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*    useful, but WITHOUT ANY WARRANTY; without even the implied        *
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------------------------------------------------------------------------
Map identifier: Mp00029

------------------------------------------------------------------------
Map name: to binary tree: left tree, up step, right tree, down step

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

------------------------------------------------------------------------
Codomain: Binary trees

------------------------------------------------------------------------
Description: Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.

A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.

This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.

This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.

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

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

def mapping(elt):
    return elt.to_binary_tree("L1R0")


------------------------------------------------------------------------
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]     => [[[.,[.,[[.,.],.]]],.],[.,.]]
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[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]     => [[[.,[[.,[[.,.],.]],.]],.],.]
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[1,1,1,0,1,0,0,1,0,1,0,0,1,0]     => [[.,[[[.,[[.,.],.]],.],.]],.]
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[1,1,1,0,1,0,0,1,0,1,1,0,0,0]     => [.,[[[.,[[.,.],.]],.],[.,.]]]
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[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]     => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
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[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] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
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[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
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[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] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
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[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
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[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] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]

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Created: Jan 29, 2020 at 13:25 by FindStatCrew

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Last Updated: Jan 29, 2020 at 13:25 by Martin Rubey