1,1,4,2] => [4,1,1,1,2]
[1,1,1,5,1] => [5,1,1,1,1]
[1,1,1,6] => [1,1,1,6]
[1,1,2,1,1,1,1,1] => [1,1,1,1,2,1,1,1]
[1,1,2,1,1,1,2] => [1,1,2,1,1,1,2]
[1,1,2,1,1,2,1] => [1,1,2,2,1,1,1]
[1,1,2,1,1,3] => [1,2,1,1,1,3]
[1,1,2,1,2,1,1] => [2,1,1,2,1,1,1]
[1,1,2,1,2,2] => [2,1,1,1,2,2]
[1,1,2,1,3,1] => [1,2,3,1,1,1]
[1,1,2,1,4] => [2,1,1,1,4]
[1,1,2,2,1,1,1] => [1,2,1,2,1,1,1]
[1,1,2,2,1,2] => [2,2,1,1,1,2]
[1,1,2,2,2,1] => [2,2,2,1,1,1]
[1,1,2,2,3] => [1,1,2,2,3]
[1,1,2,3,1,1] => [2,1,3,1,1,1]
[1,1,2,3,2] => [3,1,1,2,2]
[1,1,2,4,1] => [2,4,1,1,1]
[1,1,2,5] => [1,1,2,5]
[1,1,3,1,1,1,1] => [1,1,1,3,1,1,1]
[1,1,3,1,1,2] => [1,1,3,1,1,2]
[1,1,3,1,2,1] => [3,1,2,1,1,1]
[1,1,3,1,3] => [3,1,1,1,3]
[1,1,3,2,1,1] => [1,3,2,1,1,1]
[1,1,3,2,2] => [1,3,1,2,2]
[1,1,3,3,1] => [3,3,1,1,1]
[1,1,3,4] => [1,1,3,4]
[1,1,4,1,1,1] => [1,1,4,1,1,1]
[1,1,4,1,2] => [1,4,1,1,2]
[1,1,4,2,1] => [4,2,1,1,1]
[1,1,4,3] => [4,1,1,3]
[1,1,5,1,1] => [1,5,1,1,1]
[1,1,5,2] => [5,1,1,2]
[1,1,6,1] => [6,1,1,1]
[1,1,7] => [1,1,7]
[1,2,1,1,1,1,1,1] => [1,1,1,1,1,2,1,1]
[1,2,1,1,1,1,2] => [1,1,1,2,1,1,2]
[1,2,1,1,1,2,1] => [1,1,1,2,2,1,1]
[1,2,1,1,1,3] => [1,1,2,1,1,3]
[1,2,1,1,2,1,1] => [2,1,1,1,2,1,1]
[1,2,1,1,2,2] => [1,2,1,1,2,2]
[1,2,1,1,3,1] => [1,1,2,3,1,1]
[1,2,1,1,4] => [1,2,1,1,4]
[1,2,1,2,1,1,1] => [1,2,1,1,2,1,1]
[1,2,1,2,1,2] => [1,2,2,1,1,2]
[1,2,1,2,2,1] => [1,2,2,2,1,1]
[1,2,1,2,3] => [2,1,1,2,3]
[1,2,1,3,1,1] => [2,1,1,3,1,1]
[1,2,1,3,2] => [2,3,1,1,2]
[1,2,1,4,1] => [1,2,4,1,1]
[1,2,1,5] => [2,1,1,5]
[1,2,2,1,1,1,1] => [1,1,2,1,2,1,1]
[1,2,2,1,1,2] => [2,1,2,1,1,2]
[1,2,2,1,2,1] => [2,1,2,2,1,1]
[1,2,2,1,3] => [2,2,1,1,3]
[1,2,2,2,1,1] => [2,2,1,2,1,1]
[1,2,2,2,2] => [1,2,2,2,2]
[1,2,2,3,1] => [2,2,3,1,1]
[1,2,2,4] => [1,2,2,4]
[1,2,3,1,1,1] => [1,2,1,3,1,1]
[1,2,3,1,2] => [3,2,1,1,2]
[1,2,3,2,1] => [3,2,2,1,1]
[1,2,3,3] => [1,2,3,3]
[1,2,4,1,1] => [2,1,4,1,1]
[1,2,4,2] => [4,1,2,2]
[1,2,5,1] => [2,5,1,1]
[1,2,6] => [1,2,6]
[1,3,1,1,1,1,1] => [1,1,1,1,3,1,1]
[1,3,1,1,1,2] => [1,1,1,3,1,2]
[1,3,1,1,2,1] => [3,1,1,2,1,1]
[1,3,1,1,3] => [1,3,1,1,3]
[1,3,1,2,1,1] => [1,3,1,2,1,1]
[1,3,1,2,2] => [1,1,3,2,2]
[1,3,1,3,1] => [1,3,3,1,1]
[1,3,1,4] => [3,1,1,4]
[1,3,2,1,1,1] => [1,1,3,2,1,1]
[1,3,2,1,2] => [3,1,2,1,2]
[1,3,2,2,1] => [2,3,2,1,1]
[1,3,2,3] => [3,1,2,3]
[1,3,3,1,1] => [3,1,3,1,1]
[1,3,3,2] => [3,3,1,2]
[1,3,4,1] => [3,4,1,1]
[1,3,5] => [1,3,5]
[1,4,1,1,1,1] => [1,1,1,4,1,1]
[1,4,1,1,2] => [1,1,4,1,2]
[1,4,1,2,1] => [4,1,2,1,1]
[1,4,1,3] => [1,4,1,3]
[1,4,2,1,1] => [1,4,2,1,1]
[1,4,2,2] => [1,4,2,2]
[1,4,3,1] => [4,3,1,1]
[1,4,4] => [1,4,4]
[1,5,1,1,1] => [1,1,5,1,1]
[1,5,1,2] => [1,5,1,2]
[1,5,2,1] => [5,2,1,1]
[1,5,3] => [5,1,3]
[1,6,1,1] => [1,6,1,1]
[1,6,2] => [6,1,2]
[1,7,1] => [7,1,1]
[1,8] => [1,8]
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1]
[2,1,1,1,1,1,2] => [1,1,1,1,2,1,2]
[2,1,1,1,1,2,1] => [1,1,1,1,2,2,1]
[2,1,1,1,1,3] => [1,1,1,2,1,3]
[2,1,1,1,2,1,1] => [2,1,1,1,1,2,1]
[2,1,1,1,2,2] => [1,1,2,1,2,2]
[2,1,1,1,3,1] => [1,1,1,2,3,1]
[2,1,1,1,4] => [1,1,2,1,4]
[2,1,1,2,1,1,1] => [1,2,1,1,1,2,1]
[2,1,1,2,1,2] => [1,1,2,2,1,2]
[2,1,1,2,2,1] => [1,1,2,2,2,1]
[2,1,1,2,3] => [1,2,1,2,3]
[2,1,1,3,1,1] => [2,1,1,1,3,1]
[2,1,1,3,2] => [1,2,3,1,2]
[2,1,1,4,1] => [1,1,2,4,1]
[2,1,1,5] => [1,2,1,5]
[2,1,2,1,1,1,1] => [1,1,2,1,1,2,1]
[2,1,2,1,1,2] => [2,1,1,2,1,2]
[2,1,2,1,2,1] => [2,1,1,2,2,1]
[2,1,2,1,3] => [1,2,2,1,3]
[2,1,2,2,1,1] => [2,2,1,1,2,1]
[2,1,2,2,2] => [2,1,2,2,2]
[2,1,2,3,1] => [1,2,2,3,1]
[2,1,2,4] => [2,1,2,4]
[2,1,3,1,1,1] => [1,2,1,1,3,1]
[2,1,3,1,2] => [2,1,3,1,2]
[2,1,3,2,1] => [3,1,2,2,1]
[2,1,3,3] => [2,1,3,3]
[2,1,4,1,1] => [2,1,1,4,1]
[2,1,4,2] => [2,4,1,2]
[2,1,5,1] => [1,2,5,1]
[2,1,6] => [2,1,6]
[2,2,1,1,1,1,1] => [1,1,1,2,1,2,1]
[2,2,1,1,1,2] => [1,2,1,2,1,2]
[2,2,1,1,2,1] => [1,2,1,2,2,1]
[2,2,1,1,3] => [2,1,2,1,3]
[2,2,1,2,1,1] => [1,2,2,1,2,1]
[2,2,1,2,2] => [2,2,1,2,2]
[2,2,1,3,1] => [2,1,2,3,1]
[2,2,1,4] => [2,2,1,4]
[2,2,2,1,1,1] => [2,1,2,1,2,1]
[2,2,2,1,2] => [2,2,2,1,2]
[2,2,2,2,1] => [2,2,2,2,1]
[2,2,2,3] => [2,2,2,3]
[2,2,3,1,1] => [2,2,1,3,1]
[2,2,3,2] => [3,2,2,2]
[2,2,4,1] => [2,2,4,1]
[2,2,5] => [2,2,5]
[2,3,1,1,1,1] => [1,1,2,1,3,1]
[2,3,1,1,2] => [1,3,2,1,2]
[2,3,1,2,1] => [2,3,1,2,1]
[2,3,1,3] => [2,3,1,3]
[2,3,2,1,1] => [3,2,1,2,1]
[2,3,2,2] => [2,3,2,2]
[2,3,3,1] => [2,3,3,1]
[2,3,4] => [2,3,4]
[2,4,1,1,1] => [1,2,1,4,1]
[2,4,1,2] => [4,2,1,2]
[2,4,2,1] => [4,2,2,1]
[2,4,3] => [4,2,3]
[2,5,1,1] => [2,1,5,1]
[2,5,2] => [5,2,2]
[2,6,1] => [2,6,1]
[2,7] => [2,7]
[3,1,1,1,1,1,1] => [1,1,1,1,1,3,1]
[3,1,1,1,1,2] => [1,1,1,1,3,2]
[3,1,1,1,2,1] => [3,1,1,1,2,1]
[3,1,1,1,3] => [1,1,3,1,3]
[3,1,1,2,1,1] => [1,3,1,1,2,1]
[3,1,1,2,2] => [1,1,2,3,2]
[3,1,1,3,1] => [1,1,3,3,1]
[3,1,1,4] => [1,3,1,4]
[3,1,2,1,1,1] => [1,1,3,1,2,1]
[3,1,2,1,2] => [2,1,1,3,2]
[3,1,2,2,1] => [1,3,2,2,1]
[3,1,2,3] => [1,3,2,3]
[3,1,3,1,1] => [3,1,1,3,1]
[3,1,3,2] => [1,3,3,2]
[3,1,4,1] => [1,3,4,1]
[3,1,5] => [3,1,5]
[3,2,1,1,1,1] => [1,1,1,3,2,1]
[3,2,1,1,2] => [1,2,1,3,2]
[3,2,1,2,1] => [1,2,3,2,1]
[3,2,1,3] => [3,2,1,3]
[3,2,2,1,1] => [2,1,3,2,1]
[3,2,2,2] => [2,2,3,2]
[3,2,3,1] => [3,2,3,1]
[3,2,4] => [3,2,4]
[3,3,1,1,1] => [1,3,1,3,1]
[3,3,1,2] => [3,1,3,2]
[3,3,2,1] => [3,3,2,1]
[3,3,3] => [3,3,3]
[3,4,1,1] => [3,1,4,1]
[3,4,2] => [3,4,2]
[3,5,1] => [3,5,1]
[3,6] => [3,6]
[4,1,1,1,1,1] => [1,1,1,1,4,1]
[4,1,1,1,2] => [1,1,1,4,2]
[4,1,1,2,1] => [4,1,1,2,1]
[4,1,1,3] => [1,1,4,3]
[4,1,2,1,1] => [1,4,1,2,1]
[4,1,2,2] => [1,2,4,2]
[4,1,3,1] => [4,1,3,1]
[4,1,4] => [4,1,4]
[4,2,1,1,1] => [1,1,4,2,1]
[4,2,1,2] => [2,1,4,2]
[4,2,2,1] => [2,4,2,1]
[4,2,3] => [2,4,3]
[4,3,1,1] => [1,4,3,1]
[4,3,2] => [4,3,2]
[4,4,1] => [4,4,1]
[4,5] => [4,5]
[5,1,1,1,1] => [1,1,1,5,1]
[5,1,1,2] => [1,1,5,2]
[5,1,2,1] => [5,1,2,1]
[5,1,3] => [1,5,3]
[5,2,1,1] => [1,5,2,1]
[5,2,2] => [2,5,2]
[5,3,1] => [5,3,1]
[5,4] => [5,4]
[6,1,1,1] => [1,1,6,1]
[6,1,2] => [1,6,2]
[6,2,1] => [6,2,1]
[6,3] => [6,3]
[7,1,1] => [1,7,1]
[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] => [1,1,1,1,1,1,1,1,2]
[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] => [1,1,1,1,1,1,1,3]
[1,1,1,1,1,1,2,1,1] => [1,2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2,2] => [1,1,1,1,1,1,2,2]
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,4] => [1,1,1,1,1,1,4]
[1,1,1,1,1,2,1,1,1] => [1,1,2,1,1,1,1,1,1]
[1,1,1,1,1,2,1,2] => [2,1,1,1,1,1,1,2]
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1]
[1,1,1,1,1,2,3] => [1,1,1,1,1,2,3]
[1,1,1,1,1,3,1,1] => [1,3,1,1,1,1,1,1]
[1,1,1,1,1,3,2] => [3,1,1,1,1,1,2]
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1]
[1,1,1,1,1,5] => [1,1,1,1,1,5]
[1,1,1,1,2,1,1,1,1] => [1,1,1,2,1,1,1,1,1]
[1,1,1,1,2,1,1,2] => [1,2,1,1,1,1,1,2]
[1,1,1,1,2,1,2,1] => [1,2,2,1,1,1,1,1]
[1,1,1,1,2,1,3] => [2,1,1,1,1,1,3]
[1,1,1,1,2,2,1,1] => [2,1,2,1,1,1,1,1]
[1,1,1,1,2,2,2] => [1,1,1,1,2,2,2]
[1,1,1,1,2,3,1] => [2,3,1,1,1,1,1]
[1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,1,1,3,1,1,1] => [1,1,3,1,1,1,1,1]
[1,1,1,1,3,1,2] => [1,3,1,1,1,1,2]
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1]
[1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,1,1,1,4,1,1] => [1,4,1,1,1,1,1]
[1,1,1,1,4,2] => [4,1,1,1,1,2]
[1,1,1,1,5,1] => [5,1,1,1,1,1]
[1,1,1,1,6] => [1,1,1,1,6]
[1,1,1,2,1,1,1,1,1] => [1,1,1,1,2,1,1,1,1]
[1,1,1,2,1,1,1,2] => [1,1,2,1,1,1,1,2]
[1,1,1,2,1,1,2,1] => [1,1,2,2,1,1,1,1]
[1,1,1,2,1,1,3] => [1,2,1,1,1,1,3]
[1,1,1,2,1,2,1,1] => [2,1,1,2,1,1,1,1]
[1,1,1,2,1,2,2] => [2,1,1,1,1,2,2]
[1,1,1,2,1,3,1] => [1,2,3,1,1,1,1]
[1,1,1,2,1,4] => [2,1,1,1,1,4]
[1,1,1,2,2,1,1,1] => [1,2,1,2,1,1,1,1]
[1,1,1,2,2,1,2] => [2,2,1,1,1,1,2]
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1]
[1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,1,2,3,1,1] => [2,1,3,1,1,1,1]
[1,1,1,2,3,2] => [3,1,1,1,2,2]
[1,1,1,2,4,1] => [2,4,1,1,1,1]
[1,1,1,2,5] => [1,1,1,2,5]
[1,1,1,3,1,1,1,1] => [1,1,1,3,1,1,1,1]
[1,1,1,3,1,1,2] => [1,1,3,1,1,1,2]
[1,1,1,3,1,2,1] => [3,1,2,1,1,1,1]
[1,1,1,3,1,3] => [3,1,1,1,1,3]
[1,1,1,3,2,1,1] => [1,3,2,1,1,1,1]
[1,1,1,3,2,2] => [1,3,1,1,2,2]
[1,1,1,3,3,1] => [3,3,1,1,1,1]
[1,1,1,3,4] => [1,1,1,3,4]
[1,1,1,4,1,1,1] => [1,1,4,1,1,1,1]
[1,1,1,4,1,2] => [1,4,1,1,1,2]
[1,1,1,4,2,1] => [4,2,1,1,1,1]
[1,1,1,4,3] => [4,1,1,1,3]
[1,1,1,5,1,1] => [1,5,1,1,1,1]
[1,1,1,5,2] => [5,1,1,1,2]
[1,1,1,6,1] => [6,1,1,1,1]
[1,1,1,7] => [1,1,1,7]
[1,1,2,1,1,1,1,1,1] => [1,1,1,1,1,2,1,1,1]
[1,1,2,1,1,1,1,2] => [1,1,1,2,1,1,1,2]
[1,1,2,1,1,1,2,1] => [1,1,1,2,2,1,1,1]
[1,1,2,1,1,1,3] => [1,1,2,1,1,1,3]
[1,1,2,1,1,2,1,1] => [2,1,1,1,2,1,1,1]
[1,1,2,1,1,2,2] => [1,2,1,1,1,2,2]
[1,1,2,1,1,3,1] => [1,1,2,3,1,1,1]
[1,1,2,1,1,4] => [1,2,1,1,1,4]
[1,1,2,1,2,1,1,1] => [1,2,1,1,2,1,1,1]
[1,1,2,1,2,1,2] => [1,2,2,1,1,1,2]
[1,1,2,1,2,2,1] => [1,2,2,2,1,1,1]
[1,1,2,1,2,3] => [2,1,1,1,2,3]
[1,1,2,1,3,1,1] => [2,1,1,3,1,1,1]
[1,1,2,1,3,2] => [2,3,1,1,1,2]
[1,1,2,1,4,1] => [1,2,4,1,1,1]
[1,1,2,1,5] => [2,1,1,1,5]
[1,1,2,2,1,1,1,1] => [1,1,2,1,2,1,1,1]
[1,1,2,2,1,1,2] => [2,1,2,1,1,1,2]
[1,1,2,2,1,2,1] => [2,1,2,2,1,1,1]
[1,1,2,2,1,3] => [2,2,1,1,1,3]
[1,1,2,2,2,1,1] => [2,2,1,2,1,1,1]
[1,1,2,2,2,2] => [1,1,2,2,2,2]
[1,1,2,2,3,1] => [2,2,3,1,1,1]
[1,1,2,2,4] => [1,1,2,2,4]
[1,1,2,3,1,1,1] => [1,2,1,3,1,1,1]
[1,1,2,3,1,2] => [3,2,1,1,1,2]
[1,1,2,3,2,1] => [3,2,2,1,1,1]
[1,1,2,3,3] => [1,1,2,3,3]
[1,1,2,4,1,1] => [2,1,4,1,1,1]
[1,1,2,4,2] => [4,1,1,2,2]
[1,1,2,5,1] => [2,5,1,1,1]
[1,1,2,6] => [1,1,2,6]
[1,1,3,1,1,1,1,1] => [1,1,1,1,3,1,1,1]
[1,1,3,1,1,1,2] => [1,1,1,3,1,1,2]
[1,1,3,1,1,2,1] => [3,1,1,2,1,1,1]
[1,1,3,1,1,3] => [1,3,1,1,1,3]
[1,1,3,1,2,1,1] => [1,3,1,2,1,1,1]
[1,1,3,1,2,2] => [1,1,3,1,2,2]
[1,1,3,1,3,1] => [1,3,3,1,1,1]
[1,1,3,1,4] => [3,1,1,1,4]
[1,1,3,2,1,1,1] => [1,1,3,2,1,1,1]
[1,1,3,2,1,2] => [3,1,2,1,1,2]
[1,1,3,2,2,1] => [2,3,2,1,1,1]
[1,1,3,2,3] => [3,1,1,2,3]
[1,1,3,3,1,1] => [3,1,3,1,1,1]
[1,1,3,3,2] => [3,3,1,1,2]
[1,1,3,4,1] => [3,4,1,1,1]
[1,1,3,5] => [1,1,3,5]
[1,1,4,1,1,1,1] => [1,1,1,4,1,1,1]
[1,1,4,1,1,2] => [1,1,4,1,1,2]
[1,1,4,1,2,1] => [4,1,2,1,1,1]
[1,1,4,1,3] => [1,4,1,1,3]
[1,1,4,2,1,1] => [1,4,2,1,1,1]
[1,1,4,2,2] => [1,4,1,2,2]
[1,1,4,3,1] => [4,3,1,1,1]
[1,1,4,4] => [1,1,4,4]
[1,1,5,1,1,1] => [1,1,5,1,1,1]
[1,1,5,1,2] => [1,5,1,1,2]
[1,1,5,2,1] => [5,2,1,1,1]
[1,1,5,3] => [5,1,1,3]
[1,1,6,1,1] => [1,6,1,1,1]
[1,1,6,2] => [6,1,1,2]
[1,1,7,1] => [7,1,1,1]
[1,1,8] => [1,1,8]
[1,2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1,1]
[1,2,1,1,1,1,1,2] => [1,1,1,1,2,1,1,2]
[1,2,1,1,1,1,2,1] => [1,1,1,1,2,2,1,1]
[1,2,1,1,1,1,3] => [1,1,1,2,1,1,3]
[1,2,1,1,1,2,1,1] => [2,1,1,1,1,2,1,1]
[1,2,1,1,1,2,2] => [1,1,2,1,1,2,2]
[1,2,1,1,1,3,1] => [1,1,1,2,3,1,1]
[1,2,1,1,1,4] => [1,1,2,1,1,4]
[1,2,1,1,2,1,1,1] => [1,2,1,1,1,2,1,1]
[1,2,1,1,2,1,2] => [1,1,2,2,1,1,2]
[1,2,1,1,2,2,1] => [1,1,2,2,2,1,1]
[1,2,1,1,2,3] => [1,2,1,1,2,3]
[1,2,1,1,3,1,1] => [2,1,1,1,3,1,1]
[1,2,1,1,3,2] => [1,2,3,1,1,2]
[1,2,1,1,4,1] => [1,1,2,4,1,1]
[1,2,1,1,5] => [1,2,1,1,5]
[1,2,1,2,1,1,1,1] => [1,1,2,1,1,2,1,1]
[1,2,1,2,1,1,2] => [2,1,1,2,1,1,2]
[1,2,1,2,1,2,1] => [2,1,1,2,2,1,1]
[1,2,1,2,1,3] => [1,2,2,1,1,3]
[1,2,1,2,2,1,1] => [2,2,1,1,2,1,1]
[1,2,1,2,2,2] => [2,1,1,2,2,2]
[1,2,1,2,3,1] => [1,2,2,3,1,1]
[1,2,1,2,4] => [2,1,1,2,4]
[1,2,1,3,1,1,1] => [1,2,1,1,3,1,1]
[1,2,1,3,1,2] => [2,1,3,1,1,2]
[1,2,1,3,2,1] => [3,1,2,2,1,1]
[1,2,1,3,3] => [2,1,1,3,3]
[1,2,1,4,1,1] => [2,1,1,4,1,1]
[1,2,1,4,2] => [2,4,1,1,2]
[1,2,1,5,1] => [1,2,5,1,1]
[1,2,1,6] => [2,1,1,6]
[1,2,2,1,1,1,1,1] => [1,1,1,2,1,2,1,1]
[1,2,2,1,1,1,2] => [1,2,1,2,1,1,2]
[1,2,2,1,1,2,1] => [1,2,1,2,2,1,1]
[1,2,2,1,1,3] => [2,1,2,1,1,3]
[1,2,2,1,2,1,1] => [1,2,2,1,2,1,1]
[1,2,2,1,2,2] => [2,2,1,1,2,2]
[1,2,2,1,3,1] => [2,1,2,3,1,1]
[1,2,2,1,4] => [2,2,1,1,4]
[1,2,2,2,1,1,1] => [2,1,2,1,2,1,1]
[1,2,2,2,1,2] => [2,2,2,1,1,2]
[1,2,2,2,2,1] => [2,2,2,2,1,1]
[1,2,2,2,3] => [1,2,2,2,3]
[1,2,2,3,1,1] => [2,2,1,3,1,1]
[1,2,2,3,2] => [3,1,2,2,2]
[1,2,2,4,1] => [2,2,4,1,1]
[1,2,2,5] => [1,2,2,5]
[1,2,3,1,1,1,1] => [1,1,2,1,3,1,1]
[1,2,3,1,1,2] => [1,3,2,1,1,2]
[1,2,3,1,2,1] => [2,3,1,2,1,1]
[1,2,3,1,3] => [2,3,1,1,3]
[1,2,3,2,1,1] => [3,2,1,2,1,1]
[1,2,3,2,2] => [1,3,2,2,2]
[1,2,3,3,1] => [2,3,3,1,1]
[1,2,3,4] => [1,2,3,4]
[1,2,4,1,1,1] => [1,2,1,4,1,1]
[1,2,4,1,2] => [4,2,1,1,2]
[1,2,4,2,1] => [4,2,2,1,1]
[1,2,4,3] => [4,1,2,3]
[1,2,5,1,1] => [2,1,5,1,1]
[1,2,5,2] => [5,1,2,2]
[1,2,6,1] => [2,6,1,1]
[1,2,7] => [1,2,7]
[1,3,1,1,1,1,1,1] => [1,1,1,1,1,3,1,1]
[1,3,1,1,1,1,2] => [1,1,1,1,3,1,2]
[1,3,1,1,1,2,1] => [3,1,1,1,2,1,1]
[1,3,1,1,1,3] => [1,1,3,1,1,3]
[1,3,1,1,2,1,1] => [1,3,1,1,2,1,1]
[1,3,1,1,2,2] => [1,1,1,3,2,2]
[1,3,1,1,3,1] => [1,1,3,3,1,1]
[1,3,1,1,4] => [1,3,1,1,4]
[1,3,1,2,1,1,1] => [1,1,3,1,2,1,1]
[1,3,1,2,1,2] => [3,1,1,2,1,2]
[1,3,1,2,2,1] => [1,3,2,2,1,1]
[1,3,1,2,3] => [1,3,1,2,3]
[1,3,1,3,1,1] => [3,1,1,3,1,1]
[1,3,1,3,2] => [1,3,3,1,2]
[1,3,1,4,1] => [1,3,4,1,1]
[1,3,1,5] => [3,1,1,5]
[1,3,2,1,1,1,1] => [1,1,1,3,2,1,1]
[1,3,2,1,1,2] => [1,3,1,2,1,2]
[1,3,2,1,2,1] => [1,2,3,2,1,1]
[1,3,2,1,3] => [3,2,1,1,3]
[1,3,2,2,1,1] => [2,1,3,2,1,1]
[1,3,2,2,2] => [1,2,3,2,2]
[1,3,2,3,1] => [3,2,3,1,1]
[1,3,2,4] => [3,1,2,4]
[1,3,3,1,1,1] => [1,3,1,3,1,1]
[1,3,3,1,2] => [3,1,3,1,2]
[1,3,3,2,1] => [3,3,2,1,1]
[1,3,3,3] => [1,3,3,3]
[1,3,4,1,1] => [3,1,4,1,1]
[1,3,4,2] => [3,4,1,2]
[1,3,5,1] => [3,5,1,1]
[1,3,6] => [1,3,6]
[1,4,1,1,1,1,1] => [1,1,1,1,4,1,1]
[1,4,1,1,1,2] => [1,1,1,4,1,2]
[1,4,1,1,2,1] => [4,1,1,2,1,1]
[1,4,1,1,3] => [1,1,4,1,3]
[1,4,1,2,1,1] => [1,4,1,2,1,1]
[1,4,1,2,2] => [1,1,4,2,2]
[1,4,1,3,1] => [4,1,3,1,1]
[1,4,1,4] => [4,1,1,4]
[1,4,2,1,1,1] => [1,1,4,2,1,1]
[1,4,2,1,2] => [4,1,2,1,2]
[1,4,2,2,1] => [2,4,2,1,1]
[1,4,2,3] => [1,4,2,3]
[1,4,3,1,1] => [1,4,3,1,1]
[1,4,3,2] => [4,3,1,2]
[1,4,4,1] => [4,4,1,1]
[1,4,5] => [1,4,5]
[1,5,1,1,1,1] => [1,1,1,5,1,1]
[1,5,1,1,2] => [1,1,5,1,2]
[1,5,1,2,1] => [5,1,2,1,1]
[1,5,1,3] => [1,5,1,3]
[1,5,2,1,1] => [1,5,2,1,1]
[1,5,2,2] => [1,5,2,2]
[1,5,3,1] => [5,3,1,1]
[1,5,4] => [5,1,4]
[1,6,1,1,1] => [1,1,6,1,1]
[1,6,1,2] => [1,6,1,2]
[1,6,2,1] => [6,2,1,1]
[1,6,3] => [6,1,3]
[1,7,1,1] => [1,7,1,1]
[1,7,2] => [7,1,2]
[1,8,1] => [8,1,1]
[1,9] => [1,9]
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2,1]
[2,1,1,1,1,1,1,2] => [1,1,1,1,1,2,1,2]
[2,1,1,1,1,1,2,1] => [1,1,1,1,1,2,2,1]
[2,1,1,1,1,1,3] => [1,1,1,1,2,1,3]
[2,1,1,1,1,2,1,1] => [2,1,1,1,1,1,2,1]
[2,1,1,1,1,2,2] => [1,1,1,2,1,2,2]
[2,1,1,1,1,3,1] => [1,1,1,1,2,3,1]
[2,1,1,1,1,4] => [1,1,1,2,1,4]
[2,1,1,1,2,1,1,1] => [1,2,1,1,1,1,2,1]
[2,1,1,1,2,1,2] => [1,1,1,2,2,1,2]
[2,1,1,1,2,2,1] => [1,1,1,2,2,2,1]
[2,1,1,1,2,3] => [1,1,2,1,2,3]
[2,1,1,1,3,1,1] => [2,1,1,1,1,3,1]
[2,1,1,1,3,2] => [1,1,2,3,1,2]
[2,1,1,1,4,1] => [1,1,1,2,4,1]
[2,1,1,1,5] => [1,1,2,1,5]
[2,1,1,2,1,1,1,1] => [1,1,2,1,1,1,2,1]
[2,1,1,2,1,1,2] => [2,1,1,1,2,1,2]
[2,1,1,2,1,2,1] => [2,1,1,1,2,2,1]
[2,1,1,2,1,3] => [1,1,2,2,1,3]
[2,1,1,2,2,1,1] => [2,2,1,1,1,2,1]
[2,1,1,2,2,2] => [1,2,1,2,2,2]
[2,1,1,2,3,1] => [1,1,2,2,3,1]
[2,1,1,2,4] => [1,2,1,2,4]
[2,1,1,3,1,1,1] => [1,2,1,1,1,3,1]
[2,1,1,3,1,2] => [2,1,1,3,1,2]
[2,1,1,3,2,1] => [3,1,1,2,2,1]
[2,1,1,3,3] => [1,2,1,3,3]
[2,1,1,4,1,1] => [2,1,1,1,4,1]
[2,1,1,4,2] => [1,2,4,1,2]
[2,1,1,5,1] => [1,1,2,5,1]
[2,1,1,6] => [1,2,1,6]
[2,1,2,1,1,1,1,1] => [1,1,1,2,1,1,2,1]
[2,1,2,1,1,1,2] => [1,2,1,1,2,1,2]
[2,1,2,1,1,2,1] => [1,2,1,1,2,2,1]
[2,1,2,1,1,3] => [2,1,1,2,1,3]
[2,1,2,1,2,1,1] => [1,2,2,1,1,2,1]
[2,1,2,1,2,2] => [1,2,2,1,2,2]
[2,1,2,1,3,1] => [2,1,1,2,3,1]
[2,1,2,1,4] => [1,2,2,1,4]
[2,1,2,2,1,1,1] => [2,1,2,1,1,2,1]
[2,1,2,2,1,2] => [1,2,2,2,1,2]
[2,1,2,2,2,1] => [1,2,2,2,2,1]
[2,1,2,2,3] => [2,1,2,2,3]
[2,1,2,3,1,1] => [2,2,1,1,3,1]
[2,1,2,3,2] => [2,3,1,2,2]
[2,1,2,4,1] => [1,2,2,4,1]
[2,1,2,5] => [2,1,2,5]
[2,1,3,1,1,1,1] => [1,1,2,1,1,3,1]
[2,1,3,1,1,2] => [1,2,1,3,1,2]
[2,1,3,1,2,1] => [2,3,1,1,2,1]
[2,1,3,1,3] => [1,2,3,1,3]
[2,1,3,2,1,1] => [3,2,1,1,2,1]
[2,1,3,2,2] => [3,2,1,2,2]
[2,1,3,3,1] => [1,2,3,3,1]
[2,1,3,4] => [2,1,3,4]
[2,1,4,1,1,1] => [1,2,1,1,4,1]
[2,1,4,1,2] => [2,1,4,1,2]
[2,1,4,2,1] => [4,1,2,2,1]
[2,1,4,3] => [2,4,1,3]
[2,1,5,1,1] => [2,1,1,5,1]
[2,1,5,2] => [2,5,1,2]
[2,1,6,1] => [1,2,6,1]
[2,1,7] => [2,1,7]
[2,2,1,1,1,1,1,1] => [1,1,1,1,2,1,2,1]
[2,2,1,1,1,1,2] => [1,1,2,1,2,1,2]
[2,2,1,1,1,2,1] => [1,1,2,1,2,2,1]
[2,2,1,1,1,3] => [1,2,1,2,1,3]
[2,2,1,1,2,1,1] => [1,1,2,2,1,2,1]
[2,2,1,1,2,2] => [2,1,2,1,2,2]
[2,2,1,1,3,1] => [1,2,1,2,3,1]
[2,2,1,1,4] => [2,1,2,1,4]
[2,2,1,2,1,1,1] => [2,1,1,2,1,2,1]
[2,2,1,2,1,2] => [2,1,2,2,1,2]
[2,2,1,2,2,1] => [2,1,2,2,2,1]
[2,2,1,2,3] => [2,2,1,2,3]
[2,2,1,3,1,1] => [1,2,2,1,3,1]
[2,2,1,3,2] => [2,2,3,1,2]
[2,2,1,4,1] => [2,1,2,4,1]
[2,2,1,5] => [2,2,1,5]
[2,2,2,1,1,1,1] => [1,2,1,2,1,2,1]
[2,2,2,1,1,2] => [2,2,1,2,1,2]
[2,2,2,1,2,1] => [2,2,1,2,2,1]
[2,2,2,1,3] => [2,2,2,1,3]
[2,2,2,2,1,1] => [2,2,2,1,2,1]
[2,2,2,2,2] => [2,2,2,2,2]
[2,2,2,3,1] => [2,2,2,3,1]
[2,2,2,4] => [2,2,2,4]
[2,2,3,1,1,1] => [2,1,2,1,3,1]
[2,2,3,1,2] => [3,2,2,1,2]
[2,2,3,2,1] => [3,2,2,2,1]
[2,2,3,3] => [2,2,3,3]
[2,2,4,1,1] => [2,2,1,4,1]
[2,2,4,2] => [4,2,2,2]
[2,2,5,1] => [2,2,5,1]
[2,2,6] => [2,2,6]
[2,3,1,1,1,1,1] => [1,1,1,2,1,3,1]
[2,3,1,1,1,2] => [1,1,3,2,1,2]
[2,3,1,1,2,1] => [1,2,3,1,2,1]
[2,3,1,1,3] => [2,1,3,1,3]
[2,3,1,2,1,1] => [2,1,3,1,2,1]
[2,3,1,2,2] => [2,1,3,2,2]
[2,3,1,3,1] => [2,1,3,3,1]
[2,3,1,4] => [2,3,1,4]
[2,3,2,1,1,1] => [1,3,2,1,2,1]
[2,3,2,1,2] => [2,3,2,1,2]
[2,3,2,2,1] => [2,3,2,2,1]
[2,3,2,3] => [3,2,2,3]
[2,3,3,1,1] => [2,3,1,3,1]
[2,3,3,2] => [3,3,2,2]
[2,3,4,1] => [2,3,4,1]
[2,3,5] => [2,3,5]
[2,4,1,1,1,1] => [1,1,2,1,4,1]
[2,4,1,1,2] => [1,4,2,1,2]
[2,4,1,2,1] => [2,4,1,2,1]
[2,4,1,3] => [4,2,1,3]
[2,4,2,1,1] => [4,2,1,2,1]
[2,4,2,2] => [2,4,2,2]
[2,4,3,1] => [4,2,3,1]
[2,4,4] => [2,4,4]
[2,5,1,1,1] => [1,2,1,5,1]
[2,5,1,2] => [5,2,1,2]
[2,5,2,1] => [5,2,2,1]
[2,5,3] => [5,2,3]
[2,6,1,1] => [2,1,6,1]
[2,6,2] => [6,2,2]
[2,7,1] => [2,7,1]
[2,8] => [2,8]
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,3,1]
[3,1,1,1,1,1,2] => [1,1,1,1,1,3,2]
[3,1,1,1,1,2,1] => [3,1,1,1,1,2,1]
[3,1,1,1,1,3] => [1,1,1,3,1,3]
[3,1,1,1,2,1,1] => [1,3,1,1,1,2,1]
[3,1,1,1,2,2] => [1,1,1,2,3,2]
[3,1,1,1,3,1] => [1,1,1,3,3,1]
[3,1,1,1,4] => [1,1,3,1,4]
[3,1,1,2,1,1,1] => [1,1,3,1,1,2,1]
[3,1,1,2,1,2] => [2,1,1,1,3,2]
[3,1,1,2,2,1] => [1,3,1,2,2,1]
[3,1,1,2,3] => [1,1,3,2,3]
[3,1,1,3,1,1] => [3,1,1,1,3,1]
[3,1,1,3,2] => [1,1,3,3,2]
[3,1,1,4,1] => [1,1,3,4,1]
[3,1,1,5] => [1,3,1,5]
[3,1,2,1,1,1,1] => [1,1,1,3,1,2,1]
[3,1,2,1,1,2] => [1,2,1,1,3,2]
[3,1,2,1,2,1] => [1,1,3,2,2,1]
[3,1,2,1,3] => [3,1,2,1,3]
[3,1,2,2,1,1] => [3,1,2,1,2,1]
[3,1,2,2,2] => [1,2,2,3,2]
[3,1,2,3,1] => [3,1,2,3,1]
[3,1,2,4] => [1,3,2,4]
[3,1,3,1,1,1] => [1,3,1,1,3,1]
[3,1,3,1,2] => [3,1,1,3,2]
[3,1,3,2,1] => [3,3,1,2,1]
[3,1,3,3] => [3,1,3,3]
[3,1,4,1,1] => [3,1,1,4,1]
[3,1,4,2] => [1,3,4,2]
[3,1,5,1] => [1,3,5,1]
[3,1,6] => [3,1,6]
[3,2,1,1,1,1,1] => [1,1,1,1,3,2,1]
[3,2,1,1,1,2] => [1,1,2,1,3,2]
[3,2,1,1,2,1] => [1,1,2,3,2,1]
[3,2,1,1,3] => [1,3,2,1,3]
[3,2,1,2,1,1] => [2,1,1,3,2,1]
[3,2,1,2,2] => [2,1,2,3,2]
[3,2,1,3,1] => [1,3,2,3,1]
[3,2,1,4] => [3,2,1,4]
[3,2,2,1,1,1] => [1,2,1,3,2,1]
[3,2,2,1,2] => [2,2,1,3,2]
[3,2,2,2,1] => [2,2,3,2,1]
[3,2,2,3] => [2,3,2,3]
[3,2,3,1,1] => [3,2,1,3,1]
[3,2,3,2] => [2,3,3,2]
[3,2,4,1] => [3,2,4,1]
[3,2,5] => [3,2,5]
[3,3,1,1,1,1] => [1,1,3,1,3,1]
[3,3,1,1,2] => [1,3,1,3,2]
[3,3,1,2,1] => [1,3,3,2,1]
[3,3,1,3] => [3,3,1,3]
[3,3,2,1,1] => [3,1,3,2,1]
[3,3,2,2] => [3,2,3,2]
[3,3,3,1] => [3,3,3,1]
[3,3,4] => [3,3,4]
[3,4,1,1,1] => [1,3,1,4,1]
[3,4,1,2] => [3,1,4,2]
[3,4,2,1] => [3,4,2,1]
[3,4,3] => [4,3,3]
[3,5,1,1] => [3,1,5,1]
[3,5,2] => [3,5,2]
[3,6,1] => [3,6,1]
[3,7] => [3,7]
[4,1,1,1,1,1,1] => [1,1,1,1,1,4,1]
[4,1,1,1,1,2] => [1,1,1,1,4,2]
[4,1,1,1,2,1] => [4,1,1,1,2,1]
[4,1,1,1,3] => [1,1,1,4,3]
[4,1,1,2,1,1] => [1,4,1,1,2,1]
[4,1,1,2,2] => [1,1,2,4,2]
[4,1,1,3,1] => [4,1,1,3,1]
[4,1,1,4] => [1,4,1,4]
[4,1,2,1,1,1] => [1,1,4,1,2,1]
[4,1,2,1,2] => [2,1,1,4,2]
[4,1,2,2,1] => [1,4,2,2,1]
[4,1,2,3] => [1,2,4,3]
[4,1,3,1,1] => [1,4,1,3,1]
[4,1,3,2] => [4,1,3,2]
[4,1,4,1] => [1,4,4,1]
[4,1,5] => [4,1,5]
[4,2,1,1,1,1] => [1,1,1,4,2,1]
[4,2,1,1,2] => [1,2,1,4,2]
[4,2,1,2,1] => [1,2,4,2,1]
[4,2,1,3] => [2,1,4,3]
[4,2,2,1,1] => [2,1,4,2,1]
[4,2,2,2] => [2,2,4,2]
[4,2,3,1] => [2,4,3,1]
[4,2,4] => [4,2,4]
[4,3,1,1,1] => [1,1,4,3,1]
[4,3,1,2] => [1,4,3,2]
[4,3,2,1] => [4,3,2,1]
[4,3,3] => [3,4,3]
[4,4,1,1] => [4,1,4,1]
[4,4,2] => [4,4,2]
[4,5,1] => [4,5,1]
[4,6] => [4,6]
[5,1,1,1,1,1] => [1,1,1,1,5,1]
[5,1,1,1,2] => [1,1,1,5,2]
[5,1,1,2,1] => [5,1,1,2,1]
[5,1,1,3] => [1,1,5,3]
[5,1,2,1,1] => [1,5,1,2,1]
[5,1,2,2] => [1,2,5,2]
[5,1,3,1] => [5,1,3,1]
[5,1,4] => [1,5,4]
[5,2,1,1,1] => [1,1,5,2,1]
[5,2,1,2] => [2,1,5,2]
[5,2,2,1] => [2,5,2,1]
[5,2,3] => [2,5,3]
[5,3,1,1] => [1,5,3,1]
[5,3,2] => [5,3,2]
[5,4,1] => [5,4,1]
[5,5] => [5,5]
[6,1,1,1,1] => [1,1,1,6,1]
[6,1,1,2] => [1,1,6,2]
[6,1,2,1] => [6,1,2,1]
[6,1,3] => [1,6,3]
[6,2,1,1] => [1,6,2,1]
[6,2,2] => [2,6,2]
[6,3,1] => [6,3,1]
[6,4] => [6,4]
[7,1,1,1] => [1,1,7,1]
[7,1,2] => [1,7,2]
[7,2,1] => [7,2,1]
[7,3] => [7,3]
[8,1,1] => [1,8,1]
[8,2] => [8,2]
[9,1] => [9,1]
[10] => [10]
-----------------------------------------------------------------------------
Created: Sep 12, 2023 at 11:42 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 12, 2023 at 11:42 by Martin Rubey