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* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St000919
-----------------------------------------------------------------------------
Collection: Binary trees
-----------------------------------------------------------------------------
Description: The number of maximal left branches of a binary tree.
A maximal left branch of a binary tree is an inclusion wise maximal path which consists of left edges only. This statistic records the number of distinct maximal left branches in the tree.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(B):
return B.twisting_number()[0]
-----------------------------------------------------------------------------
Statistic values:
[.,[.,.]] => 0
[[.,.],.] => 1
[.,[.,[.,.]]] => 0
[.,[[.,.],.]] => 1
[[.,.],[.,.]] => 1
[[.,[.,.]],.] => 1
[[[.,.],.],.] => 1
[.,[.,[.,[.,.]]]] => 0
[.,[.,[[.,.],.]]] => 1
[.,[[.,.],[.,.]]] => 1
[.,[[.,[.,.]],.]] => 1
[.,[[[.,.],.],.]] => 1
[[.,.],[.,[.,.]]] => 1
[[.,.],[[.,.],.]] => 2
[[.,[.,.]],[.,.]] => 1
[[[.,.],.],[.,.]] => 1
[[.,[.,[.,.]]],.] => 1
[[.,[[.,.],.]],.] => 2
[[[.,.],[.,.]],.] => 1
[[[.,[.,.]],.],.] => 1
[[[[.,.],.],.],.] => 1
[.,[.,[.,[.,[.,.]]]]] => 0
[.,[.,[.,[[.,.],.]]]] => 1
[.,[.,[[.,.],[.,.]]]] => 1
[.,[.,[[.,[.,.]],.]]] => 1
[.,[.,[[[.,.],.],.]]] => 1
[.,[[.,.],[.,[.,.]]]] => 1
[.,[[.,.],[[.,.],.]]] => 2
[.,[[.,[.,.]],[.,.]]] => 1
[.,[[[.,.],.],[.,.]]] => 1
[.,[[.,[.,[.,.]]],.]] => 1
[.,[[.,[[.,.],.]],.]] => 2
[.,[[[.,.],[.,.]],.]] => 1
[.,[[[.,[.,.]],.],.]] => 1
[.,[[[[.,.],.],.],.]] => 1
[[.,.],[.,[.,[.,.]]]] => 1
[[.,.],[.,[[.,.],.]]] => 2
[[.,.],[[.,.],[.,.]]] => 2
[[.,.],[[.,[.,.]],.]] => 2
[[.,.],[[[.,.],.],.]] => 2
[[.,[.,.]],[.,[.,.]]] => 1
[[.,[.,.]],[[.,.],.]] => 2
[[[.,.],.],[.,[.,.]]] => 1
[[[.,.],.],[[.,.],.]] => 2
[[.,[.,[.,.]]],[.,.]] => 1
[[.,[[.,.],.]],[.,.]] => 2
[[[.,.],[.,.]],[.,.]] => 1
[[[.,[.,.]],.],[.,.]] => 1
[[[[.,.],.],.],[.,.]] => 1
[[.,[.,[.,[.,.]]]],.] => 1
[[.,[.,[[.,.],.]]],.] => 2
[[.,[[.,.],[.,.]]],.] => 2
[[.,[[.,[.,.]],.]],.] => 2
[[.,[[[.,.],.],.]],.] => 2
[[[.,.],[.,[.,.]]],.] => 1
[[[.,.],[[.,.],.]],.] => 2
[[[.,[.,.]],[.,.]],.] => 1
[[[[.,.],.],[.,.]],.] => 1
[[[.,[.,[.,.]]],.],.] => 1
[[[.,[[.,.],.]],.],.] => 2
[[[[.,.],[.,.]],.],.] => 1
[[[[.,[.,.]],.],.],.] => 1
[[[[[.,.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => 1
[.,[.,[.,[[.,[.,.]],.]]]] => 1
[.,[.,[.,[[[.,.],.],.]]]] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => 1
[.,[.,[[.,.],[[.,.],.]]]] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => 1
[.,[.,[[[.,.],.],[.,.]]]] => 1
[.,[.,[[.,[.,[.,.]]],.]]] => 1
[.,[.,[[.,[[.,.],.]],.]]] => 2
[.,[.,[[[.,.],[.,.]],.]]] => 1
[.,[.,[[[.,[.,.]],.],.]]] => 1
[.,[.,[[[[.,.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => 1
[.,[[.,.],[.,[[.,.],.]]]] => 2
[.,[[.,.],[[.,.],[.,.]]]] => 2
[.,[[.,.],[[.,[.,.]],.]]] => 2
[.,[[.,.],[[[.,.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => 1
[.,[[.,[.,.]],[[.,.],.]]] => 2
[.,[[[.,.],.],[.,[.,.]]]] => 1
[.,[[[.,.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => 1
[.,[[.,[[.,.],.]],[.,.]]] => 2
[.,[[[.,.],[.,.]],[.,.]]] => 1
[.,[[[.,[.,.]],.],[.,.]]] => 1
[.,[[[[.,.],.],.],[.,.]]] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => 1
[.,[[.,[.,[[.,.],.]]],.]] => 2
[.,[[.,[[.,.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,.]],.]],.]] => 2
[.,[[.,[[[.,.],.],.]],.]] => 2
[.,[[[.,.],[.,[.,.]]],.]] => 1
[.,[[[.,.],[[.,.],.]],.]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => 1
[.,[[[[.,.],.],[.,.]],.]] => 1
[.,[[[.,[.,[.,.]]],.],.]] => 1
[.,[[[.,[[.,.],.]],.],.]] => 2
[.,[[[[.,.],[.,.]],.],.]] => 1
[.,[[[[.,[.,.]],.],.],.]] => 1
[.,[[[[[.,.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => 1
[[.,.],[.,[.,[[.,.],.]]]] => 2
[[.,.],[.,[[.,.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,.]],.]]] => 2
[[.,.],[.,[[[.,.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => 2
[[.,.],[[.,.],[[.,.],.]]] => 3
[[.,.],[[.,[.,.]],[.,.]]] => 2
[[.,.],[[[.,.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => 2
[[.,.],[[.,[[.,.],.]],.]] => 3
[[.,.],[[[.,.],[.,.]],.]] => 2
[[.,.],[[[.,[.,.]],.],.]] => 2
[[.,.],[[[[.,.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => 1
[[.,[.,.]],[.,[[.,.],.]]] => 2
[[.,[.,.]],[[.,.],[.,.]]] => 2
[[.,[.,.]],[[.,[.,.]],.]] => 2
[[.,[.,.]],[[[.,.],.],.]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => 1
[[[.,.],.],[.,[[.,.],.]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => 2
[[[.,.],.],[[.,[.,.]],.]] => 2
[[[.,.],.],[[[.,.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => 1
[[.,[.,[.,.]]],[[.,.],.]] => 2
[[.,[[.,.],.]],[.,[.,.]]] => 2
[[.,[[.,.],.]],[[.,.],.]] => 3
[[[.,.],[.,.]],[.,[.,.]]] => 1
[[[.,.],[.,.]],[[.,.],.]] => 2
[[[.,[.,.]],.],[.,[.,.]]] => 1
[[[.,[.,.]],.],[[.,.],.]] => 2
[[[[.,.],.],.],[.,[.,.]]] => 1
[[[[.,.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => 1
[[.,[.,[[.,.],.]]],[.,.]] => 2
[[.,[[.,.],[.,.]]],[.,.]] => 2
[[.,[[.,[.,.]],.]],[.,.]] => 2
[[.,[[[.,.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => 1
[[[.,.],[[.,.],.]],[.,.]] => 2
[[[.,[.,.]],[.,.]],[.,.]] => 1
[[[[.,.],.],[.,.]],[.,.]] => 1
[[[.,[.,[.,.]]],.],[.,.]] => 1
[[[.,[[.,.],.]],.],[.,.]] => 2
[[[[.,.],[.,.]],.],[.,.]] => 1
[[[[.,[.,.]],.],.],[.,.]] => 1
[[[[[.,.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => 1
[[.,[.,[.,[[.,.],.]]]],.] => 2
[[.,[.,[[.,.],[.,.]]]],.] => 2
[[.,[.,[[.,[.,.]],.]]],.] => 2
[[.,[.,[[[.,.],.],.]]],.] => 2
[[.,[[.,.],[.,[.,.]]]],.] => 2
[[.,[[.,.],[[.,.],.]]],.] => 3
[[.,[[.,[.,.]],[.,.]]],.] => 2
[[.,[[[.,.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,.]]],.]],.] => 2
[[.,[[.,[[.,.],.]],.]],.] => 3
[[.,[[[.,.],[.,.]],.]],.] => 2
[[.,[[[.,[.,.]],.],.]],.] => 2
[[.,[[[[.,.],.],.],.]],.] => 2
[[[.,.],[.,[.,[.,.]]]],.] => 1
[[[.,.],[.,[[.,.],.]]],.] => 2
[[[.,.],[[.,.],[.,.]]],.] => 2
[[[.,.],[[.,[.,.]],.]],.] => 2
[[[.,.],[[[.,.],.],.]],.] => 2
[[[.,[.,.]],[.,[.,.]]],.] => 1
[[[.,[.,.]],[[.,.],.]],.] => 2
[[[[.,.],.],[.,[.,.]]],.] => 1
[[[[.,.],.],[[.,.],.]],.] => 2
[[[.,[.,[.,.]]],[.,.]],.] => 1
[[[.,[[.,.],.]],[.,.]],.] => 2
[[[[.,.],[.,.]],[.,.]],.] => 1
[[[[.,[.,.]],.],[.,.]],.] => 1
[[[[[.,.],.],.],[.,.]],.] => 1
[[[.,[.,[.,[.,.]]]],.],.] => 1
[[[.,[.,[[.,.],.]]],.],.] => 2
[[[.,[[.,.],[.,.]]],.],.] => 2
[[[.,[[.,[.,.]],.]],.],.] => 2
[[[.,[[[.,.],.],.]],.],.] => 2
[[[[.,.],[.,[.,.]]],.],.] => 1
[[[[.,.],[[.,.],.]],.],.] => 2
[[[[.,[.,.]],[.,.]],.],.] => 1
[[[[[.,.],.],[.,.]],.],.] => 1
[[[[.,[.,[.,.]]],.],.],.] => 1
[[[[.,[[.,.],.]],.],.],.] => 2
[[[[[.,.],[.,.]],.],.],.] => 1
[[[[[.,[.,.]],.],.],.],.] => 1
[[[[[[.,.],.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 2
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 1
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 1
[.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 1
[.,[.,[[[.,.],.],[[.,.],.]]]] => 2
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 1
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 1
[.,[.,[[[[.,.],.],.],[.,.]]]] => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 2
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 2
[.,[.,[[.,[[[.,.],.],.]],.]]] => 2
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 1
[.,[.,[[[.,.],[[.,.],.]],.]]] => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 1
[.,[.,[[[[.,.],.],[.,.]],.]]] => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => 2
[.,[.,[[[[.,.],[.,.]],.],.]]] => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
[.,[[.,.],[[.,[[.,.],.]],.]]] => 3
[.,[[.,.],[[[.,.],[.,.]],.]]] => 2
[.,[[.,.],[[[.,[.,.]],.],.]]] => 2
[.,[[.,.],[[[[.,.],.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[.,[[.,[.,.]],[[[.,.],.],.]]] => 2
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 1
[.,[[[.,.],.],[.,[[.,.],.]]]] => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => 2
[.,[[[.,.],.],[[[.,.],.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => 3
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 1
[.,[[[.,.],[.,.]],[[.,.],.]]] => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 1
[.,[[[.,[.,.]],.],[[.,.],.]]] => 2
[.,[[[[.,.],.],.],[.,[.,.]]]] => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 1
[.,[[[.,.],[[.,.],.]],[.,.]]] => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 1
[.,[[[[.,.],.],[.,.]],[.,.]]] => 1
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => 1
[.,[[[[.,[.,.]],.],.],[.,.]]] => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 2
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 2
[.,[[.,[.,[[[.,.],.],.]]],.]] => 2
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[.,[[.,[[.,.],[[.,.],.]]],.]] => 3
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[.,[[.,[[[.,.],.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 2
[.,[[.,[[.,[[.,.],.]],.]],.]] => 3
[.,[[.,[[[.,.],[.,.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],.],.]],.]] => 2
[.,[[.,[[[[.,.],.],.],.]],.]] => 2
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 1
[.,[[[.,.],[.,[[.,.],.]]],.]] => 2
[.,[[[.,.],[[.,.],[.,.]]],.]] => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => 2
[.,[[[.,.],[[[.,.],.],.]],.]] => 2
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 1
[.,[[[.,[.,.]],[[.,.],.]],.]] => 2
[.,[[[[.,.],.],[.,[.,.]]],.]] => 1
[.,[[[[.,.],.],[[.,.],.]],.]] => 2
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 1
[.,[[[.,[[.,.],.]],[.,.]],.]] => 2
[.,[[[[.,.],[.,.]],[.,.]],.]] => 1
[.,[[[[.,[.,.]],.],[.,.]],.]] => 1
[.,[[[[[.,.],.],.],[.,.]],.]] => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => 2
[.,[[[.,[[.,.],[.,.]]],.],.]] => 2
[.,[[[.,[[.,[.,.]],.]],.],.]] => 2
[.,[[[.,[[[.,.],.],.]],.],.]] => 2
[.,[[[[.,.],[.,[.,.]]],.],.]] => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => 2
[.,[[[[.,[.,.]],[.,.]],.],.]] => 1
[.,[[[[[.,.],.],[.,.]],.],.]] => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => 2
[.,[[[[[.,.],[.,.]],.],.],.]] => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => 3
[[.,.],[.,[[[.,.],[.,.]],.]]] => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[[.,.],[[.,.],[[[.,.],.],.]]] => 3
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => 3
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => 3
[[.,.],[[[.,.],[.,.]],[.,.]]] => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[[.,.],[[.,[[.,[.,.]],.]],.]] => 3
[[.,.],[[.,[[[.,.],.],.]],.]] => 3
[[.,.],[[[.,.],[.,[.,.]]],.]] => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => 3
[[.,.],[[[.,[.,.]],[.,.]],.]] => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => 3
[[.,.],[[[[.,.],[.,.]],.],.]] => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => 2
[[.,.],[[[[[.,.],.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[[.,[.,.]],[.,[[[.,.],.],.]]] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[[.,[.,.]],[[.,[[.,.],.]],.]] => 3
[[.,[.,.]],[[[.,.],[.,.]],.]] => 2
[[.,[.,.]],[[[.,[.,.]],.],.]] => 2
[[.,[.,.]],[[[[.,.],.],.],.]] => 2
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 1
[[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => 3
[[[.,.],.],[[[.,.],[.,.]],.]] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => 2
[[[.,.],.],[[[[.,.],.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[[.,[.,[.,.]]],[[[.,.],.],.]] => 2
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => 3
[[.,[[.,.],.]],[[.,.],[.,.]]] => 3
[[.,[[.,.],.]],[[.,[.,.]],.]] => 3
[[.,[[.,.],.]],[[[.,.],.],.]] => 3
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[[[.,.],[.,.]],[.,[[.,.],.]]] => 2
[[[.,.],[.,.]],[[.,.],[.,.]]] => 2
[[[.,.],[.,.]],[[.,[.,.]],.]] => 2
[[[.,.],[.,.]],[[[.,.],.],.]] => 2
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[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
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[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 4
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => 2
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => 3
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[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => 3
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[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 3
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 3
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 3
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 3
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 2
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 3
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 2
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 2
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 2
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 3
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 2
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 2
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 3
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 3
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 3
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 3
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 4
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 3
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 3
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 4
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 3
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => 3
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 2
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 3
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 3
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 3
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => 3
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 2
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 3
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 2
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 2
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 2
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 2
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 2
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 3
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 3
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 3
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => 3
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 2
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => 3
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 2
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => 2
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 2
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => 3
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => 2
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => 2
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 1
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 2
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 2
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 3
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 2
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 2
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 2
-----------------------------------------------------------------------------
Created: Jul 29, 2017 at 22:17 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Jul 29, 2017 at 22:17 by Martin Rubey