*****************************************************************************
*       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: St000118

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

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

[[oeis:A001006]] counts binary trees avoiding this pattern.


-----------------------------------------------------------------------------
References: [1]   Donaghey, R., Shapiro, L. W. Motzkin numbers [[MathSciNet:0505544]]
[2]   Rowland, E. S. Pattern avoidance in binary trees [[MathSciNet:2645188]] [[arXiv:0809.0488]]

-----------------------------------------------------------------------------
Code:


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

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

-----------------------------------------------------------------------------
Created: Jun 18, 2013 at 16:59 by Eric Rowland

-----------------------------------------------------------------------------
Last Updated: Oct 17, 2015 at 11:05 by Christian Stump