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*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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*    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: St000196

-----------------------------------------------------------------------------
Collection: Binary trees

-----------------------------------------------------------------------------
Description: The number of occurrences of the contiguous pattern {{{[[.,.],[.,.]]}}} in a binary tree.

Equivalently, this is the number of branches in the tree, i.e. the number of nodes with two children. Binary trees avoiding this pattern are counted by $2^{n-2}$.



-----------------------------------------------------------------------------
References: 

-----------------------------------------------------------------------------
Code:
# BinaryTree -> Bool
def is_leaf(b):
    return b == BinaryTree('.')

# BinaryTree -> Int
def hat_count(b):
    if is_leaf(b):
        return 0
    if not is_leaf(b[0]) and not is_leaf(b[1]):
        return 1
    return 0

# (a -> a -> a) -> (BinaryTree -> a) -> BinaryTree -> a
def fold_tree(f, g, b):
    if is_leaf(b):
        return g(b)
    else:
        return f(g(b), f(fold_tree(f, g, b[0]), fold_tree(f, g, b[1])))

def statistic(b):
    return fold_tree(lambda a,b: a+b, hat_count, b)


-----------------------------------------------------------------------------
Statistic values:

[.,.]                         => 0
[.,[.,.]]                     => 0
[[.,.],.]                     => 0
[.,[.,[.,.]]]                 => 0
[.,[[.,.],.]]                 => 0
[[.,.],[.,.]]                 => 1
[[.,[.,.]],.]                 => 0
[[[.,.],.],.]                 => 0
[.,[.,[.,[.,.]]]]             => 0
[.,[.,[[.,.],.]]]             => 0
[.,[[.,.],[.,.]]]             => 1
[.,[[.,[.,.]],.]]             => 0
[.,[[[.,.],.],.]]             => 0
[[.,.],[.,[.,.]]]             => 1
[[.,.],[[.,.],.]]             => 1
[[.,[.,.]],[.,.]]             => 1
[[[.,.],.],[.,.]]             => 1
[[.,[.,[.,.]]],.]             => 0
[[.,[[.,.],.]],.]             => 0
[[[.,.],[.,.]],.]             => 1
[[[.,[.,.]],.],.]             => 0
[[[[.,.],.],.],.]             => 0
[.,[.,[.,[.,[.,.]]]]]         => 0
[.,[.,[.,[[.,.],.]]]]         => 0
[.,[.,[[.,.],[.,.]]]]         => 1
[.,[.,[[.,[.,.]],.]]]         => 0
[.,[.,[[[.,.],.],.]]]         => 0
[.,[[.,.],[.,[.,.]]]]         => 1
[.,[[.,.],[[.,.],.]]]         => 1
[.,[[.,[.,.]],[.,.]]]         => 1
[.,[[[.,.],.],[.,.]]]         => 1
[.,[[.,[.,[.,.]]],.]]         => 0
[.,[[.,[[.,.],.]],.]]         => 0
[.,[[[.,.],[.,.]],.]]         => 1
[.,[[[.,[.,.]],.],.]]         => 0
[.,[[[[.,.],.],.],.]]         => 0
[[.,.],[.,[.,[.,.]]]]         => 1
[[.,.],[.,[[.,.],.]]]         => 1
[[.,.],[[.,.],[.,.]]]         => 2
[[.,.],[[.,[.,.]],.]]         => 1
[[.,.],[[[.,.],.],.]]         => 1
[[.,[.,.]],[.,[.,.]]]         => 1
[[.,[.,.]],[[.,.],.]]         => 1
[[[.,.],.],[.,[.,.]]]         => 1
[[[.,.],.],[[.,.],.]]         => 1
[[.,[.,[.,.]]],[.,.]]         => 1
[[.,[[.,.],.]],[.,.]]         => 1
[[[.,.],[.,.]],[.,.]]         => 2
[[[.,[.,.]],.],[.,.]]         => 1
[[[[.,.],.],.],[.,.]]         => 1
[[.,[.,[.,[.,.]]]],.]         => 0
[[.,[.,[[.,.],.]]],.]         => 0
[[.,[[.,.],[.,.]]],.]         => 1
[[.,[[.,[.,.]],.]],.]         => 0
[[.,[[[.,.],.],.]],.]         => 0
[[[.,.],[.,[.,.]]],.]         => 1
[[[.,.],[[.,.],.]],.]         => 1
[[[.,[.,.]],[.,.]],.]         => 1
[[[[.,.],.],[.,.]],.]         => 1
[[[.,[.,[.,.]]],.],.]         => 0
[[[.,[[.,.],.]],.],.]         => 0
[[[[.,.],[.,.]],.],.]         => 1
[[[[.,[.,.]],.],.],.]         => 0
[[[[[.,.],.],.],.],.]         => 0
[.,[.,[.,[.,[.,[.,.]]]]]]     => 0
[.,[.,[.,[.,[[.,.],.]]]]]     => 0
[.,[.,[.,[[.,.],[.,.]]]]]     => 1
[.,[.,[.,[[.,[.,.]],.]]]]     => 0
[.,[.,[.,[[[.,.],.],.]]]]     => 0
[.,[.,[[.,.],[.,[.,.]]]]]     => 1
[.,[.,[[.,.],[[.,.],.]]]]     => 1
[.,[.,[[.,[.,.]],[.,.]]]]     => 1
[.,[.,[[[.,.],.],[.,.]]]]     => 1
[.,[.,[[.,[.,[.,.]]],.]]]     => 0
[.,[.,[[.,[[.,.],.]],.]]]     => 0
[.,[.,[[[.,.],[.,.]],.]]]     => 1
[.,[.,[[[.,[.,.]],.],.]]]     => 0
[.,[.,[[[[.,.],.],.],.]]]     => 0
[.,[[.,.],[.,[.,[.,.]]]]]     => 1
[.,[[.,.],[.,[[.,.],.]]]]     => 1
[.,[[.,.],[[.,.],[.,.]]]]     => 2
[.,[[.,.],[[.,[.,.]],.]]]     => 1
[.,[[.,.],[[[.,.],.],.]]]     => 1
[.,[[.,[.,.]],[.,[.,.]]]]     => 1
[.,[[.,[.,.]],[[.,.],.]]]     => 1
[.,[[[.,.],.],[.,[.,.]]]]     => 1
[.,[[[.,.],.],[[.,.],.]]]     => 1
[.,[[.,[.,[.,.]]],[.,.]]]     => 1
[.,[[.,[[.,.],.]],[.,.]]]     => 1
[.,[[[.,.],[.,.]],[.,.]]]     => 2
[.,[[[.,[.,.]],.],[.,.]]]     => 1
[.,[[[[.,.],.],.],[.,.]]]     => 1
[.,[[.,[.,[.,[.,.]]]],.]]     => 0
[.,[[.,[.,[[.,.],.]]],.]]     => 0
[.,[[.,[[.,.],[.,.]]],.]]     => 1
[.,[[.,[[.,[.,.]],.]],.]]     => 0
[.,[[.,[[[.,.],.],.]],.]]     => 0
[.,[[[.,.],[.,[.,.]]],.]]     => 1
[.,[[[.,.],[[.,.],.]],.]]     => 1
[.,[[[.,[.,.]],[.,.]],.]]     => 1
[.,[[[[.,.],.],[.,.]],.]]     => 1
[.,[[[.,[.,[.,.]]],.],.]]     => 0
[.,[[[.,[[.,.],.]],.],.]]     => 0
[.,[[[[.,.],[.,.]],.],.]]     => 1
[.,[[[[.,[.,.]],.],.],.]]     => 0
[.,[[[[[.,.],.],.],.],.]]     => 0
[[.,.],[.,[.,[.,[.,.]]]]]     => 1
[[.,.],[.,[.,[[.,.],.]]]]     => 1
[[.,.],[.,[[.,.],[.,.]]]]     => 2
[[.,.],[.,[[.,[.,.]],.]]]     => 1
[[.,.],[.,[[[.,.],.],.]]]     => 1
[[.,.],[[.,.],[.,[.,.]]]]     => 2
[[.,.],[[.,.],[[.,.],.]]]     => 2
[[.,.],[[.,[.,.]],[.,.]]]     => 2
[[.,.],[[[.,.],.],[.,.]]]     => 2
[[.,.],[[.,[.,[.,.]]],.]]     => 1
[[.,.],[[.,[[.,.],.]],.]]     => 1
[[.,.],[[[.,.],[.,.]],.]]     => 2
[[.,.],[[[.,[.,.]],.],.]]     => 1
[[.,.],[[[[.,.],.],.],.]]     => 1
[[.,[.,.]],[.,[.,[.,.]]]]     => 1
[[.,[.,.]],[.,[[.,.],.]]]     => 1
[[.,[.,.]],[[.,.],[.,.]]]     => 2
[[.,[.,.]],[[.,[.,.]],.]]     => 1
[[.,[.,.]],[[[.,.],.],.]]     => 1
[[[.,.],.],[.,[.,[.,.]]]]     => 1
[[[.,.],.],[.,[[.,.],.]]]     => 1
[[[.,.],.],[[.,.],[.,.]]]     => 2
[[[.,.],.],[[.,[.,.]],.]]     => 1
[[[.,.],.],[[[.,.],.],.]]     => 1
[[.,[.,[.,.]]],[.,[.,.]]]     => 1
[[.,[.,[.,.]]],[[.,.],.]]     => 1
[[.,[[.,.],.]],[.,[.,.]]]     => 1
[[.,[[.,.],.]],[[.,.],.]]     => 1
[[[.,.],[.,.]],[.,[.,.]]]     => 2
[[[.,.],[.,.]],[[.,.],.]]     => 2
[[[.,[.,.]],.],[.,[.,.]]]     => 1
[[[.,[.,.]],.],[[.,.],.]]     => 1
[[[[.,.],.],.],[.,[.,.]]]     => 1
[[[[.,.],.],.],[[.,.],.]]     => 1
[[.,[.,[.,[.,.]]]],[.,.]]     => 1
[[.,[.,[[.,.],.]]],[.,.]]     => 1
[[.,[[.,.],[.,.]]],[.,.]]     => 2
[[.,[[.,[.,.]],.]],[.,.]]     => 1
[[.,[[[.,.],.],.]],[.,.]]     => 1
[[[.,.],[.,[.,.]]],[.,.]]     => 2
[[[.,.],[[.,.],.]],[.,.]]     => 2
[[[.,[.,.]],[.,.]],[.,.]]     => 2
[[[[.,.],.],[.,.]],[.,.]]     => 2
[[[.,[.,[.,.]]],.],[.,.]]     => 1
[[[.,[[.,.],.]],.],[.,.]]     => 1
[[[[.,.],[.,.]],.],[.,.]]     => 2
[[[[.,[.,.]],.],.],[.,.]]     => 1
[[[[[.,.],.],.],.],[.,.]]     => 1
[[.,[.,[.,[.,[.,.]]]]],.]     => 0
[[.,[.,[.,[[.,.],.]]]],.]     => 0
[[.,[.,[[.,.],[.,.]]]],.]     => 1
[[.,[.,[[.,[.,.]],.]]],.]     => 0
[[.,[.,[[[.,.],.],.]]],.]     => 0
[[.,[[.,.],[.,[.,.]]]],.]     => 1
[[.,[[.,.],[[.,.],.]]],.]     => 1
[[.,[[.,[.,.]],[.,.]]],.]     => 1
[[.,[[[.,.],.],[.,.]]],.]     => 1
[[.,[[.,[.,[.,.]]],.]],.]     => 0
[[.,[[.,[[.,.],.]],.]],.]     => 0
[[.,[[[.,.],[.,.]],.]],.]     => 1
[[.,[[[.,[.,.]],.],.]],.]     => 0
[[.,[[[[.,.],.],.],.]],.]     => 0
[[[.,.],[.,[.,[.,.]]]],.]     => 1
[[[.,.],[.,[[.,.],.]]],.]     => 1
[[[.,.],[[.,.],[.,.]]],.]     => 2
[[[.,.],[[.,[.,.]],.]],.]     => 1
[[[.,.],[[[.,.],.],.]],.]     => 1
[[[.,[.,.]],[.,[.,.]]],.]     => 1
[[[.,[.,.]],[[.,.],.]],.]     => 1
[[[[.,.],.],[.,[.,.]]],.]     => 1
[[[[.,.],.],[[.,.],.]],.]     => 1
[[[.,[.,[.,.]]],[.,.]],.]     => 1
[[[.,[[.,.],.]],[.,.]],.]     => 1
[[[[.,.],[.,.]],[.,.]],.]     => 2
[[[[.,[.,.]],.],[.,.]],.]     => 1
[[[[[.,.],.],.],[.,.]],.]     => 1
[[[.,[.,[.,[.,.]]]],.],.]     => 0
[[[.,[.,[[.,.],.]]],.],.]     => 0
[[[.,[[.,.],[.,.]]],.],.]     => 1
[[[.,[[.,[.,.]],.]],.],.]     => 0
[[[.,[[[.,.],.],.]],.],.]     => 0
[[[[.,.],[.,[.,.]]],.],.]     => 1
[[[[.,.],[[.,.],.]],.],.]     => 1
[[[[.,[.,.]],[.,.]],.],.]     => 1
[[[[[.,.],.],[.,.]],.],.]     => 1
[[[[.,[.,[.,.]]],.],.],.]     => 0
[[[[.,[[.,.],.]],.],.],.]     => 0
[[[[[.,.],[.,.]],.],.],.]     => 1
[[[[[.,[.,.]],.],.],.],.]     => 0
[[[[[[.,.],.],.],.],.],.]     => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 0
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 0
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 0
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 1
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 0
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 0
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 1
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 0
[.,[.,[.,[[[[.,.],.],.],.]]]] => 0
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 1
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 1
[.,[.,[[.,.],[[[.,.],.],.]]]] => 1
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 1
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 1
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 1
[.,[.,[[[.,.],.],[[.,.],.]]]] => 1
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 1
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 1
[.,[.,[[[[.,.],.],.],[.,.]]]] => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 0
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 0
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 1
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 0
[.,[.,[[.,[[[.,.],.],.]],.]]] => 0
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 1
[.,[.,[[[.,.],[[.,.],.]],.]]] => 1
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 1
[.,[.,[[[[.,.],.],[.,.]],.]]] => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 0
[.,[.,[[[.,[[.,.],.]],.],.]]] => 0
[.,[.,[[[[.,.],[.,.]],.],.]]] => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => 0
[.,[.,[[[[[.,.],.],.],.],.]]] => 0
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 1
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 1
[.,[[.,.],[.,[[[.,.],.],.]]]] => 1
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[.,[[.,.],[[.,.],[[.,.],.]]]] => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 1
[.,[[.,.],[[.,[[.,.],.]],.]]] => 1
[.,[[.,.],[[[.,.],[.,.]],.]]] => 2
[.,[[.,.],[[[.,[.,.]],.],.]]] => 1
[.,[[.,.],[[[[.,.],.],.],.]]] => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 1
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 1
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 1
[.,[[.,[.,.]],[[[.,.],.],.]]] => 1
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 1
[.,[[[.,.],.],[.,[[.,.],.]]]] => 1
[.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => 1
[.,[[[.,.],.],[[[.,.],.],.]]] => 1
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 1
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 1
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 1
[.,[[.,[[.,.],.]],[[.,.],.]]] => 1
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 1
[.,[[[.,[.,.]],.],[[.,.],.]]] => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 1
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 1
[.,[[.,[[[.,.],.],.]],[.,.]]] => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 2
[.,[[[[.,.],.],[.,.]],[.,.]]] => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => 2
[.,[[[[.,[.,.]],.],.],[.,.]]] => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 0
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 1
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => 0
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 1
[.,[[.,[[.,.],[[.,.],.]]],.]] => 1
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 1
[.,[[.,[[[.,.],.],[.,.]]],.]] => 1
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => 1
[.,[[.,[[[.,[.,.]],.],.]],.]] => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => 0
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 1
[.,[[[.,.],[.,[[.,.],.]]],.]] => 1
[.,[[[.,.],[[.,.],[.,.]]],.]] => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => 1
[.,[[[.,.],[[[.,.],.],.]],.]] => 1
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 1
[.,[[[.,[.,.]],[[.,.],.]],.]] => 1
[.,[[[[.,.],.],[.,[.,.]]],.]] => 1
[.,[[[[.,.],.],[[.,.],.]],.]] => 1
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 1
[.,[[[.,[[.,.],.]],[.,.]],.]] => 1
[.,[[[[.,.],[.,.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],.],[.,.]],.]] => 1
[.,[[[[[.,.],.],.],[.,.]],.]] => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => 0
[.,[[[.,[[.,.],[.,.]]],.],.]] => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => 0
[.,[[[.,[[[.,.],.],.]],.],.]] => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => 1
[.,[[[[.,[.,.]],[.,.]],.],.]] => 1
[.,[[[[[.,.],.],[.,.]],.],.]] => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => 0
[.,[[[[[[.,.],.],.],.],.],.]] => 0
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 1
[[.,.],[.,[.,[[[.,.],.],.]]]] => 1
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 1
[[.,.],[.,[[.,[[.,.],.]],.]]] => 1
[[.,.],[.,[[[.,.],[.,.]],.]]] => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => 1
[[.,.],[.,[[[[.,.],.],.],.]]] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[[.,.],[[.,.],[[.,[.,.]],.]]] => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => 3
[[.,.],[[[.,[.,.]],.],[.,.]]] => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 1
[[.,.],[[.,[.,[[.,.],.]]],.]] => 1
[[.,.],[[.,[[.,.],[.,.]]],.]] => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => 1
[[.,.],[[.,[[[.,.],.],.]],.]] => 1
[[.,.],[[[.,.],[.,[.,.]]],.]] => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => 1
[[.,.],[[[.,[[.,.],.]],.],.]] => 1
[[.,.],[[[[.,.],[.,.]],.],.]] => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => 1
[[.,.],[[[[[.,.],.],.],.],.]] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 1
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 1
[[.,[.,.]],[.,[[[.,.],.],.]]] => 1
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 1
[[.,[.,.]],[[.,[[.,.],.]],.]] => 1
[[.,[.,.]],[[[.,.],[.,.]],.]] => 2
[[.,[.,.]],[[[.,[.,.]],.],.]] => 1
[[.,[.,.]],[[[[.,.],.],.],.]] => 1
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 1
[[[.,.],.],[.,[.,[[.,.],.]]]] => 1
[[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => 1
[[[.,.],.],[.,[[[.,.],.],.]]] => 1
[[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => 2
[[[.,.],.],[[.,[.,.]],[.,.]]] => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => 1
[[[.,.],.],[[.,[[.,.],.]],.]] => 1
[[[.,.],.],[[[.,.],[.,.]],.]] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => 1
[[[.,.],.],[[[[.,.],.],.],.]] => 1
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 1
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 1
[[.,[.,[.,.]]],[[[.,.],.],.]] => 1
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 1
[[.,[[.,.],.]],[.,[[.,.],.]]] => 1
[[.,[[.,.],.]],[[.,.],[.,.]]] => 2
[[.,[[.,.],.]],[[.,[.,.]],.]] => 1
[[.,[[.,.],.]],[[[.,.],.],.]] => 1
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 2
[[[.,.],[.,.]],[.,[[.,.],.]]] => 2
[[[.,.],[.,.]],[[.,.],[.,.]]] => 3
[[[.,.],[.,.]],[[.,[.,.]],.]] => 2
[[[.,.],[.,.]],[[[.,.],.],.]] => 2
[[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[[[.,[.,.]],.],[.,[[.,.],.]]] => 1
[[[.,[.,.]],.],[[.,.],[.,.]]] => 2
[[[.,[.,.]],.],[[.,[.,.]],.]] => 1
[[[.,[.,.]],.],[[[.,.],.],.]] => 1
[[[[.,.],.],.],[.,[.,[.,.]]]] => 1
[[[[.,.],.],.],[.,[[.,.],.]]] => 1
[[[[.,.],.],.],[[.,.],[.,.]]] => 2
[[[[.,.],.],.],[[.,[.,.]],.]] => 1
[[[[.,.],.],.],[[[.,.],.],.]] => 1
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[[.,[.,[.,[.,.]]]],[[.,.],.]] => 1
[[.,[.,[[.,.],.]]],[.,[.,.]]] => 1
[[.,[.,[[.,.],.]]],[[.,.],.]] => 1
[[.,[[.,.],[.,.]]],[.,[.,.]]] => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => 2
[[.,[[.,[.,.]],.]],[.,[.,.]]] => 1
[[.,[[.,[.,.]],.]],[[.,.],.]] => 1
[[.,[[[.,.],.],.]],[.,[.,.]]] => 1
[[.,[[[.,.],.],.]],[[.,.],.]] => 1
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => 2
[[[.,.],[[.,.],.]],[.,[.,.]]] => 2
[[[.,.],[[.,.],.]],[[.,.],.]] => 2
[[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[[[.,[.,.]],[.,.]],[[.,.],.]] => 2
[[[[.,.],.],[.,.]],[.,[.,.]]] => 2
[[[[.,.],.],[.,.]],[[.,.],.]] => 2
[[[.,[.,[.,.]]],.],[.,[.,.]]] => 1
[[[.,[.,[.,.]]],.],[[.,.],.]] => 1
[[[.,[[.,.],.]],.],[.,[.,.]]] => 1
[[[.,[[.,.],.]],.],[[.,.],.]] => 1
[[[[.,.],[.,.]],.],[.,[.,.]]] => 2
[[[[.,.],[.,.]],.],[[.,.],.]] => 2
[[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[[[[.,[.,.]],.],.],[[.,.],.]] => 1
[[[[[.,.],.],.],.],[.,[.,.]]] => 1
[[[[[.,.],.],.],.],[[.,.],.]] => 1
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[[.,[.,[.,[[.,.],.]]]],[.,.]] => 1
[[.,[.,[[.,.],[.,.]]]],[.,.]] => 2
[[.,[.,[[.,[.,.]],.]]],[.,.]] => 1
[[.,[.,[[[.,.],.],.]]],[.,.]] => 1
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 2
[[.,[[.,.],[[.,.],.]]],[.,.]] => 2
[[.,[[.,[.,.]],[.,.]]],[.,.]] => 2
[[.,[[[.,.],.],[.,.]]],[.,.]] => 2
[[.,[[.,[.,[.,.]]],.]],[.,.]] => 1
[[.,[[.,[[.,.],.]],.]],[.,.]] => 1
[[.,[[[.,.],[.,.]],.]],[.,.]] => 2
[[.,[[[.,[.,.]],.],.]],[.,.]] => 1
[[.,[[[[.,.],.],.],.]],[.,.]] => 1
[[[.,.],[.,[.,[.,.]]]],[.,.]] => 2
[[[.,.],[.,[[.,.],.]]],[.,.]] => 2
[[[.,.],[[.,.],[.,.]]],[.,.]] => 3
[[[.,.],[[.,[.,.]],.]],[.,.]] => 2
[[[.,.],[[[.,.],.],.]],[.,.]] => 2
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 2
[[[.,[.,.]],[[.,.],.]],[.,.]] => 2
[[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[[[[.,.],.],[[.,.],.]],[.,.]] => 2
[[[.,[.,[.,.]]],[.,.]],[.,.]] => 2
[[[.,[[.,.],.]],[.,.]],[.,.]] => 2
[[[[.,.],[.,.]],[.,.]],[.,.]] => 3
[[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[[[[[.,.],.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,[.,.]]]],.],[.,.]] => 1
[[[.,[.,[[.,.],.]]],.],[.,.]] => 1
[[[.,[[.,.],[.,.]]],.],[.,.]] => 2
[[[.,[[.,[.,.]],.]],.],[.,.]] => 1
[[[.,[[[.,.],.],.]],.],[.,.]] => 1
[[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[[[[.,.],[[.,.],.]],.],[.,.]] => 2
[[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[[[[[.,.],.],[.,.]],.],[.,.]] => 2
[[[[.,[.,[.,.]]],.],.],[.,.]] => 1
[[[[.,[[.,.],.]],.],.],[.,.]] => 1
[[[[[.,.],[.,.]],.],.],[.,.]] => 2
[[[[[.,[.,.]],.],.],.],[.,.]] => 1
[[[[[[.,.],.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 0
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 1
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 0
[[.,[.,[.,[[[.,.],.],.]]]],.] => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 1
[[.,[.,[[.,.],[[.,.],.]]]],.] => 1
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 1
[[.,[.,[[[.,.],.],[.,.]]]],.] => 1
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 0
[[.,[.,[[.,[[.,.],.]],.]]],.] => 0
[[.,[.,[[[.,.],[.,.]],.]]],.] => 1
[[.,[.,[[[.,[.,.]],.],.]]],.] => 0
[[.,[.,[[[[.,.],.],.],.]]],.] => 0
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 1
[[.,[[.,.],[.,[[.,.],.]]]],.] => 1
[[.,[[.,.],[[.,.],[.,.]]]],.] => 2
[[.,[[.,.],[[.,[.,.]],.]]],.] => 1
[[.,[[.,.],[[[.,.],.],.]]],.] => 1
[[.,[[.,[.,.]],[.,[.,.]]]],.] => 1
[[.,[[.,[.,.]],[[.,.],.]]],.] => 1
[[.,[[[.,.],.],[.,[.,.]]]],.] => 1
[[.,[[[.,.],.],[[.,.],.]]],.] => 1
[[.,[[.,[.,[.,.]]],[.,.]]],.] => 1
[[.,[[.,[[.,.],.]],[.,.]]],.] => 1
[[.,[[[.,.],[.,.]],[.,.]]],.] => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => 1
[[.,[[[[.,.],.],.],[.,.]]],.] => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] => 1
[[.,[[.,[[.,[.,.]],.]],.]],.] => 0
[[.,[[.,[[[.,.],.],.]],.]],.] => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => 1
[[.,[[[.,.],[[.,.],.]],.]],.] => 1
[[.,[[[.,[.,.]],[.,.]],.]],.] => 1
[[.,[[[[.,.],.],[.,.]],.]],.] => 1
[[.,[[[.,[.,[.,.]]],.],.]],.] => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => 1
[[.,[[[[.,[.,.]],.],.],.]],.] => 0
[[.,[[[[[.,.],.],.],.],.]],.] => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] => 1
[[[.,.],[.,[.,[[.,.],.]]]],.] => 1
[[[.,.],[.,[[.,.],[.,.]]]],.] => 2
[[[.,.],[.,[[.,[.,.]],.]]],.] => 1
[[[.,.],[.,[[[.,.],.],.]]],.] => 1
[[[.,.],[[.,.],[.,[.,.]]]],.] => 2
[[[.,.],[[.,.],[[.,.],.]]],.] => 2
[[[.,.],[[.,[.,.]],[.,.]]],.] => 2
[[[.,.],[[[.,.],.],[.,.]]],.] => 2
[[[.,.],[[.,[.,[.,.]]],.]],.] => 1
[[[.,.],[[.,[[.,.],.]],.]],.] => 1
[[[.,.],[[[.,.],[.,.]],.]],.] => 2
[[[.,.],[[[.,[.,.]],.],.]],.] => 1
[[[.,.],[[[[.,.],.],.],.]],.] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],.] => 1
[[[.,[.,.]],[.,[[.,.],.]]],.] => 1
[[[.,[.,.]],[[.,.],[.,.]]],.] => 2
[[[.,[.,.]],[[.,[.,.]],.]],.] => 1
[[[.,[.,.]],[[[.,.],.],.]],.] => 1
[[[[.,.],.],[.,[.,[.,.]]]],.] => 1
[[[[.,.],.],[.,[[.,.],.]]],.] => 1
[[[[.,.],.],[[.,.],[.,.]]],.] => 2
[[[[.,.],.],[[.,[.,.]],.]],.] => 1
[[[[.,.],.],[[[.,.],.],.]],.] => 1
[[[.,[.,[.,.]]],[.,[.,.]]],.] => 1
[[[.,[.,[.,.]]],[[.,.],.]],.] => 1
[[[.,[[.,.],.]],[.,[.,.]]],.] => 1
[[[.,[[.,.],.]],[[.,.],.]],.] => 1
[[[[.,.],[.,.]],[.,[.,.]]],.] => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => 2
[[[[.,[.,.]],.],[.,[.,.]]],.] => 1
[[[[.,[.,.]],.],[[.,.],.]],.] => 1
[[[[[.,.],.],.],[.,[.,.]]],.] => 1
[[[[[.,.],.],.],[[.,.],.]],.] => 1
[[[.,[.,[.,[.,.]]]],[.,.]],.] => 1
[[[.,[.,[[.,.],.]]],[.,.]],.] => 1
[[[.,[[.,.],[.,.]]],[.,.]],.] => 2
[[[.,[[.,[.,.]],.]],[.,.]],.] => 1
[[[.,[[[.,.],.],.]],[.,.]],.] => 1
[[[[.,.],[.,[.,.]]],[.,.]],.] => 2
[[[[.,.],[[.,.],.]],[.,.]],.] => 2
[[[[.,[.,.]],[.,.]],[.,.]],.] => 2
[[[[[.,.],.],[.,.]],[.,.]],.] => 2
[[[[.,[.,[.,.]]],.],[.,.]],.] => 1
[[[[.,[[.,.],.]],.],[.,.]],.] => 1
[[[[[.,.],[.,.]],.],[.,.]],.] => 2
[[[[[.,[.,.]],.],.],[.,.]],.] => 1
[[[[[[.,.],.],.],.],[.,.]],.] => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] => 1
[[[.,[.,[[.,[.,.]],.]]],.],.] => 0
[[[.,[.,[[[.,.],.],.]]],.],.] => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] => 1
[[[.,[[.,.],[[.,.],.]]],.],.] => 1
[[[.,[[.,[.,.]],[.,.]]],.],.] => 1
[[[.,[[[.,.],.],[.,.]]],.],.] => 1
[[[.,[[.,[.,[.,.]]],.]],.],.] => 0
[[[.,[[.,[[.,.],.]],.]],.],.] => 0
[[[.,[[[.,.],[.,.]],.]],.],.] => 1
[[[.,[[[.,[.,.]],.],.]],.],.] => 0
[[[.,[[[[.,.],.],.],.]],.],.] => 0
[[[[.,.],[.,[.,[.,.]]]],.],.] => 1
[[[[.,.],[.,[[.,.],.]]],.],.] => 1
[[[[.,.],[[.,.],[.,.]]],.],.] => 2
[[[[.,.],[[.,[.,.]],.]],.],.] => 1
[[[[.,.],[[[.,.],.],.]],.],.] => 1
[[[[.,[.,.]],[.,[.,.]]],.],.] => 1
[[[[.,[.,.]],[[.,.],.]],.],.] => 1
[[[[[.,.],.],[.,[.,.]]],.],.] => 1
[[[[[.,.],.],[[.,.],.]],.],.] => 1
[[[[.,[.,[.,.]]],[.,.]],.],.] => 1
[[[[.,[[.,.],.]],[.,.]],.],.] => 1
[[[[[.,.],[.,.]],[.,.]],.],.] => 2
[[[[[.,[.,.]],.],[.,.]],.],.] => 1
[[[[[[.,.],.],.],[.,.]],.],.] => 1
[[[[.,[.,[.,[.,.]]]],.],.],.] => 0
[[[[.,[.,[[.,.],.]]],.],.],.] => 0
[[[[.,[[.,.],[.,.]]],.],.],.] => 1
[[[[.,[[.,[.,.]],.]],.],.],.] => 0
[[[[.,[[[.,.],.],.]],.],.],.] => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => 1
[[[[[.,.],[[.,.],.]],.],.],.] => 1
[[[[[.,[.,.]],[.,.]],.],.],.] => 1
[[[[[[.,.],.],[.,.]],.],.],.] => 1
[[[[[.,[.,[.,.]]],.],.],.],.] => 0
[[[[[.,[[.,.],.]],.],.],.],.] => 0
[[[[[[.,.],[.,.]],.],.],.],.] => 1
[[[[[[.,[.,.]],.],.],.],.],.] => 0
[[[[[[[.,.],.],.],.],.],.],.] => 0

-----------------------------------------------------------------------------
Created: May 15, 2014 at 08:57 by Joseph Ching

-----------------------------------------------------------------------------
Last Updated: May 30, 2016 at 11:58 by Christian Stump