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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
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-----------------------------------------------------------------------------
Statistic identifier: St000201
-----------------------------------------------------------------------------
Collection: Binary trees
-----------------------------------------------------------------------------
Description: The number of leaf nodes in a binary tree.
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
-----------------------------------------------------------------------------
References: [1] Billey, S., Konvalinka, M., Matsen, F. A. I. On the enumeration of tanglegrams and tangled chains [[arXiv:1507.04976]]
[2] Powers of 2: a(n) = 2^n. [[OEIS:A000079]]
[3] a(n) = n*(n+1)*2^(n-2). [[OEIS:A001788]]
-----------------------------------------------------------------------------
Code:
def statistic(B):
if B == BinaryTree():
return 0
if B == BinaryTree([]):
return 1
return sum(statistic(S) for S in B)
-----------------------------------------------------------------------------
Statistic values:
[.,.] => 1
[.,[.,.]] => 1
[[.,.],.] => 1
[.,[.,[.,.]]] => 1
[.,[[.,.],.]] => 1
[[.,.],[.,.]] => 2
[[.,[.,.]],.] => 1
[[[.,.],.],.] => 1
[.,[.,[.,[.,.]]]] => 1
[.,[.,[[.,.],.]]] => 1
[.,[[.,.],[.,.]]] => 2
[.,[[.,[.,.]],.]] => 1
[.,[[[.,.],.],.]] => 1
[[.,.],[.,[.,.]]] => 2
[[.,.],[[.,.],.]] => 2
[[.,[.,.]],[.,.]] => 2
[[[.,.],.],[.,.]] => 2
[[.,[.,[.,.]]],.] => 1
[[.,[[.,.],.]],.] => 1
[[[.,.],[.,.]],.] => 2
[[[.,[.,.]],.],.] => 1
[[[[.,.],.],.],.] => 1
[.,[.,[.,[.,[.,.]]]]] => 1
[.,[.,[.,[[.,.],.]]]] => 1
[.,[.,[[.,.],[.,.]]]] => 2
[.,[.,[[.,[.,.]],.]]] => 1
[.,[.,[[[.,.],.],.]]] => 1
[.,[[.,.],[.,[.,.]]]] => 2
[.,[[.,.],[[.,.],.]]] => 2
[.,[[.,[.,.]],[.,.]]] => 2
[.,[[[.,.],.],[.,.]]] => 2
[.,[[.,[.,[.,.]]],.]] => 1
[.,[[.,[[.,.],.]],.]] => 1
[.,[[[.,.],[.,.]],.]] => 2
[.,[[[.,[.,.]],.],.]] => 1
[.,[[[[.,.],.],.],.]] => 1
[[.,.],[.,[.,[.,.]]]] => 2
[[.,.],[.,[[.,.],.]]] => 2
[[.,.],[[.,.],[.,.]]] => 3
[[.,.],[[.,[.,.]],.]] => 2
[[.,.],[[[.,.],.],.]] => 2
[[.,[.,.]],[.,[.,.]]] => 2
[[.,[.,.]],[[.,.],.]] => 2
[[[.,.],.],[.,[.,.]]] => 2
[[[.,.],.],[[.,.],.]] => 2
[[.,[.,[.,.]]],[.,.]] => 2
[[.,[[.,.],.]],[.,.]] => 2
[[[.,.],[.,.]],[.,.]] => 3
[[[.,[.,.]],.],[.,.]] => 2
[[[[.,.],.],.],[.,.]] => 2
[[.,[.,[.,[.,.]]]],.] => 1
[[.,[.,[[.,.],.]]],.] => 1
[[.,[[.,.],[.,.]]],.] => 2
[[.,[[.,[.,.]],.]],.] => 1
[[.,[[[.,.],.],.]],.] => 1
[[[.,.],[.,[.,.]]],.] => 2
[[[.,.],[[.,.],.]],.] => 2
[[[.,[.,.]],[.,.]],.] => 2
[[[[.,.],.],[.,.]],.] => 2
[[[.,[.,[.,.]]],.],.] => 1
[[[.,[[.,.],.]],.],.] => 1
[[[[.,.],[.,.]],.],.] => 2
[[[[.,[.,.]],.],.],.] => 1
[[[[[.,.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => 1
[.,[.,[.,[[[.,.],.],.]]]] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => 2
[.,[.,[[.,.],[[.,.],.]]]] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => 2
[.,[.,[[[.,.],.],[.,.]]]] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => 1
[.,[.,[[.,[[.,.],.]],.]]] => 1
[.,[.,[[[.,.],[.,.]],.]]] => 2
[.,[.,[[[.,[.,.]],.],.]]] => 1
[.,[.,[[[[.,.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => 2
[.,[[.,.],[.,[[.,.],.]]]] => 2
[.,[[.,.],[[.,.],[.,.]]]] => 3
[.,[[.,.],[[.,[.,.]],.]]] => 2
[.,[[.,.],[[[.,.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => 2
[.,[[.,[.,.]],[[.,.],.]]] => 2
[.,[[[.,.],.],[.,[.,.]]]] => 2
[.,[[[.,.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => 2
[.,[[.,[[.,.],.]],[.,.]]] => 2
[.,[[[.,.],[.,.]],[.,.]]] => 3
[.,[[[.,[.,.]],.],[.,.]]] => 2
[.,[[[[.,.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => 1
[.,[[.,[.,[[.,.],.]]],.]] => 1
[.,[[.,[[.,.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,.]],.]],.]] => 1
[.,[[.,[[[.,.],.],.]],.]] => 1
[.,[[[.,.],[.,[.,.]]],.]] => 2
[.,[[[.,.],[[.,.],.]],.]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => 2
[.,[[[[.,.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,.]]],.],.]] => 1
[.,[[[.,[[.,.],.]],.],.]] => 1
[.,[[[[.,.],[.,.]],.],.]] => 2
[.,[[[[.,[.,.]],.],.],.]] => 1
[.,[[[[[.,.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => 2
[[.,.],[.,[.,[[.,.],.]]]] => 2
[[.,.],[.,[[.,.],[.,.]]]] => 3
[[.,.],[.,[[.,[.,.]],.]]] => 2
[[.,.],[.,[[[.,.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => 3
[[.,.],[[.,.],[[.,.],.]]] => 3
[[.,.],[[.,[.,.]],[.,.]]] => 3
[[.,.],[[[.,.],.],[.,.]]] => 3
[[.,.],[[.,[.,[.,.]]],.]] => 2
[[.,.],[[.,[[.,.],.]],.]] => 2
[[.,.],[[[.,.],[.,.]],.]] => 3
[[.,.],[[[.,[.,.]],.],.]] => 2
[[.,.],[[[[.,.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => 2
[[.,[.,.]],[.,[[.,.],.]]] => 2
[[.,[.,.]],[[.,.],[.,.]]] => 3
[[.,[.,.]],[[.,[.,.]],.]] => 2
[[.,[.,.]],[[[.,.],.],.]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => 2
[[[.,.],.],[.,[[.,.],.]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => 3
[[[.,.],.],[[.,[.,.]],.]] => 2
[[[.,.],.],[[[.,.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => 2
[[.,[.,[.,.]]],[[.,.],.]] => 2
[[.,[[.,.],.]],[.,[.,.]]] => 2
[[.,[[.,.],.]],[[.,.],.]] => 2
[[[.,.],[.,.]],[.,[.,.]]] => 3
[[[.,.],[.,.]],[[.,.],.]] => 3
[[[.,[.,.]],.],[.,[.,.]]] => 2
[[[.,[.,.]],.],[[.,.],.]] => 2
[[[[.,.],.],.],[.,[.,.]]] => 2
[[[[.,.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => 2
[[.,[.,[[.,.],.]]],[.,.]] => 2
[[.,[[.,.],[.,.]]],[.,.]] => 3
[[.,[[.,[.,.]],.]],[.,.]] => 2
[[.,[[[.,.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => 3
[[[.,.],[[.,.],.]],[.,.]] => 3
[[[.,[.,.]],[.,.]],[.,.]] => 3
[[[[.,.],.],[.,.]],[.,.]] => 3
[[[.,[.,[.,.]]],.],[.,.]] => 2
[[[.,[[.,.],.]],.],[.,.]] => 2
[[[[.,.],[.,.]],.],[.,.]] => 3
[[[[.,[.,.]],.],.],[.,.]] => 2
[[[[[.,.],.],.],.],[.,.]] => 2
[[.,[.,[.,[.,[.,.]]]]],.] => 1
[[.,[.,[.,[[.,.],.]]]],.] => 1
[[.,[.,[[.,.],[.,.]]]],.] => 2
[[.,[.,[[.,[.,.]],.]]],.] => 1
[[.,[.,[[[.,.],.],.]]],.] => 1
[[.,[[.,.],[.,[.,.]]]],.] => 2
[[.,[[.,.],[[.,.],.]]],.] => 2
[[.,[[.,[.,.]],[.,.]]],.] => 2
[[.,[[[.,.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,.]]],.]],.] => 1
[[.,[[.,[[.,.],.]],.]],.] => 1
[[.,[[[.,.],[.,.]],.]],.] => 2
[[.,[[[.,[.,.]],.],.]],.] => 1
[[.,[[[[.,.],.],.],.]],.] => 1
[[[.,.],[.,[.,[.,.]]]],.] => 2
[[[.,.],[.,[[.,.],.]]],.] => 2
[[[.,.],[[.,.],[.,.]]],.] => 3
[[[.,.],[[.,[.,.]],.]],.] => 2
[[[.,.],[[[.,.],.],.]],.] => 2
[[[.,[.,.]],[.,[.,.]]],.] => 2
[[[.,[.,.]],[[.,.],.]],.] => 2
[[[[.,.],.],[.,[.,.]]],.] => 2
[[[[.,.],.],[[.,.],.]],.] => 2
[[[.,[.,[.,.]]],[.,.]],.] => 2
[[[.,[[.,.],.]],[.,.]],.] => 2
[[[[.,.],[.,.]],[.,.]],.] => 3
[[[[.,[.,.]],.],[.,.]],.] => 2
[[[[[.,.],.],.],[.,.]],.] => 2
[[[.,[.,[.,[.,.]]]],.],.] => 1
[[[.,[.,[[.,.],.]]],.],.] => 1
[[[.,[[.,.],[.,.]]],.],.] => 2
[[[.,[[.,[.,.]],.]],.],.] => 1
[[[.,[[[.,.],.],.]],.],.] => 1
[[[[.,.],[.,[.,.]]],.],.] => 2
[[[[.,.],[[.,.],.]],.],.] => 2
[[[[.,[.,.]],[.,.]],.],.] => 2
[[[[[.,.],.],[.,.]],.],.] => 2
[[[[.,[.,[.,.]]],.],.],.] => 1
[[[[.,[[.,.],.]],.],.],.] => 1
[[[[[.,.],[.,.]],.],.],.] => 2
[[[[[.,[.,.]],.],.],.],.] => 1
[[[[[[.,.],.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 2
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 1
[.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[.,[.,[[[.,.],.],[[.,.],.]]]] => 2
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 3
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[.,[.,[[.,[[[.,.],.],.]],.]]] => 1
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 2
[.,[.,[[[.,.],[[.,.],.]],.]]] => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 2
[.,[.,[[[[.,.],.],[.,.]],.]]] => 2
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => 1
[.,[.,[[[[.,.],[.,.]],.],.]]] => 2
[.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[.,[[.,.],[[[.,.],.],[.,.]]]] => 3
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
[.,[[.,.],[[.,[[.,.],.]],.]]] => 2
[.,[[.,.],[[[.,.],[.,.]],.]]] => 3
[.,[[.,.],[[[.,[.,.]],.],.]]] => 2
[.,[[.,.],[[[[.,.],.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[.,[[.,[.,.]],[[[.,.],.],.]]] => 2
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => 3
[.,[[[.,.],.],[[.,[.,.]],.]]] => 2
[.,[[[.,.],.],[[[.,.],.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => 2
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 3
[.,[[[.,.],[.,.]],[[.,.],.]]] => 3
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => 2
[.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 3
[.,[[[.,.],[[.,.],.]],[.,.]]] => 3
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 3
[.,[[[[.,.],.],[.,.]],[.,.]]] => 3
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 2
[.,[[[.,[[.,.],.]],.],[.,.]]] => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => 3
[.,[[[[.,[.,.]],.],.],[.,.]]] => 2
[.,[[[[[.,.],.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[.,[[.,[.,[[[.,.],.],.]]],.]] => 1
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[.,[[.,[[.,.],[[.,.],.]]],.]] => 2
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[.,[[.,[[[.,.],.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[.,[[.,[[[.,.],[.,.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],.],.]],.]] => 1
[.,[[.,[[[[.,.],.],.],.]],.]] => 1
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 2
[.,[[[.,.],[.,[[.,.],.]]],.]] => 2
[.,[[[.,.],[[.,.],[.,.]]],.]] => 3
[.,[[[.,.],[[.,[.,.]],.]],.]] => 2
[.,[[[.,.],[[[.,.],.],.]],.]] => 2
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 2
[.,[[[.,[.,.]],[[.,.],.]],.]] => 2
[.,[[[[.,.],.],[.,[.,.]]],.]] => 2
[.,[[[[.,.],.],[[.,.],.]],.]] => 2
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 2
[.,[[[.,[[.,.],.]],[.,.]],.]] => 2
[.,[[[[.,.],[.,.]],[.,.]],.]] => 3
[.,[[[[.,[.,.]],.],[.,.]],.]] => 2
[.,[[[[[.,.],.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => 1
[.,[[[.,[[.,.],[.,.]]],.],.]] => 2
[.,[[[.,[[.,[.,.]],.]],.],.]] => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => 1
[.,[[[[.,.],[.,[.,.]]],.],.]] => 2
[.,[[[[.,.],[[.,.],.]],.],.]] => 2
[.,[[[[.,[.,.]],[.,.]],.],.]] => 2
[.,[[[[[.,.],.],[.,.]],.],.]] => 2
[.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => 2
[.,[[[[[.,[.,.]],.],.],.],.]] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 3
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 3
[[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 3
[[.,.],[.,[[[.,.],.],[.,.]]]] => 3
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => 2
[[.,.],[.,[[[.,.],[.,.]],.]]] => 3
[[.,.],[.,[[[.,[.,.]],.],.]]] => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 3
[[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[[.,.],[[.,.],[[.,.],[.,.]]]] => 4
[[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[[.,.],[[.,.],[[[.,.],.],.]]] => 3
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 3
[[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[[.,.],[[[.,.],.],[.,[.,.]]]] => 3
[[.,.],[[[.,.],.],[[.,.],.]]] => 3
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[[.,.],[[.,[[.,.],.]],[.,.]]] => 3
[[.,.],[[[.,.],[.,.]],[.,.]]] => 4
[[.,.],[[[.,[.,.]],.],[.,.]]] => 3
[[.,.],[[[[.,.],.],.],[.,.]]] => 3
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => 2
[[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[[.,.],[[.,[[.,[.,.]],.]],.]] => 2
[[.,.],[[.,[[[.,.],.],.]],.]] => 2
[[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[[.,.],[[[.,.],[[.,.],.]],.]] => 3
[[.,.],[[[.,[.,.]],[.,.]],.]] => 3
[[.,.],[[[[.,.],.],[.,.]],.]] => 3
[[.,.],[[[.,[.,[.,.]]],.],.]] => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => 2
[[.,.],[[[[.,.],[.,.]],.],.]] => 3
[[.,.],[[[[.,[.,.]],.],.],.]] => 2
[[.,.],[[[[[.,.],.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[[.,[.,.]],[.,[[[.,.],.],.]]] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[[.,[.,.]],[[[.,.],.],[.,.]]] => 3
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[[.,[.,.]],[[.,[[.,.],.]],.]] => 2
[[.,[.,.]],[[[.,.],[.,.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],.],.]] => 2
[[.,[.,.]],[[[[.,.],.],.],.]] => 2
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => 3
[[[.,.],.],[.,[[.,[.,.]],.]]] => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => 3
[[[.,.],.],[[.,.],[[.,.],.]]] => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => 3
[[[.,.],.],[[[.,.],.],[.,.]]] => 3
[[[.,.],.],[[.,[.,[.,.]]],.]] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => 2
[[[.,.],.],[[[.,.],[.,.]],.]] => 3
[[[.,.],.],[[[.,[.,.]],.],.]] => 2
[[[.,.],.],[[[[.,.],.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[[.,[.,[.,.]]],[[[.,.],.],.]] => 2
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => 2
[[.,[[.,.],.]],[[.,.],[.,.]]] => 3
[[.,[[.,.],.]],[[.,[.,.]],.]] => 2
[[.,[[.,.],.]],[[[.,.],.],.]] => 2
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 3
[[[.,.],[.,.]],[.,[[.,.],.]]] => 3
[[[.,.],[.,.]],[[.,.],[.,.]]] => 4
[[[.,.],[.,.]],[[.,[.,.]],.]] => 3
[[[.,.],[.,.]],[[[.,.],.],.]] => 3
[[[.,[.,.]],.],[.,[.,[.,.]]]] => 2
[[[.,[.,.]],.],[.,[[.,.],.]]] => 2
[[[.,[.,.]],.],[[.,.],[.,.]]] => 3
[[[.,[.,.]],.],[[.,[.,.]],.]] => 2
[[[.,[.,.]],.],[[[.,.],.],.]] => 2
[[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[[[[.,.],.],.],[.,[[.,.],.]]] => 2
[[[[.,.],.],.],[[.,.],[.,.]]] => 3
[[[[.,.],.],.],[[.,[.,.]],.]] => 2
[[[[.,.],.],.],[[[.,.],.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[[.,[.,[[.,.],.]]],[[.,.],.]] => 2
[[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[[.,[[.,.],[.,.]]],[[.,.],.]] => 3
[[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[[.,[[.,[.,.]],.]],[[.,.],.]] => 2
[[.,[[[.,.],.],.]],[.,[.,.]]] => 2
[[.,[[[.,.],.],.]],[[.,.],.]] => 2
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 3
[[[.,.],[.,[.,.]]],[[.,.],.]] => 3
[[[.,.],[[.,.],.]],[.,[.,.]]] => 3
[[[.,.],[[.,.],.]],[[.,.],.]] => 3
[[[.,[.,.]],[.,.]],[.,[.,.]]] => 3
[[[.,[.,.]],[.,.]],[[.,.],.]] => 3
[[[[.,.],.],[.,.]],[.,[.,.]]] => 3
[[[[.,.],.],[.,.]],[[.,.],.]] => 3
[[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[[[.,[.,[.,.]]],.],[[.,.],.]] => 2
[[[.,[[.,.],.]],.],[.,[.,.]]] => 2
[[[.,[[.,.],.]],.],[[.,.],.]] => 2
[[[[.,.],[.,.]],.],[.,[.,.]]] => 3
[[[[.,.],[.,.]],.],[[.,.],.]] => 3
[[[[.,[.,.]],.],.],[.,[.,.]]] => 2
[[[[.,[.,.]],.],.],[[.,.],.]] => 2
[[[[[.,.],.],.],.],[.,[.,.]]] => 2
[[[[[.,.],.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[[.,[.,[[[.,.],.],.]]],[.,.]] => 2
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[[.,[[.,.],[[.,.],.]]],[.,.]] => 3
[[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[[.,[[[.,.],.],[.,.]]],[.,.]] => 3
[[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[[.,[[[.,.],[.,.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],.],.]],[.,.]] => 2
[[.,[[[[.,.],.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[[[.,.],[.,[[.,.],.]]],[.,.]] => 3
[[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[[[.,.],[[.,[.,.]],.]],[.,.]] => 3
[[[.,.],[[[.,.],.],.]],[.,.]] => 3
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[[[.,[.,.]],[[.,.],.]],[.,.]] => 3
[[[[.,.],.],[.,[.,.]]],[.,.]] => 3
[[[[.,.],.],[[.,.],.]],[.,.]] => 3
[[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[[[.,[[.,.],.]],[.,.]],[.,.]] => 3
[[[[.,.],[.,.]],[.,.]],[.,.]] => 4
[[[[.,[.,.]],.],[.,.]],[.,.]] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => 3
[[[.,[.,[.,[.,.]]]],.],[.,.]] => 2
[[[.,[.,[[.,.],.]]],.],[.,.]] => 2
[[[.,[[.,.],[.,.]]],.],[.,.]] => 3
[[[.,[[.,[.,.]],.]],.],[.,.]] => 2
[[[.,[[[.,.],.],.]],.],[.,.]] => 2
[[[[.,.],[.,[.,.]]],.],[.,.]] => 3
[[[[.,.],[[.,.],.]],.],[.,.]] => 3
[[[[.,[.,.]],[.,.]],.],[.,.]] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => 3
[[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[[[[.,[[.,.],.]],.],.],[.,.]] => 2
[[[[[.,.],[.,.]],.],.],[.,.]] => 3
[[[[[.,[.,.]],.],.],.],[.,.]] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[[.,[.,[.,[[[.,.],.],.]]]],.] => 1
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[[.,[.,[[.,.],[[.,.],.]]]],.] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => 2
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 1
[[.,[.,[[.,[[.,.],.]],.]]],.] => 1
[[.,[.,[[[.,.],[.,.]],.]]],.] => 2
[[.,[.,[[[.,[.,.]],.],.]]],.] => 1
[[.,[.,[[[[.,.],.],.],.]]],.] => 1
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[[.,[[.,.],[.,[[.,.],.]]]],.] => 2
[[.,[[.,.],[[.,.],[.,.]]]],.] => 3
[[.,[[.,.],[[.,[.,.]],.]]],.] => 2
[[.,[[.,.],[[[.,.],.],.]]],.] => 2
[[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[[.,[[.,[.,.]],[[.,.],.]]],.] => 2
[[.,[[[.,.],.],[.,[.,.]]]],.] => 2
[[.,[[[.,.],.],[[.,.],.]]],.] => 2
[[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => 3
[[.,[[[.,[.,.]],.],[.,.]]],.] => 2
[[.,[[[[.,.],.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 1
[[.,[[.,[.,[[.,.],.]]],.]],.] => 1
[[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[[.,[[.,[[.,[.,.]],.]],.]],.] => 1
[[.,[[.,[[[.,.],.],.]],.]],.] => 1
[[.,[[[.,.],[.,[.,.]]],.]],.] => 2
[[.,[[[.,.],[[.,.],.]],.]],.] => 2
[[.,[[[.,[.,.]],[.,.]],.]],.] => 2
[[.,[[[[.,.],.],[.,.]],.]],.] => 2
[[.,[[[.,[.,[.,.]]],.],.]],.] => 1
[[.,[[[.,[[.,.],.]],.],.]],.] => 1
[[.,[[[[.,.],[.,.]],.],.]],.] => 2
[[.,[[[[.,[.,.]],.],.],.]],.] => 1
[[.,[[[[[.,.],.],.],.],.]],.] => 1
[[[.,.],[.,[.,[.,[.,.]]]]],.] => 2
[[[.,.],[.,[.,[[.,.],.]]]],.] => 2
[[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[[[.,.],[.,[[.,[.,.]],.]]],.] => 2
[[[.,.],[.,[[[.,.],.],.]]],.] => 2
[[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[[[.,.],[[.,.],[[.,.],.]]],.] => 3
[[[.,.],[[.,[.,.]],[.,.]]],.] => 3
[[[.,.],[[[.,.],.],[.,.]]],.] => 3
[[[.,.],[[.,[.,[.,.]]],.]],.] => 2
[[[.,.],[[.,[[.,.],.]],.]],.] => 2
[[[.,.],[[[.,.],[.,.]],.]],.] => 3
[[[.,.],[[[.,[.,.]],.],.]],.] => 2
[[[.,.],[[[[.,.],.],.],.]],.] => 2
[[[.,[.,.]],[.,[.,[.,.]]]],.] => 2
[[[.,[.,.]],[.,[[.,.],.]]],.] => 2
[[[.,[.,.]],[[.,.],[.,.]]],.] => 3
[[[.,[.,.]],[[.,[.,.]],.]],.] => 2
[[[.,[.,.]],[[[.,.],.],.]],.] => 2
[[[[.,.],.],[.,[.,[.,.]]]],.] => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => 2
[[[[.,.],.],[[.,.],[.,.]]],.] => 3
[[[[.,.],.],[[.,[.,.]],.]],.] => 2
[[[[.,.],.],[[[.,.],.],.]],.] => 2
[[[.,[.,[.,.]]],[.,[.,.]]],.] => 2
[[[.,[.,[.,.]]],[[.,.],.]],.] => 2
[[[.,[[.,.],.]],[.,[.,.]]],.] => 2
[[[.,[[.,.],.]],[[.,.],.]],.] => 2
[[[[.,.],[.,.]],[.,[.,.]]],.] => 3
[[[[.,.],[.,.]],[[.,.],.]],.] => 3
[[[[.,[.,.]],.],[.,[.,.]]],.] => 2
[[[[.,[.,.]],.],[[.,.],.]],.] => 2
[[[[[.,.],.],.],[.,[.,.]]],.] => 2
[[[[[.,.],.],.],[[.,.],.]],.] => 2
[[[.,[.,[.,[.,.]]]],[.,.]],.] => 2
[[[.,[.,[[.,.],.]]],[.,.]],.] => 2
[[[.,[[.,.],[.,.]]],[.,.]],.] => 3
[[[.,[[.,[.,.]],.]],[.,.]],.] => 2
[[[.,[[[.,.],.],.]],[.,.]],.] => 2
[[[[.,.],[.,[.,.]]],[.,.]],.] => 3
[[[[.,.],[[.,.],.]],[.,.]],.] => 3
[[[[.,[.,.]],[.,.]],[.,.]],.] => 3
[[[[[.,.],.],[.,.]],[.,.]],.] => 3
[[[[.,[.,[.,.]]],.],[.,.]],.] => 2
[[[[.,[[.,.],.]],.],[.,.]],.] => 2
[[[[[.,.],[.,.]],.],[.,.]],.] => 3
[[[[[.,[.,.]],.],.],[.,.]],.] => 2
[[[[[[.,.],.],.],.],[.,.]],.] => 2
[[[.,[.,[.,[.,[.,.]]]]],.],.] => 1
[[[.,[.,[.,[[.,.],.]]]],.],.] => 1
[[[.,[.,[[.,.],[.,.]]]],.],.] => 2
[[[.,[.,[[.,[.,.]],.]]],.],.] => 1
[[[.,[.,[[[.,.],.],.]]],.],.] => 1
[[[.,[[.,.],[.,[.,.]]]],.],.] => 2
[[[.,[[.,.],[[.,.],.]]],.],.] => 2
[[[.,[[.,[.,.]],[.,.]]],.],.] => 2
[[[.,[[[.,.],.],[.,.]]],.],.] => 2
[[[.,[[.,[.,[.,.]]],.]],.],.] => 1
[[[.,[[.,[[.,.],.]],.]],.],.] => 1
[[[.,[[[.,.],[.,.]],.]],.],.] => 2
[[[.,[[[.,[.,.]],.],.]],.],.] => 1
[[[.,[[[[.,.],.],.],.]],.],.] => 1
[[[[.,.],[.,[.,[.,.]]]],.],.] => 2
[[[[.,.],[.,[[.,.],.]]],.],.] => 2
[[[[.,.],[[.,.],[.,.]]],.],.] => 3
[[[[.,.],[[.,[.,.]],.]],.],.] => 2
[[[[.,.],[[[.,.],.],.]],.],.] => 2
[[[[.,[.,.]],[.,[.,.]]],.],.] => 2
[[[[.,[.,.]],[[.,.],.]],.],.] => 2
[[[[[.,.],.],[.,[.,.]]],.],.] => 2
[[[[[.,.],.],[[.,.],.]],.],.] => 2
[[[[.,[.,[.,.]]],[.,.]],.],.] => 2
[[[[.,[[.,.],.]],[.,.]],.],.] => 2
[[[[[.,.],[.,.]],[.,.]],.],.] => 3
[[[[[.,[.,.]],.],[.,.]],.],.] => 2
[[[[[[.,.],.],.],[.,.]],.],.] => 2
[[[[.,[.,[.,[.,.]]]],.],.],.] => 1
[[[[.,[.,[[.,.],.]]],.],.],.] => 1
[[[[.,[[.,.],[.,.]]],.],.],.] => 2
[[[[.,[[.,[.,.]],.]],.],.],.] => 1
[[[[.,[[[.,.],.],.]],.],.],.] => 1
[[[[[.,.],[.,[.,.]]],.],.],.] => 2
[[[[[.,.],[[.,.],.]],.],.],.] => 2
[[[[[.,[.,.]],[.,.]],.],.],.] => 2
[[[[[[.,.],.],[.,.]],.],.],.] => 2
[[[[[.,[.,[.,.]]],.],.],.],.] => 1
[[[[[.,[[.,.],.]],.],.],.],.] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => 2
[[[[[[.,[.,.]],.],.],.],.],.] => 1
[[[[[[[.,.],.],.],.],.],.],.] => 1
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 3
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 3
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 3
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 3
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 3
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 3
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 4
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 3
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 3
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 2
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 2
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 3
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => 1
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => 2
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 1
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => 1
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => 2
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => 1
[.,[[[[[[[.,.],.],.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 3
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 3
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 4
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 4
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 3
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => 3
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 3
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 4
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 3
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 3
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 3
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 4
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 4
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 3
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 2
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 4
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 3
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 3
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 3
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 4
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 3
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 3
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => 3
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 4
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 3
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 3
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 3
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 2
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 3
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 2
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 3
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 2
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 3
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 3
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 3
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => 3
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 3
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 3
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => 2
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 3
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => 2
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 4
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 4
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => 3
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 3
[[[[.,.],.],.],[[[[.,.],.],.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 2
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 4
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 3
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 3
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 2
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => 2
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 3
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 3
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 3
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 3
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 3
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 3
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 4
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => 3
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 3
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 4
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => 3
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 2
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => 3
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => 2
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => 2
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 3
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 3
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => 3
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 4
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 4
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 3
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 3
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 3
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 3
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => 3
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 3
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 3
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 2
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => 2
[[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 3
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 4
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 3
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 4
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 3
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => 3
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 4
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 4
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 3
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 3
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 4
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 4
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 4
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => 3
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 3
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => 3
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => 2
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => 3
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 2
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => 2
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => 3
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => 2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 1
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 1
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 1
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 1
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 3
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 2
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 3
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 2
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 3
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 1
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => 3
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 3
[[[[.,.],.],[[[[.,.],.],.],.]],.] => 2
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 3
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => 3
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 3
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => 3
[[[[[[.,.],.],.],.],[[.,.],.]],.] => 2
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => 3
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => 3
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => 3
[[[[[[.,.],.],.],[[.,.],.]],.],.] => 2
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => 3
[[[[[[[[.,.],.],.],.],.],.],.],.] => 1
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 1
[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]] => 4
[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]] => 4
[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 4
[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]] => 4
[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]] => 4
[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]] => 4
[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]] => 4
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 1
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 2
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 2
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 3
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 2
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 2
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 2
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 1
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 1
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 3
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 1
[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 5
[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 5
[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,.]]]] => 4
[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]] => 4
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 1
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 5
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 4
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 4
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 3
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 4
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 3
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 3
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 4
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 2
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => 4
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]] => 3
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => 3
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => 2
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => 2
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => 4
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => 2
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => 4
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.] => 3
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.] => 3
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.] => 3
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.] => 3
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.] => 3
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.] => 3
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 1
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 3
[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 4
[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 3
[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 4
[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 4
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 5
[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 4
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 3
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 4
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 5
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 4
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 5
[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]] => 4
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 5
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]] => 4
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => 5
[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.] => 3
[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.] => 4
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]] => 4
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]] => 5
[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.] => 3
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.] => 4
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => 5
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]] => 4
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => 5
[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.] => 2
[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.] => 3
[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 4
[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.] => 3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 4
[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 4
[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 5
[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]] => 4
[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 5
[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]] => 3
[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]] => 4
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 5
[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]] => 4
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 2
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => 2
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 2
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 1
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 2
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 1
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 2
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 3
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 2
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 3
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 2
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 3
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 2
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 3
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 3
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 3
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 4
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 2
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 3
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 4
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 2
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 3
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 3
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 4
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 2
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 3
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 3
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 3
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 2
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 4
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 3
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 4
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 3
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 4
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 3
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 4
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 4
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 4
[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]] => 5
[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]] => 5
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 2
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 1
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 2
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 6
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]] => 5
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => 5
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]] => 5
[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]] => 4
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]] => 4
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]] => 5
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]] => 4
[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]] => 5
[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]] => 3
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => 5
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]] => 4
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => 4
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]] => 4
[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]] => 3
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => 5
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]] => 4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] => 4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]] => 3
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => 5
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] => 3
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => 5
[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => 4
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => 4
[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => 4
[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => 4
[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => 4
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => 4
[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => 2
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 5
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 4
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 4
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 4
[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 3
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 3
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 3
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 4
[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 2
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] => 4
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] => 2
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] => 5
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => 4
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] => 3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] => 2
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => 5
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => 4
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => 4
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => 4
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] => 4
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] => 4
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] => 4
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] => 2
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] => 5
[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.] => 4
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.] => 4
[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.] => 4
[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.] => 3
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.] => 4
[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.] => 3
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.] => 4
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.] => 3
[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.] => 4
[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.] => 3
[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.] => 3
[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.] => 3
[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.] => 4
[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.] => 3
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.] => 3
[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.] => 3
[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.] => 4
[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.] => 3
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.] => 3
[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.] => 4
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.] => 3
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.] => 3
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.] => 3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.] => 4
[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.] => 3
[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.] => 3
[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.] => 3
[[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]],.] => 3
[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.] => 3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.] => 3
[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 1
[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]] => 3
[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]] => 4
[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]] => 3
[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]] => 4
[.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]] => 4
[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]] => 5
[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]] => 4
[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]] => 5
[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]] => 3
[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]] => 4
[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]] => 5
[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]] => 4
[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]] => 5
[.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 4
[.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 5
[.,[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 5
[.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 5
[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 6
[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => 4
[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]] => 5
[.,[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 5
[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 6
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => 4
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]] => 5
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]] => 6
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]] => 5
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]] => 6
[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]] => 3
[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]] => 4
[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]] => 5
[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => 4
[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]] => 5
[.,[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]] => 5
[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]] => 6
[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]] => 5
[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]] => 6
[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]] => 4
[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]] => 5
[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]] => 6
[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]] => 5
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => 6
[[.,[.,.]],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 4
[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 5
[[.,[.,.]],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 4
[[.,[.,.]],[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 5
[[.,[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 5
[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 6
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 5
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 6
[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 4
[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 5
[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 6
[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 5
[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 6
[[.,[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.] => 3
[[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]],.] => 4
[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 6
[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.] => 4
[[.,[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.] => 5
[[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]] => 5
[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 6
[[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]] => 5
[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => 6
[[.,[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]],.] => 3
[[.,[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.] => 4
[[.,[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]],.] => 4
[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.] => 5
[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]] => 5
[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]] => 6
[[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.],[.,.]] => 4
[[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]] => 5
[[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]] => 5
[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] => 6
[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.] => 3
[[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.] => 4
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.] => 5
[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.] => 4
[[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.] => 5
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]] => 5
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] => 6
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]] => 5
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => 6
[[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]] => 4
[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]] => 5
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => 6
[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]] => 5
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => 6
[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.] => 2
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.] => 3
[[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.] => 4
[[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.] => 3
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.] => 4
[[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.] => 4
[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.] => 5
[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.] => 4
[[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.] => 5
[[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.] => 3
[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.] => 4
[[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.] => 5
[[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.] => 4
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => 5
[[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 4
[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 5
[[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 5
[[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 5
[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 6
[[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]] => 4
[[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]] => 5
[[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 5
[[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 6
[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]] => 4
[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]] => 5
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]] => 6
[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]] => 5
[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 6
[[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]] => 3
[[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]] => 4
[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]] => 5
[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]] => 4
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]] => 5
[[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]] => 5
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]] => 6
[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]] => 5
[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 6
[[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]] => 4
[[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]] => 5
[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]] => 6
[[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]] => 5
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 1
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => 2
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => 3
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => 3
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => 2
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => 3
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => 2
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => 3
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => 3
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => 3
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => 4
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 3
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 3
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 3
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 4
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => 2
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => 3
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 3
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 4
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => 2
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => 3
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 3
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => 3
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 4
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => 2
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => 3
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => 3
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => 3
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => 4
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 3
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 4
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => 3
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 4
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => 3
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => 4
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 4
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => 4
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => 5
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 3
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 4
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 4
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 3
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 4
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 3
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 4
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 4
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 4
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 5
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 2
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 3
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 3
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 3
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 4
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 3
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 4
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 4
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 4
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 5
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => 2
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 4
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 3
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 4
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 3
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 4
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 4
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 5
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => 2
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 4
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 4
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 3
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 4
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => 3
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 4
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 4
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 5
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => 2
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => 3
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => 3
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => 4
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 4
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 3
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 4
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 3
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => 4
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 4
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => 4
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => 5
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 4
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 5
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 3
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 4
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 4
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 5
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => 3
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 4
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 4
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 4
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 5
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => 3
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => 4
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 4
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => 4
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => 5
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 4
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 5
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 4
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 5
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 4
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 5
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 5
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
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Created: May 16, 2014 at 09:02 by Joseph Ching
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Last Updated: Mar 31, 2019 at 22:07 by Martin Rubey