*****************************************************************************
*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
*                                                                           *
*    This information is distributed in the hope that it will be useful,    *
*    but WITHOUT ANY WARRANTY; without even the implied warranty of         *
*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                   *
*****************************************************************************

-----------------------------------------------------------------------------
Statistic identifier: St000414

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

-----------------------------------------------------------------------------
Description: The binary logarithm of the number of binary trees with the same underlying unordered tree.

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

-----------------------------------------------------------------------------
Code:
@cached_function
def Binary_to_Rooted(n):
    return [RootedTree(S) for S in BinaryTrees(n)]

def statistic(tree):
    T = RootedTree(tree)
    return ZZ(Binary_to_Rooted(tree.node_number()).count(T)).log(2)


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

[.,[.,.]]                         => 1
[[.,.],.]                         => 1
[.,[.,[.,.]]]                     => 2
[.,[[.,.],.]]                     => 2
[[.,.],[.,.]]                     => 0
[[.,[.,.]],.]                     => 2
[[[.,.],.],.]                     => 2
[.,[.,[.,[.,.]]]]                 => 3
[.,[.,[[.,.],.]]]                 => 3
[.,[[.,.],[.,.]]]                 => 1
[.,[[.,[.,.]],.]]                 => 3
[.,[[[.,.],.],.]]                 => 3
[[.,.],[.,[.,.]]]                 => 2
[[.,.],[[.,.],.]]                 => 2
[[.,[.,.]],[.,.]]                 => 2
[[[.,.],.],[.,.]]                 => 2
[[.,[.,[.,.]]],.]                 => 3
[[.,[[.,.],.]],.]                 => 3
[[[.,.],[.,.]],.]                 => 1
[[[.,[.,.]],.],.]                 => 3
[[[[.,.],.],.],.]                 => 3
[.,[.,[.,[.,[.,.]]]]]             => 4
[.,[.,[.,[[.,.],.]]]]             => 4
[.,[.,[[.,.],[.,.]]]]             => 2
[.,[.,[[.,[.,.]],.]]]             => 4
[.,[.,[[[.,.],.],.]]]             => 4
[.,[[.,.],[.,[.,.]]]]             => 3
[.,[[.,.],[[.,.],.]]]             => 3
[.,[[.,[.,.]],[.,.]]]             => 3
[.,[[[.,.],.],[.,.]]]             => 3
[.,[[.,[.,[.,.]]],.]]             => 4
[.,[[.,[[.,.],.]],.]]             => 4
[.,[[[.,.],[.,.]],.]]             => 2
[.,[[[.,[.,.]],.],.]]             => 4
[.,[[[[.,.],.],.],.]]             => 4
[[.,.],[.,[.,[.,.]]]]             => 3
[[.,.],[.,[[.,.],.]]]             => 3
[[.,.],[[.,.],[.,.]]]             => 1
[[.,.],[[.,[.,.]],.]]             => 3
[[.,.],[[[.,.],.],.]]             => 3
[[.,[.,.]],[.,[.,.]]]             => 2
[[.,[.,.]],[[.,.],.]]             => 2
[[[.,.],.],[.,[.,.]]]             => 2
[[[.,.],.],[[.,.],.]]             => 2
[[.,[.,[.,.]]],[.,.]]             => 3
[[.,[[.,.],.]],[.,.]]             => 3
[[[.,.],[.,.]],[.,.]]             => 1
[[[.,[.,.]],.],[.,.]]             => 3
[[[[.,.],.],.],[.,.]]             => 3
[[.,[.,[.,[.,.]]]],.]             => 4
[[.,[.,[[.,.],.]]],.]             => 4
[[.,[[.,.],[.,.]]],.]             => 2
[[.,[[.,[.,.]],.]],.]             => 4
[[.,[[[.,.],.],.]],.]             => 4
[[[.,.],[.,[.,.]]],.]             => 3
[[[.,.],[[.,.],.]],.]             => 3
[[[.,[.,.]],[.,.]],.]             => 3
[[[[.,.],.],[.,.]],.]             => 3
[[[.,[.,[.,.]]],.],.]             => 4
[[[.,[[.,.],.]],.],.]             => 4
[[[[.,.],[.,.]],.],.]             => 2
[[[[.,[.,.]],.],.],.]             => 4
[[[[[.,.],.],.],.],.]             => 4
[.,[.,[.,[.,[.,[.,.]]]]]]         => 5
[.,[.,[.,[.,[[.,.],.]]]]]         => 5
[.,[.,[.,[[.,.],[.,.]]]]]         => 3
[.,[.,[.,[[.,[.,.]],.]]]]         => 5
[.,[.,[.,[[[.,.],.],.]]]]         => 5
[.,[.,[[.,.],[.,[.,.]]]]]         => 4
[.,[.,[[.,.],[[.,.],.]]]]         => 4
[.,[.,[[.,[.,.]],[.,.]]]]         => 4
[.,[.,[[[.,.],.],[.,.]]]]         => 4
[.,[.,[[.,[.,[.,.]]],.]]]         => 5
[.,[.,[[.,[[.,.],.]],.]]]         => 5
[.,[.,[[[.,.],[.,.]],.]]]         => 3
[.,[.,[[[.,[.,.]],.],.]]]         => 5
[.,[.,[[[[.,.],.],.],.]]]         => 5
[.,[[.,.],[.,[.,[.,.]]]]]         => 4
[.,[[.,.],[.,[[.,.],.]]]]         => 4
[.,[[.,.],[[.,.],[.,.]]]]         => 2
[.,[[.,.],[[.,[.,.]],.]]]         => 4
[.,[[.,.],[[[.,.],.],.]]]         => 4
[.,[[.,[.,.]],[.,[.,.]]]]         => 3
[.,[[.,[.,.]],[[.,.],.]]]         => 3
[.,[[[.,.],.],[.,[.,.]]]]         => 3
[.,[[[.,.],.],[[.,.],.]]]         => 3
[.,[[.,[.,[.,.]]],[.,.]]]         => 4
[.,[[.,[[.,.],.]],[.,.]]]         => 4
[.,[[[.,.],[.,.]],[.,.]]]         => 2
[.,[[[.,[.,.]],.],[.,.]]]         => 4
[.,[[[[.,.],.],.],[.,.]]]         => 4
[.,[[.,[.,[.,[.,.]]]],.]]         => 5
[.,[[.,[.,[[.,.],.]]],.]]         => 5
[.,[[.,[[.,.],[.,.]]],.]]         => 3
[.,[[.,[[.,[.,.]],.]],.]]         => 5
[.,[[.,[[[.,.],.],.]],.]]         => 5
[.,[[[.,.],[.,[.,.]]],.]]         => 4
[.,[[[.,.],[[.,.],.]],.]]         => 4
[.,[[[.,[.,.]],[.,.]],.]]         => 4
[.,[[[[.,.],.],[.,.]],.]]         => 4
[.,[[[.,[.,[.,.]]],.],.]]         => 5
[.,[[[.,[[.,.],.]],.],.]]         => 5
[.,[[[[.,.],[.,.]],.],.]]         => 3
[.,[[[[.,[.,.]],.],.],.]]         => 5
[.,[[[[[.,.],.],.],.],.]]         => 5
[[.,.],[.,[.,[.,[.,.]]]]]         => 4
[[.,.],[.,[.,[[.,.],.]]]]         => 4
[[.,.],[.,[[.,.],[.,.]]]]         => 2
[[.,.],[.,[[.,[.,.]],.]]]         => 4
[[.,.],[.,[[[.,.],.],.]]]         => 4
[[.,.],[[.,.],[.,[.,.]]]]         => 3
[[.,.],[[.,.],[[.,.],.]]]         => 3
[[.,.],[[.,[.,.]],[.,.]]]         => 3
[[.,.],[[[.,.],.],[.,.]]]         => 3
[[.,.],[[.,[.,[.,.]]],.]]         => 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
[[[.,.],[.,[.,.]]],[.,.]]         => 3
[[[.,.],[[.,.],.]],[.,.]]         => 3
[[[.,[.,.]],[.,.]],[.,.]]         => 3
[[[[.,.],.],[.,.]],[.,.]]         => 3
[[[.,[.,[.,.]]],.],[.,.]]         => 4
[[[.,[[.,.],.]],.],[.,.]]         => 4
[[[[.,.],[.,.]],.],[.,.]]         => 2
[[[[.,[.,.]],.],.],[.,.]]         => 4
[[[[[.,.],.],.],.],[.,.]]         => 4
[[.,[.,[.,[.,[.,.]]]]],.]         => 5
[[.,[.,[.,[[.,.],.]]]],.]         => 5
[[.,[.,[[.,.],[.,.]]]],.]         => 3
[[.,[.,[[.,[.,.]],.]]],.]         => 5
[[.,[.,[[[.,.],.],.]]],.]         => 5
[[.,[[.,.],[.,[.,.]]]],.]         => 4
[[.,[[.,.],[[.,.],.]]],.]         => 4
[[.,[[.,[.,.]],[.,.]]],.]         => 4
[[.,[[[.,.],.],[.,.]]],.]         => 4
[[.,[[.,[.,[.,.]]],.]],.]         => 5
[[.,[[.,[[.,.],.]],.]],.]         => 5
[[.,[[[.,.],[.,.]],.]],.]         => 3
[[.,[[[.,[.,.]],.],.]],.]         => 5
[[.,[[[[.,.],.],.],.]],.]         => 5
[[[.,.],[.,[.,[.,.]]]],.]         => 4
[[[.,.],[.,[[.,.],.]]],.]         => 4
[[[.,.],[[.,.],[.,.]]],.]         => 2
[[[.,.],[[.,[.,.]],.]],.]         => 4
[[[.,.],[[[.,.],.],.]],.]         => 4
[[[.,[.,.]],[.,[.,.]]],.]         => 3
[[[.,[.,.]],[[.,.],.]],.]         => 3
[[[[.,.],.],[.,[.,.]]],.]         => 3
[[[[.,.],.],[[.,.],.]],.]         => 3
[[[.,[.,[.,.]]],[.,.]],.]         => 4
[[[.,[[.,.],.]],[.,.]],.]         => 4
[[[[.,.],[.,.]],[.,.]],.]         => 2
[[[[.,[.,.]],.],[.,.]],.]         => 4
[[[[[.,.],.],.],[.,.]],.]         => 4
[[[.,[.,[.,[.,.]]]],.],.]         => 5
[[[.,[.,[[.,.],.]]],.],.]         => 5
[[[.,[[.,.],[.,.]]],.],.]         => 3
[[[.,[[.,[.,.]],.]],.],.]         => 5
[[[.,[[[.,.],.],.]],.],.]         => 5
[[[[.,.],[.,[.,.]]],.],.]         => 4
[[[[.,.],[[.,.],.]],.],.]         => 4
[[[[.,[.,.]],[.,.]],.],.]         => 4
[[[[[.,.],.],[.,.]],.],.]         => 4
[[[[.,[.,[.,.]]],.],.],.]         => 5
[[[[.,[[.,.],.]],.],.],.]         => 5
[[[[[.,.],[.,.]],.],.],.]         => 3
[[[[[.,[.,.]],.],.],.],.]         => 5
[[[[[[.,.],.],.],.],.],.]         => 5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]     => 6
[.,[.,[.,[.,[.,[[.,.],.]]]]]]     => 6
[.,[.,[.,[.,[[.,.],[.,.]]]]]]     => 4
[.,[.,[.,[.,[[.,[.,.]],.]]]]]     => 6
[.,[.,[.,[.,[[[.,.],.],.]]]]]     => 6
[.,[.,[.,[[.,.],[.,[.,.]]]]]]     => 5
[.,[.,[.,[[.,.],[[.,.],.]]]]]     => 5
[.,[.,[.,[[.,[.,.]],[.,.]]]]]     => 5
[.,[.,[.,[[[.,.],.],[.,.]]]]]     => 5
[.,[.,[.,[[.,[.,[.,.]]],.]]]]     => 6
[.,[.,[.,[[.,[[.,.],.]],.]]]]     => 6
[.,[.,[.,[[[.,.],[.,.]],.]]]]     => 4
[.,[.,[.,[[[.,[.,.]],.],.]]]]     => 6
[.,[.,[.,[[[[.,.],.],.],.]]]]     => 6
[.,[.,[[.,.],[.,[.,[.,.]]]]]]     => 5
[.,[.,[[.,.],[.,[[.,.],.]]]]]     => 5
[.,[.,[[.,.],[[.,.],[.,.]]]]]     => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]]     => 5
[.,[.,[[.,.],[[[.,.],.],.]]]]     => 5
[.,[.,[[.,[.,.]],[.,[.,.]]]]]     => 4
[.,[.,[[.,[.,.]],[[.,.],.]]]]     => 4
[.,[.,[[[.,.],.],[.,[.,.]]]]]     => 4
[.,[.,[[[.,.],.],[[.,.],.]]]]     => 4
[.,[.,[[.,[.,[.,.]]],[.,.]]]]     => 5
[.,[.,[[.,[[.,.],.]],[.,.]]]]     => 5
[.,[.,[[[.,.],[.,.]],[.,.]]]]     => 3
[.,[.,[[[.,[.,.]],.],[.,.]]]]     => 5
[.,[.,[[[[.,.],.],.],[.,.]]]]     => 5
[.,[.,[[.,[.,[.,[.,.]]]],.]]]     => 6
[.,[.,[[.,[.,[[.,.],.]]],.]]]     => 6
[.,[.,[[.,[[.,.],[.,.]]],.]]]     => 4
[.,[.,[[.,[[.,[.,.]],.]],.]]]     => 6
[.,[.,[[.,[[[.,.],.],.]],.]]]     => 6
[.,[.,[[[.,.],[.,[.,.]]],.]]]     => 5
[.,[.,[[[.,.],[[.,.],.]],.]]]     => 5
[.,[.,[[[.,[.,.]],[.,.]],.]]]     => 5
[.,[.,[[[[.,.],.],[.,.]],.]]]     => 5
[.,[.,[[[.,[.,[.,.]]],.],.]]]     => 6
[.,[.,[[[.,[[.,.],.]],.],.]]]     => 6
[.,[.,[[[[.,.],[.,.]],.],.]]]     => 4
[.,[.,[[[[.,[.,.]],.],.],.]]]     => 6
[.,[.,[[[[[.,.],.],.],.],.]]]     => 6
[.,[[.,.],[.,[.,[.,[.,.]]]]]]     => 5
[.,[[.,.],[.,[.,[[.,.],.]]]]]     => 5
[.,[[.,.],[.,[[.,.],[.,.]]]]]     => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]]     => 5
[.,[[.,.],[.,[[[.,.],.],.]]]]     => 5
[.,[[.,.],[[.,.],[.,[.,.]]]]]     => 4
[.,[[.,.],[[.,.],[[.,.],.]]]]     => 4
[.,[[.,.],[[.,[.,.]],[.,.]]]]     => 4
[.,[[.,.],[[[.,.],.],[.,.]]]]     => 4
[.,[[.,.],[[.,[.,[.,.]]],.]]]     => 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
[.,[[[.,.],[.,[.,.]]],[.,.]]]     => 4
[.,[[[.,.],[[.,.],.]],[.,.]]]     => 4
[.,[[[.,[.,.]],[.,.]],[.,.]]]     => 4
[.,[[[[.,.],.],[.,.]],[.,.]]]     => 4
[.,[[[.,[.,[.,.]]],.],[.,.]]]     => 5
[.,[[[.,[[.,.],.]],.],[.,.]]]     => 5
[.,[[[[.,.],[.,.]],.],[.,.]]]     => 3
[.,[[[[.,[.,.]],.],.],[.,.]]]     => 5
[.,[[[[[.,.],.],.],.],[.,.]]]     => 5
[.,[[.,[.,[.,[.,[.,.]]]]],.]]     => 6
[.,[[.,[.,[.,[[.,.],.]]]],.]]     => 6
[.,[[.,[.,[[.,.],[.,.]]]],.]]     => 4
[.,[[.,[.,[[.,[.,.]],.]]],.]]     => 6
[.,[[.,[.,[[[.,.],.],.]]],.]]     => 6
[.,[[.,[[.,.],[.,[.,.]]]],.]]     => 5
[.,[[.,[[.,.],[[.,.],.]]],.]]     => 5
[.,[[.,[[.,[.,.]],[.,.]]],.]]     => 5
[.,[[.,[[[.,.],.],[.,.]]],.]]     => 5
[.,[[.,[[.,[.,[.,.]]],.]],.]]     => 6
[.,[[.,[[.,[[.,.],.]],.]],.]]     => 6
[.,[[.,[[[.,.],[.,.]],.]],.]]     => 4
[.,[[.,[[[.,[.,.]],.],.]],.]]     => 6
[.,[[.,[[[[.,.],.],.],.]],.]]     => 6
[.,[[[.,.],[.,[.,[.,.]]]],.]]     => 5
[.,[[[.,.],[.,[[.,.],.]]],.]]     => 5
[.,[[[.,.],[[.,.],[.,.]]],.]]     => 3
[.,[[[.,.],[[.,[.,.]],.]],.]]     => 5
[.,[[[.,.],[[[.,.],.],.]],.]]     => 5
[.,[[[.,[.,.]],[.,[.,.]]],.]]     => 4
[.,[[[.,[.,.]],[[.,.],.]],.]]     => 4
[.,[[[[.,.],.],[.,[.,.]]],.]]     => 4
[.,[[[[.,.],.],[[.,.],.]],.]]     => 4
[.,[[[.,[.,[.,.]]],[.,.]],.]]     => 5
[.,[[[.,[[.,.],.]],[.,.]],.]]     => 5
[.,[[[[.,.],[.,.]],[.,.]],.]]     => 3
[.,[[[[.,[.,.]],.],[.,.]],.]]     => 5
[.,[[[[[.,.],.],.],[.,.]],.]]     => 5
[.,[[[.,[.,[.,[.,.]]]],.],.]]     => 6
[.,[[[.,[.,[[.,.],.]]],.],.]]     => 6
[.,[[[.,[[.,.],[.,.]]],.],.]]     => 4
[.,[[[.,[[.,[.,.]],.]],.],.]]     => 6
[.,[[[.,[[[.,.],.],.]],.],.]]     => 6
[.,[[[[.,.],[.,[.,.]]],.],.]]     => 5
[.,[[[[.,.],[[.,.],.]],.],.]]     => 5
[.,[[[[.,[.,.]],[.,.]],.],.]]     => 5
[.,[[[[[.,.],.],[.,.]],.],.]]     => 5
[.,[[[[.,[.,[.,.]]],.],.],.]]     => 6
[.,[[[[.,[[.,.],.]],.],.],.]]     => 6
[.,[[[[[.,.],[.,.]],.],.],.]]     => 4
[.,[[[[[.,[.,.]],.],.],.],.]]     => 6
[.,[[[[[[.,.],.],.],.],.],.]]     => 6
[[.,.],[.,[.,[.,[.,[.,.]]]]]]     => 5
[[.,.],[.,[.,[.,[[.,.],.]]]]]     => 5
[[.,.],[.,[.,[[.,.],[.,.]]]]]     => 3
[[.,.],[.,[.,[[.,[.,.]],.]]]]     => 5
[[.,.],[.,[.,[[[.,.],.],.]]]]     => 5
[[.,.],[.,[[.,.],[.,[.,.]]]]]     => 4
[[.,.],[.,[[.,.],[[.,.],.]]]]     => 4
[[.,.],[.,[[.,[.,.]],[.,.]]]]     => 4
[[.,.],[.,[[[.,.],.],[.,.]]]]     => 4
[[.,.],[.,[[.,[.,[.,.]]],.]]]     => 5
[[.,.],[.,[[.,[[.,.],.]],.]]]     => 5
[[.,.],[.,[[[.,.],[.,.]],.]]]     => 3
[[.,.],[.,[[[.,[.,.]],.],.]]]     => 5
[[.,.],[.,[[[[.,.],.],.],.]]]     => 5
[[.,.],[[.,.],[.,[.,[.,.]]]]]     => 4
[[.,.],[[.,.],[.,[[.,.],.]]]]     => 4
[[.,.],[[.,.],[[.,.],[.,.]]]]     => 2
[[.,.],[[.,.],[[.,[.,.]],.]]]     => 4
[[.,.],[[.,.],[[[.,.],.],.]]]     => 4
[[.,.],[[.,[.,.]],[.,[.,.]]]]     => 3
[[.,.],[[.,[.,.]],[[.,.],.]]]     => 3
[[.,.],[[[.,.],.],[.,[.,.]]]]     => 3
[[.,.],[[[.,.],.],[[.,.],.]]]     => 3
[[.,.],[[.,[.,[.,.]]],[.,.]]]     => 4
[[.,.],[[.,[[.,.],.]],[.,.]]]     => 4
[[.,.],[[[.,.],[.,.]],[.,.]]]     => 2
[[.,.],[[[.,[.,.]],.],[.,.]]]     => 4
[[.,.],[[[[.,.],.],.],[.,.]]]     => 4
[[.,.],[[.,[.,[.,[.,.]]]],.]]     => 5
[[.,.],[[.,[.,[[.,.],.]]],.]]     => 5
[[.,.],[[.,[[.,.],[.,.]]],.]]     => 3
[[.,.],[[.,[[.,[.,.]],.]],.]]     => 5
[[.,.],[[.,[[[.,.],.],.]],.]]     => 5
[[.,.],[[[.,.],[.,[.,.]]],.]]     => 4
[[.,.],[[[.,.],[[.,.],.]],.]]     => 4
[[.,.],[[[.,[.,.]],[.,.]],.]]     => 4
[[.,.],[[[[.,.],.],[.,.]],.]]     => 4
[[.,.],[[[.,[.,[.,.]]],.],.]]     => 5
[[.,.],[[[.,[[.,.],.]],.],.]]     => 5
[[.,.],[[[[.,.],[.,.]],.],.]]     => 3
[[.,.],[[[[.,[.,.]],.],.],.]]     => 5
[[.,.],[[[[[.,.],.],.],.],.]]     => 5
[[.,[.,.]],[.,[.,[.,[.,.]]]]]     => 5
[[.,[.,.]],[.,[.,[[.,.],.]]]]     => 5
[[.,[.,.]],[.,[[.,.],[.,.]]]]     => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]]     => 5
[[.,[.,.]],[.,[[[.,.],.],.]]]     => 5
[[.,[.,.]],[[.,.],[.,[.,.]]]]     => 4
[[.,[.,.]],[[.,.],[[.,.],.]]]     => 4
[[.,[.,.]],[[.,[.,.]],[.,.]]]     => 4
[[.,[.,.]],[[[.,.],.],[.,.]]]     => 4
[[.,[.,.]],[[.,[.,[.,.]]],.]]     => 5
[[.,[.,.]],[[.,[[.,.],.]],.]]     => 5
[[.,[.,.]],[[[.,.],[.,.]],.]]     => 3
[[.,[.,.]],[[[.,[.,.]],.],.]]     => 5
[[.,[.,.]],[[[[.,.],.],.],.]]     => 5
[[[.,.],.],[.,[.,[.,[.,.]]]]]     => 5
[[[.,.],.],[.,[.,[[.,.],.]]]]     => 5
[[[.,.],.],[.,[[.,.],[.,.]]]]     => 3
[[[.,.],.],[.,[[.,[.,.]],.]]]     => 5
[[[.,.],.],[.,[[[.,.],.],.]]]     => 5
[[[.,.],.],[[.,.],[.,[.,.]]]]     => 4
[[[.,.],.],[[.,.],[[.,.],.]]]     => 4
[[[.,.],.],[[.,[.,.]],[.,.]]]     => 4
[[[.,.],.],[[[.,.],.],[.,.]]]     => 4
[[[.,.],.],[[.,[.,[.,.]]],.]]     => 5
[[[.,.],.],[[.,[[.,.],.]],.]]     => 5
[[[.,.],.],[[[.,.],[.,.]],.]]     => 3
[[[.,.],.],[[[.,[.,.]],.],.]]     => 5
[[[.,.],.],[[[[.,.],.],.],.]]     => 5
[[.,[.,[.,.]]],[.,[.,[.,.]]]]     => 4
[[.,[.,[.,.]]],[.,[[.,.],.]]]     => 4
[[.,[.,[.,.]]],[[.,.],[.,.]]]     => 3
[[.,[.,[.,.]]],[[.,[.,.]],.]]     => 4
[[.,[.,[.,.]]],[[[.,.],.],.]]     => 4
[[.,[[.,.],.]],[.,[.,[.,.]]]]     => 4
[[.,[[.,.],.]],[.,[[.,.],.]]]     => 4
[[.,[[.,.],.]],[[.,.],[.,.]]]     => 3
[[.,[[.,.],.]],[[.,[.,.]],.]]     => 4
[[.,[[.,.],.]],[[[.,.],.],.]]     => 4
[[[.,.],[.,.]],[.,[.,[.,.]]]]     => 3
[[[.,.],[.,.]],[.,[[.,.],.]]]     => 3
[[[.,.],[.,.]],[[.,.],[.,.]]]     => 0
[[[.,.],[.,.]],[[.,[.,.]],.]]     => 3
[[[.,.],[.,.]],[[[.,.],.],.]]     => 3
[[[.,[.,.]],.],[.,[.,[.,.]]]]     => 4
[[[.,[.,.]],.],[.,[[.,.],.]]]     => 4
[[[.,[.,.]],.],[[.,.],[.,.]]]     => 3
[[[.,[.,.]],.],[[.,[.,.]],.]]     => 4
[[[.,[.,.]],.],[[[.,.],.],.]]     => 4
[[[[.,.],.],.],[.,[.,[.,.]]]]     => 4
[[[[.,.],.],.],[.,[[.,.],.]]]     => 4
[[[[.,.],.],.],[[.,.],[.,.]]]     => 3
[[[[.,.],.],.],[[.,[.,.]],.]]     => 4
[[[[.,.],.],.],[[[.,.],.],.]]     => 4
[[.,[.,[.,[.,.]]]],[.,[.,.]]]     => 5
[[.,[.,[.,[.,.]]]],[[.,.],.]]     => 5
[[.,[.,[[.,.],.]]],[.,[.,.]]]     => 5
[[.,[.,[[.,.],.]]],[[.,.],.]]     => 5
[[.,[[.,.],[.,.]]],[.,[.,.]]]     => 3
[[.,[[.,.],[.,.]]],[[.,.],.]]     => 3
[[.,[[.,[.,.]],.]],[.,[.,.]]]     => 5
[[.,[[.,[.,.]],.]],[[.,.],.]]     => 5
[[.,[[[.,.],.],.]],[.,[.,.]]]     => 5
[[.,[[[.,.],.],.]],[[.,.],.]]     => 5
[[[.,.],[.,[.,.]]],[.,[.,.]]]     => 4
[[[.,.],[.,[.,.]]],[[.,.],.]]     => 4
[[[.,.],[[.,.],.]],[.,[.,.]]]     => 4
[[[.,.],[[.,.],.]],[[.,.],.]]     => 4
[[[.,[.,.]],[.,.]],[.,[.,.]]]     => 4
[[[.,[.,.]],[.,.]],[[.,.],.]]     => 4
[[[[.,.],.],[.,.]],[.,[.,.]]]     => 4
[[[[.,.],.],[.,.]],[[.,.],.]]     => 4
[[[.,[.,[.,.]]],.],[.,[.,.]]]     => 5
[[[.,[.,[.,.]]],.],[[.,.],.]]     => 5
[[[.,[[.,.],.]],.],[.,[.,.]]]     => 5
[[[.,[[.,.],.]],.],[[.,.],.]]     => 5
[[[[.,.],[.,.]],.],[.,[.,.]]]     => 3
[[[[.,.],[.,.]],.],[[.,.],.]]     => 3
[[[[.,[.,.]],.],.],[.,[.,.]]]     => 5
[[[[.,[.,.]],.],.],[[.,.],.]]     => 5
[[[[[.,.],.],.],.],[.,[.,.]]]     => 5
[[[[[.,.],.],.],.],[[.,.],.]]     => 5
[[.,[.,[.,[.,[.,.]]]]],[.,.]]     => 5
[[.,[.,[.,[[.,.],.]]]],[.,.]]     => 5
[[.,[.,[[.,.],[.,.]]]],[.,.]]     => 3
[[.,[.,[[.,[.,.]],.]]],[.,.]]     => 5
[[.,[.,[[[.,.],.],.]]],[.,.]]     => 5
[[.,[[.,.],[.,[.,.]]]],[.,.]]     => 4
[[.,[[.,.],[[.,.],.]]],[.,.]]     => 4
[[.,[[.,[.,.]],[.,.]]],[.,.]]     => 4
[[.,[[[.,.],.],[.,.]]],[.,.]]     => 4
[[.,[[.,[.,[.,.]]],.]],[.,.]]     => 5
[[.,[[.,[[.,.],.]],.]],[.,.]]     => 5
[[.,[[[.,.],[.,.]],.]],[.,.]]     => 3
[[.,[[[.,[.,.]],.],.]],[.,.]]     => 5
[[.,[[[[.,.],.],.],.]],[.,.]]     => 5
[[[.,.],[.,[.,[.,.]]]],[.,.]]     => 4
[[[.,.],[.,[[.,.],.]]],[.,.]]     => 4
[[[.,.],[[.,.],[.,.]]],[.,.]]     => 2
[[[.,.],[[.,[.,.]],.]],[.,.]]     => 4
[[[.,.],[[[.,.],.],.]],[.,.]]     => 4
[[[.,[.,.]],[.,[.,.]]],[.,.]]     => 3
[[[.,[.,.]],[[.,.],.]],[.,.]]     => 3
[[[[.,.],.],[.,[.,.]]],[.,.]]     => 3
[[[[.,.],.],[[.,.],.]],[.,.]]     => 3
[[[.,[.,[.,.]]],[.,.]],[.,.]]     => 4
[[[.,[[.,.],.]],[.,.]],[.,.]]     => 4
[[[[.,.],[.,.]],[.,.]],[.,.]]     => 2
[[[[.,[.,.]],.],[.,.]],[.,.]]     => 4
[[[[[.,.],.],.],[.,.]],[.,.]]     => 4
[[[.,[.,[.,[.,.]]]],.],[.,.]]     => 5
[[[.,[.,[[.,.],.]]],.],[.,.]]     => 5
[[[.,[[.,.],[.,.]]],.],[.,.]]     => 3
[[[.,[[.,[.,.]],.]],.],[.,.]]     => 5
[[[.,[[[.,.],.],.]],.],[.,.]]     => 5
[[[[.,.],[.,[.,.]]],.],[.,.]]     => 4
[[[[.,.],[[.,.],.]],.],[.,.]]     => 4
[[[[.,[.,.]],[.,.]],.],[.,.]]     => 4
[[[[[.,.],.],[.,.]],.],[.,.]]     => 4
[[[[.,[.,[.,.]]],.],.],[.,.]]     => 5
[[[[.,[[.,.],.]],.],.],[.,.]]     => 5
[[[[[.,.],[.,.]],.],.],[.,.]]     => 3
[[[[[.,[.,.]],.],.],.],[.,.]]     => 5
[[[[[[.,.],.],.],.],.],[.,.]]     => 5
[[.,[.,[.,[.,[.,[.,.]]]]]],.]     => 6
[[.,[.,[.,[.,[[.,.],.]]]]],.]     => 6
[[.,[.,[.,[[.,.],[.,.]]]]],.]     => 4
[[.,[.,[.,[[.,[.,.]],.]]]],.]     => 6
[[.,[.,[.,[[[.,.],.],.]]]],.]     => 6
[[.,[.,[[.,.],[.,[.,.]]]]],.]     => 5
[[.,[.,[[.,.],[[.,.],.]]]],.]     => 5
[[.,[.,[[.,[.,.]],[.,.]]]],.]     => 5
[[.,[.,[[[.,.],.],[.,.]]]],.]     => 5
[[.,[.,[[.,[.,[.,.]]],.]]],.]     => 6
[[.,[.,[[.,[[.,.],.]],.]]],.]     => 6
[[.,[.,[[[.,.],[.,.]],.]]],.]     => 4
[[.,[.,[[[.,[.,.]],.],.]]],.]     => 6
[[.,[.,[[[[.,.],.],.],.]]],.]     => 6
[[.,[[.,.],[.,[.,[.,.]]]]],.]     => 5
[[.,[[.,.],[.,[[.,.],.]]]],.]     => 5
[[.,[[.,.],[[.,.],[.,.]]]],.]     => 3
[[.,[[.,.],[[.,[.,.]],.]]],.]     => 5
[[.,[[.,.],[[[.,.],.],.]]],.]     => 5
[[.,[[.,[.,.]],[.,[.,.]]]],.]     => 4
[[.,[[.,[.,.]],[[.,.],.]]],.]     => 4
[[.,[[[.,.],.],[.,[.,.]]]],.]     => 4
[[.,[[[.,.],.],[[.,.],.]]],.]     => 4
[[.,[[.,[.,[.,.]]],[.,.]]],.]     => 5
[[.,[[.,[[.,.],.]],[.,.]]],.]     => 5
[[.,[[[.,.],[.,.]],[.,.]]],.]     => 3
[[.,[[[.,[.,.]],.],[.,.]]],.]     => 5
[[.,[[[[.,.],.],.],[.,.]]],.]     => 5
[[.,[[.,[.,[.,[.,.]]]],.]],.]     => 6
[[.,[[.,[.,[[.,.],.]]],.]],.]     => 6
[[.,[[.,[[.,.],[.,.]]],.]],.]     => 4
[[.,[[.,[[.,[.,.]],.]],.]],.]     => 6
[[.,[[.,[[[.,.],.],.]],.]],.]     => 6
[[.,[[[.,.],[.,[.,.]]],.]],.]     => 5
[[.,[[[.,.],[[.,.],.]],.]],.]     => 5
[[.,[[[.,[.,.]],[.,.]],.]],.]     => 5
[[.,[[[[.,.],.],[.,.]],.]],.]     => 5
[[.,[[[.,[.,[.,.]]],.],.]],.]     => 6
[[.,[[[.,[[.,.],.]],.],.]],.]     => 6
[[.,[[[[.,.],[.,.]],.],.]],.]     => 4
[[.,[[[[.,[.,.]],.],.],.]],.]     => 6
[[.,[[[[[.,.],.],.],.],.]],.]     => 6
[[[.,.],[.,[.,[.,[.,.]]]]],.]     => 5
[[[.,.],[.,[.,[[.,.],.]]]],.]     => 5
[[[.,.],[.,[[.,.],[.,.]]]],.]     => 3
[[[.,.],[.,[[.,[.,.]],.]]],.]     => 5
[[[.,.],[.,[[[.,.],.],.]]],.]     => 5
[[[.,.],[[.,.],[.,[.,.]]]],.]     => 4
[[[.,.],[[.,.],[[.,.],.]]],.]     => 4
[[[.,.],[[.,[.,.]],[.,.]]],.]     => 4
[[[.,.],[[[.,.],.],[.,.]]],.]     => 4
[[[.,.],[[.,[.,[.,.]]],.]],.]     => 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
[[[[.,.],[.,[.,.]]],[.,.]],.]     => 4
[[[[.,.],[[.,.],.]],[.,.]],.]     => 4
[[[[.,[.,.]],[.,.]],[.,.]],.]     => 4
[[[[[.,.],.],[.,.]],[.,.]],.]     => 4
[[[[.,[.,[.,.]]],.],[.,.]],.]     => 5
[[[[.,[[.,.],.]],.],[.,.]],.]     => 5
[[[[[.,.],[.,.]],.],[.,.]],.]     => 3
[[[[[.,[.,.]],.],.],[.,.]],.]     => 5
[[[[[[.,.],.],.],.],[.,.]],.]     => 5
[[[.,[.,[.,[.,[.,.]]]]],.],.]     => 6
[[[.,[.,[.,[[.,.],.]]]],.],.]     => 6
[[[.,[.,[[.,.],[.,.]]]],.],.]     => 4
[[[.,[.,[[.,[.,.]],.]]],.],.]     => 6
[[[.,[.,[[[.,.],.],.]]],.],.]     => 6
[[[.,[[.,.],[.,[.,.]]]],.],.]     => 5
[[[.,[[.,.],[[.,.],.]]],.],.]     => 5
[[[.,[[.,[.,.]],[.,.]]],.],.]     => 5
[[[.,[[[.,.],.],[.,.]]],.],.]     => 5
[[[.,[[.,[.,[.,.]]],.]],.],.]     => 6
[[[.,[[.,[[.,.],.]],.]],.],.]     => 6
[[[.,[[[.,.],[.,.]],.]],.],.]     => 4
[[[.,[[[.,[.,.]],.],.]],.],.]     => 6
[[[.,[[[[.,.],.],.],.]],.],.]     => 6
[[[[.,.],[.,[.,[.,.]]]],.],.]     => 5
[[[[.,.],[.,[[.,.],.]]],.],.]     => 5
[[[[.,.],[[.,.],[.,.]]],.],.]     => 3
[[[[.,.],[[.,[.,.]],.]],.],.]     => 5
[[[[.,.],[[[.,.],.],.]],.],.]     => 5
[[[[.,[.,.]],[.,[.,.]]],.],.]     => 4
[[[[.,[.,.]],[[.,.],.]],.],.]     => 4
[[[[[.,.],.],[.,[.,.]]],.],.]     => 4
[[[[[.,.],.],[[.,.],.]],.],.]     => 4
[[[[.,[.,[.,.]]],[.,.]],.],.]     => 5
[[[[.,[[.,.],.]],[.,.]],.],.]     => 5
[[[[[.,.],[.,.]],[.,.]],.],.]     => 3
[[[[[.,[.,.]],.],[.,.]],.],.]     => 5
[[[[[[.,.],.],.],[.,.]],.],.]     => 5
[[[[.,[.,[.,[.,.]]]],.],.],.]     => 6
[[[[.,[.,[[.,.],.]]],.],.],.]     => 6
[[[[.,[[.,.],[.,.]]],.],.],.]     => 4
[[[[.,[[.,[.,.]],.]],.],.],.]     => 6
[[[[.,[[[.,.],.],.]],.],.],.]     => 6
[[[[[.,.],[.,[.,.]]],.],.],.]     => 5
[[[[[.,.],[[.,.],.]],.],.],.]     => 5
[[[[[.,[.,.]],[.,.]],.],.],.]     => 5
[[[[[[.,.],.],[.,.]],.],.],.]     => 5
[[[[[.,[.,[.,.]]],.],.],.],.]     => 6
[[[[[.,[[.,.],.]],.],.],.],.]     => 6
[[[[[[.,.],[.,.]],.],.],.],.]     => 4
[[[[[[.,[.,.]],.],.],.],.],.]     => 6
[[[[[[[.,.],.],.],.],.],.],.]     => 6
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 7
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 7
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 5
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 7
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => 7
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 6
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 6
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 6
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => 6
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => 7
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => 7
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => 5
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => 7
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => 7
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => 6
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 6
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => 4
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => 6
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => 6
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => 5
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => 5
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => 5
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => 5
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => 6
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => 6
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => 4
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => 6
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => 6
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 7
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => 7
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => 5
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => 7
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => 7
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => 6
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => 6
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => 6
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => 6
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => 7
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => 7
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => 5
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => 7
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => 7
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => 6
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 6
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => 4
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => 6
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => 6
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => 5
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => 5
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => 5
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => 5
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => 6
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => 6
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => 4
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => 6
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => 6
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => 6
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => 6
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => 4
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => 6
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => 6
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => 6
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => 6
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => 4
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => 6
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => 6
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => 6
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => 6
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => 6
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => 6
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => 4
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => 4
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => 6
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => 6
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => 6
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => 6
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => 6
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => 6
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => 4
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => 6
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => 6
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => 5
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => 5
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => 5
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => 5
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => 6
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => 6
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => 4
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => 6
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => 6
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => 7
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => 7
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => 5
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => 7
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => 7
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => 6
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => 6
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => 6
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => 6
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => 7
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => 7
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => 5
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => 7
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => 7
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => 6
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => 6
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => 4
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => 6
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => 6
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => 5
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => 5
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => 5
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => 5
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => 6
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => 6
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => 4
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => 6
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => 6
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => 7
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => 7
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => 5
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => 7
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => 7
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => 6
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => 6
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => 6
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => 6
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => 7
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => 7
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => 5
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => 7
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => 7
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 6
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[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => 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
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 4
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 4
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 4
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 4
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 5
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 5
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 3
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 5
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => 5
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 6
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 6
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 4
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 6
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 6
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 5
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 5
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 5
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 5
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 6
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 6
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 4
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 6
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => 6
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 5
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 5
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 3
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 5
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => 5
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 4
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 4
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 4
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 4
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 5
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 5
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 3
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 5
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => 5
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 6
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 6
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 4
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 6
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => 6
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 5
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => 5
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 5
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => 5
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 6
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => 6
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => 4
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => 6
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 6
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 6
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 6
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 4
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 6
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 6
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 5
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 5
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 5
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 5
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 6
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 6
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 4
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 6
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 6
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => 5

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Created: Feb 25, 2016 at 11:21 by Martin Rubey

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Last Updated: Mar 31, 2019 at 22:32 by Martin Rubey