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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
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-----------------------------------------------------------------------------
Statistic identifier: St000398
-----------------------------------------------------------------------------
Collection: Binary trees
-----------------------------------------------------------------------------
Description: The sum of the depths of the vertices (or total internal path length) of a binary tree.
The depth of a vertex is the number of edges to the tree's root, see Section 2.3.4.5 of [1] and [3].
This statistic is the very first entry of the OEIS, see [2]. Observe that there the term '''height''' is used instead.
-----------------------------------------------------------------------------
References: [1] Knuth, D. E. The art of computer programming. Vol. 1 [[MathSciNet:3077152]]
[2] Normalized total height of all nodes in all rooted trees with n labeled nodes. [[OEIS:A000435]]
[3] [[wikipedia:Tree (data_structure)]]
-----------------------------------------------------------------------------
Code:
def statistic(T):
return path_length_aux(T, 0)
def path_length_aux(T, n):
return n+sum(path_length_aux(S, n+1) for S in T if not S.is_empty())
-----------------------------------------------------------------------------
Statistic values:
[.,.] => 0
[.,[.,.]] => 1
[[.,.],.] => 1
[.,[.,[.,.]]] => 3
[.,[[.,.],.]] => 3
[[.,.],[.,.]] => 2
[[.,[.,.]],.] => 3
[[[.,.],.],.] => 3
[.,[.,[.,[.,.]]]] => 6
[.,[.,[[.,.],.]]] => 6
[.,[[.,.],[.,.]]] => 5
[.,[[.,[.,.]],.]] => 6
[.,[[[.,.],.],.]] => 6
[[.,.],[.,[.,.]]] => 4
[[.,.],[[.,.],.]] => 4
[[.,[.,.]],[.,.]] => 4
[[[.,.],.],[.,.]] => 4
[[.,[.,[.,.]]],.] => 6
[[.,[[.,.],.]],.] => 6
[[[.,.],[.,.]],.] => 5
[[[.,[.,.]],.],.] => 6
[[[[.,.],.],.],.] => 6
[.,[.,[.,[.,[.,.]]]]] => 10
[.,[.,[.,[[.,.],.]]]] => 10
[.,[.,[[.,.],[.,.]]]] => 9
[.,[.,[[.,[.,.]],.]]] => 10
[.,[.,[[[.,.],.],.]]] => 10
[.,[[.,.],[.,[.,.]]]] => 8
[.,[[.,.],[[.,.],.]]] => 8
[.,[[.,[.,.]],[.,.]]] => 8
[.,[[[.,.],.],[.,.]]] => 8
[.,[[.,[.,[.,.]]],.]] => 10
[.,[[.,[[.,.],.]],.]] => 10
[.,[[[.,.],[.,.]],.]] => 9
[.,[[[.,[.,.]],.],.]] => 10
[.,[[[[.,.],.],.],.]] => 10
[[.,.],[.,[.,[.,.]]]] => 7
[[.,.],[.,[[.,.],.]]] => 7
[[.,.],[[.,.],[.,.]]] => 6
[[.,.],[[.,[.,.]],.]] => 7
[[.,.],[[[.,.],.],.]] => 7
[[.,[.,.]],[.,[.,.]]] => 6
[[.,[.,.]],[[.,.],.]] => 6
[[[.,.],.],[.,[.,.]]] => 6
[[[.,.],.],[[.,.],.]] => 6
[[.,[.,[.,.]]],[.,.]] => 7
[[.,[[.,.],.]],[.,.]] => 7
[[[.,.],[.,.]],[.,.]] => 6
[[[.,[.,.]],.],[.,.]] => 7
[[[[.,.],.],.],[.,.]] => 7
[[.,[.,[.,[.,.]]]],.] => 10
[[.,[.,[[.,.],.]]],.] => 10
[[.,[[.,.],[.,.]]],.] => 9
[[.,[[.,[.,.]],.]],.] => 10
[[.,[[[.,.],.],.]],.] => 10
[[[.,.],[.,[.,.]]],.] => 8
[[[.,.],[[.,.],.]],.] => 8
[[[.,[.,.]],[.,.]],.] => 8
[[[[.,.],.],[.,.]],.] => 8
[[[.,[.,[.,.]]],.],.] => 10
[[[.,[[.,.],.]],.],.] => 10
[[[[.,.],[.,.]],.],.] => 9
[[[[.,[.,.]],.],.],.] => 10
[[[[[.,.],.],.],.],.] => 10
[.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[.,[.,[[.,.],.]]]]] => 15
[.,[.,[.,[[.,.],[.,.]]]]] => 14
[.,[.,[.,[[.,[.,.]],.]]]] => 15
[.,[.,[.,[[[.,.],.],.]]]] => 15
[.,[.,[[.,.],[.,[.,.]]]]] => 13
[.,[.,[[.,.],[[.,.],.]]]] => 13
[.,[.,[[.,[.,.]],[.,.]]]] => 13
[.,[.,[[[.,.],.],[.,.]]]] => 13
[.,[.,[[.,[.,[.,.]]],.]]] => 15
[.,[.,[[.,[[.,.],.]],.]]] => 15
[.,[.,[[[.,.],[.,.]],.]]] => 14
[.,[.,[[[.,[.,.]],.],.]]] => 15
[.,[.,[[[[.,.],.],.],.]]] => 15
[.,[[.,.],[.,[.,[.,.]]]]] => 12
[.,[[.,.],[.,[[.,.],.]]]] => 12
[.,[[.,.],[[.,.],[.,.]]]] => 11
[.,[[.,.],[[.,[.,.]],.]]] => 12
[.,[[.,.],[[[.,.],.],.]]] => 12
[.,[[.,[.,.]],[.,[.,.]]]] => 11
[.,[[.,[.,.]],[[.,.],.]]] => 11
[.,[[[.,.],.],[.,[.,.]]]] => 11
[.,[[[.,.],.],[[.,.],.]]] => 11
[.,[[.,[.,[.,.]]],[.,.]]] => 12
[.,[[.,[[.,.],.]],[.,.]]] => 12
[.,[[[.,.],[.,.]],[.,.]]] => 11
[.,[[[.,[.,.]],.],[.,.]]] => 12
[.,[[[[.,.],.],.],[.,.]]] => 12
[.,[[.,[.,[.,[.,.]]]],.]] => 15
[.,[[.,[.,[[.,.],.]]],.]] => 15
[.,[[.,[[.,.],[.,.]]],.]] => 14
[.,[[.,[[.,[.,.]],.]],.]] => 15
[.,[[.,[[[.,.],.],.]],.]] => 15
[.,[[[.,.],[.,[.,.]]],.]] => 13
[.,[[[.,.],[[.,.],.]],.]] => 13
[.,[[[.,[.,.]],[.,.]],.]] => 13
[.,[[[[.,.],.],[.,.]],.]] => 13
[.,[[[.,[.,[.,.]]],.],.]] => 15
[.,[[[.,[[.,.],.]],.],.]] => 15
[.,[[[[.,.],[.,.]],.],.]] => 14
[.,[[[[.,[.,.]],.],.],.]] => 15
[.,[[[[[.,.],.],.],.],.]] => 15
[[.,.],[.,[.,[.,[.,.]]]]] => 11
[[.,.],[.,[.,[[.,.],.]]]] => 11
[[.,.],[.,[[.,.],[.,.]]]] => 10
[[.,.],[.,[[.,[.,.]],.]]] => 11
[[.,.],[.,[[[.,.],.],.]]] => 11
[[.,.],[[.,.],[.,[.,.]]]] => 9
[[.,.],[[.,.],[[.,.],.]]] => 9
[[.,.],[[.,[.,.]],[.,.]]] => 9
[[.,.],[[[.,.],.],[.,.]]] => 9
[[.,.],[[.,[.,[.,.]]],.]] => 11
[[.,.],[[.,[[.,.],.]],.]] => 11
[[.,.],[[[.,.],[.,.]],.]] => 10
[[.,.],[[[.,[.,.]],.],.]] => 11
[[.,.],[[[[.,.],.],.],.]] => 11
[[.,[.,.]],[.,[.,[.,.]]]] => 9
[[.,[.,.]],[.,[[.,.],.]]] => 9
[[.,[.,.]],[[.,.],[.,.]]] => 8
[[.,[.,.]],[[.,[.,.]],.]] => 9
[[.,[.,.]],[[[.,.],.],.]] => 9
[[[.,.],.],[.,[.,[.,.]]]] => 9
[[[.,.],.],[.,[[.,.],.]]] => 9
[[[.,.],.],[[.,.],[.,.]]] => 8
[[[.,.],.],[[.,[.,.]],.]] => 9
[[[.,.],.],[[[.,.],.],.]] => 9
[[.,[.,[.,.]]],[.,[.,.]]] => 9
[[.,[.,[.,.]]],[[.,.],.]] => 9
[[.,[[.,.],.]],[.,[.,.]]] => 9
[[.,[[.,.],.]],[[.,.],.]] => 9
[[[.,.],[.,.]],[.,[.,.]]] => 8
[[[.,.],[.,.]],[[.,.],.]] => 8
[[[.,[.,.]],.],[.,[.,.]]] => 9
[[[.,[.,.]],.],[[.,.],.]] => 9
[[[[.,.],.],.],[.,[.,.]]] => 9
[[[[.,.],.],.],[[.,.],.]] => 9
[[.,[.,[.,[.,.]]]],[.,.]] => 11
[[.,[.,[[.,.],.]]],[.,.]] => 11
[[.,[[.,.],[.,.]]],[.,.]] => 10
[[.,[[.,[.,.]],.]],[.,.]] => 11
[[.,[[[.,.],.],.]],[.,.]] => 11
[[[.,.],[.,[.,.]]],[.,.]] => 9
[[[.,.],[[.,.],.]],[.,.]] => 9
[[[.,[.,.]],[.,.]],[.,.]] => 9
[[[[.,.],.],[.,.]],[.,.]] => 9
[[[.,[.,[.,.]]],.],[.,.]] => 11
[[[.,[[.,.],.]],.],[.,.]] => 11
[[[[.,.],[.,.]],.],[.,.]] => 10
[[[[.,[.,.]],.],.],[.,.]] => 11
[[[[[.,.],.],.],.],[.,.]] => 11
[[.,[.,[.,[.,[.,.]]]]],.] => 15
[[.,[.,[.,[[.,.],.]]]],.] => 15
[[.,[.,[[.,.],[.,.]]]],.] => 14
[[.,[.,[[.,[.,.]],.]]],.] => 15
[[.,[.,[[[.,.],.],.]]],.] => 15
[[.,[[.,.],[.,[.,.]]]],.] => 13
[[.,[[.,.],[[.,.],.]]],.] => 13
[[.,[[.,[.,.]],[.,.]]],.] => 13
[[.,[[[.,.],.],[.,.]]],.] => 13
[[.,[[.,[.,[.,.]]],.]],.] => 15
[[.,[[.,[[.,.],.]],.]],.] => 15
[[.,[[[.,.],[.,.]],.]],.] => 14
[[.,[[[.,[.,.]],.],.]],.] => 15
[[.,[[[[.,.],.],.],.]],.] => 15
[[[.,.],[.,[.,[.,.]]]],.] => 12
[[[.,.],[.,[[.,.],.]]],.] => 12
[[[.,.],[[.,.],[.,.]]],.] => 11
[[[.,.],[[.,[.,.]],.]],.] => 12
[[[.,.],[[[.,.],.],.]],.] => 12
[[[.,[.,.]],[.,[.,.]]],.] => 11
[[[.,[.,.]],[[.,.],.]],.] => 11
[[[[.,.],.],[.,[.,.]]],.] => 11
[[[[.,.],.],[[.,.],.]],.] => 11
[[[.,[.,[.,.]]],[.,.]],.] => 12
[[[.,[[.,.],.]],[.,.]],.] => 12
[[[[.,.],[.,.]],[.,.]],.] => 11
[[[[.,[.,.]],.],[.,.]],.] => 12
[[[[[.,.],.],.],[.,.]],.] => 12
[[[.,[.,[.,[.,.]]]],.],.] => 15
[[[.,[.,[[.,.],.]]],.],.] => 15
[[[.,[[.,.],[.,.]]],.],.] => 14
[[[.,[[.,[.,.]],.]],.],.] => 15
[[[.,[[[.,.],.],.]],.],.] => 15
[[[[.,.],[.,[.,.]]],.],.] => 13
[[[[.,.],[[.,.],.]],.],.] => 13
[[[[.,[.,.]],[.,.]],.],.] => 13
[[[[[.,.],.],[.,.]],.],.] => 13
[[[[.,[.,[.,.]]],.],.],.] => 15
[[[[.,[[.,.],.]],.],.],.] => 15
[[[[[.,.],[.,.]],.],.],.] => 14
[[[[[.,[.,.]],.],.],.],.] => 15
[[[[[[.,.],.],.],.],.],.] => 15
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 21
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 21
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 20
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 21
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 21
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 19
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 19
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 19
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 19
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 21
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 21
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 20
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 21
[.,[.,[.,[[[[.,.],.],.],.]]]] => 21
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 18
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 18
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 17
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 18
[.,[.,[[.,.],[[[.,.],.],.]]]] => 18
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 17
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 17
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 17
[.,[.,[[[.,.],.],[[.,.],.]]]] => 17
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 18
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 18
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 17
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 18
[.,[.,[[[[.,.],.],.],[.,.]]]] => 18
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 21
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 21
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 20
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 21
[.,[.,[[.,[[[.,.],.],.]],.]]] => 21
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 19
[.,[.,[[[.,.],[[.,.],.]],.]]] => 19
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 19
[.,[.,[[[[.,.],.],[.,.]],.]]] => 19
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 21
[.,[.,[[[.,[[.,.],.]],.],.]]] => 21
[.,[.,[[[[.,.],[.,.]],.],.]]] => 20
[.,[.,[[[[.,[.,.]],.],.],.]]] => 21
[.,[.,[[[[[.,.],.],.],.],.]]] => 21
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 17
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 17
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 16
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 17
[.,[[.,.],[.,[[[.,.],.],.]]]] => 17
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 15
[.,[[.,.],[[.,.],[[.,.],.]]]] => 15
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 15
[.,[[.,.],[[[.,.],.],[.,.]]]] => 15
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 17
[.,[[.,.],[[.,[[.,.],.]],.]]] => 17
[.,[[.,.],[[[.,.],[.,.]],.]]] => 16
[.,[[.,.],[[[.,[.,.]],.],.]]] => 17
[.,[[.,.],[[[[.,.],.],.],.]]] => 17
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 15
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 15
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 14
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 15
[.,[[.,[.,.]],[[[.,.],.],.]]] => 15
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 15
[.,[[[.,.],.],[.,[[.,.],.]]]] => 15
[.,[[[.,.],.],[[.,.],[.,.]]]] => 14
[.,[[[.,.],.],[[.,[.,.]],.]]] => 15
[.,[[[.,.],.],[[[.,.],.],.]]] => 15
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 15
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 15
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 15
[.,[[.,[[.,.],.]],[[.,.],.]]] => 15
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 14
[.,[[[.,.],[.,.]],[[.,.],.]]] => 14
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 15
[.,[[[.,[.,.]],.],[[.,.],.]]] => 15
[.,[[[[.,.],.],.],[.,[.,.]]]] => 15
[.,[[[[.,.],.],.],[[.,.],.]]] => 15
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 17
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 17
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 16
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 17
[.,[[.,[[[.,.],.],.]],[.,.]]] => 17
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 15
[.,[[[.,.],[[.,.],.]],[.,.]]] => 15
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 15
[.,[[[[.,.],.],[.,.]],[.,.]]] => 15
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 17
[.,[[[.,[[.,.],.]],.],[.,.]]] => 17
[.,[[[[.,.],[.,.]],.],[.,.]]] => 16
[.,[[[[.,[.,.]],.],.],[.,.]]] => 17
[.,[[[[[.,.],.],.],.],[.,.]]] => 17
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 21
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 21
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 20
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 21
[.,[[.,[.,[[[.,.],.],.]]],.]] => 21
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 19
[.,[[.,[[.,.],[[.,.],.]]],.]] => 19
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 19
[.,[[.,[[[.,.],.],[.,.]]],.]] => 19
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 21
[.,[[.,[[.,[[.,.],.]],.]],.]] => 21
[.,[[.,[[[.,.],[.,.]],.]],.]] => 20
[.,[[.,[[[.,[.,.]],.],.]],.]] => 21
[.,[[.,[[[[.,.],.],.],.]],.]] => 21
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 18
[.,[[[.,.],[.,[[.,.],.]]],.]] => 18
[.,[[[.,.],[[.,.],[.,.]]],.]] => 17
[.,[[[.,.],[[.,[.,.]],.]],.]] => 18
[.,[[[.,.],[[[.,.],.],.]],.]] => 18
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 17
[.,[[[.,[.,.]],[[.,.],.]],.]] => 17
[.,[[[[.,.],.],[.,[.,.]]],.]] => 17
[.,[[[[.,.],.],[[.,.],.]],.]] => 17
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 18
[.,[[[.,[[.,.],.]],[.,.]],.]] => 18
[.,[[[[.,.],[.,.]],[.,.]],.]] => 17
[.,[[[[.,[.,.]],.],[.,.]],.]] => 18
[.,[[[[[.,.],.],.],[.,.]],.]] => 18
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 21
[.,[[[.,[.,[[.,.],.]]],.],.]] => 21
[.,[[[.,[[.,.],[.,.]]],.],.]] => 20
[.,[[[.,[[.,[.,.]],.]],.],.]] => 21
[.,[[[.,[[[.,.],.],.]],.],.]] => 21
[.,[[[[.,.],[.,[.,.]]],.],.]] => 19
[.,[[[[.,.],[[.,.],.]],.],.]] => 19
[.,[[[[.,[.,.]],[.,.]],.],.]] => 19
[.,[[[[[.,.],.],[.,.]],.],.]] => 19
[.,[[[[.,[.,[.,.]]],.],.],.]] => 21
[.,[[[[.,[[.,.],.]],.],.],.]] => 21
[.,[[[[[.,.],[.,.]],.],.],.]] => 20
[.,[[[[[.,[.,.]],.],.],.],.]] => 21
[.,[[[[[[.,.],.],.],.],.],.]] => 21
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 16
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 16
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 15
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 16
[[.,.],[.,[.,[[[.,.],.],.]]]] => 16
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 14
[[.,.],[.,[[.,.],[[.,.],.]]]] => 14
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 14
[[.,.],[.,[[[.,.],.],[.,.]]]] => 14
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 16
[[.,.],[.,[[.,[[.,.],.]],.]]] => 16
[[.,.],[.,[[[.,.],[.,.]],.]]] => 15
[[.,.],[.,[[[.,[.,.]],.],.]]] => 16
[[.,.],[.,[[[[.,.],.],.],.]]] => 16
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 13
[[.,.],[[.,.],[.,[[.,.],.]]]] => 13
[[.,.],[[.,.],[[.,.],[.,.]]]] => 12
[[.,.],[[.,.],[[.,[.,.]],.]]] => 13
[[.,.],[[.,.],[[[.,.],.],.]]] => 13
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 12
[[.,.],[[.,[.,.]],[[.,.],.]]] => 12
[[.,.],[[[.,.],.],[.,[.,.]]]] => 12
[[.,.],[[[.,.],.],[[.,.],.]]] => 12
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 13
[[.,.],[[.,[[.,.],.]],[.,.]]] => 13
[[.,.],[[[.,.],[.,.]],[.,.]]] => 12
[[.,.],[[[.,[.,.]],.],[.,.]]] => 13
[[.,.],[[[[.,.],.],.],[.,.]]] => 13
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 16
[[.,.],[[.,[.,[[.,.],.]]],.]] => 16
[[.,.],[[.,[[.,.],[.,.]]],.]] => 15
[[.,.],[[.,[[.,[.,.]],.]],.]] => 16
[[.,.],[[.,[[[.,.],.],.]],.]] => 16
[[.,.],[[[.,.],[.,[.,.]]],.]] => 14
[[.,.],[[[.,.],[[.,.],.]],.]] => 14
[[.,.],[[[.,[.,.]],[.,.]],.]] => 14
[[.,.],[[[[.,.],.],[.,.]],.]] => 14
[[.,.],[[[.,[.,[.,.]]],.],.]] => 16
[[.,.],[[[.,[[.,.],.]],.],.]] => 16
[[.,.],[[[[.,.],[.,.]],.],.]] => 15
[[.,.],[[[[.,[.,.]],.],.],.]] => 16
[[.,.],[[[[[.,.],.],.],.],.]] => 16
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 13
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 13
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 12
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 13
[[.,[.,.]],[.,[[[.,.],.],.]]] => 13
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 11
[[.,[.,.]],[[.,.],[[.,.],.]]] => 11
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 11
[[.,[.,.]],[[[.,.],.],[.,.]]] => 11
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 13
[[.,[.,.]],[[.,[[.,.],.]],.]] => 13
[[.,[.,.]],[[[.,.],[.,.]],.]] => 12
[[.,[.,.]],[[[.,[.,.]],.],.]] => 13
[[.,[.,.]],[[[[.,.],.],.],.]] => 13
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 13
[[[.,.],.],[.,[.,[[.,.],.]]]] => 13
[[[.,.],.],[.,[[.,.],[.,.]]]] => 12
[[[.,.],.],[.,[[.,[.,.]],.]]] => 13
[[[.,.],.],[.,[[[.,.],.],.]]] => 13
[[[.,.],.],[[.,.],[.,[.,.]]]] => 11
[[[.,.],.],[[.,.],[[.,.],.]]] => 11
[[[.,.],.],[[.,[.,.]],[.,.]]] => 11
[[[.,.],.],[[[.,.],.],[.,.]]] => 11
[[[.,.],.],[[.,[.,[.,.]]],.]] => 13
[[[.,.],.],[[.,[[.,.],.]],.]] => 13
[[[.,.],.],[[[.,.],[.,.]],.]] => 12
[[[.,.],.],[[[.,[.,.]],.],.]] => 13
[[[.,.],.],[[[[.,.],.],.],.]] => 13
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 12
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 12
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 11
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 12
[[.,[.,[.,.]]],[[[.,.],.],.]] => 12
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 12
[[.,[[.,.],.]],[.,[[.,.],.]]] => 12
[[.,[[.,.],.]],[[.,.],[.,.]]] => 11
[[.,[[.,.],.]],[[.,[.,.]],.]] => 12
[[.,[[.,.],.]],[[[.,.],.],.]] => 12
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 11
[[[.,.],[.,.]],[.,[[.,.],.]]] => 11
[[[.,.],[.,.]],[[.,.],[.,.]]] => 10
[[[.,.],[.,.]],[[.,[.,.]],.]] => 11
[[[.,.],[.,.]],[[[.,.],.],.]] => 11
[[[.,[.,.]],.],[.,[.,[.,.]]]] => 12
[[[.,[.,.]],.],[.,[[.,.],.]]] => 12
[[[.,[.,.]],.],[[.,.],[.,.]]] => 11
[[[.,[.,.]],.],[[.,[.,.]],.]] => 12
[[[.,[.,.]],.],[[[.,.],.],.]] => 12
[[[[.,.],.],.],[.,[.,[.,.]]]] => 12
[[[[.,.],.],.],[.,[[.,.],.]]] => 12
[[[[.,.],.],.],[[.,.],[.,.]]] => 11
[[[[.,.],.],.],[[.,[.,.]],.]] => 12
[[[[.,.],.],.],[[[.,.],.],.]] => 12
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => 13
[[.,[.,[.,[.,.]]]],[[.,.],.]] => 13
[[.,[.,[[.,.],.]]],[.,[.,.]]] => 13
[[.,[.,[[.,.],.]]],[[.,.],.]] => 13
[[.,[[.,.],[.,.]]],[.,[.,.]]] => 12
[[.,[[.,.],[.,.]]],[[.,.],.]] => 12
[[.,[[.,[.,.]],.]],[.,[.,.]]] => 13
[[.,[[.,[.,.]],.]],[[.,.],.]] => 13
[[.,[[[.,.],.],.]],[.,[.,.]]] => 13
[[.,[[[.,.],.],.]],[[.,.],.]] => 13
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 11
[[[.,.],[.,[.,.]]],[[.,.],.]] => 11
[[[.,.],[[.,.],.]],[.,[.,.]]] => 11
[[[.,.],[[.,.],.]],[[.,.],.]] => 11
[[[.,[.,.]],[.,.]],[.,[.,.]]] => 11
[[[.,[.,.]],[.,.]],[[.,.],.]] => 11
[[[[.,.],.],[.,.]],[.,[.,.]]] => 11
[[[[.,.],.],[.,.]],[[.,.],.]] => 11
[[[.,[.,[.,.]]],.],[.,[.,.]]] => 13
[[[.,[.,[.,.]]],.],[[.,.],.]] => 13
[[[.,[[.,.],.]],.],[.,[.,.]]] => 13
[[[.,[[.,.],.]],.],[[.,.],.]] => 13
[[[[.,.],[.,.]],.],[.,[.,.]]] => 12
[[[[.,.],[.,.]],.],[[.,.],.]] => 12
[[[[.,[.,.]],.],.],[.,[.,.]]] => 13
[[[[.,[.,.]],.],.],[[.,.],.]] => 13
[[[[[.,.],.],.],.],[.,[.,.]]] => 13
[[[[[.,.],.],.],.],[[.,.],.]] => 13
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 16
[[.,[.,[.,[[.,.],.]]]],[.,.]] => 16
[[.,[.,[[.,.],[.,.]]]],[.,.]] => 15
[[.,[.,[[.,[.,.]],.]]],[.,.]] => 16
[[.,[.,[[[.,.],.],.]]],[.,.]] => 16
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 14
[[.,[[.,.],[[.,.],.]]],[.,.]] => 14
[[.,[[.,[.,.]],[.,.]]],[.,.]] => 14
[[.,[[[.,.],.],[.,.]]],[.,.]] => 14
[[.,[[.,[.,[.,.]]],.]],[.,.]] => 16
[[.,[[.,[[.,.],.]],.]],[.,.]] => 16
[[.,[[[.,.],[.,.]],.]],[.,.]] => 15
[[.,[[[.,[.,.]],.],.]],[.,.]] => 16
[[.,[[[[.,.],.],.],.]],[.,.]] => 16
[[[.,.],[.,[.,[.,.]]]],[.,.]] => 13
[[[.,.],[.,[[.,.],.]]],[.,.]] => 13
[[[.,.],[[.,.],[.,.]]],[.,.]] => 12
[[[.,.],[[.,[.,.]],.]],[.,.]] => 13
[[[.,.],[[[.,.],.],.]],[.,.]] => 13
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 12
[[[.,[.,.]],[[.,.],.]],[.,.]] => 12
[[[[.,.],.],[.,[.,.]]],[.,.]] => 12
[[[[.,.],.],[[.,.],.]],[.,.]] => 12
[[[.,[.,[.,.]]],[.,.]],[.,.]] => 13
[[[.,[[.,.],.]],[.,.]],[.,.]] => 13
[[[[.,.],[.,.]],[.,.]],[.,.]] => 12
[[[[.,[.,.]],.],[.,.]],[.,.]] => 13
[[[[[.,.],.],.],[.,.]],[.,.]] => 13
[[[.,[.,[.,[.,.]]]],.],[.,.]] => 16
[[[.,[.,[[.,.],.]]],.],[.,.]] => 16
[[[.,[[.,.],[.,.]]],.],[.,.]] => 15
[[[.,[[.,[.,.]],.]],.],[.,.]] => 16
[[[.,[[[.,.],.],.]],.],[.,.]] => 16
[[[[.,.],[.,[.,.]]],.],[.,.]] => 14
[[[[.,.],[[.,.],.]],.],[.,.]] => 14
[[[[.,[.,.]],[.,.]],.],[.,.]] => 14
[[[[[.,.],.],[.,.]],.],[.,.]] => 14
[[[[.,[.,[.,.]]],.],.],[.,.]] => 16
[[[[.,[[.,.],.]],.],.],[.,.]] => 16
[[[[[.,.],[.,.]],.],.],[.,.]] => 15
[[[[[.,[.,.]],.],.],.],[.,.]] => 16
[[[[[[.,.],.],.],.],.],[.,.]] => 16
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 21
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 21
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 20
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 21
[[.,[.,[.,[[[.,.],.],.]]]],.] => 21
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 19
[[.,[.,[[.,.],[[.,.],.]]]],.] => 19
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 19
[[.,[.,[[[.,.],.],[.,.]]]],.] => 19
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 21
[[.,[.,[[.,[[.,.],.]],.]]],.] => 21
[[.,[.,[[[.,.],[.,.]],.]]],.] => 20
[[.,[.,[[[.,[.,.]],.],.]]],.] => 21
[[.,[.,[[[[.,.],.],.],.]]],.] => 21
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 18
[[.,[[.,.],[.,[[.,.],.]]]],.] => 18
[[.,[[.,.],[[.,.],[.,.]]]],.] => 17
[[.,[[.,.],[[.,[.,.]],.]]],.] => 18
[[.,[[.,.],[[[.,.],.],.]]],.] => 18
[[.,[[.,[.,.]],[.,[.,.]]]],.] => 17
[[.,[[.,[.,.]],[[.,.],.]]],.] => 17
[[.,[[[.,.],.],[.,[.,.]]]],.] => 17
[[.,[[[.,.],.],[[.,.],.]]],.] => 17
[[.,[[.,[.,[.,.]]],[.,.]]],.] => 18
[[.,[[.,[[.,.],.]],[.,.]]],.] => 18
[[.,[[[.,.],[.,.]],[.,.]]],.] => 17
[[.,[[[.,[.,.]],.],[.,.]]],.] => 18
[[.,[[[[.,.],.],.],[.,.]]],.] => 18
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 21
[[.,[[.,[.,[[.,.],.]]],.]],.] => 21
[[.,[[.,[[.,.],[.,.]]],.]],.] => 20
[[.,[[.,[[.,[.,.]],.]],.]],.] => 21
[[.,[[.,[[[.,.],.],.]],.]],.] => 21
[[.,[[[.,.],[.,[.,.]]],.]],.] => 19
[[.,[[[.,.],[[.,.],.]],.]],.] => 19
[[.,[[[.,[.,.]],[.,.]],.]],.] => 19
[[.,[[[[.,.],.],[.,.]],.]],.] => 19
[[.,[[[.,[.,[.,.]]],.],.]],.] => 21
[[.,[[[.,[[.,.],.]],.],.]],.] => 21
[[.,[[[[.,.],[.,.]],.],.]],.] => 20
[[.,[[[[.,[.,.]],.],.],.]],.] => 21
[[.,[[[[[.,.],.],.],.],.]],.] => 21
[[[.,.],[.,[.,[.,[.,.]]]]],.] => 17
[[[.,.],[.,[.,[[.,.],.]]]],.] => 17
[[[.,.],[.,[[.,.],[.,.]]]],.] => 16
[[[.,.],[.,[[.,[.,.]],.]]],.] => 17
[[[.,.],[.,[[[.,.],.],.]]],.] => 17
[[[.,.],[[.,.],[.,[.,.]]]],.] => 15
[[[.,.],[[.,.],[[.,.],.]]],.] => 15
[[[.,.],[[.,[.,.]],[.,.]]],.] => 15
[[[.,.],[[[.,.],.],[.,.]]],.] => 15
[[[.,.],[[.,[.,[.,.]]],.]],.] => 17
[[[.,.],[[.,[[.,.],.]],.]],.] => 17
[[[.,.],[[[.,.],[.,.]],.]],.] => 16
[[[.,.],[[[.,[.,.]],.],.]],.] => 17
[[[.,.],[[[[.,.],.],.],.]],.] => 17
[[[.,[.,.]],[.,[.,[.,.]]]],.] => 15
[[[.,[.,.]],[.,[[.,.],.]]],.] => 15
[[[.,[.,.]],[[.,.],[.,.]]],.] => 14
[[[.,[.,.]],[[.,[.,.]],.]],.] => 15
[[[.,[.,.]],[[[.,.],.],.]],.] => 15
[[[[.,.],.],[.,[.,[.,.]]]],.] => 15
[[[[.,.],.],[.,[[.,.],.]]],.] => 15
[[[[.,.],.],[[.,.],[.,.]]],.] => 14
[[[[.,.],.],[[.,[.,.]],.]],.] => 15
[[[[.,.],.],[[[.,.],.],.]],.] => 15
[[[.,[.,[.,.]]],[.,[.,.]]],.] => 15
[[[.,[.,[.,.]]],[[.,.],.]],.] => 15
[[[.,[[.,.],.]],[.,[.,.]]],.] => 15
[[[.,[[.,.],.]],[[.,.],.]],.] => 15
[[[[.,.],[.,.]],[.,[.,.]]],.] => 14
[[[[.,.],[.,.]],[[.,.],.]],.] => 14
[[[[.,[.,.]],.],[.,[.,.]]],.] => 15
[[[[.,[.,.]],.],[[.,.],.]],.] => 15
[[[[[.,.],.],.],[.,[.,.]]],.] => 15
[[[[[.,.],.],.],[[.,.],.]],.] => 15
[[[.,[.,[.,[.,.]]]],[.,.]],.] => 17
[[[.,[.,[[.,.],.]]],[.,.]],.] => 17
[[[.,[[.,.],[.,.]]],[.,.]],.] => 16
[[[.,[[.,[.,.]],.]],[.,.]],.] => 17
[[[.,[[[.,.],.],.]],[.,.]],.] => 17
[[[[.,.],[.,[.,.]]],[.,.]],.] => 15
[[[[.,.],[[.,.],.]],[.,.]],.] => 15
[[[[.,[.,.]],[.,.]],[.,.]],.] => 15
[[[[[.,.],.],[.,.]],[.,.]],.] => 15
[[[[.,[.,[.,.]]],.],[.,.]],.] => 17
[[[[.,[[.,.],.]],.],[.,.]],.] => 17
[[[[[.,.],[.,.]],.],[.,.]],.] => 16
[[[[[.,[.,.]],.],.],[.,.]],.] => 17
[[[[[[.,.],.],.],.],[.,.]],.] => 17
[[[.,[.,[.,[.,[.,.]]]]],.],.] => 21
[[[.,[.,[.,[[.,.],.]]]],.],.] => 21
[[[.,[.,[[.,.],[.,.]]]],.],.] => 20
[[[.,[.,[[.,[.,.]],.]]],.],.] => 21
[[[.,[.,[[[.,.],.],.]]],.],.] => 21
[[[.,[[.,.],[.,[.,.]]]],.],.] => 19
[[[.,[[.,.],[[.,.],.]]],.],.] => 19
[[[.,[[.,[.,.]],[.,.]]],.],.] => 19
[[[.,[[[.,.],.],[.,.]]],.],.] => 19
[[[.,[[.,[.,[.,.]]],.]],.],.] => 21
[[[.,[[.,[[.,.],.]],.]],.],.] => 21
[[[.,[[[.,.],[.,.]],.]],.],.] => 20
[[[.,[[[.,[.,.]],.],.]],.],.] => 21
[[[.,[[[[.,.],.],.],.]],.],.] => 21
[[[[.,.],[.,[.,[.,.]]]],.],.] => 18
[[[[.,.],[.,[[.,.],.]]],.],.] => 18
[[[[.,.],[[.,.],[.,.]]],.],.] => 17
[[[[.,.],[[.,[.,.]],.]],.],.] => 18
[[[[.,.],[[[.,.],.],.]],.],.] => 18
[[[[.,[.,.]],[.,[.,.]]],.],.] => 17
[[[[.,[.,.]],[[.,.],.]],.],.] => 17
[[[[[.,.],.],[.,[.,.]]],.],.] => 17
[[[[[.,.],.],[[.,.],.]],.],.] => 17
[[[[.,[.,[.,.]]],[.,.]],.],.] => 18
[[[[.,[[.,.],.]],[.,.]],.],.] => 18
[[[[[.,.],[.,.]],[.,.]],.],.] => 17
[[[[[.,[.,.]],.],[.,.]],.],.] => 18
[[[[[[.,.],.],.],[.,.]],.],.] => 18
[[[[.,[.,[.,[.,.]]]],.],.],.] => 21
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[[[[.,[[.,.],[.,.]]],.],.],.] => 20
[[[[.,[[.,[.,.]],.]],.],.],.] => 21
[[[[.,[[[.,.],.],.]],.],.],.] => 21
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[[[[[.,.],[[.,.],.]],.],.],.] => 19
[[[[[.,[.,.]],[.,.]],.],.],.] => 19
[[[[[[.,.],.],[.,.]],.],.],.] => 19
[[[[[.,[.,[.,.]]],.],.],.],.] => 21
[[[[[.,[[.,.],.]],.],.],.],.] => 21
[[[[[[.,.],[.,.]],.],.],.],.] => 20
[[[[[[.,[.,.]],.],.],.],.],.] => 21
[[[[[[[.,.],.],.],.],.],.],.] => 21
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 28
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 28
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 27
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 28
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => 28
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 26
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[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 26
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => 26
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => 28
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => 28
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => 27
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => 28
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => 28
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 25
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[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 24
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 25
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => 25
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[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => 24
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[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => 24
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[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => 22
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[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => 22
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[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => 24
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[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => 27
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => 28
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[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => 23
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[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => 23
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => 23
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[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => 23
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[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 20
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[[.,.],[[[[.,.],.],.],[[.,.],.]]] => 16
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 18
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 18
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 17
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 18
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 18
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 16
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 16
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 16
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 16
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 18
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 18
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 17
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 18
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => 18
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 22
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 22
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 21
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 22
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 22
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 20
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 20
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 20
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 20
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 22
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 22
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 21
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 22
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => 22
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 19
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 19
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 18
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 19
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => 19
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 18
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 18
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 18
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 18
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 19
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 19
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 18
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 19
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => 19
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 22
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 22
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 21
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 22
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => 22
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 20
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => 20
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 20
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => 20
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 22
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => 22
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => 21
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => 22
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 22
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 18
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 18
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 17
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 18
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 18
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 16
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 16
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 16
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 16
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 18
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 18
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 17
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 18
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 18
-----------------------------------------------------------------------------
Created: Feb 22, 2016 at 15:54 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Aug 10, 2016 at 11:38 by Christian Stump