************************************************************************
*    www.FindStat.org - The Combinatorial Statistic Finder             *
*                                                                      *
*    Copyright (C) 2013 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.  *
************************************************************************

------------------------------------------------------------------------
Map identifier: Mp00026

------------------------------------------------------------------------
Map name: to ordered tree

------------------------------------------------------------------------
Domain: Dyck paths

------------------------------------------------------------------------
Codomain: Ordered trees

------------------------------------------------------------------------
Description: Sends a Dyck path to the ordered tree encoding the heights of the path.

This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns ([[St000011]]), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.

This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.

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

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

def mapping(elt):
    levels = [OrderedTree().clone()]
    for u in elt:
        if u == 1:
            levels.append(OrderedTree().clone())
        else:
            tree = levels.pop()
            tree.set_immutable()
            root = levels.pop()
            root.append(tree)
            levels.append(root)
    root = levels[0]
    root.set_immutable()
    return root


------------------------------------------------------------------------
Map images:

[1,0]                             => [[]]
[1,0,1,0]                         => [[],[]]
[1,1,0,0]                         => [[[]]]
[1,0,1,0,1,0]                     => [[],[],[]]
[1,0,1,1,0,0]                     => [[],[[]]]
[1,1,0,0,1,0]                     => [[[]],[]]
[1,1,0,1,0,0]                     => [[[],[]]]
[1,1,1,0,0,0]                     => [[[[]]]]
[1,0,1,0,1,0,1,0]                 => [[],[],[],[]]
[1,0,1,0,1,1,0,0]                 => [[],[],[[]]]
[1,0,1,1,0,0,1,0]                 => [[],[[]],[]]
[1,0,1,1,0,1,0,0]                 => [[],[[],[]]]
[1,0,1,1,1,0,0,0]                 => [[],[[[]]]]
[1,1,0,0,1,0,1,0]                 => [[[]],[],[]]
[1,1,0,0,1,1,0,0]                 => [[[]],[[]]]
[1,1,0,1,0,0,1,0]                 => [[[],[]],[]]
[1,1,0,1,0,1,0,0]                 => [[[],[],[]]]
[1,1,0,1,1,0,0,0]                 => [[[],[[]]]]
[1,1,1,0,0,0,1,0]                 => [[[[]]],[]]
[1,1,1,0,0,1,0,0]                 => [[[[]],[]]]
[1,1,1,0,1,0,0,0]                 => [[[[],[]]]]
[1,1,1,1,0,0,0,0]                 => [[[[[]]]]]
[1,0,1,0,1,0,1,0,1,0]             => [[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0]             => [[],[],[],[[]]]
[1,0,1,0,1,1,0,0,1,0]             => [[],[],[[]],[]]
[1,0,1,0,1,1,0,1,0,0]             => [[],[],[[],[]]]
[1,0,1,0,1,1,1,0,0,0]             => [[],[],[[[]]]]
[1,0,1,1,0,0,1,0,1,0]             => [[],[[]],[],[]]
[1,0,1,1,0,0,1,1,0,0]             => [[],[[]],[[]]]
[1,0,1,1,0,1,0,0,1,0]             => [[],[[],[]],[]]
[1,0,1,1,0,1,0,1,0,0]             => [[],[[],[],[]]]
[1,0,1,1,0,1,1,0,0,0]             => [[],[[],[[]]]]
[1,0,1,1,1,0,0,0,1,0]             => [[],[[[]]],[]]
[1,0,1,1,1,0,0,1,0,0]             => [[],[[[]],[]]]
[1,0,1,1,1,0,1,0,0,0]             => [[],[[[],[]]]]
[1,0,1,1,1,1,0,0,0,0]             => [[],[[[[]]]]]
[1,1,0,0,1,0,1,0,1,0]             => [[[]],[],[],[]]
[1,1,0,0,1,0,1,1,0,0]             => [[[]],[],[[]]]
[1,1,0,0,1,1,0,0,1,0]             => [[[]],[[]],[]]
[1,1,0,0,1,1,0,1,0,0]             => [[[]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0]             => [[[]],[[[]]]]
[1,1,0,1,0,0,1,0,1,0]             => [[[],[]],[],[]]
[1,1,0,1,0,0,1,1,0,0]             => [[[],[]],[[]]]
[1,1,0,1,0,1,0,0,1,0]             => [[[],[],[]],[]]
[1,1,0,1,0,1,0,1,0,0]             => [[[],[],[],[]]]
[1,1,0,1,0,1,1,0,0,0]             => [[[],[],[[]]]]
[1,1,0,1,1,0,0,0,1,0]             => [[[],[[]]],[]]
[1,1,0,1,1,0,0,1,0,0]             => [[[],[[]],[]]]
[1,1,0,1,1,0,1,0,0,0]             => [[[],[[],[]]]]
[1,1,0,1,1,1,0,0,0,0]             => [[[],[[[]]]]]
[1,1,1,0,0,0,1,0,1,0]             => [[[[]]],[],[]]
[1,1,1,0,0,0,1,1,0,0]             => [[[[]]],[[]]]
[1,1,1,0,0,1,0,0,1,0]             => [[[[]],[]],[]]
[1,1,1,0,0,1,0,1,0,0]             => [[[[]],[],[]]]
[1,1,1,0,0,1,1,0,0,0]             => [[[[]],[[]]]]
[1,1,1,0,1,0,0,0,1,0]             => [[[[],[]]],[]]
[1,1,1,0,1,0,0,1,0,0]             => [[[[],[]],[]]]
[1,1,1,0,1,0,1,0,0,0]             => [[[[],[],[]]]]
[1,1,1,0,1,1,0,0,0,0]             => [[[[],[[]]]]]
[1,1,1,1,0,0,0,0,1,0]             => [[[[[]]]],[]]
[1,1,1,1,0,0,0,1,0,0]             => [[[[[]]],[]]]
[1,1,1,1,0,0,1,0,0,0]             => [[[[[]],[]]]]
[1,1,1,1,0,1,0,0,0,0]             => [[[[[],[]]]]]
[1,1,1,1,1,0,0,0,0,0]             => [[[[[[]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]         => [[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0]         => [[],[],[],[],[[]]]
[1,0,1,0,1,0,1,1,0,0,1,0]         => [[],[],[],[[]],[]]
[1,0,1,0,1,0,1,1,0,1,0,0]         => [[],[],[],[[],[]]]
[1,0,1,0,1,0,1,1,1,0,0,0]         => [[],[],[],[[[]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]         => [[],[],[[]],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0]         => [[],[],[[]],[[]]]
[1,0,1,0,1,1,0,1,0,0,1,0]         => [[],[],[[],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,0]         => [[],[],[[],[],[]]]
[1,0,1,0,1,1,0,1,1,0,0,0]         => [[],[],[[],[[]]]]
[1,0,1,0,1,1,1,0,0,0,1,0]         => [[],[],[[[]]],[]]
[1,0,1,0,1,1,1,0,0,1,0,0]         => [[],[],[[[]],[]]]
[1,0,1,0,1,1,1,0,1,0,0,0]         => [[],[],[[[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,0]         => [[],[],[[[[]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]         => [[],[[]],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0]         => [[],[[]],[],[[]]]
[1,0,1,1,0,0,1,1,0,0,1,0]         => [[],[[]],[[]],[]]
[1,0,1,1,0,0,1,1,0,1,0,0]         => [[],[[]],[[],[]]]
[1,0,1,1,0,0,1,1,1,0,0,0]         => [[],[[]],[[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,0]         => [[],[[],[]],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0]         => [[],[[],[]],[[]]]
[1,0,1,1,0,1,0,1,0,0,1,0]         => [[],[[],[],[]],[]]
[1,0,1,1,0,1,0,1,0,1,0,0]         => [[],[[],[],[],[]]]
[1,0,1,1,0,1,0,1,1,0,0,0]         => [[],[[],[],[[]]]]
[1,0,1,1,0,1,1,0,0,0,1,0]         => [[],[[],[[]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,0]         => [[],[[],[[]],[]]]
[1,0,1,1,0,1,1,0,1,0,0,0]         => [[],[[],[[],[]]]]
[1,0,1,1,0,1,1,1,0,0,0,0]         => [[],[[],[[[]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]         => [[],[[[]]],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0]         => [[],[[[]]],[[]]]
[1,0,1,1,1,0,0,1,0,0,1,0]         => [[],[[[]],[]],[]]
[1,0,1,1,1,0,0,1,0,1,0,0]         => [[],[[[]],[],[]]]
[1,0,1,1,1,0,0,1,1,0,0,0]         => [[],[[[]],[[]]]]
[1,0,1,1,1,0,1,0,0,0,1,0]         => [[],[[[],[]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,0]         => [[],[[[],[]],[]]]
[1,0,1,1,1,0,1,0,1,0,0,0]         => [[],[[[],[],[]]]]
[1,0,1,1,1,0,1,1,0,0,0,0]         => [[],[[[],[[]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]         => [[],[[[[]]]],[]]
[1,0,1,1,1,1,0,0,0,1,0,0]         => [[],[[[[]]],[]]]
[1,0,1,1,1,1,0,0,1,0,0,0]         => [[],[[[[]],[]]]]
[1,0,1,1,1,1,0,1,0,0,0,0]         => [[],[[[[],[]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]         => [[],[[[[[]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]         => [[[]],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0]         => [[[]],[],[],[[]]]
[1,1,0,0,1,0,1,1,0,0,1,0]         => [[[]],[],[[]],[]]
[1,1,0,0,1,0,1,1,0,1,0,0]         => [[[]],[],[[],[]]]
[1,1,0,0,1,0,1,1,1,0,0,0]         => [[[]],[],[[[]]]]
[1,1,0,0,1,1,0,0,1,0,1,0]         => [[[]],[[]],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0]         => [[[]],[[]],[[]]]
[1,1,0,0,1,1,0,1,0,0,1,0]         => [[[]],[[],[]],[]]
[1,1,0,0,1,1,0,1,0,1,0,0]         => [[[]],[[],[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0]         => [[[]],[[],[[]]]]
[1,1,0,0,1,1,1,0,0,0,1,0]         => [[[]],[[[]]],[]]
[1,1,0,0,1,1,1,0,0,1,0,0]         => [[[]],[[[]],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0]         => [[[]],[[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,0]         => [[[]],[[[[]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]         => [[[],[]],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0]         => [[[],[]],[],[[]]]
[1,1,0,1,0,0,1,1,0,0,1,0]         => [[[],[]],[[]],[]]
[1,1,0,1,0,0,1,1,0,1,0,0]         => [[[],[]],[[],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0]         => [[[],[]],[[[]]]]
[1,1,0,1,0,1,0,0,1,0,1,0]         => [[[],[],[]],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0]         => [[[],[],[]],[[]]]
[1,1,0,1,0,1,0,1,0,0,1,0]         => [[[],[],[],[]],[]]
[1,1,0,1,0,1,0,1,0,1,0,0]         => [[[],[],[],[],[]]]
[1,1,0,1,0,1,0,1,1,0,0,0]         => [[[],[],[],[[]]]]
[1,1,0,1,0,1,1,0,0,0,1,0]         => [[[],[],[[]]],[]]
[1,1,0,1,0,1,1,0,0,1,0,0]         => [[[],[],[[]],[]]]
[1,1,0,1,0,1,1,0,1,0,0,0]         => [[[],[],[[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,0]         => [[[],[],[[[]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]         => [[[],[[]]],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0]         => [[[],[[]]],[[]]]
[1,1,0,1,1,0,0,1,0,0,1,0]         => [[[],[[]],[]],[]]
[1,1,0,1,1,0,0,1,0,1,0,0]         => [[[],[[]],[],[]]]
[1,1,0,1,1,0,0,1,1,0,0,0]         => [[[],[[]],[[]]]]
[1,1,0,1,1,0,1,0,0,0,1,0]         => [[[],[[],[]]],[]]
[1,1,0,1,1,0,1,0,0,1,0,0]         => [[[],[[],[]],[]]]
[1,1,0,1,1,0,1,0,1,0,0,0]         => [[[],[[],[],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,0]         => [[[],[[],[[]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]         => [[[],[[[]]]],[]]
[1,1,0,1,1,1,0,0,0,1,0,0]         => [[[],[[[]]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,0]         => [[[],[[[]],[]]]]
[1,1,0,1,1,1,0,1,0,0,0,0]         => [[[],[[[],[]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]         => [[[],[[[[]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]         => [[[[]]],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0]         => [[[[]]],[],[[]]]
[1,1,1,0,0,0,1,1,0,0,1,0]         => [[[[]]],[[]],[]]
[1,1,1,0,0,0,1,1,0,1,0,0]         => [[[[]]],[[],[]]]
[1,1,1,0,0,0,1,1,1,0,0,0]         => [[[[]]],[[[]]]]
[1,1,1,0,0,1,0,0,1,0,1,0]         => [[[[]],[]],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0]         => [[[[]],[]],[[]]]
[1,1,1,0,0,1,0,1,0,0,1,0]         => [[[[]],[],[]],[]]
[1,1,1,0,0,1,0,1,0,1,0,0]         => [[[[]],[],[],[]]]
[1,1,1,0,0,1,0,1,1,0,0,0]         => [[[[]],[],[[]]]]
[1,1,1,0,0,1,1,0,0,0,1,0]         => [[[[]],[[]]],[]]
[1,1,1,0,0,1,1,0,0,1,0,0]         => [[[[]],[[]],[]]]
[1,1,1,0,0,1,1,0,1,0,0,0]         => [[[[]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,0]         => [[[[]],[[[]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]         => [[[[],[]]],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0]         => [[[[],[]]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,0]         => [[[[],[]],[]],[]]
[1,1,1,0,1,0,0,1,0,1,0,0]         => [[[[],[]],[],[]]]
[1,1,1,0,1,0,0,1,1,0,0,0]         => [[[[],[]],[[]]]]
[1,1,1,0,1,0,1,0,0,0,1,0]         => [[[[],[],[]]],[]]
[1,1,1,0,1,0,1,0,0,1,0,0]         => [[[[],[],[]],[]]]
[1,1,1,0,1,0,1,0,1,0,0,0]         => [[[[],[],[],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]         => [[[[],[],[[]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]         => [[[[],[[]]]],[]]
[1,1,1,0,1,1,0,0,0,1,0,0]         => [[[[],[[]]],[]]]
[1,1,1,0,1,1,0,0,1,0,0,0]         => [[[[],[[]],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,0]         => [[[[],[[],[]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]         => [[[[],[[[]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]         => [[[[[]]]],[],[]]
[1,1,1,1,0,0,0,0,1,1,0,0]         => [[[[[]]]],[[]]]
[1,1,1,1,0,0,0,1,0,0,1,0]         => [[[[[]]],[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0]         => [[[[[]]],[],[]]]
[1,1,1,1,0,0,0,1,1,0,0,0]         => [[[[[]]],[[]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]         => [[[[[]],[]]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0]         => [[[[[]],[]],[]]]
[1,1,1,1,0,0,1,0,1,0,0,0]         => [[[[[]],[],[]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]         => [[[[[]],[[]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]         => [[[[[],[]]]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0]         => [[[[[],[]]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,0]         => [[[[[],[]],[]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]         => [[[[[],[],[]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]         => [[[[[],[[]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]         => [[[[[[]]]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0]         => [[[[[[]]]],[]]]
[1,1,1,1,1,0,0,0,1,0,0,0]         => [[[[[[]]],[]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]         => [[[[[[]],[]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]         => [[[[[[],[]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]         => [[[[[[[]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]     => [[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]     => [[],[],[],[],[],[[]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]     => [[],[],[],[],[[]],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]     => [[],[],[],[],[[],[]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]     => [[],[],[],[],[[[]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]     => [[],[],[],[[]],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]     => [[],[],[],[[]],[[]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]     => [[],[],[],[[],[]],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]     => [[],[],[],[[],[],[]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]     => [[],[],[],[[],[[]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]     => [[],[],[],[[[]]],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]     => [[],[],[],[[[]],[]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]     => [[],[],[],[[[],[]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]     => [[],[],[],[[[[]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]     => [[],[],[[]],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]     => [[],[],[[]],[],[[]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]     => [[],[],[[]],[[]],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]     => [[],[],[[]],[[],[]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]     => [[],[],[[]],[[[]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]     => [[],[],[[],[]],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]     => [[],[],[[],[]],[[]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]     => [[],[],[[],[],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]     => [[],[],[[],[],[],[]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]     => [[],[],[[],[],[[]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]     => [[],[],[[],[[]]],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]     => [[],[],[[],[[]],[]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]     => [[],[],[[],[[],[]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]     => [[],[],[[],[[[]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]     => [[],[],[[[]]],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]     => [[],[],[[[]]],[[]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]     => [[],[],[[[]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]     => [[],[],[[[]],[],[]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]     => [[],[],[[[]],[[]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]     => [[],[],[[[],[]]],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]     => [[],[],[[[],[]],[]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]     => [[],[],[[[],[],[]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]     => [[],[],[[[],[[]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]     => [[],[],[[[[]]]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]     => [[],[],[[[[]]],[]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]     => [[],[],[[[[]],[]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]     => [[],[],[[[[],[]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]     => [[],[],[[[[[]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]     => [[],[[]],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]     => [[],[[]],[],[],[[]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]     => [[],[[]],[],[[]],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]     => [[],[[]],[],[[],[]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]     => [[],[[]],[],[[[]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]     => [[],[[]],[[]],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]     => [[],[[]],[[]],[[]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]     => [[],[[]],[[],[]],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]     => [[],[[]],[[],[],[]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]     => [[],[[]],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]     => [[],[[]],[[[]]],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]     => [[],[[]],[[[]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]     => [[],[[]],[[[],[]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]     => [[],[[]],[[[[]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]     => [[],[[],[]],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]     => [[],[[],[]],[],[[]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]     => [[],[[],[]],[[]],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]     => [[],[[],[]],[[],[]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]     => [[],[[],[]],[[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]     => [[],[[],[],[]],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]     => [[],[[],[],[]],[[]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]     => [[],[[],[],[],[]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]     => [[],[[],[],[],[],[]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]     => [[],[[],[],[],[[]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]     => [[],[[],[],[[]]],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]     => [[],[[],[],[[]],[]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]     => [[],[[],[],[[],[]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]     => [[],[[],[],[[[]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]     => [[],[[],[[]]],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]     => [[],[[],[[]]],[[]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]     => [[],[[],[[]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]     => [[],[[],[[]],[],[]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]     => [[],[[],[[]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]     => [[],[[],[[],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]     => [[],[[],[[],[]],[]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]     => [[],[[],[[],[],[]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]     => [[],[[],[[],[[]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]     => [[],[[],[[[]]]],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]     => [[],[[],[[[]]],[]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]     => [[],[[],[[[]],[]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]     => [[],[[],[[[],[]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]     => [[],[[],[[[[]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]     => [[],[[[]]],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]     => [[],[[[]]],[],[[]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]     => [[],[[[]]],[[]],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]     => [[],[[[]]],[[],[]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]     => [[],[[[]]],[[[]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]     => [[],[[[]],[]],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]     => [[],[[[]],[]],[[]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]     => [[],[[[]],[],[]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]     => [[],[[[]],[],[],[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]     => [[],[[[]],[],[[]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]     => [[],[[[]],[[]]],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]     => [[],[[[]],[[]],[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]     => [[],[[[]],[[],[]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]     => [[],[[[]],[[[]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]     => [[],[[[],[]]],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]     => [[],[[[],[]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]     => [[],[[[],[]],[]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]     => [[],[[[],[]],[],[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]     => [[],[[[],[]],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]     => [[],[[[],[],[]]],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]     => [[],[[[],[],[]],[]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]     => [[],[[[],[],[],[]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]     => [[],[[[],[],[[]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]     => [[],[[[],[[]]]],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]     => [[],[[[],[[]]],[]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]     => [[],[[[],[[]],[]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]     => [[],[[[],[[],[]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]     => [[],[[[],[[[]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]     => [[],[[[[]]]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]     => [[],[[[[]]]],[[]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]     => [[],[[[[]]],[]],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]     => [[],[[[[]]],[],[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]     => [[],[[[[]]],[[]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]     => [[],[[[[]],[]]],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]     => [[],[[[[]],[]],[]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]     => [[],[[[[]],[],[]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]     => [[],[[[[]],[[]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]     => [[],[[[[],[]]]],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]     => [[],[[[[],[]]],[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]     => [[],[[[[],[]],[]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]     => [[],[[[[],[],[]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]     => [[],[[[[],[[]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]     => [[],[[[[[]]]]],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]     => [[],[[[[[]]]],[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]     => [[],[[[[[]]],[]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]     => [[],[[[[[]],[]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]     => [[],[[[[[],[]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]     => [[],[[[[[[]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]     => [[[]],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]     => [[[]],[],[],[],[[]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]     => [[[]],[],[],[[]],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]     => [[[]],[],[],[[],[]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]     => [[[]],[],[],[[[]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]     => [[[]],[],[[]],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]     => [[[]],[],[[]],[[]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]     => [[[]],[],[[],[]],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]     => [[[]],[],[[],[],[]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]     => [[[]],[],[[],[[]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]     => [[[]],[],[[[]]],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]     => [[[]],[],[[[]],[]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]     => [[[]],[],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]     => [[[]],[],[[[[]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]     => [[[]],[[]],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]     => [[[]],[[]],[],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]     => [[[]],[[]],[[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]     => [[[]],[[]],[[],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]     => [[[]],[[]],[[[]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]     => [[[]],[[],[]],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]     => [[[]],[[],[]],[[]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]     => [[[]],[[],[],[]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]     => [[[]],[[],[],[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]     => [[[]],[[],[],[[]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]     => [[[]],[[],[[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]     => [[[]],[[],[[]],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]     => [[[]],[[],[[],[]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]     => [[[]],[[],[[[]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]     => [[[]],[[[]]],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]     => [[[]],[[[]]],[[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]     => [[[]],[[[]],[]],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]     => [[[]],[[[]],[],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]     => [[[]],[[[]],[[]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]     => [[[]],[[[],[]]],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]     => [[[]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]     => [[[]],[[[],[],[]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]     => [[[]],[[[],[[]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]     => [[[]],[[[[]]]],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]     => [[[]],[[[[]]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]     => [[[]],[[[[]],[]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]     => [[[]],[[[[],[]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]     => [[[]],[[[[[]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]     => [[[],[]],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]     => [[[],[]],[],[],[[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]     => [[[],[]],[],[[]],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]     => [[[],[]],[],[[],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]     => [[[],[]],[],[[[]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]     => [[[],[]],[[]],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]     => [[[],[]],[[]],[[]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]     => [[[],[]],[[],[]],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]     => [[[],[]],[[],[],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]     => [[[],[]],[[],[[]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]     => [[[],[]],[[[]]],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]     => [[[],[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]     => [[[],[]],[[[],[]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]     => [[[],[]],[[[[]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]     => [[[],[],[]],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]     => [[[],[],[]],[],[[]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]     => [[[],[],[]],[[]],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]     => [[[],[],[]],[[],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]     => [[[],[],[]],[[[]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]     => [[[],[],[],[]],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]     => [[[],[],[],[]],[[]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]     => [[[],[],[],[],[]],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]     => [[[],[],[],[],[],[]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]     => [[[],[],[],[],[[]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]     => [[[],[],[],[[]]],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]     => [[[],[],[],[[]],[]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]     => [[[],[],[],[[],[]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]     => [[[],[],[],[[[]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]     => [[[],[],[[]]],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]     => [[[],[],[[]]],[[]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]     => [[[],[],[[]],[]],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]     => [[[],[],[[]],[],[]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]     => [[[],[],[[]],[[]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]     => [[[],[],[[],[]]],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]     => [[[],[],[[],[]],[]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]     => [[[],[],[[],[],[]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]     => [[[],[],[[],[[]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]     => [[[],[],[[[]]]],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]     => [[[],[],[[[]]],[]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]     => [[[],[],[[[]],[]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]     => [[[],[],[[[],[]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]     => [[[],[],[[[[]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]     => [[[],[[]]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]     => [[[],[[]]],[],[[]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]     => [[[],[[]]],[[]],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]     => [[[],[[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]     => [[[],[[]]],[[[]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]     => [[[],[[]],[]],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]     => [[[],[[]],[]],[[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]     => [[[],[[]],[],[]],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]     => [[[],[[]],[],[],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]     => [[[],[[]],[],[[]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]     => [[[],[[]],[[]]],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]     => [[[],[[]],[[]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]     => [[[],[[]],[[],[]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]     => [[[],[[]],[[[]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]     => [[[],[[],[]]],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]     => [[[],[[],[]]],[[]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]     => [[[],[[],[]],[]],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]     => [[[],[[],[]],[],[]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]     => [[[],[[],[]],[[]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]     => [[[],[[],[],[]]],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]     => [[[],[[],[],[]],[]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]     => [[[],[[],[],[],[]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]     => [[[],[[],[],[[]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]     => [[[],[[],[[]]]],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]     => [[[],[[],[[]]],[]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]     => [[[],[[],[[]],[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]     => [[[],[[],[[],[]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]     => [[[],[[],[[[]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]     => [[[],[[[]]]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]     => [[[],[[[]]]],[[]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]     => [[[],[[[]]],[]],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]     => [[[],[[[]]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]     => [[[],[[[]]],[[]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]     => [[[],[[[]],[]]],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]     => [[[],[[[]],[]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]     => [[[],[[[]],[],[]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]     => [[[],[[[]],[[]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]     => [[[],[[[],[]]]],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]     => [[[],[[[],[]]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]     => [[[],[[[],[]],[]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]     => [[[],[[[],[],[]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]     => [[[],[[[],[[]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]     => [[[],[[[[]]]]],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]     => [[[],[[[[]]]],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]     => [[[],[[[[]]],[]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]     => [[[],[[[[]],[]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]     => [[[],[[[[],[]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]     => [[[],[[[[[]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]     => [[[[]]],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]     => [[[[]]],[],[],[[]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]     => [[[[]]],[],[[]],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]     => [[[[]]],[],[[],[]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]     => [[[[]]],[],[[[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]     => [[[[]]],[[]],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]     => [[[[]]],[[]],[[]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]     => [[[[]]],[[],[]],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]     => [[[[]]],[[],[],[]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]     => [[[[]]],[[],[[]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]     => [[[[]]],[[[]]],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]     => [[[[]]],[[[]],[]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]     => [[[[]]],[[[],[]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]     => [[[[]]],[[[[]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]     => [[[[]],[]],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]     => [[[[]],[]],[],[[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]     => [[[[]],[]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]     => [[[[]],[]],[[],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]     => [[[[]],[]],[[[]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]     => [[[[]],[],[]],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]     => [[[[]],[],[]],[[]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]     => [[[[]],[],[],[]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]     => [[[[]],[],[],[],[]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]     => [[[[]],[],[],[[]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]     => [[[[]],[],[[]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]     => [[[[]],[],[[]],[]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]     => [[[[]],[],[[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]     => [[[[]],[],[[[]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]     => [[[[]],[[]]],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]     => [[[[]],[[]]],[[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]     => [[[[]],[[]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]     => [[[[]],[[]],[],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]     => [[[[]],[[]],[[]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]     => [[[[]],[[],[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]     => [[[[]],[[],[]],[]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]     => [[[[]],[[],[],[]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]     => [[[[]],[[],[[]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]     => [[[[]],[[[]]]],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]     => [[[[]],[[[]]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]     => [[[[]],[[[]],[]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]     => [[[[]],[[[],[]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]     => [[[[]],[[[[]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]     => [[[[],[]]],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]     => [[[[],[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]     => [[[[],[]]],[[]],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]     => [[[[],[]]],[[],[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]     => [[[[],[]]],[[[]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]     => [[[[],[]],[]],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]     => [[[[],[]],[]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]     => [[[[],[]],[],[]],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]     => [[[[],[]],[],[],[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]     => [[[[],[]],[],[[]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]     => [[[[],[]],[[]]],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]     => [[[[],[]],[[]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]     => [[[[],[]],[[],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]     => [[[[],[]],[[[]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]     => [[[[],[],[]]],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]     => [[[[],[],[]]],[[]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]     => [[[[],[],[]],[]],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]     => [[[[],[],[]],[],[]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]     => [[[[],[],[]],[[]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]     => [[[[],[],[],[]]],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]     => [[[[],[],[],[]],[]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]     => [[[[],[],[],[],[]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]     => [[[[],[],[],[[]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]     => [[[[],[],[[]]]],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]     => [[[[],[],[[]]],[]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]     => [[[[],[],[[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]     => [[[[],[],[[],[]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]     => [[[[],[],[[[]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]     => [[[[],[[]]]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]     => [[[[],[[]]]],[[]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]     => [[[[],[[]]],[]],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]     => [[[[],[[]]],[],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]     => [[[[],[[]]],[[]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]     => [[[[],[[]],[]]],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]     => [[[[],[[]],[]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]     => [[[[],[[]],[],[]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]     => [[[[],[[]],[[]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]     => [[[[],[[],[]]]],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]     => [[[[],[[],[]]],[]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]     => [[[[],[[],[]],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]     => [[[[],[[],[],[]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]     => [[[[],[[],[[]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]     => [[[[],[[[]]]]],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]     => [[[[],[[[]]]],[]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]     => [[[[],[[[]]],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]     => [[[[],[[[]],[]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]     => [[[[],[[[],[]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]     => [[[[],[[[[]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]     => [[[[[]]]],[],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]     => [[[[[]]]],[],[[]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]     => [[[[[]]]],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]     => [[[[[]]]],[[],[]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]     => [[[[[]]]],[[[]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]     => [[[[[]]],[]],[],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]     => [[[[[]]],[]],[[]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]     => [[[[[]]],[],[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]     => [[[[[]]],[],[],[]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]     => [[[[[]]],[],[[]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]     => [[[[[]]],[[]]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]     => [[[[[]]],[[]],[]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]     => [[[[[]]],[[],[]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]     => [[[[[]]],[[[]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]     => [[[[[]],[]]],[],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]     => [[[[[]],[]]],[[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]     => [[[[[]],[]],[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]     => [[[[[]],[]],[],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]     => [[[[[]],[]],[[]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]     => [[[[[]],[],[]]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]     => [[[[[]],[],[]],[]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]     => [[[[[]],[],[],[]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]     => [[[[[]],[],[[]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]     => [[[[[]],[[]]]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]     => [[[[[]],[[]]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]     => [[[[[]],[[]],[]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]     => [[[[[]],[[],[]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]     => [[[[[]],[[[]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]     => [[[[[],[]]]],[],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]     => [[[[[],[]]]],[[]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]     => [[[[[],[]]],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]     => [[[[[],[]]],[],[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]     => [[[[[],[]]],[[]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]     => [[[[[],[]],[]]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]     => [[[[[],[]],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]     => [[[[[],[]],[],[]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]     => [[[[[],[]],[[]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]     => [[[[[],[],[]]]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]     => [[[[[],[],[]]],[]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]     => [[[[[],[],[]],[]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]     => [[[[[],[],[],[]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]     => [[[[[],[],[[]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]     => [[[[[],[[]]]]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]     => [[[[[],[[]]]],[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]     => [[[[[],[[]]],[]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]     => [[[[[],[[]],[]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]     => [[[[[],[[],[]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]     => [[[[[],[[[]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]     => [[[[[[]]]]],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]     => [[[[[[]]]]],[[]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]     => [[[[[[]]]],[]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]     => [[[[[[]]]],[],[]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]     => [[[[[[]]]],[[]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]     => [[[[[[]]],[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]     => [[[[[[]]],[]],[]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]     => [[[[[[]]],[],[]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]     => [[[[[[]]],[[]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]     => [[[[[[]],[]]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]     => [[[[[[]],[]]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]     => [[[[[[]],[]],[]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]     => [[[[[[]],[],[]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]     => [[[[[[]],[[]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]     => [[[[[[],[]]]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]     => [[[[[[],[]]]],[]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]     => [[[[[[],[]]],[]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]     => [[[[[[],[]],[]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]     => [[[[[[],[],[]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]     => [[[[[[],[[]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]     => [[[[[[[]]]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]     => [[[[[[[]]]]],[]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]     => [[[[[[[]]]],[]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]     => [[[[[[[]]],[]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]     => [[[[[[[]],[]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]     => [[[[[[[],[]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]     => [[[[[[[[]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[],[[]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[],[[]],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[],[[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[],[[[]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[],[[]],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[[]],[[]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[],[],[],[],[[],[]],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[],[],[[],[],[]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[],[],[],[],[[],[[]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[],[[[]]],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[],[],[[[]],[]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[],[],[[[],[]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[],[[[[]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[],[[]],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[],[[]],[],[[]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[],[],[],[[]],[[],[]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[],[[]],[[[]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[],[],[],[[],[]],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[],[],[],[[],[]],[[]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[],[],[],[[],[],[]],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[],[],[],[[],[],[],[]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[],[],[],[[],[],[[]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[],[],[],[[],[[]]],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[],[],[],[[],[[]],[]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[],[],[],[[],[[],[]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[],[],[],[[],[[[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[],[[[]]],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[],[[[]]],[[]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[],[],[],[[[]],[]],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[],[],[],[[[]],[],[]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[],[],[],[[[]],[[]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[],[],[],[[[],[]]],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[],[],[],[[[],[]],[]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[],[],[],[[[],[],[]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[],[],[],[[[],[[]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[],[[[[]]]],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[],[],[],[[[[]]],[]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[],[],[],[[[[]],[]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[],[[[[],[]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[],[[[[[]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[],[[]],[],[],[[]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[],[[]],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[],[],[[]],[],[[],[]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[],[[]],[],[[[]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]],[[]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[],[],[[]],[[],[]],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[],[],[[]],[[],[],[]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[],[],[[]],[[],[[]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[],[[]],[[[]]],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[],[],[[]],[[[]],[]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[],[],[[]],[[[],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[],[[]],[[[[]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[],[],[[],[]],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[],[],[[],[]],[],[[]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[],[],[[],[]],[[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[],[],[[],[]],[[],[]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[],[],[[],[]],[[[]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[],[],[[],[],[]],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[],[],[[],[],[]],[[]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[],[],[[],[],[],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[[],[],[],[],[]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[],[],[[],[],[],[[]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[],[],[[],[],[[]]],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[],[],[[],[],[[]],[]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[],[],[[],[],[[],[]]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[],[],[[],[],[[[]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[],[],[[],[[]]],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[],[],[[],[[]]],[[]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[],[],[[],[[]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[],[],[[],[[]],[],[]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[],[],[[],[[]],[[]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[],[],[[],[[],[]]],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[],[],[[],[[],[]],[]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[],[],[[],[[],[],[]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[],[],[[],[[],[[]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[],[],[[],[[[]]]],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[],[],[[],[[[]]],[]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[],[],[[],[[[]],[]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[],[],[[],[[[],[]]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[],[[],[[[[]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[],[[[]]],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[],[[[]]],[],[[]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[],[[[]]],[[]],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[],[],[[[]]],[[],[]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[],[],[[[]],[]],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[],[],[[[]],[]],[[]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[],[],[[[]],[],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[],[],[[[]],[],[],[]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[],[],[[[]],[],[[]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[],[],[[[]],[[]]],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[],[],[[[]],[[]],[]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[],[],[[[]],[[],[]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[],[],[[[]],[[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[],[],[[[],[]]],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[],[],[[[],[]]],[[]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[],[],[[[],[]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[],[],[[[],[]],[],[]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[],[],[[[],[]],[[]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[],[],[[[],[],[]]],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[],[],[[[],[],[]],[]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[],[],[[[],[],[],[]]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[],[],[[[],[],[[]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[],[],[[[],[[]]]],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[],[],[[[],[[]]],[]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[],[],[[[],[[]],[]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[],[[[],[[],[]]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[],[[[],[[[]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[],[[[[]]]],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[],[],[[[[]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[],[],[[[[]]],[],[]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[],[],[[[[]]],[[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[],[],[[[[]],[]]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[],[],[[[[]],[]],[]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[],[],[[[[]],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[],[[[[]],[[]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[],[],[[[[],[]]]],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[],[[[[],[]]],[]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[],[[[[],[]],[]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[],[[[[],[],[]]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[],[[[[],[[]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[],[[[[[]]]],[]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[],[[[[[]]],[]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[],[[[[[]],[]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[],[[[[[],[]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[],[[[[[[]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[],[[]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[],[[]],[],[],[[],[]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[],[[[]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[[]],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[],[[]],[],[[],[]],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[],[[]],[],[[],[],[]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[],[[]],[],[[],[[]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[],[[]],[],[[[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[],[[]],[],[[[]],[]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[],[[]],[],[[[],[]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[]],[[],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[],[[]],[[],[]],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[],[[]],[[],[]],[[]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[],[[]],[[],[],[]],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[],[[]],[[],[],[],[]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[],[[]],[[],[],[[]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[],[[]],[[],[[]]],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[],[[]],[[],[[]],[]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[],[[]],[[],[[],[]]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[],[[]],[[],[[[]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[],[[]],[[[]],[]],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[],[[]],[[[]],[],[]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[],[[]],[[[]],[[]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[],[[]],[[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[],[[]],[[[],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[],[[]],[[[],[],[]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[],[[]],[[[],[[]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[],[[]],[[[[]]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[],[[]],[[[[]],[]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[],[[]],[[[[],[]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[],[[],[]],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[],[[],[]],[],[],[[]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[],[[],[]],[],[[]],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[],[[],[]],[],[[],[]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[],[[],[]],[],[[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[],[[],[]],[[]],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[],[[],[]],[[]],[[]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[[],[]],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[],[[],[]],[[],[],[]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[],[[],[]],[[],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[],[[],[]],[[[]]],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[],[[],[]],[[[]],[]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[],[[],[]],[[[],[]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[],[[],[]],[[[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[],[[],[],[]],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[],[[],[],[]],[],[[]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[],[[],[],[]],[[]],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[],[[],[],[]],[[],[]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[],[[],[],[]],[[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[],[[],[],[],[]],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[],[[],[],[],[]],[[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[],[[],[],[],[],[]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[],[],[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[],[[],[],[],[],[[]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[],[[],[],[],[[]]],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[],[[],[],[],[[]],[]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[],[[],[],[],[[],[]]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[],[[],[],[],[[[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[],[[],[],[[]]],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[],[[],[],[[]]],[[]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[],[[],[],[[]],[]],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[],[[],[],[[]],[],[]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[],[[],[],[[]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[],[[],[],[[],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[],[[],[],[[],[]],[]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[],[[],[],[[],[],[]]]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[],[[],[],[[],[[]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[],[[],[],[[[]]]],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[],[[],[],[[[]]],[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[],[[],[],[[[]],[]]]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[],[[],[],[[[],[]]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[],[[[[]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[],[[],[[]]],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[],[[],[[]]],[],[[]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[],[[],[[]]],[[]],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[],[[],[[]]],[[],[]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[],[[],[[]]],[[[]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[],[[],[[]],[]],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[],[[],[[]],[]],[[]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[],[[],[[]],[],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[],[[],[[]],[],[],[]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[],[[],[[]],[],[[]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[],[[],[[]],[[]]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[],[[],[[]],[[]],[]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[],[[],[[]],[[],[]]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[],[[],[[]],[[[]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[],[[],[[],[]]],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[],[[],[[],[]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[],[[],[[],[]],[]],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[],[[],[[],[]],[],[]]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[],[[],[[],[]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[],[[],[[],[],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[],[[],[[],[],[]],[]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[],[[],[[],[],[],[]]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[],[[],[[],[],[[]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[],[[],[[],[[]]]],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[],[[],[[],[[]]],[]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[],[[],[[],[[]],[]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[],[[],[[],[]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[],[[],[[],[[[]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[],[[],[[[]]]],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[],[[],[[[]]]],[[]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[],[[],[[[]]],[]],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[],[[],[[[]]],[],[]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[],[[],[[[]]],[[]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[],[[],[[[]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[],[[],[[[]],[]],[]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[],[[],[[[]],[],[]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[],[[],[[[]],[[]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[],[[],[[[],[]]]],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[],[[],[[[],[]]],[]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[],[[],[[[],[]],[]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[],[[],[[[],[],[]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[],[[],[[[],[[]]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[],[[],[[[[]]]]],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[],[[],[[[[]]]],[]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[],[[],[[[[]]],[]]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[],[[],[[[[]],[]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[],[[],[[[[],[]]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[],[[],[[[[[]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[],[[[]]],[],[],[[]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[],[[[]]],[],[[],[]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[],[[[]]],[[],[]],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[],[[[]]],[[],[],[]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[],[[[]]],[[],[[]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[],[[[]]],[[[]],[]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[],[[[]]],[[[],[]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[],[[[]],[]],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[],[[[]],[]],[],[[]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[],[[[]],[]],[[]],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[],[[[]],[]],[[],[]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[],[[[]],[]],[[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[],[[[]],[],[]],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[],[[[]],[],[]],[[]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[],[[[]],[],[],[]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[],[[[]],[],[],[],[]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[],[[[]],[],[],[[]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[],[[[]],[],[[]]],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[],[[[]],[],[[]],[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[],[[[]],[],[[],[]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[],[[[]],[],[[[]]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[],[[[]],[[]]],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[],[[[]],[[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[],[[[]],[[]],[]],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[],[[[]],[[]],[],[]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]],[[]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[],[[[]],[[],[]]],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[],[[[]],[[],[]],[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[],[[[]],[[],[],[]]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[],[[[]],[[],[[]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[],[[[]],[[[]]]],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[],[[[]],[[[]]],[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[],[[[]],[[[]],[]]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[],[[[]],[[[],[]]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[],[[[]],[[[[]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[],[[[],[]]],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[],[[[],[]]],[],[[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[],[[[],[]]],[[]],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[],[[[],[]]],[[],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[],[[[],[]]],[[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[],[[[],[]],[]],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[],[[[],[]],[]],[[]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[],[[[],[]],[],[]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[],[[[],[]],[],[],[]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[],[[[],[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[],[[[],[]],[[]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[],[[[],[]],[[]],[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[],[[[],[]],[[],[]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[],[[[],[]],[[[]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[],[[[],[],[]]],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[],[[[],[],[]]],[[]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[],[[[],[],[]],[]],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[],[[[],[],[]],[],[]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[],[[[],[],[]],[[]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[],[[[],[],[],[]]],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[],[[[],[],[],[]],[]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[],[]]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[],[[[],[],[],[[]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[],[[[],[],[[]]]],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[],[[[],[],[[]]],[]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[],[[[],[],[[]],[]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[],[[],[]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[],[[[]]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[],[[[],[[]]]],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[],[[[],[[]]]],[[]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[],[[[],[[]]],[]],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[],[[[],[[]]],[],[]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[],[[[],[[]]],[[]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[],[[[],[[]],[]]],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[],[[[],[[]],[]],[]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[],[[[],[[]],[],[]]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[],[[[],[[]],[[]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[],[[[],[[],[]]]],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[],[[[],[[],[]]],[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[],[[[],[[],[]],[]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[],[[[],[[],[],[]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[],[[[],[[],[[]]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[],[[[],[[[]]]]],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[],[[[],[[[]]]],[]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[],[[[],[[[]]],[]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[],[[[],[[[]],[]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[],[[[],[[[],[]]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[],[[[],[[[[]]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[],[[[[]]]],[[],[]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[],[[[[]]],[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[],[[[[]]],[]],[[]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[],[[[[]]],[],[]],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[],[[[[]]],[],[],[]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[],[[[[]]],[],[[]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[],[[[[]]],[[]]],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[],[[[[]]],[[]],[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[],[[[[]]],[[],[]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[],[[[[]]],[[[]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[],[[[[]],[]]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[],[[[[]],[]]],[[]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[],[[[[]],[]],[]],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[],[[[[]],[]],[],[]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[],[[[[]],[]],[[]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[],[[[[]],[],[]]],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[],[[[[]],[],[]],[]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[],[[[[]],[],[],[]]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[],[[[[]],[],[[]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[],[[[[]],[[]]]],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[],[[[[]],[[]]],[]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[],[[[[]],[[]],[]]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[],[[[[]],[[],[]]]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[],[[[[]],[[[]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[],[[[[],[]]]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[],[[[[],[]]]],[[]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[],[[[[],[]]],[]],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[],[[[[],[]]],[],[]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[],[[[[],[]]],[[]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[],[[[[],[]],[]]],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[],[[[[],[]],[]],[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[],[[[[],[]],[],[]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[],[[[[],[]],[[]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[],[[[[],[],[]]]],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[],[[[[],[],[]]],[]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[],[[[[],[],[]],[]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[],[]]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[],[[[[],[],[[]]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[],[[[[],[[]]]]],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[],[[[[],[[]]]],[]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[],[[[[],[[]]],[]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[],[[[[],[[]],[]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[[[],[[],[]]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[],[[[[[]]]],[]],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[],[[[[[]]]],[],[]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[],[[[[[]]]],[[]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[],[[[[[]]],[]]],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[],[[[[[]]],[]],[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[],[[[[[]]],[],[]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[],[[[[[]]],[[]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[],[[[[[]],[]]]],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[],[[[[[]],[]]],[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[],[[[[[]],[]],[]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[],[[[[[]],[],[]]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[],[[[[[]],[[]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[],[[[[[],[]]]]],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[],[[[[[],[]]]],[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[],[[[[[],[]]],[]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[],[[[[[],[]],[]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[],[[[[[[]]]]],[]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[],[[[[[[]]]],[]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[],[[[[[[[]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[],[[],[]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[]],[],[],[[],[]],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[]],[],[],[[],[],[]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[]],[],[],[[],[[]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[],[[[]]],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[]],[],[],[[[]],[]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[]],[],[],[[[],[]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[],[[[[]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[]],[],[[]],[[],[]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[]],[],[[],[]],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[]],[],[[],[]],[[]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[]],[],[[],[],[]],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[]],[],[[],[],[],[]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[]],[],[[],[],[[]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[]],[],[[],[[]]],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[]],[],[[],[[]],[]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[]],[],[[],[[],[]]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[]],[],[[],[[[]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[]],[],[[[]],[]],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[]],[],[[[]],[],[]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[]],[],[[[]],[[]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[]],[],[[[],[]]],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[]],[],[[[],[]],[]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[]],[],[[[],[],[]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[]],[],[[[],[[]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[]],[],[[[[]]],[]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[]],[],[[[[]],[]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[]],[],[[[[],[]]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[],[[[[[]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[[]],[],[[],[]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[]],[[],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[]],[[]],[[],[],[]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[]],[[],[[]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[]],[[[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[]],[[[],[]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[]],[[],[]],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[]],[[],[]],[],[[]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[]],[[],[]],[[]],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]],[[],[]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[]],[[],[]],[[[]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[]],[[],[],[]],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[]],[[],[],[]],[[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[]],[[],[],[],[]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[]],[[],[],[],[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[[]],[[],[],[],[[]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[]],[[],[],[[]]],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[[]],[[],[],[[]],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[[]],[[],[],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[[]],[[],[],[[[]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[]],[[],[[]]],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[]],[[],[[]]],[[]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[]],[[],[[]],[]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[[]],[[],[[]],[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[[]],[[],[[]],[[]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[]],[[],[[],[]]],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[[]],[[],[[],[]],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[[]],[[],[[],[],[]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[[]],[[],[[],[[]]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[]],[[],[[[]]]],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[]],[[],[[[]]],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[[]],[[],[[[]],[]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[[]],[[],[[[],[]]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[[]],[[],[[[[]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[]],[[[]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[]],[[[]],[]],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[]],[[[]],[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[]],[[[]],[],[]],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[]],[[[]],[],[],[]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[[]],[[[]],[],[[]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[]],[[[]],[[]]],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[]],[[[]],[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[[]],[[[]],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[[]],[[[]],[[[]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[]],[[[],[]]],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[]],[[[],[]]],[[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[]],[[[],[]],[]],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[]],[[[],[]],[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[[]],[[[],[]],[[]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[]],[[[],[],[]]],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[[]],[[[],[],[]],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[[]],[[[],[],[],[]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[]],[[[],[],[[]]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[]],[[[],[[]]]],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[[]],[[[],[[]]],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[]],[[[],[[]],[]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[[]],[[[],[[],[]]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[]],[[[],[[[]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[]],[[[[]]],[]],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[[]],[[[[]]],[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[[]],[[[[]]],[[]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[]],[[[[]],[]]],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[]],[[[[]],[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[[]],[[[[]],[],[]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[[]],[[[[]],[[]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[]],[[[[],[]]]],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[]],[[[[],[]]],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[[]],[[[[],[]],[]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[]],[[[[],[],[]]]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[[]],[[[[],[[]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[[]],[[[[[]]]],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[[]],[[[[[]]],[]]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[]],[[[[[]],[]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[]],[[[[[],[]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[],[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[],[]],[],[],[],[[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[],[]],[],[],[[]],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[],[]],[],[],[[],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[],[]],[],[],[[[]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[],[]],[],[[]],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[],[]],[],[[]],[[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[],[]],[],[[],[]],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[],[]],[],[[],[],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[],[]],[],[[],[[]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[],[]],[],[[[]]],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[],[]],[],[[[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[],[]],[],[[[],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[],[]],[],[[[[]]]]]

-----------------------------------------------------------------------------
Created: Jan 19, 2020 at 07:29 by FindStatCrew

-----------------------------------------------------------------------------
Last Updated: Jan 19, 2020 at 07:29 by Martin Rubey