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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St000568
-----------------------------------------------------------------------------
Collection: Binary trees
-----------------------------------------------------------------------------
Description: The hook number of a binary tree.
A hook of a binary tree is a vertex together with is left- and its right-most branch. Then there is a unique decomposition of the tree into hooks and the hook number is the number of hooks in this decomposition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(T):
return T.hook_number()
-----------------------------------------------------------------------------
Statistic values:
[.,[.,.]] => 1
[[.,.],.] => 1
[.,[.,[.,.]]] => 1
[.,[[.,.],.]] => 2
[[.,.],[.,.]] => 1
[[.,[.,.]],.] => 2
[[[.,.],.],.] => 1
[.,[.,[.,[.,.]]]] => 1
[.,[.,[[.,.],.]]] => 2
[.,[[.,.],[.,.]]] => 2
[.,[[.,[.,.]],.]] => 2
[.,[[[.,.],.],.]] => 2
[[.,.],[.,[.,.]]] => 1
[[.,.],[[.,.],.]] => 2
[[.,[.,.]],[.,.]] => 2
[[[.,.],.],[.,.]] => 1
[[.,[.,[.,.]]],.] => 2
[[.,[[.,.],.]],.] => 2
[[[.,.],[.,.]],.] => 2
[[[.,[.,.]],.],.] => 2
[[[[.,.],.],.],.] => 1
[.,[.,[.,[.,[.,.]]]]] => 1
[.,[.,[.,[[.,.],.]]]] => 2
[.,[.,[[.,.],[.,.]]]] => 2
[.,[.,[[.,[.,.]],.]]] => 2
[.,[.,[[[.,.],.],.]]] => 2
[.,[[.,.],[.,[.,.]]]] => 2
[.,[[.,.],[[.,.],.]]] => 3
[.,[[.,[.,.]],[.,.]]] => 2
[.,[[[.,.],.],[.,.]]] => 2
[.,[[.,[.,[.,.]]],.]] => 2
[.,[[.,[[.,.],.]],.]] => 3
[.,[[[.,.],[.,.]],.]] => 2
[.,[[[.,[.,.]],.],.]] => 3
[.,[[[[.,.],.],.],.]] => 2
[[.,.],[.,[.,[.,.]]]] => 1
[[.,.],[.,[[.,.],.]]] => 2
[[.,.],[[.,.],[.,.]]] => 2
[[.,.],[[.,[.,.]],.]] => 2
[[.,.],[[[.,.],.],.]] => 2
[[.,[.,.]],[.,[.,.]]] => 2
[[.,[.,.]],[[.,.],.]] => 3
[[[.,.],.],[.,[.,.]]] => 1
[[[.,.],.],[[.,.],.]] => 2
[[.,[.,[.,.]]],[.,.]] => 2
[[.,[[.,.],.]],[.,.]] => 2
[[[.,.],[.,.]],[.,.]] => 2
[[[.,[.,.]],.],[.,.]] => 2
[[[[.,.],.],.],[.,.]] => 1
[[.,[.,[.,[.,.]]]],.] => 2
[[.,[.,[[.,.],.]]],.] => 3
[[.,[[.,.],[.,.]]],.] => 2
[[.,[[.,[.,.]],.]],.] => 3
[[.,[[[.,.],.],.]],.] => 2
[[[.,.],[.,[.,.]]],.] => 2
[[[.,.],[[.,.],.]],.] => 2
[[[.,[.,.]],[.,.]],.] => 3
[[[[.,.],.],[.,.]],.] => 2
[[[.,[.,[.,.]]],.],.] => 2
[[[.,[[.,.],.]],.],.] => 2
[[[[.,.],[.,.]],.],.] => 2
[[[[.,[.,.]],.],.],.] => 2
[[[[[.,.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => 2
[.,[.,[.,[[.,.],[.,.]]]]] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => 2
[.,[.,[.,[[[.,.],.],.]]]] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => 2
[.,[.,[[.,.],[[.,.],.]]]] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => 2
[.,[.,[[[.,.],.],[.,.]]]] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => 2
[.,[.,[[.,[[.,.],.]],.]]] => 3
[.,[.,[[[.,.],[.,.]],.]]] => 2
[.,[.,[[[.,[.,.]],.],.]]] => 3
[.,[.,[[[[.,.],.],.],.]]] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => 2
[.,[[.,.],[.,[[.,.],.]]]] => 3
[.,[[.,.],[[.,.],[.,.]]]] => 3
[.,[[.,.],[[.,[.,.]],.]]] => 3
[.,[[.,.],[[[.,.],.],.]]] => 3
[.,[[.,[.,.]],[.,[.,.]]]] => 2
[.,[[.,[.,.]],[[.,.],.]]] => 3
[.,[[[.,.],.],[.,[.,.]]]] => 2
[.,[[[.,.],.],[[.,.],.]]] => 3
[.,[[.,[.,[.,.]]],[.,.]]] => 2
[.,[[.,[[.,.],.]],[.,.]]] => 3
[.,[[[.,.],[.,.]],[.,.]]] => 2
[.,[[[.,[.,.]],.],[.,.]]] => 3
[.,[[[[.,.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => 2
[.,[[.,[.,[[.,.],.]]],.]] => 3
[.,[[.,[[.,.],[.,.]]],.]] => 3
[.,[[.,[[.,[.,.]],.]],.]] => 3
[.,[[.,[[[.,.],.],.]],.]] => 3
[.,[[[.,.],[.,[.,.]]],.]] => 2
[.,[[[.,.],[[.,.],.]],.]] => 3
[.,[[[.,[.,.]],[.,.]],.]] => 3
[.,[[[[.,.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,.]]],.],.]] => 3
[.,[[[.,[[.,.],.]],.],.]] => 3
[.,[[[[.,.],[.,.]],.],.]] => 3
[.,[[[[.,[.,.]],.],.],.]] => 3
[.,[[[[[.,.],.],.],.],.]] => 2
[[.,.],[.,[.,[.,[.,.]]]]] => 1
[[.,.],[.,[.,[[.,.],.]]]] => 2
[[.,.],[.,[[.,.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,.]],.]]] => 2
[[.,.],[.,[[[.,.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => 2
[[.,.],[[.,.],[[.,.],.]]] => 3
[[.,.],[[.,[.,.]],[.,.]]] => 2
[[.,.],[[[.,.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => 2
[[.,.],[[.,[[.,.],.]],.]] => 3
[[.,.],[[[.,.],[.,.]],.]] => 2
[[.,.],[[[.,[.,.]],.],.]] => 3
[[.,.],[[[[.,.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => 2
[[.,[.,.]],[.,[[.,.],.]]] => 3
[[.,[.,.]],[[.,.],[.,.]]] => 3
[[.,[.,.]],[[.,[.,.]],.]] => 3
[[.,[.,.]],[[[.,.],.],.]] => 3
[[[.,.],.],[.,[.,[.,.]]]] => 1
[[[.,.],.],[.,[[.,.],.]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => 2
[[[.,.],.],[[.,[.,.]],.]] => 2
[[[.,.],.],[[[.,.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => 2
[[.,[.,[.,.]]],[[.,.],.]] => 3
[[.,[[.,.],.]],[.,[.,.]]] => 2
[[.,[[.,.],.]],[[.,.],.]] => 3
[[[.,.],[.,.]],[.,[.,.]]] => 2
[[[.,.],[.,.]],[[.,.],.]] => 3
[[[.,[.,.]],.],[.,[.,.]]] => 2
[[[.,[.,.]],.],[[.,.],.]] => 3
[[[[.,.],.],.],[.,[.,.]]] => 1
[[[[.,.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => 2
[[.,[.,[[.,.],.]]],[.,.]] => 3
[[.,[[.,.],[.,.]]],[.,.]] => 2
[[.,[[.,[.,.]],.]],[.,.]] => 3
[[.,[[[.,.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => 2
[[[.,.],[[.,.],.]],[.,.]] => 2
[[[.,[.,.]],[.,.]],[.,.]] => 3
[[[[.,.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,.]]],.],[.,.]] => 2
[[[.,[[.,.],.]],.],[.,.]] => 2
[[[[.,.],[.,.]],.],[.,.]] => 2
[[[[.,[.,.]],.],.],[.,.]] => 2
[[[[[.,.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => 2
[[.,[.,[.,[[.,.],.]]]],.] => 3
[[.,[.,[[.,.],[.,.]]]],.] => 3
[[.,[.,[[.,[.,.]],.]]],.] => 3
[[.,[.,[[[.,.],.],.]]],.] => 3
[[.,[[.,.],[.,[.,.]]]],.] => 2
[[.,[[.,.],[[.,.],.]]],.] => 3
[[.,[[.,[.,.]],[.,.]]],.] => 3
[[.,[[[.,.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,.]]],.]],.] => 3
[[.,[[.,[[.,.],.]],.]],.] => 3
[[.,[[[.,.],[.,.]],.]],.] => 3
[[.,[[[.,[.,.]],.],.]],.] => 3
[[.,[[[[.,.],.],.],.]],.] => 2
[[[.,.],[.,[.,[.,.]]]],.] => 2
[[[.,.],[.,[[.,.],.]]],.] => 3
[[[.,.],[[.,.],[.,.]]],.] => 2
[[[.,.],[[.,[.,.]],.]],.] => 3
[[[.,.],[[[.,.],.],.]],.] => 2
[[[.,[.,.]],[.,[.,.]]],.] => 3
[[[.,[.,.]],[[.,.],.]],.] => 3
[[[[.,.],.],[.,[.,.]]],.] => 2
[[[[.,.],.],[[.,.],.]],.] => 2
[[[.,[.,[.,.]]],[.,.]],.] => 3
[[[.,[[.,.],.]],[.,.]],.] => 3
[[[[.,.],[.,.]],[.,.]],.] => 3
[[[[.,[.,.]],.],[.,.]],.] => 3
[[[[[.,.],.],.],[.,.]],.] => 2
[[[.,[.,[.,[.,.]]]],.],.] => 2
[[[.,[.,[[.,.],.]]],.],.] => 3
[[[.,[[.,.],[.,.]]],.],.] => 2
[[[.,[[.,[.,.]],.]],.],.] => 3
[[[.,[[[.,.],.],.]],.],.] => 2
[[[[.,.],[.,[.,.]]],.],.] => 2
[[[[.,.],[[.,.],.]],.],.] => 2
[[[[.,[.,.]],[.,.]],.],.] => 3
[[[[[.,.],.],[.,.]],.],.] => 2
[[[[.,[.,[.,.]]],.],.],.] => 2
[[[[.,[[.,.],.]],.],.],.] => 2
[[[[[.,.],[.,.]],.],.],.] => 2
[[[[[.,[.,.]],.],.],.],.] => 2
[[[[[[.,.],.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 2
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 3
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 3
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 2
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 3
[.,[.,[.,[[[[.,.],.],.],.]]]] => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 3
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 3
[.,[.,[[.,.],[[[.,.],.],.]]]] => 3
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 3
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[.,[.,[[[.,.],.],[[.,.],.]]]] => 3
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 3
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 3
[.,[.,[[[[.,.],.],.],[.,.]]]] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 2
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 3
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 3
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 3
[.,[.,[[.,[[[.,.],.],.]],.]]] => 3
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 2
[.,[.,[[[.,.],[[.,.],.]],.]]] => 3
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 3
[.,[.,[[[[.,.],.],[.,.]],.]]] => 2
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 3
[.,[.,[[[.,[[.,.],.]],.],.]]] => 3
[.,[.,[[[[.,.],[.,.]],.],.]]] => 3
[.,[.,[[[[.,[.,.]],.],.],.]]] => 3
[.,[.,[[[[[.,.],.],.],.],.]]] => 2
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 3
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 3
[.,[[.,.],[.,[[[.,.],.],.]]]] => 3
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[.,[[.,.],[[.,.],[[.,.],.]]]] => 4
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[.,[[.,.],[[[.,.],.],[.,.]]]] => 3
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 3
[.,[[.,.],[[.,[[.,.],.]],.]]] => 4
[.,[[.,.],[[[.,.],[.,.]],.]]] => 3
[.,[[.,.],[[[.,[.,.]],.],.]]] => 4
[.,[[.,.],[[[[.,.],.],.],.]]] => 3
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 3
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 3
[.,[[.,[.,.]],[[[.,.],.],.]]] => 3
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => 3
[.,[[[.,.],.],[[.,.],[.,.]]]] => 3
[.,[[[.,.],.],[[.,[.,.]],.]]] => 3
[.,[[[.,.],.],[[[.,.],.],.]]] => 3
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 3
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 3
[.,[[.,[[.,.],.]],[[.,.],.]]] => 4
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => 3
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 3
[.,[[[.,[.,.]],.],[[.,.],.]]] => 4
[.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => 3
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 3
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 3
[.,[[.,[[[.,.],.],.]],[.,.]]] => 3
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => 3
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 3
[.,[[[[.,.],.],[.,.]],[.,.]]] => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 3
[.,[[[.,[[.,.],.]],.],[.,.]]] => 3
[.,[[[[.,.],[.,.]],.],[.,.]]] => 3
[.,[[[[.,[.,.]],.],.],[.,.]]] => 3
[.,[[[[[.,.],.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 3
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 3
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 3
[.,[[.,[.,[[[.,.],.],.]]],.]] => 3
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 3
[.,[[.,[[.,.],[[.,.],.]]],.]] => 4
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 3
[.,[[.,[[[.,.],.],[.,.]]],.]] => 3
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 3
[.,[[.,[[.,[[.,.],.]],.]],.]] => 4
[.,[[.,[[[.,.],[.,.]],.]],.]] => 3
[.,[[.,[[[.,[.,.]],.],.]],.]] => 4
[.,[[.,[[[[.,.],.],.],.]],.]] => 3
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 2
[.,[[[.,.],[.,[[.,.],.]]],.]] => 3
[.,[[[.,.],[[.,.],[.,.]]],.]] => 3
[.,[[[.,.],[[.,[.,.]],.]],.]] => 3
[.,[[[.,.],[[[.,.],.],.]],.]] => 3
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 3
[.,[[[.,[.,.]],[[.,.],.]],.]] => 4
[.,[[[[.,.],.],[.,[.,.]]],.]] => 2
[.,[[[[.,.],.],[[.,.],.]],.]] => 3
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 3
[.,[[[.,[[.,.],.]],[.,.]],.]] => 3
[.,[[[[.,.],[.,.]],[.,.]],.]] => 3
[.,[[[[.,[.,.]],.],[.,.]],.]] => 3
[.,[[[[[.,.],.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 3
[.,[[[.,[.,[[.,.],.]]],.],.]] => 4
[.,[[[.,[[.,.],[.,.]]],.],.]] => 3
[.,[[[.,[[.,[.,.]],.]],.],.]] => 4
[.,[[[.,[[[.,.],.],.]],.],.]] => 3
[.,[[[[.,.],[.,[.,.]]],.],.]] => 3
[.,[[[[.,.],[[.,.],.]],.],.]] => 3
[.,[[[[.,[.,.]],[.,.]],.],.]] => 4
[.,[[[[[.,.],.],[.,.]],.],.]] => 3
[.,[[[[.,[.,[.,.]]],.],.],.]] => 3
[.,[[[[.,[[.,.],.]],.],.],.]] => 3
[.,[[[[[.,.],[.,.]],.],.],.]] => 3
[.,[[[[[.,[.,.]],.],.],.],.]] => 3
[.,[[[[[[.,.],.],.],.],.],.]] => 2
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => 3
[[.,.],[.,[[[.,.],[.,.]],.]]] => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => 3
[[.,.],[.,[[[[.,.],.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[[.,.],[[.,.],[[[.,.],.],.]]] => 3
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => 3
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => 3
[[.,.],[[[.,.],[.,.]],[.,.]]] => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => 3
[[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[[.,.],[[.,[[.,[.,.]],.]],.]] => 3
[[.,.],[[.,[[[.,.],.],.]],.]] => 3
[[.,.],[[[.,.],[.,[.,.]]],.]] => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => 3
[[.,.],[[[.,[.,.]],[.,.]],.]] => 3
[[.,.],[[[[.,.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => 3
[[.,.],[[[.,[[.,.],.]],.],.]] => 3
[[.,.],[[[[.,.],[.,.]],.],.]] => 3
[[.,.],[[[[.,[.,.]],.],.],.]] => 3
[[.,.],[[[[[.,.],.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 3
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 3
[[.,[.,.]],[.,[[[.,.],.],.]]] => 3
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => 4
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[[.,[.,.]],[[[.,.],.],[.,.]]] => 3
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 3
[[.,[.,.]],[[.,[[.,.],.]],.]] => 4
[[.,[.,.]],[[[.,.],[.,.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],.],.]] => 4
[[.,[.,.]],[[[[.,.],.],.],.]] => 3
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 1
[[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => 3
[[[.,.],.],[[[.,.],[.,.]],.]] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => 3
[[[.,.],.],[[[[.,.],.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 3
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 3
[[.,[.,[.,.]]],[[[.,.],.],.]] => 3
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => 3
[[.,[[.,.],.]],[[.,.],[.,.]]] => 3
[[.,[[.,.],.]],[[.,[.,.]],.]] => 3
[[.,[[.,.],.]],[[[.,.],.],.]] => 3
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 2
[[[.,.],[.,.]],[.,[[.,.],.]]] => 3
[[[.,.],[.,.]],[[.,.],[.,.]]] => 3
[[[.,.],[.,.]],[[.,[.,.]],.]] => 3
[[[.,.],[.,.]],[[[.,.],.],.]] => 3
[[[.,[.,.]],.],[.,[.,[.,.]]]] => 2
[[[.,[.,.]],.],[.,[[.,.],.]]] => 3
[[[.,[.,.]],.],[[.,.],[.,.]]] => 3
[[[.,[.,.]],.],[[.,[.,.]],.]] => 3
[[[.,[.,.]],.],[[[.,.],.],.]] => 3
[[[[.,.],.],.],[.,[.,[.,.]]]] => 1
[[[[.,.],.],.],[.,[[.,.],.]]] => 2
[[[[.,.],.],.],[[.,.],[.,.]]] => 2
[[[[.,.],.],.],[[.,[.,.]],.]] => 2
[[[[.,.],.],.],[[[.,.],.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[[.,[.,[.,[.,.]]]],[[.,.],.]] => 3
[[.,[.,[[.,.],.]]],[.,[.,.]]] => 3
[[.,[.,[[.,.],.]]],[[.,.],.]] => 4
[[.,[[.,.],[.,.]]],[.,[.,.]]] => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => 3
[[.,[[.,[.,.]],.]],[.,[.,.]]] => 3
[[.,[[.,[.,.]],.]],[[.,.],.]] => 4
[[.,[[[.,.],.],.]],[.,[.,.]]] => 2
[[.,[[[.,.],.],.]],[[.,.],.]] => 3
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => 3
[[[.,.],[[.,.],.]],[.,[.,.]]] => 2
[[[.,.],[[.,.],.]],[[.,.],.]] => 3
[[[.,[.,.]],[.,.]],[.,[.,.]]] => 3
[[[.,[.,.]],[.,.]],[[.,.],.]] => 4
[[[[.,.],.],[.,.]],[.,[.,.]]] => 2
[[[[.,.],.],[.,.]],[[.,.],.]] => 3
[[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[[[.,[.,[.,.]]],.],[[.,.],.]] => 3
[[[.,[[.,.],.]],.],[.,[.,.]]] => 2
[[[.,[[.,.],.]],.],[[.,.],.]] => 3
[[[[.,.],[.,.]],.],[.,[.,.]]] => 2
[[[[.,.],[.,.]],.],[[.,.],.]] => 3
[[[[.,[.,.]],.],.],[.,[.,.]]] => 2
[[[[.,[.,.]],.],.],[[.,.],.]] => 3
[[[[[.,.],.],.],.],[.,[.,.]]] => 1
[[[[[.,.],.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
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[[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[[.,[.,[[.,[.,.]],.]]],[.,.]] => 3
[[.,[.,[[[.,.],.],.]]],[.,.]] => 3
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 2
[[.,[[.,.],[[.,.],.]]],[.,.]] => 3
[[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[[.,[[[.,.],.],[.,.]]],[.,.]] => 2
[[.,[[.,[.,[.,.]]],.]],[.,.]] => 3
[[.,[[.,[[.,.],.]],.]],[.,.]] => 3
[[.,[[[.,.],[.,.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],.],.]],[.,.]] => 3
[[.,[[[[.,.],.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,[.,.]]]],[.,.]] => 2
[[[.,.],[.,[[.,.],.]]],[.,.]] => 3
[[[.,.],[[.,.],[.,.]]],[.,.]] => 2
[[[.,.],[[.,[.,.]],.]],[.,.]] => 3
[[[.,.],[[[.,.],.],.]],[.,.]] => 2
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[[[.,[.,.]],[[.,.],.]],[.,.]] => 3
[[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[[[[.,.],.],[[.,.],.]],[.,.]] => 2
[[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[[[.,[[.,.],.]],[.,.]],[.,.]] => 3
[[[[.,.],[.,.]],[.,.]],[.,.]] => 3
[[[[.,[.,.]],.],[.,.]],[.,.]] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,[.,.]]]],.],[.,.]] => 2
[[[.,[.,[[.,.],.]]],.],[.,.]] => 3
[[[.,[[.,.],[.,.]]],.],[.,.]] => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => 3
[[[.,[[[.,.],.],.]],.],[.,.]] => 2
[[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[[[[.,.],[[.,.],.]],.],[.,.]] => 2
[[[[.,[.,.]],[.,.]],.],[.,.]] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => 2
[[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[[[[.,[[.,.],.]],.],.],[.,.]] => 2
[[[[[.,.],[.,.]],.],.],[.,.]] => 2
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[[[[[[.,.],.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 2
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 3
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 3
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 3
[[.,[.,[.,[[[.,.],.],.]]]],.] => 3
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 3
[[.,[.,[[.,.],[[.,.],.]]]],.] => 4
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 3
[[.,[.,[[[.,.],.],[.,.]]]],.] => 3
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 3
[[.,[.,[[.,[[.,.],.]],.]]],.] => 4
[[.,[.,[[[.,.],[.,.]],.]]],.] => 3
[[.,[.,[[[.,[.,.]],.],.]]],.] => 4
[[.,[.,[[[[.,.],.],.],.]]],.] => 3
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
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[[.,[[.,[.,.]],[.,[.,.]]]],.] => 3
[[.,[[.,[.,.]],[[.,.],.]]],.] => 4
[[.,[[[.,.],.],[.,[.,.]]]],.] => 2
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[[.,[[[.,.],[.,.]],[.,.]]],.] => 3
[[.,[[[.,[.,.]],.],[.,.]]],.] => 3
[[.,[[[[.,.],.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 3
[[.,[[.,[.,[[.,.],.]]],.]],.] => 4
[[.,[[.,[[.,.],[.,.]]],.]],.] => 3
[[.,[[.,[[.,[.,.]],.]],.]],.] => 4
[[.,[[.,[[[.,.],.],.]],.]],.] => 3
[[.,[[[.,.],[.,[.,.]]],.]],.] => 3
[[.,[[[.,.],[[.,.],.]],.]],.] => 3
[[.,[[[.,[.,.]],[.,.]],.]],.] => 4
[[.,[[[[.,.],.],[.,.]],.]],.] => 3
[[.,[[[.,[.,[.,.]]],.],.]],.] => 3
[[.,[[[.,[[.,.],.]],.],.]],.] => 3
[[.,[[[[.,.],[.,.]],.],.]],.] => 3
[[.,[[[[.,[.,.]],.],.],.]],.] => 3
[[.,[[[[[.,.],.],.],.],.]],.] => 2
[[[.,.],[.,[.,[.,[.,.]]]]],.] => 2
[[[.,.],[.,[.,[[.,.],.]]]],.] => 3
[[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[[[.,.],[.,[[.,[.,.]],.]]],.] => 3
[[[.,.],[.,[[[.,.],.],.]]],.] => 3
[[[.,.],[[.,.],[.,[.,.]]]],.] => 2
[[[.,.],[[.,.],[[.,.],.]]],.] => 3
[[[.,.],[[.,[.,.]],[.,.]]],.] => 3
[[[.,.],[[[.,.],.],[.,.]]],.] => 2
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[[[.,.],[[.,[[.,.],.]],.]],.] => 3
[[[.,.],[[[.,.],[.,.]],.]],.] => 3
[[[.,.],[[[.,[.,.]],.],.]],.] => 3
[[[.,.],[[[[.,.],.],.],.]],.] => 2
[[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[[[.,[.,.]],[.,[[.,.],.]]],.] => 4
[[[.,[.,.]],[[.,.],[.,.]]],.] => 3
[[[.,[.,.]],[[.,[.,.]],.]],.] => 4
[[[.,[.,.]],[[[.,.],.],.]],.] => 3
[[[[.,.],.],[.,[.,[.,.]]]],.] => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => 3
[[[[.,.],.],[[.,.],[.,.]]],.] => 2
[[[[.,.],.],[[.,[.,.]],.]],.] => 3
[[[[.,.],.],[[[.,.],.],.]],.] => 2
[[[.,[.,[.,.]]],[.,[.,.]]],.] => 3
[[[.,[.,[.,.]]],[[.,.],.]],.] => 3
[[[.,[[.,.],.]],[.,[.,.]]],.] => 3
[[[.,[[.,.],.]],[[.,.],.]],.] => 3
[[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[[[[.,.],[.,.]],[[.,.],.]],.] => 3
[[[[.,[.,.]],.],[.,[.,.]]],.] => 3
[[[[.,[.,.]],.],[[.,.],.]],.] => 3
[[[[[.,.],.],.],[.,[.,.]]],.] => 2
[[[[[.,.],.],.],[[.,.],.]],.] => 2
[[[.,[.,[.,[.,.]]]],[.,.]],.] => 3
[[[.,[.,[[.,.],.]]],[.,.]],.] => 4
[[[.,[[.,.],[.,.]]],[.,.]],.] => 3
[[[.,[[.,[.,.]],.]],[.,.]],.] => 4
[[[.,[[[.,.],.],.]],[.,.]],.] => 3
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[[[[.,[.,.]],[.,.]],[.,.]],.] => 4
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[[[.,[[.,[.,.]],[.,.]]],.],.] => 3
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[[[.,[[[.,.],[.,.]],.]],.],.] => 3
[[[.,[[[.,[.,.]],.],.]],.],.] => 3
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[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 3
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[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => 4
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[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => 4
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[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 4
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[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 4
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => 4
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[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => 4
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[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 3
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[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
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[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 4
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[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => 4
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[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
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[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 3
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => 3
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 4
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => 2
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => 3
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => 3
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => 4
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => 2
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 3
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 3
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 3
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 3
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 2
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 3
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 3
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 2
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 3
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 3
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 3
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 3
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 3
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 3
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 3
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 3
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 4
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 3
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 3
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 4
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 4
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => 3
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 2
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 3
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 3
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 3
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => 3
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 3
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 4
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 2
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 3
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 3
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 3
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 3
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 4
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 3
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 4
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => 3
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 3
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => 3
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 4
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => 3
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 3
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => 3
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => 3
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => 3
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 2
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 3
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 3
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 3
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 3
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 3
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 4
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 3
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 3
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 3
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 4
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 3
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 4
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 3
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 3
-----------------------------------------------------------------------------
Created: Aug 09, 2016 at 11:12 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Aug 09, 2016 at 11:12 by Christian Stump