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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St000385
-----------------------------------------------------------------------------
Collection: Binary trees
-----------------------------------------------------------------------------
Description: The number of vertices with out-degree 1 in a binary tree.
See the references for several connections of this statistic.
In particular, the number $T(n,k)$ of binary trees with $n$ vertices and $k$ out-degree $1$ vertices is given by $T(n,k) = 0$ for $n-k$ odd and
$$T(n,k)=\frac{2^k}{n+1}\binom{n+1}{k}\binom{n+1-k}{(n-k)/2}$$
for $n-k$ is even.
-----------------------------------------------------------------------------
References: [1] Triangle read by rows: T(n,k) is the number of binary trees with n edges and having k vertices of outdegree 1 (n>=0, k>=0). A binary tree is a rooted tree in which each vertex has at most two children and each child of a vertex is designated as its left or right child. [[OEIS:A121448]]
[2] Copeland, T. Has anyone seen these binary trees (Catalan-type related to the Gegenbauer polynomials and Motzkin paths)? [[MathOverflow:230714]]
-----------------------------------------------------------------------------
Code:
def statistic(tree):
return tree.graph(with_leaves=False).out_degree_sequence().count(1)
-----------------------------------------------------------------------------
Statistic values:
[.,[.,.]] => 1
[[.,.],.] => 1
[.,[.,[.,.]]] => 2
[.,[[.,.],.]] => 2
[[.,.],[.,.]] => 0
[[.,[.,.]],.] => 2
[[[.,.],.],.] => 2
[.,[.,[.,[.,.]]]] => 3
[.,[.,[[.,.],.]]] => 3
[.,[[.,.],[.,.]]] => 1
[.,[[.,[.,.]],.]] => 3
[.,[[[.,.],.],.]] => 3
[[.,.],[.,[.,.]]] => 1
[[.,.],[[.,.],.]] => 1
[[.,[.,.]],[.,.]] => 1
[[[.,.],.],[.,.]] => 1
[[.,[.,[.,.]]],.] => 3
[[.,[[.,.],.]],.] => 3
[[[.,.],[.,.]],.] => 1
[[[.,[.,.]],.],.] => 3
[[[[.,.],.],.],.] => 3
[.,[.,[.,[.,[.,.]]]]] => 4
[.,[.,[.,[[.,.],.]]]] => 4
[.,[.,[[.,.],[.,.]]]] => 2
[.,[.,[[.,[.,.]],.]]] => 4
[.,[.,[[[.,.],.],.]]] => 4
[.,[[.,.],[.,[.,.]]]] => 2
[.,[[.,.],[[.,.],.]]] => 2
[.,[[.,[.,.]],[.,.]]] => 2
[.,[[[.,.],.],[.,.]]] => 2
[.,[[.,[.,[.,.]]],.]] => 4
[.,[[.,[[.,.],.]],.]] => 4
[.,[[[.,.],[.,.]],.]] => 2
[.,[[[.,[.,.]],.],.]] => 4
[.,[[[[.,.],.],.],.]] => 4
[[.,.],[.,[.,[.,.]]]] => 2
[[.,.],[.,[[.,.],.]]] => 2
[[.,.],[[.,.],[.,.]]] => 0
[[.,.],[[.,[.,.]],.]] => 2
[[.,.],[[[.,.],.],.]] => 2
[[.,[.,.]],[.,[.,.]]] => 2
[[.,[.,.]],[[.,.],.]] => 2
[[[.,.],.],[.,[.,.]]] => 2
[[[.,.],.],[[.,.],.]] => 2
[[.,[.,[.,.]]],[.,.]] => 2
[[.,[[.,.],.]],[.,.]] => 2
[[[.,.],[.,.]],[.,.]] => 0
[[[.,[.,.]],.],[.,.]] => 2
[[[[.,.],.],.],[.,.]] => 2
[[.,[.,[.,[.,.]]]],.] => 4
[[.,[.,[[.,.],.]]],.] => 4
[[.,[[.,.],[.,.]]],.] => 2
[[.,[[.,[.,.]],.]],.] => 4
[[.,[[[.,.],.],.]],.] => 4
[[[.,.],[.,[.,.]]],.] => 2
[[[.,.],[[.,.],.]],.] => 2
[[[.,[.,.]],[.,.]],.] => 2
[[[[.,.],.],[.,.]],.] => 2
[[[.,[.,[.,.]]],.],.] => 4
[[[.,[[.,.],.]],.],.] => 4
[[[[.,.],[.,.]],.],.] => 2
[[[[.,[.,.]],.],.],.] => 4
[[[[[.,.],.],.],.],.] => 4
[.,[.,[.,[.,[.,[.,.]]]]]] => 5
[.,[.,[.,[.,[[.,.],.]]]]] => 5
[.,[.,[.,[[.,.],[.,.]]]]] => 3
[.,[.,[.,[[.,[.,.]],.]]]] => 5
[.,[.,[.,[[[.,.],.],.]]]] => 5
[.,[.,[[.,.],[.,[.,.]]]]] => 3
[.,[.,[[.,.],[[.,.],.]]]] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => 3
[.,[.,[[[.,.],.],[.,.]]]] => 3
[.,[.,[[.,[.,[.,.]]],.]]] => 5
[.,[.,[[.,[[.,.],.]],.]]] => 5
[.,[.,[[[.,.],[.,.]],.]]] => 3
[.,[.,[[[.,[.,.]],.],.]]] => 5
[.,[.,[[[[.,.],.],.],.]]] => 5
[.,[[.,.],[.,[.,[.,.]]]]] => 3
[.,[[.,.],[.,[[.,.],.]]]] => 3
[.,[[.,.],[[.,.],[.,.]]]] => 1
[.,[[.,.],[[.,[.,.]],.]]] => 3
[.,[[.,.],[[[.,.],.],.]]] => 3
[.,[[.,[.,.]],[.,[.,.]]]] => 3
[.,[[.,[.,.]],[[.,.],.]]] => 3
[.,[[[.,.],.],[.,[.,.]]]] => 3
[.,[[[.,.],.],[[.,.],.]]] => 3
[.,[[.,[.,[.,.]]],[.,.]]] => 3
[.,[[.,[[.,.],.]],[.,.]]] => 3
[.,[[[.,.],[.,.]],[.,.]]] => 1
[.,[[[.,[.,.]],.],[.,.]]] => 3
[.,[[[[.,.],.],.],[.,.]]] => 3
[.,[[.,[.,[.,[.,.]]]],.]] => 5
[.,[[.,[.,[[.,.],.]]],.]] => 5
[.,[[.,[[.,.],[.,.]]],.]] => 3
[.,[[.,[[.,[.,.]],.]],.]] => 5
[.,[[.,[[[.,.],.],.]],.]] => 5
[.,[[[.,.],[.,[.,.]]],.]] => 3
[.,[[[.,.],[[.,.],.]],.]] => 3
[.,[[[.,[.,.]],[.,.]],.]] => 3
[.,[[[[.,.],.],[.,.]],.]] => 3
[.,[[[.,[.,[.,.]]],.],.]] => 5
[.,[[[.,[[.,.],.]],.],.]] => 5
[.,[[[[.,.],[.,.]],.],.]] => 3
[.,[[[[.,[.,.]],.],.],.]] => 5
[.,[[[[[.,.],.],.],.],.]] => 5
[[.,.],[.,[.,[.,[.,.]]]]] => 3
[[.,.],[.,[.,[[.,.],.]]]] => 3
[[.,.],[.,[[.,.],[.,.]]]] => 1
[[.,.],[.,[[.,[.,.]],.]]] => 3
[[.,.],[.,[[[.,.],.],.]]] => 3
[[.,.],[[.,.],[.,[.,.]]]] => 1
[[.,.],[[.,.],[[.,.],.]]] => 1
[[.,.],[[.,[.,.]],[.,.]]] => 1
[[.,.],[[[.,.],.],[.,.]]] => 1
[[.,.],[[.,[.,[.,.]]],.]] => 3
[[.,.],[[.,[[.,.],.]],.]] => 3
[[.,.],[[[.,.],[.,.]],.]] => 1
[[.,.],[[[.,[.,.]],.],.]] => 3
[[.,.],[[[[.,.],.],.],.]] => 3
[[.,[.,.]],[.,[.,[.,.]]]] => 3
[[.,[.,.]],[.,[[.,.],.]]] => 3
[[.,[.,.]],[[.,.],[.,.]]] => 1
[[.,[.,.]],[[.,[.,.]],.]] => 3
[[.,[.,.]],[[[.,.],.],.]] => 3
[[[.,.],.],[.,[.,[.,.]]]] => 3
[[[.,.],.],[.,[[.,.],.]]] => 3
[[[.,.],.],[[.,.],[.,.]]] => 1
[[[.,.],.],[[.,[.,.]],.]] => 3
[[[.,.],.],[[[.,.],.],.]] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => 3
[[.,[.,[.,.]]],[[.,.],.]] => 3
[[.,[[.,.],.]],[.,[.,.]]] => 3
[[.,[[.,.],.]],[[.,.],.]] => 3
[[[.,.],[.,.]],[.,[.,.]]] => 1
[[[.,.],[.,.]],[[.,.],.]] => 1
[[[.,[.,.]],.],[.,[.,.]]] => 3
[[[.,[.,.]],.],[[.,.],.]] => 3
[[[[.,.],.],.],[.,[.,.]]] => 3
[[[[.,.],.],.],[[.,.],.]] => 3
[[.,[.,[.,[.,.]]]],[.,.]] => 3
[[.,[.,[[.,.],.]]],[.,.]] => 3
[[.,[[.,.],[.,.]]],[.,.]] => 1
[[.,[[.,[.,.]],.]],[.,.]] => 3
[[.,[[[.,.],.],.]],[.,.]] => 3
[[[.,.],[.,[.,.]]],[.,.]] => 1
[[[.,.],[[.,.],.]],[.,.]] => 1
[[[.,[.,.]],[.,.]],[.,.]] => 1
[[[[.,.],.],[.,.]],[.,.]] => 1
[[[.,[.,[.,.]]],.],[.,.]] => 3
[[[.,[[.,.],.]],.],[.,.]] => 3
[[[[.,.],[.,.]],.],[.,.]] => 1
[[[[.,[.,.]],.],.],[.,.]] => 3
[[[[[.,.],.],.],.],[.,.]] => 3
[[.,[.,[.,[.,[.,.]]]]],.] => 5
[[.,[.,[.,[[.,.],.]]]],.] => 5
[[.,[.,[[.,.],[.,.]]]],.] => 3
[[.,[.,[[.,[.,.]],.]]],.] => 5
[[.,[.,[[[.,.],.],.]]],.] => 5
[[.,[[.,.],[.,[.,.]]]],.] => 3
[[.,[[.,.],[[.,.],.]]],.] => 3
[[.,[[.,[.,.]],[.,.]]],.] => 3
[[.,[[[.,.],.],[.,.]]],.] => 3
[[.,[[.,[.,[.,.]]],.]],.] => 5
[[.,[[.,[[.,.],.]],.]],.] => 5
[[.,[[[.,.],[.,.]],.]],.] => 3
[[.,[[[.,[.,.]],.],.]],.] => 5
[[.,[[[[.,.],.],.],.]],.] => 5
[[[.,.],[.,[.,[.,.]]]],.] => 3
[[[.,.],[.,[[.,.],.]]],.] => 3
[[[.,.],[[.,.],[.,.]]],.] => 1
[[[.,.],[[.,[.,.]],.]],.] => 3
[[[.,.],[[[.,.],.],.]],.] => 3
[[[.,[.,.]],[.,[.,.]]],.] => 3
[[[.,[.,.]],[[.,.],.]],.] => 3
[[[[.,.],.],[.,[.,.]]],.] => 3
[[[[.,.],.],[[.,.],.]],.] => 3
[[[.,[.,[.,.]]],[.,.]],.] => 3
[[[.,[[.,.],.]],[.,.]],.] => 3
[[[[.,.],[.,.]],[.,.]],.] => 1
[[[[.,[.,.]],.],[.,.]],.] => 3
[[[[[.,.],.],.],[.,.]],.] => 3
[[[.,[.,[.,[.,.]]]],.],.] => 5
[[[.,[.,[[.,.],.]]],.],.] => 5
[[[.,[[.,.],[.,.]]],.],.] => 3
[[[.,[[.,[.,.]],.]],.],.] => 5
[[[.,[[[.,.],.],.]],.],.] => 5
[[[[.,.],[.,[.,.]]],.],.] => 3
[[[[.,.],[[.,.],.]],.],.] => 3
[[[[.,[.,.]],[.,.]],.],.] => 3
[[[[[.,.],.],[.,.]],.],.] => 3
[[[[.,[.,[.,.]]],.],.],.] => 5
[[[[.,[[.,.],.]],.],.],.] => 5
[[[[[.,.],[.,.]],.],.],.] => 3
[[[[[.,[.,.]],.],.],.],.] => 5
[[[[[[.,.],.],.],.],.],.] => 5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 6
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 4
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 6
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 6
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 4
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 4
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 4
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 4
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 6
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 6
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 4
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 6
[.,[.,[.,[[[[.,.],.],.],.]]]] => 6
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 4
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 4
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 4
[.,[.,[[.,.],[[[.,.],.],.]]]] => 4
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 4
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 4
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 4
[.,[.,[[[.,.],.],[[.,.],.]]]] => 4
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 4
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 4
[.,[.,[[[[.,.],.],.],[.,.]]]] => 4
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 6
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 6
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 4
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 6
[.,[.,[[.,[[[.,.],.],.]],.]]] => 6
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 4
[.,[.,[[[.,.],[[.,.],.]],.]]] => 4
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 4
[.,[.,[[[[.,.],.],[.,.]],.]]] => 4
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 6
[.,[.,[[[.,[[.,.],.]],.],.]]] => 6
[.,[.,[[[[.,.],[.,.]],.],.]]] => 4
[.,[.,[[[[.,[.,.]],.],.],.]]] => 6
[.,[.,[[[[[.,.],.],.],.],.]]] => 6
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 4
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 4
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 4
[.,[[.,.],[.,[[[.,.],.],.]]]] => 4
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[.,[[.,.],[[.,.],[[.,.],.]]]] => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 4
[.,[[.,.],[[.,[[.,.],.]],.]]] => 4
[.,[[.,.],[[[.,.],[.,.]],.]]] => 2
[.,[[.,.],[[[.,[.,.]],.],.]]] => 4
[.,[[.,.],[[[[.,.],.],.],.]]] => 4
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 4
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 4
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 4
[.,[[.,[.,.]],[[[.,.],.],.]]] => 4
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 4
[.,[[[.,.],.],[.,[[.,.],.]]]] => 4
[.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => 4
[.,[[[.,.],.],[[[.,.],.],.]]] => 4
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 4
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 4
[.,[[.,[[.,.],.]],[[.,.],.]]] => 4
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 4
[.,[[[.,[.,.]],.],[[.,.],.]]] => 4
[.,[[[[.,.],.],.],[.,[.,.]]]] => 4
[.,[[[[.,.],.],.],[[.,.],.]]] => 4
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 4
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 4
[.,[[.,[[[.,.],.],.]],[.,.]]] => 4
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 2
[.,[[[[.,.],.],[.,.]],[.,.]]] => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 4
[.,[[[.,[[.,.],.]],.],[.,.]]] => 4
[.,[[[[.,.],[.,.]],.],[.,.]]] => 2
[.,[[[[.,[.,.]],.],.],[.,.]]] => 4
[.,[[[[[.,.],.],.],.],[.,.]]] => 4
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 6
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 6
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 4
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 6
[.,[[.,[.,[[[.,.],.],.]]],.]] => 6
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 4
[.,[[.,[[.,.],[[.,.],.]]],.]] => 4
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 4
[.,[[.,[[[.,.],.],[.,.]]],.]] => 4
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 6
[.,[[.,[[.,[[.,.],.]],.]],.]] => 6
[.,[[.,[[[.,.],[.,.]],.]],.]] => 4
[.,[[.,[[[.,[.,.]],.],.]],.]] => 6
[.,[[.,[[[[.,.],.],.],.]],.]] => 6
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 4
[.,[[[.,.],[.,[[.,.],.]]],.]] => 4
[.,[[[.,.],[[.,.],[.,.]]],.]] => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => 4
[.,[[[.,.],[[[.,.],.],.]],.]] => 4
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 4
[.,[[[.,[.,.]],[[.,.],.]],.]] => 4
[.,[[[[.,.],.],[.,[.,.]]],.]] => 4
[.,[[[[.,.],.],[[.,.],.]],.]] => 4
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 4
[.,[[[.,[[.,.],.]],[.,.]],.]] => 4
[.,[[[[.,.],[.,.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],.],[.,.]],.]] => 4
[.,[[[[[.,.],.],.],[.,.]],.]] => 4
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 6
[.,[[[.,[.,[[.,.],.]]],.],.]] => 6
[.,[[[.,[[.,.],[.,.]]],.],.]] => 4
[.,[[[.,[[.,[.,.]],.]],.],.]] => 6
[.,[[[.,[[[.,.],.],.]],.],.]] => 6
[.,[[[[.,.],[.,[.,.]]],.],.]] => 4
[.,[[[[.,.],[[.,.],.]],.],.]] => 4
[.,[[[[.,[.,.]],[.,.]],.],.]] => 4
[.,[[[[[.,.],.],[.,.]],.],.]] => 4
[.,[[[[.,[.,[.,.]]],.],.],.]] => 6
[.,[[[[.,[[.,.],.]],.],.],.]] => 6
[.,[[[[[.,.],[.,.]],.],.],.]] => 4
[.,[[[[[.,[.,.]],.],.],.],.]] => 6
[.,[[[[[[.,.],.],.],.],.],.]] => 6
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 4
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 4
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 4
[[.,.],[.,[.,[[[.,.],.],.]]]] => 4
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 4
[[.,.],[.,[[.,[[.,.],.]],.]]] => 4
[[.,.],[.,[[[.,.],[.,.]],.]]] => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => 4
[[.,.],[.,[[[[.,.],.],.],.]]] => 4
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => 0
[[.,.],[[.,.],[[.,[.,.]],.]]] => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => 0
[[.,.],[[[.,[.,.]],.],[.,.]]] => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 4
[[.,.],[[.,[.,[[.,.],.]]],.]] => 4
[[.,.],[[.,[[.,.],[.,.]]],.]] => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => 4
[[.,.],[[.,[[[.,.],.],.]],.]] => 4
[[.,.],[[[.,.],[.,[.,.]]],.]] => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => 4
[[.,.],[[[.,[[.,.],.]],.],.]] => 4
[[.,.],[[[[.,.],[.,.]],.],.]] => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => 4
[[.,.],[[[[[.,.],.],.],.],.]] => 4
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 4
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 4
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 4
[[.,[.,.]],[.,[[[.,.],.],.]]] => 4
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 4
[[.,[.,.]],[[.,[[.,.],.]],.]] => 4
[[.,[.,.]],[[[.,.],[.,.]],.]] => 2
[[.,[.,.]],[[[.,[.,.]],.],.]] => 4
[[.,[.,.]],[[[[.,.],.],.],.]] => 4
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 4
[[[.,.],.],[.,[.,[[.,.],.]]]] => 4
[[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => 4
[[[.,.],.],[.,[[[.,.],.],.]]] => 4
[[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => 2
[[[.,.],.],[[.,[.,.]],[.,.]]] => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[[[.,.],.],[[.,[[.,.],.]],.]] => 4
[[[.,.],.],[[[.,.],[.,.]],.]] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => 4
[[[.,.],.],[[[[.,.],.],.],.]] => 4
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 4
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 4
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 4
[[.,[.,[.,.]]],[[[.,.],.],.]] => 4
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 4
[[.,[[.,.],.]],[.,[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,.],[.,.]]] => 2
[[.,[[.,.],.]],[[.,[.,.]],.]] => 4
[[.,[[.,.],.]],[[[.,.],.],.]] => 4
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 2
[[[.,.],[.,.]],[.,[[.,.],.]]] => 2
[[[.,.],[.,.]],[[.,.],[.,.]]] => 0
[[[.,.],[.,.]],[[.,[.,.]],.]] => 2
[[[.,.],[.,.]],[[[.,.],.],.]] => 2
[[[.,[.,.]],.],[.,[.,[.,.]]]] => 4
[[[.,[.,.]],.],[.,[[.,.],.]]] => 4
[[[.,[.,.]],.],[[.,.],[.,.]]] => 2
[[[.,[.,.]],.],[[.,[.,.]],.]] => 4
[[[.,[.,.]],.],[[[.,.],.],.]] => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => 4
[[[[.,.],.],.],[.,[[.,.],.]]] => 4
[[[[.,.],.],.],[[.,.],[.,.]]] => 2
[[[[.,.],.],.],[[.,[.,.]],.]] => 4
[[[[.,.],.],.],[[[.,.],.],.]] => 4
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => 4
[[.,[.,[.,[.,.]]]],[[.,.],.]] => 4
[[.,[.,[[.,.],.]]],[.,[.,.]]] => 4
[[.,[.,[[.,.],.]]],[[.,.],.]] => 4
[[.,[[.,.],[.,.]]],[.,[.,.]]] => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => 2
[[.,[[.,[.,.]],.]],[.,[.,.]]] => 4
[[.,[[.,[.,.]],.]],[[.,.],.]] => 4
[[.,[[[.,.],.],.]],[.,[.,.]]] => 4
[[.,[[[.,.],.],.]],[[.,.],.]] => 4
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => 2
[[[.,.],[[.,.],.]],[.,[.,.]]] => 2
[[[.,.],[[.,.],.]],[[.,.],.]] => 2
[[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[[[.,[.,.]],[.,.]],[[.,.],.]] => 2
[[[[.,.],.],[.,.]],[.,[.,.]]] => 2
[[[[.,.],.],[.,.]],[[.,.],.]] => 2
[[[.,[.,[.,.]]],.],[.,[.,.]]] => 4
[[[.,[.,[.,.]]],.],[[.,.],.]] => 4
[[[.,[[.,.],.]],.],[.,[.,.]]] => 4
[[[.,[[.,.],.]],.],[[.,.],.]] => 4
[[[[.,.],[.,.]],.],[.,[.,.]]] => 2
[[[[.,.],[.,.]],.],[[.,.],.]] => 2
[[[[.,[.,.]],.],.],[.,[.,.]]] => 4
[[[[.,[.,.]],.],.],[[.,.],.]] => 4
[[[[[.,.],.],.],.],[.,[.,.]]] => 4
[[[[[.,.],.],.],.],[[.,.],.]] => 4
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[[.,[.,[.,[[.,.],.]]]],[.,.]] => 4
[[.,[.,[[.,.],[.,.]]]],[.,.]] => 2
[[.,[.,[[.,[.,.]],.]]],[.,.]] => 4
[[.,[.,[[[.,.],.],.]]],[.,.]] => 4
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 2
[[.,[[.,.],[[.,.],.]]],[.,.]] => 2
[[.,[[.,[.,.]],[.,.]]],[.,.]] => 2
[[.,[[[.,.],.],[.,.]]],[.,.]] => 2
[[.,[[.,[.,[.,.]]],.]],[.,.]] => 4
[[.,[[.,[[.,.],.]],.]],[.,.]] => 4
[[.,[[[.,.],[.,.]],.]],[.,.]] => 2
[[.,[[[.,[.,.]],.],.]],[.,.]] => 4
[[.,[[[[.,.],.],.],.]],[.,.]] => 4
[[[.,.],[.,[.,[.,.]]]],[.,.]] => 2
[[[.,.],[.,[[.,.],.]]],[.,.]] => 2
[[[.,.],[[.,.],[.,.]]],[.,.]] => 0
[[[.,.],[[.,[.,.]],.]],[.,.]] => 2
[[[.,.],[[[.,.],.],.]],[.,.]] => 2
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 2
[[[.,[.,.]],[[.,.],.]],[.,.]] => 2
[[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[[[[.,.],.],[[.,.],.]],[.,.]] => 2
[[[.,[.,[.,.]]],[.,.]],[.,.]] => 2
[[[.,[[.,.],.]],[.,.]],[.,.]] => 2
[[[[.,.],[.,.]],[.,.]],[.,.]] => 0
[[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[[[[[.,.],.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,[.,.]]]],.],[.,.]] => 4
[[[.,[.,[[.,.],.]]],.],[.,.]] => 4
[[[.,[[.,.],[.,.]]],.],[.,.]] => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => 4
[[[.,[[[.,.],.],.]],.],[.,.]] => 4
[[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[[[[.,.],[[.,.],.]],.],[.,.]] => 2
[[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[[[[[.,.],.],[.,.]],.],[.,.]] => 2
[[[[.,[.,[.,.]]],.],.],[.,.]] => 4
[[[[.,[[.,.],.]],.],.],[.,.]] => 4
[[[[[.,.],[.,.]],.],.],[.,.]] => 2
[[[[[.,[.,.]],.],.],.],[.,.]] => 4
[[[[[[.,.],.],.],.],.],[.,.]] => 4
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 6
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 6
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 4
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 6
[[.,[.,[.,[[[.,.],.],.]]]],.] => 6
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 4
[[.,[.,[[.,.],[[.,.],.]]]],.] => 4
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 4
[[.,[.,[[[.,.],.],[.,.]]]],.] => 4
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 6
[[.,[.,[[.,[[.,.],.]],.]]],.] => 6
[[.,[.,[[[.,.],[.,.]],.]]],.] => 4
[[.,[.,[[[.,[.,.]],.],.]]],.] => 6
[[.,[.,[[[[.,.],.],.],.]]],.] => 6
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 4
[[.,[[.,.],[.,[[.,.],.]]]],.] => 4
[[.,[[.,.],[[.,.],[.,.]]]],.] => 2
[[.,[[.,.],[[.,[.,.]],.]]],.] => 4
[[.,[[.,.],[[[.,.],.],.]]],.] => 4
[[.,[[.,[.,.]],[.,[.,.]]]],.] => 4
[[.,[[.,[.,.]],[[.,.],.]]],.] => 4
[[.,[[[.,.],.],[.,[.,.]]]],.] => 4
[[.,[[[.,.],.],[[.,.],.]]],.] => 4
[[.,[[.,[.,[.,.]]],[.,.]]],.] => 4
[[.,[[.,[[.,.],.]],[.,.]]],.] => 4
[[.,[[[.,.],[.,.]],[.,.]]],.] => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => 4
[[.,[[[[.,.],.],.],[.,.]]],.] => 4
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 6
[[.,[[.,[.,[[.,.],.]]],.]],.] => 6
[[.,[[.,[[.,.],[.,.]]],.]],.] => 4
[[.,[[.,[[.,[.,.]],.]],.]],.] => 6
[[.,[[.,[[[.,.],.],.]],.]],.] => 6
[[.,[[[.,.],[.,[.,.]]],.]],.] => 4
[[.,[[[.,.],[[.,.],.]],.]],.] => 4
[[.,[[[.,[.,.]],[.,.]],.]],.] => 4
[[.,[[[[.,.],.],[.,.]],.]],.] => 4
[[.,[[[.,[.,[.,.]]],.],.]],.] => 6
[[.,[[[.,[[.,.],.]],.],.]],.] => 6
[[.,[[[[.,.],[.,.]],.],.]],.] => 4
[[.,[[[[.,[.,.]],.],.],.]],.] => 6
[[.,[[[[[.,.],.],.],.],.]],.] => 6
[[[.,.],[.,[.,[.,[.,.]]]]],.] => 4
[[[.,.],[.,[.,[[.,.],.]]]],.] => 4
[[[.,.],[.,[[.,.],[.,.]]]],.] => 2
[[[.,.],[.,[[.,[.,.]],.]]],.] => 4
[[[.,.],[.,[[[.,.],.],.]]],.] => 4
[[[.,.],[[.,.],[.,[.,.]]]],.] => 2
[[[.,.],[[.,.],[[.,.],.]]],.] => 2
[[[.,.],[[.,[.,.]],[.,.]]],.] => 2
[[[.,.],[[[.,.],.],[.,.]]],.] => 2
[[[.,.],[[.,[.,[.,.]]],.]],.] => 4
[[[.,.],[[.,[[.,.],.]],.]],.] => 4
[[[.,.],[[[.,.],[.,.]],.]],.] => 2
[[[.,.],[[[.,[.,.]],.],.]],.] => 4
[[[.,.],[[[[.,.],.],.],.]],.] => 4
[[[.,[.,.]],[.,[.,[.,.]]]],.] => 4
[[[.,[.,.]],[.,[[.,.],.]]],.] => 4
[[[.,[.,.]],[[.,.],[.,.]]],.] => 2
[[[.,[.,.]],[[.,[.,.]],.]],.] => 4
[[[.,[.,.]],[[[.,.],.],.]],.] => 4
[[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[[[[.,.],.],[.,[[.,.],.]]],.] => 4
[[[[.,.],.],[[.,.],[.,.]]],.] => 2
[[[[.,.],.],[[.,[.,.]],.]],.] => 4
[[[[.,.],.],[[[.,.],.],.]],.] => 4
[[[.,[.,[.,.]]],[.,[.,.]]],.] => 4
[[[.,[.,[.,.]]],[[.,.],.]],.] => 4
[[[.,[[.,.],.]],[.,[.,.]]],.] => 4
[[[.,[[.,.],.]],[[.,.],.]],.] => 4
[[[[.,.],[.,.]],[.,[.,.]]],.] => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => 2
[[[[.,[.,.]],.],[.,[.,.]]],.] => 4
[[[[.,[.,.]],.],[[.,.],.]],.] => 4
[[[[[.,.],.],.],[.,[.,.]]],.] => 4
[[[[[.,.],.],.],[[.,.],.]],.] => 4
[[[.,[.,[.,[.,.]]]],[.,.]],.] => 4
[[[.,[.,[[.,.],.]]],[.,.]],.] => 4
[[[.,[[.,.],[.,.]]],[.,.]],.] => 2
[[[.,[[.,[.,.]],.]],[.,.]],.] => 4
[[[.,[[[.,.],.],.]],[.,.]],.] => 4
[[[[.,.],[.,[.,.]]],[.,.]],.] => 2
[[[[.,.],[[.,.],.]],[.,.]],.] => 2
[[[[.,[.,.]],[.,.]],[.,.]],.] => 2
[[[[[.,.],.],[.,.]],[.,.]],.] => 2
[[[[.,[.,[.,.]]],.],[.,.]],.] => 4
[[[[.,[[.,.],.]],.],[.,.]],.] => 4
[[[[[.,.],[.,.]],.],[.,.]],.] => 2
[[[[[.,[.,.]],.],.],[.,.]],.] => 4
[[[[[[.,.],.],.],.],[.,.]],.] => 4
[[[.,[.,[.,[.,[.,.]]]]],.],.] => 6
[[[.,[.,[.,[[.,.],.]]]],.],.] => 6
[[[.,[.,[[.,.],[.,.]]]],.],.] => 4
[[[.,[.,[[.,[.,.]],.]]],.],.] => 6
[[[.,[.,[[[.,.],.],.]]],.],.] => 6
[[[.,[[.,.],[.,[.,.]]]],.],.] => 4
[[[.,[[.,.],[[.,.],.]]],.],.] => 4
[[[.,[[.,[.,.]],[.,.]]],.],.] => 4
[[[.,[[[.,.],.],[.,.]]],.],.] => 4
[[[.,[[.,[.,[.,.]]],.]],.],.] => 6
[[[.,[[.,[[.,.],.]],.]],.],.] => 6
[[[.,[[[.,.],[.,.]],.]],.],.] => 4
[[[.,[[[.,[.,.]],.],.]],.],.] => 6
[[[.,[[[[.,.],.],.],.]],.],.] => 6
[[[[.,.],[.,[.,[.,.]]]],.],.] => 4
[[[[.,.],[.,[[.,.],.]]],.],.] => 4
[[[[.,.],[[.,.],[.,.]]],.],.] => 2
[[[[.,.],[[.,[.,.]],.]],.],.] => 4
[[[[.,.],[[[.,.],.],.]],.],.] => 4
[[[[.,[.,.]],[.,[.,.]]],.],.] => 4
[[[[.,[.,.]],[[.,.],.]],.],.] => 4
[[[[[.,.],.],[.,[.,.]]],.],.] => 4
[[[[[.,.],.],[[.,.],.]],.],.] => 4
[[[[.,[.,[.,.]]],[.,.]],.],.] => 4
[[[[.,[[.,.],.]],[.,.]],.],.] => 4
[[[[[.,.],[.,.]],[.,.]],.],.] => 2
[[[[[.,[.,.]],.],[.,.]],.],.] => 4
[[[[[[.,.],.],.],[.,.]],.],.] => 4
[[[[.,[.,[.,[.,.]]]],.],.],.] => 6
[[[[.,[.,[[.,.],.]]],.],.],.] => 6
[[[[.,[[.,.],[.,.]]],.],.],.] => 4
[[[[.,[[.,[.,.]],.]],.],.],.] => 6
[[[[.,[[[.,.],.],.]],.],.],.] => 6
[[[[[.,.],[.,[.,.]]],.],.],.] => 4
[[[[[.,.],[[.,.],.]],.],.],.] => 4
[[[[[.,[.,.]],[.,.]],.],.],.] => 4
[[[[[[.,.],.],[.,.]],.],.],.] => 4
[[[[[.,[.,[.,.]]],.],.],.],.] => 6
[[[[[.,[[.,.],.]],.],.],.],.] => 6
[[[[[[.,.],[.,.]],.],.],.],.] => 4
[[[[[[.,[.,.]],.],.],.],.],.] => 6
[[[[[[[.,.],.],.],.],.],.],.] => 6
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 7
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 7
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 5
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 7
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => 7
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 5
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 5
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 5
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => 5
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => 7
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => 7
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => 5
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => 7
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => 7
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 5
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 5
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 3
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 5
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => 5
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 5
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => 5
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => 5
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => 5
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 5
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => 5
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => 3
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[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => 5
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 7
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => 7
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => 5
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => 7
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => 7
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => 5
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => 5
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => 5
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => 5
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => 7
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => 7
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => 5
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => 7
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => 7
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 5
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 5
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 3
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => 5
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => 5
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 3
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 3
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 3
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => 3
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => 5
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => 5
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => 3
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => 5
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => 5
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 5
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 5
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 3
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => 5
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => 5
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => 5
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => 5
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => 3
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => 5
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => 5
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 5
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => 5
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => 5
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => 5
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => 3
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => 3
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => 5
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => 5
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => 5
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => 5
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 5
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => 5
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => 3
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => 5
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => 5
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => 3
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => 3
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => 3
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => 3
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => 5
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => 5
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => 3
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => 5
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => 5
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => 7
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => 7
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => 5
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => 7
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => 7
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => 5
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => 5
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => 5
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => 5
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => 7
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => 7
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => 5
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => 7
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => 7
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => 5
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => 5
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => 3
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => 5
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => 5
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => 5
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => 5
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => 5
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => 5
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => 5
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => 5
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => 3
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => 5
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => 5
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => 7
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => 7
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => 5
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => 7
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => 7
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => 5
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => 5
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => 5
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => 5
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => 7
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => 7
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => 5
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => 7
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => 7
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 5
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 5
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => 3
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => 5
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => 5
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => 3
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => 3
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => 3
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => 3
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => 5
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => 5
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => 3
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => 5
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => 5
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => 3
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => 3
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => 1
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => 3
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => 3
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => 3
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[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => 3
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 3
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 1
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 3
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 3
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 1
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 1
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 1
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 1
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 3
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 3
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 1
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 3
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => 3
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 5
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 5
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 3
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 5
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 5
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 3
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 3
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 5
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 5
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 5
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => 5
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 3
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 3
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 1
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 3
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => 3
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 3
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 3
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 3
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 3
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 1
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 3
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => 3
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 5
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 5
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 3
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 5
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => 5
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 3
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => 3
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 3
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => 3
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 5
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => 5
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => 3
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => 5
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 5
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 5
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 5
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 3
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 5
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 5
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 3
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 3
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 3
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 5
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 5
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 3
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 5
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 5
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 3
-----------------------------------------------------------------------------
Created: Feb 10, 2016 at 09:37 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Feb 10, 2016 at 09:57 by Christian Stump