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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: St000203
-----------------------------------------------------------------------------
Collection: Binary trees
-----------------------------------------------------------------------------
Description: The number of external nodes of a binary tree.
That is, the number of nodes that can be reached from the root by only left steps or only right steps, plus $1$ for the root node itself. A counting formula for the number of external node in all binary trees of size $n$ can be found in [1].
-----------------------------------------------------------------------------
References: [1] Expansion of (1+x*C)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108. [[OEIS:A070031]]
-----------------------------------------------------------------------------
Code:
# BinaryTree -> Bool
def is_leaf(b):
return b == BinaryTree('.')
# BinaryTree -> Int
def get_external_node(b, flag):
count = 0;
if is_leaf(b):
return 0
else:
if (flag): # True counts the left side
if not is_leaf(b[0]):
return 1 + get_external_node(b[0], True)
else: # False counts the right side
if not is_leaf(b[1]):
return 1 + get_external_node(b[1], False)
return count
# BinaryTree -> Int
def statistic(b):
"""
sage: [sum(statistic(b) for b in BinaryTrees(n)) for n in range(1,8)]
[1, 4, 13, 42, 138, 462, 1573]
"""
return 1 + get_external_node(b, True) + get_external_node(b, False)
-----------------------------------------------------------------------------
Statistic values:
[.,.] => 1
[.,[.,.]] => 2
[[.,.],.] => 2
[.,[.,[.,.]]] => 3
[.,[[.,.],.]] => 2
[[.,.],[.,.]] => 3
[[.,[.,.]],.] => 2
[[[.,.],.],.] => 3
[.,[.,[.,[.,.]]]] => 4
[.,[.,[[.,.],.]]] => 3
[.,[[.,.],[.,.]]] => 3
[.,[[.,[.,.]],.]] => 2
[.,[[[.,.],.],.]] => 2
[[.,.],[.,[.,.]]] => 4
[[.,.],[[.,.],.]] => 3
[[.,[.,.]],[.,.]] => 3
[[[.,.],.],[.,.]] => 4
[[.,[.,[.,.]]],.] => 2
[[.,[[.,.],.]],.] => 2
[[[.,.],[.,.]],.] => 3
[[[.,[.,.]],.],.] => 3
[[[[.,.],.],.],.] => 4
[.,[.,[.,[.,[.,.]]]]] => 5
[.,[.,[.,[[.,.],.]]]] => 4
[.,[.,[[.,.],[.,.]]]] => 4
[.,[.,[[.,[.,.]],.]]] => 3
[.,[.,[[[.,.],.],.]]] => 3
[.,[[.,.],[.,[.,.]]]] => 4
[.,[[.,.],[[.,.],.]]] => 3
[.,[[.,[.,.]],[.,.]]] => 3
[.,[[[.,.],.],[.,.]]] => 3
[.,[[.,[.,[.,.]]],.]] => 2
[.,[[.,[[.,.],.]],.]] => 2
[.,[[[.,.],[.,.]],.]] => 2
[.,[[[.,[.,.]],.],.]] => 2
[.,[[[[.,.],.],.],.]] => 2
[[.,.],[.,[.,[.,.]]]] => 5
[[.,.],[.,[[.,.],.]]] => 4
[[.,.],[[.,.],[.,.]]] => 4
[[.,.],[[.,[.,.]],.]] => 3
[[.,.],[[[.,.],.],.]] => 3
[[.,[.,.]],[.,[.,.]]] => 4
[[.,[.,.]],[[.,.],.]] => 3
[[[.,.],.],[.,[.,.]]] => 5
[[[.,.],.],[[.,.],.]] => 4
[[.,[.,[.,.]]],[.,.]] => 3
[[.,[[.,.],.]],[.,.]] => 3
[[[.,.],[.,.]],[.,.]] => 4
[[[.,[.,.]],.],[.,.]] => 4
[[[[.,.],.],.],[.,.]] => 5
[[.,[.,[.,[.,.]]]],.] => 2
[[.,[.,[[.,.],.]]],.] => 2
[[.,[[.,.],[.,.]]],.] => 2
[[.,[[.,[.,.]],.]],.] => 2
[[.,[[[.,.],.],.]],.] => 2
[[[.,.],[.,[.,.]]],.] => 3
[[[.,.],[[.,.],.]],.] => 3
[[[.,[.,.]],[.,.]],.] => 3
[[[[.,.],.],[.,.]],.] => 4
[[[.,[.,[.,.]]],.],.] => 3
[[[.,[[.,.],.]],.],.] => 3
[[[[.,.],[.,.]],.],.] => 4
[[[[.,[.,.]],.],.],.] => 4
[[[[[.,.],.],.],.],.] => 5
[.,[.,[.,[.,[.,[.,.]]]]]] => 6
[.,[.,[.,[.,[[.,.],.]]]]] => 5
[.,[.,[.,[[.,.],[.,.]]]]] => 5
[.,[.,[.,[[.,[.,.]],.]]]] => 4
[.,[.,[.,[[[.,.],.],.]]]] => 4
[.,[.,[[.,.],[.,[.,.]]]]] => 5
[.,[.,[[.,.],[[.,.],.]]]] => 4
[.,[.,[[.,[.,.]],[.,.]]]] => 4
[.,[.,[[[.,.],.],[.,.]]]] => 4
[.,[.,[[.,[.,[.,.]]],.]]] => 3
[.,[.,[[.,[[.,.],.]],.]]] => 3
[.,[.,[[[.,.],[.,.]],.]]] => 3
[.,[.,[[[.,[.,.]],.],.]]] => 3
[.,[.,[[[[.,.],.],.],.]]] => 3
[.,[[.,.],[.,[.,[.,.]]]]] => 5
[.,[[.,.],[.,[[.,.],.]]]] => 4
[.,[[.,.],[[.,.],[.,.]]]] => 4
[.,[[.,.],[[.,[.,.]],.]]] => 3
[.,[[.,.],[[[.,.],.],.]]] => 3
[.,[[.,[.,.]],[.,[.,.]]]] => 4
[.,[[.,[.,.]],[[.,.],.]]] => 3
[.,[[[.,.],.],[.,[.,.]]]] => 4
[.,[[[.,.],.],[[.,.],.]]] => 3
[.,[[.,[.,[.,.]]],[.,.]]] => 3
[.,[[.,[[.,.],.]],[.,.]]] => 3
[.,[[[.,.],[.,.]],[.,.]]] => 3
[.,[[[.,[.,.]],.],[.,.]]] => 3
[.,[[[[.,.],.],.],[.,.]]] => 3
[.,[[.,[.,[.,[.,.]]]],.]] => 2
[.,[[.,[.,[[.,.],.]]],.]] => 2
[.,[[.,[[.,.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,.]],.]],.]] => 2
[.,[[.,[[[.,.],.],.]],.]] => 2
[.,[[[.,.],[.,[.,.]]],.]] => 2
[.,[[[.,.],[[.,.],.]],.]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => 2
[.,[[[[.,.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,.]]],.],.]] => 2
[.,[[[.,[[.,.],.]],.],.]] => 2
[.,[[[[.,.],[.,.]],.],.]] => 2
[.,[[[[.,[.,.]],.],.],.]] => 2
[.,[[[[[.,.],.],.],.],.]] => 2
[[.,.],[.,[.,[.,[.,.]]]]] => 6
[[.,.],[.,[.,[[.,.],.]]]] => 5
[[.,.],[.,[[.,.],[.,.]]]] => 5
[[.,.],[.,[[.,[.,.]],.]]] => 4
[[.,.],[.,[[[.,.],.],.]]] => 4
[[.,.],[[.,.],[.,[.,.]]]] => 5
[[.,.],[[.,.],[[.,.],.]]] => 4
[[.,.],[[.,[.,.]],[.,.]]] => 4
[[.,.],[[[.,.],.],[.,.]]] => 4
[[.,.],[[.,[.,[.,.]]],.]] => 3
[[.,.],[[.,[[.,.],.]],.]] => 3
[[.,.],[[[.,.],[.,.]],.]] => 3
[[.,.],[[[.,[.,.]],.],.]] => 3
[[.,.],[[[[.,.],.],.],.]] => 3
[[.,[.,.]],[.,[.,[.,.]]]] => 5
[[.,[.,.]],[.,[[.,.],.]]] => 4
[[.,[.,.]],[[.,.],[.,.]]] => 4
[[.,[.,.]],[[.,[.,.]],.]] => 3
[[.,[.,.]],[[[.,.],.],.]] => 3
[[[.,.],.],[.,[.,[.,.]]]] => 6
[[[.,.],.],[.,[[.,.],.]]] => 5
[[[.,.],.],[[.,.],[.,.]]] => 5
[[[.,.],.],[[.,[.,.]],.]] => 4
[[[.,.],.],[[[.,.],.],.]] => 4
[[.,[.,[.,.]]],[.,[.,.]]] => 4
[[.,[.,[.,.]]],[[.,.],.]] => 3
[[.,[[.,.],.]],[.,[.,.]]] => 4
[[.,[[.,.],.]],[[.,.],.]] => 3
[[[.,.],[.,.]],[.,[.,.]]] => 5
[[[.,.],[.,.]],[[.,.],.]] => 4
[[[.,[.,.]],.],[.,[.,.]]] => 5
[[[.,[.,.]],.],[[.,.],.]] => 4
[[[[.,.],.],.],[.,[.,.]]] => 6
[[[[.,.],.],.],[[.,.],.]] => 5
[[.,[.,[.,[.,.]]]],[.,.]] => 3
[[.,[.,[[.,.],.]]],[.,.]] => 3
[[.,[[.,.],[.,.]]],[.,.]] => 3
[[.,[[.,[.,.]],.]],[.,.]] => 3
[[.,[[[.,.],.],.]],[.,.]] => 3
[[[.,.],[.,[.,.]]],[.,.]] => 4
[[[.,.],[[.,.],.]],[.,.]] => 4
[[[.,[.,.]],[.,.]],[.,.]] => 4
[[[[.,.],.],[.,.]],[.,.]] => 5
[[[.,[.,[.,.]]],.],[.,.]] => 4
[[[.,[[.,.],.]],.],[.,.]] => 4
[[[[.,.],[.,.]],.],[.,.]] => 5
[[[[.,[.,.]],.],.],[.,.]] => 5
[[[[[.,.],.],.],.],[.,.]] => 6
[[.,[.,[.,[.,[.,.]]]]],.] => 2
[[.,[.,[.,[[.,.],.]]]],.] => 2
[[.,[.,[[.,.],[.,.]]]],.] => 2
[[.,[.,[[.,[.,.]],.]]],.] => 2
[[.,[.,[[[.,.],.],.]]],.] => 2
[[.,[[.,.],[.,[.,.]]]],.] => 2
[[.,[[.,.],[[.,.],.]]],.] => 2
[[.,[[.,[.,.]],[.,.]]],.] => 2
[[.,[[[.,.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,.]]],.]],.] => 2
[[.,[[.,[[.,.],.]],.]],.] => 2
[[.,[[[.,.],[.,.]],.]],.] => 2
[[.,[[[.,[.,.]],.],.]],.] => 2
[[.,[[[[.,.],.],.],.]],.] => 2
[[[.,.],[.,[.,[.,.]]]],.] => 3
[[[.,.],[.,[[.,.],.]]],.] => 3
[[[.,.],[[.,.],[.,.]]],.] => 3
[[[.,.],[[.,[.,.]],.]],.] => 3
[[[.,.],[[[.,.],.],.]],.] => 3
[[[.,[.,.]],[.,[.,.]]],.] => 3
[[[.,[.,.]],[[.,.],.]],.] => 3
[[[[.,.],.],[.,[.,.]]],.] => 4
[[[[.,.],.],[[.,.],.]],.] => 4
[[[.,[.,[.,.]]],[.,.]],.] => 3
[[[.,[[.,.],.]],[.,.]],.] => 3
[[[[.,.],[.,.]],[.,.]],.] => 4
[[[[.,[.,.]],.],[.,.]],.] => 4
[[[[[.,.],.],.],[.,.]],.] => 5
[[[.,[.,[.,[.,.]]]],.],.] => 3
[[[.,[.,[[.,.],.]]],.],.] => 3
[[[.,[[.,.],[.,.]]],.],.] => 3
[[[.,[[.,[.,.]],.]],.],.] => 3
[[[.,[[[.,.],.],.]],.],.] => 3
[[[[.,.],[.,[.,.]]],.],.] => 4
[[[[.,.],[[.,.],.]],.],.] => 4
[[[[.,[.,.]],[.,.]],.],.] => 4
[[[[[.,.],.],[.,.]],.],.] => 5
[[[[.,[.,[.,.]]],.],.],.] => 4
[[[[.,[[.,.],.]],.],.],.] => 4
[[[[[.,.],[.,.]],.],.],.] => 5
[[[[[.,[.,.]],.],.],.],.] => 5
[[[[[[.,.],.],.],.],.],.] => 6
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 7
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 6
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 5
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 6
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 5
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 5
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 5
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 4
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 4
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 4
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 4
[.,[.,[.,[[[[.,.],.],.],.]]]] => 4
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 6
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 5
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 5
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 4
[.,[.,[[.,.],[[[.,.],.],.]]]] => 4
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 5
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 4
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 5
[.,[.,[[[.,.],.],[[.,.],.]]]] => 4
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 4
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 4
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 4
[.,[.,[[[[.,.],.],.],[.,.]]]] => 4
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 3
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 3
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 3
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 3
[.,[.,[[.,[[[.,.],.],.]],.]]] => 3
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 3
[.,[.,[[[.,.],[[.,.],.]],.]]] => 3
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 3
[.,[.,[[[[.,.],.],[.,.]],.]]] => 3
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 3
[.,[.,[[[.,[[.,.],.]],.],.]]] => 3
[.,[.,[[[[.,.],[.,.]],.],.]]] => 3
[.,[.,[[[[.,[.,.]],.],.],.]]] => 3
[.,[.,[[[[[.,.],.],.],.],.]]] => 3
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 6
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 5
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 5
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 4
[.,[[.,.],[.,[[[.,.],.],.]]]] => 4
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 5
[.,[[.,.],[[.,.],[[.,.],.]]]] => 4
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 4
[.,[[.,.],[[[.,.],.],[.,.]]]] => 4
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 3
[.,[[.,.],[[.,[[.,.],.]],.]]] => 3
[.,[[.,.],[[[.,.],[.,.]],.]]] => 3
[.,[[.,.],[[[.,[.,.]],.],.]]] => 3
[.,[[.,.],[[[[.,.],.],.],.]]] => 3
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 5
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 4
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 4
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 3
[.,[[.,[.,.]],[[[.,.],.],.]]] => 3
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 5
[.,[[[.,.],.],[.,[[.,.],.]]]] => 4
[.,[[[.,.],.],[[.,.],[.,.]]]] => 4
[.,[[[.,.],.],[[.,[.,.]],.]]] => 3
[.,[[[.,.],.],[[[.,.],.],.]]] => 3
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 3
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 4
[.,[[.,[[.,.],.]],[[.,.],.]]] => 3
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[.,.],.]]] => 3
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 4
[.,[[[.,[.,.]],.],[[.,.],.]]] => 3
[.,[[[[.,.],.],.],[.,[.,.]]]] => 4
[.,[[[[.,.],.],.],[[.,.],.]]] => 3
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 3
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 3
[.,[[.,[[[.,.],.],.]],[.,.]]] => 3
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 3
[.,[[[.,.],[[.,.],.]],[.,.]]] => 3
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 3
[.,[[[[.,.],.],[.,.]],[.,.]]] => 3
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 3
[.,[[[.,[[.,.],.]],.],[.,.]]] => 3
[.,[[[[.,.],[.,.]],.],[.,.]]] => 3
[.,[[[[.,[.,.]],.],.],[.,.]]] => 3
[.,[[[[[.,.],.],.],.],[.,.]]] => 3
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 2
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 2
[.,[[.,[.,[[[.,.],.],.]]],.]] => 2
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[.,[[.,[[.,.],[[.,.],.]]],.]] => 2
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[.,[[.,[[[.,.],.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 2
[.,[[.,[[.,[[.,.],.]],.]],.]] => 2
[.,[[.,[[[.,.],[.,.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],.],.]],.]] => 2
[.,[[.,[[[[.,.],.],.],.]],.]] => 2
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 2
[.,[[[.,.],[.,[[.,.],.]]],.]] => 2
[.,[[[.,.],[[.,.],[.,.]]],.]] => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => 2
[.,[[[.,.],[[[.,.],.],.]],.]] => 2
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 2
[.,[[[.,[.,.]],[[.,.],.]],.]] => 2
[.,[[[[.,.],.],[.,[.,.]]],.]] => 2
[.,[[[[.,.],.],[[.,.],.]],.]] => 2
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 2
[.,[[[.,[[.,.],.]],[.,.]],.]] => 2
[.,[[[[.,.],[.,.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],.],[.,.]],.]] => 2
[.,[[[[[.,.],.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 2
[.,[[[.,[.,[[.,.],.]]],.],.]] => 2
[.,[[[.,[[.,.],[.,.]]],.],.]] => 2
[.,[[[.,[[.,[.,.]],.]],.],.]] => 2
[.,[[[.,[[[.,.],.],.]],.],.]] => 2
[.,[[[[.,.],[.,[.,.]]],.],.]] => 2
[.,[[[[.,.],[[.,.],.]],.],.]] => 2
[.,[[[[.,[.,.]],[.,.]],.],.]] => 2
[.,[[[[[.,.],.],[.,.]],.],.]] => 2
[.,[[[[.,[.,[.,.]]],.],.],.]] => 2
[.,[[[[.,[[.,.],.]],.],.],.]] => 2
[.,[[[[[.,.],[.,.]],.],.],.]] => 2
[.,[[[[[.,[.,.]],.],.],.],.]] => 2
[.,[[[[[[.,.],.],.],.],.],.]] => 2
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 7
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 6
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 6
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 5
[[.,.],[.,[.,[[[.,.],.],.]]]] => 5
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 6
[[.,.],[.,[[.,.],[[.,.],.]]]] => 5
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 5
[[.,.],[.,[[[.,.],.],[.,.]]]] => 5
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 4
[[.,.],[.,[[.,[[.,.],.]],.]]] => 4
[[.,.],[.,[[[.,.],[.,.]],.]]] => 4
[[.,.],[.,[[[.,[.,.]],.],.]]] => 4
[[.,.],[.,[[[[.,.],.],.],.]]] => 4
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 6
[[.,.],[[.,.],[.,[[.,.],.]]]] => 5
[[.,.],[[.,.],[[.,.],[.,.]]]] => 5
[[.,.],[[.,.],[[.,[.,.]],.]]] => 4
[[.,.],[[.,.],[[[.,.],.],.]]] => 4
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 5
[[.,.],[[.,[.,.]],[[.,.],.]]] => 4
[[.,.],[[[.,.],.],[.,[.,.]]]] => 5
[[.,.],[[[.,.],.],[[.,.],.]]] => 4
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 4
[[.,.],[[.,[[.,.],.]],[.,.]]] => 4
[[.,.],[[[.,.],[.,.]],[.,.]]] => 4
[[.,.],[[[.,[.,.]],.],[.,.]]] => 4
[[.,.],[[[[.,.],.],.],[.,.]]] => 4
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 3
[[.,.],[[.,[.,[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[[.,.],[[.,[[.,[.,.]],.]],.]] => 3
[[.,.],[[.,[[[.,.],.],.]],.]] => 3
[[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[[.,.],[[[.,.],[[.,.],.]],.]] => 3
[[.,.],[[[.,[.,.]],[.,.]],.]] => 3
[[.,.],[[[[.,.],.],[.,.]],.]] => 3
[[.,.],[[[.,[.,[.,.]]],.],.]] => 3
[[.,.],[[[.,[[.,.],.]],.],.]] => 3
[[.,.],[[[[.,.],[.,.]],.],.]] => 3
[[.,.],[[[[.,[.,.]],.],.],.]] => 3
[[.,.],[[[[[.,.],.],.],.],.]] => 3
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 6
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 5
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 5
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 4
[[.,[.,.]],[.,[[[.,.],.],.]]] => 4
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 5
[[.,[.,.]],[[.,.],[[.,.],.]]] => 4
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 4
[[.,[.,.]],[[[.,.],.],[.,.]]] => 4
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 3
[[.,[.,.]],[[.,[[.,.],.]],.]] => 3
[[.,[.,.]],[[[.,.],[.,.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],.],.]] => 3
[[.,[.,.]],[[[[.,.],.],.],.]] => 3
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 7
[[[.,.],.],[.,[.,[[.,.],.]]]] => 6
[[[.,.],.],[.,[[.,.],[.,.]]]] => 6
[[[.,.],.],[.,[[.,[.,.]],.]]] => 5
[[[.,.],.],[.,[[[.,.],.],.]]] => 5
[[[.,.],.],[[.,.],[.,[.,.]]]] => 6
[[[.,.],.],[[.,.],[[.,.],.]]] => 5
[[[.,.],.],[[.,[.,.]],[.,.]]] => 5
[[[.,.],.],[[[.,.],.],[.,.]]] => 5
[[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[[[.,.],.],[[.,[[.,.],.]],.]] => 4
[[[.,.],.],[[[.,.],[.,.]],.]] => 4
[[[.,.],.],[[[.,[.,.]],.],.]] => 4
[[[.,.],.],[[[[.,.],.],.],.]] => 4
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 5
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 4
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 4
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 3
[[.,[.,[.,.]]],[[[.,.],.],.]] => 3
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 5
[[.,[[.,.],.]],[.,[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,.],[.,.]]] => 4
[[.,[[.,.],.]],[[.,[.,.]],.]] => 3
[[.,[[.,.],.]],[[[.,.],.],.]] => 3
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 6
[[[.,.],[.,.]],[.,[[.,.],.]]] => 5
[[[.,.],[.,.]],[[.,.],[.,.]]] => 5
[[[.,.],[.,.]],[[.,[.,.]],.]] => 4
[[[.,.],[.,.]],[[[.,.],.],.]] => 4
[[[.,[.,.]],.],[.,[.,[.,.]]]] => 6
[[[.,[.,.]],.],[.,[[.,.],.]]] => 5
[[[.,[.,.]],.],[[.,.],[.,.]]] => 5
[[[.,[.,.]],.],[[.,[.,.]],.]] => 4
[[[.,[.,.]],.],[[[.,.],.],.]] => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => 7
[[[[.,.],.],.],[.,[[.,.],.]]] => 6
[[[[.,.],.],.],[[.,.],[.,.]]] => 6
[[[[.,.],.],.],[[.,[.,.]],.]] => 5
[[[[.,.],.],.],[[[.,.],.],.]] => 5
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => 4
[[.,[.,[.,[.,.]]]],[[.,.],.]] => 3
[[.,[.,[[.,.],.]]],[.,[.,.]]] => 4
[[.,[.,[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,.],[.,.]]],[.,[.,.]]] => 4
[[.,[[.,.],[.,.]]],[[.,.],.]] => 3
[[.,[[.,[.,.]],.]],[.,[.,.]]] => 4
[[.,[[.,[.,.]],.]],[[.,.],.]] => 3
[[.,[[[.,.],.],.]],[.,[.,.]]] => 4
[[.,[[[.,.],.],.]],[[.,.],.]] => 3
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 5
[[[.,.],[.,[.,.]]],[[.,.],.]] => 4
[[[.,.],[[.,.],.]],[.,[.,.]]] => 5
[[[.,.],[[.,.],.]],[[.,.],.]] => 4
[[[.,[.,.]],[.,.]],[.,[.,.]]] => 5
[[[.,[.,.]],[.,.]],[[.,.],.]] => 4
[[[[.,.],.],[.,.]],[.,[.,.]]] => 6
[[[[.,.],.],[.,.]],[[.,.],.]] => 5
[[[.,[.,[.,.]]],.],[.,[.,.]]] => 5
[[[.,[.,[.,.]]],.],[[.,.],.]] => 4
[[[.,[[.,.],.]],.],[.,[.,.]]] => 5
[[[.,[[.,.],.]],.],[[.,.],.]] => 4
[[[[.,.],[.,.]],.],[.,[.,.]]] => 6
[[[[.,.],[.,.]],.],[[.,.],.]] => 5
[[[[.,[.,.]],.],.],[.,[.,.]]] => 6
[[[[.,[.,.]],.],.],[[.,.],.]] => 5
[[[[[.,.],.],.],.],[.,[.,.]]] => 7
[[[[[.,.],.],.],.],[[.,.],.]] => 6
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 3
[[.,[.,[.,[[.,.],.]]]],[.,.]] => 3
[[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[[.,[.,[[.,[.,.]],.]]],[.,.]] => 3
[[.,[.,[[[.,.],.],.]]],[.,.]] => 3
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[[.,[[.,.],[[.,.],.]]],[.,.]] => 3
[[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[[.,[[[.,.],.],[.,.]]],[.,.]] => 3
[[.,[[.,[.,[.,.]]],.]],[.,.]] => 3
[[.,[[.,[[.,.],.]],.]],[.,.]] => 3
[[.,[[[.,.],[.,.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],.],.]],[.,.]] => 3
[[.,[[[[.,.],.],.],.]],[.,.]] => 3
[[[.,.],[.,[.,[.,.]]]],[.,.]] => 4
[[[.,.],[.,[[.,.],.]]],[.,.]] => 4
[[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[[[.,.],[[.,[.,.]],.]],[.,.]] => 4
[[[.,.],[[[.,.],.],.]],[.,.]] => 4
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 4
[[[.,[.,.]],[[.,.],.]],[.,.]] => 4
[[[[.,.],.],[.,[.,.]]],[.,.]] => 5
[[[[.,.],.],[[.,.],.]],[.,.]] => 5
[[[.,[.,[.,.]]],[.,.]],[.,.]] => 4
[[[.,[[.,.],.]],[.,.]],[.,.]] => 4
[[[[.,.],[.,.]],[.,.]],[.,.]] => 5
[[[[.,[.,.]],.],[.,.]],[.,.]] => 5
[[[[[.,.],.],.],[.,.]],[.,.]] => 6
[[[.,[.,[.,[.,.]]]],.],[.,.]] => 4
[[[.,[.,[[.,.],.]]],.],[.,.]] => 4
[[[.,[[.,.],[.,.]]],.],[.,.]] => 4
[[[.,[[.,[.,.]],.]],.],[.,.]] => 4
[[[.,[[[.,.],.],.]],.],[.,.]] => 4
[[[[.,.],[.,[.,.]]],.],[.,.]] => 5
[[[[.,.],[[.,.],.]],.],[.,.]] => 5
[[[[.,[.,.]],[.,.]],.],[.,.]] => 5
[[[[[.,.],.],[.,.]],.],[.,.]] => 6
[[[[.,[.,[.,.]]],.],.],[.,.]] => 5
[[[[.,[[.,.],.]],.],.],[.,.]] => 5
[[[[[.,.],[.,.]],.],.],[.,.]] => 6
[[[[[.,[.,.]],.],.],.],[.,.]] => 6
[[[[[[.,.],.],.],.],.],[.,.]] => 7
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 2
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 2
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 2
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 2
[[.,[.,[.,[[[.,.],.],.]]]],.] => 2
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 2
[[.,[.,[[.,.],[[.,.],.]]]],.] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => 2
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => 2
[[.,[.,[[[.,.],[.,.]],.]]],.] => 2
[[.,[.,[[[.,[.,.]],.],.]]],.] => 2
[[.,[.,[[[[.,.],.],.],.]]],.] => 2
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 2
[[.,[[.,.],[.,[[.,.],.]]]],.] => 2
[[.,[[.,.],[[.,.],[.,.]]]],.] => 2
[[.,[[.,.],[[.,[.,.]],.]]],.] => 2
[[.,[[.,.],[[[.,.],.],.]]],.] => 2
[[.,[[.,[.,.]],[.,[.,.]]]],.] => 2
[[.,[[.,[.,.]],[[.,.],.]]],.] => 2
[[.,[[[.,.],.],[.,[.,.]]]],.] => 2
[[.,[[[.,.],.],[[.,.],.]]],.] => 2
[[.,[[.,[.,[.,.]]],[.,.]]],.] => 2
[[.,[[.,[[.,.],.]],[.,.]]],.] => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => 2
[[.,[[[[.,.],.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 2
[[.,[[.,[.,[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,.],[.,.]]],.]],.] => 2
[[.,[[.,[[.,[.,.]],.]],.]],.] => 2
[[.,[[.,[[[.,.],.],.]],.]],.] => 2
[[.,[[[.,.],[.,[.,.]]],.]],.] => 2
[[.,[[[.,.],[[.,.],.]],.]],.] => 2
[[.,[[[.,[.,.]],[.,.]],.]],.] => 2
[[.,[[[[.,.],.],[.,.]],.]],.] => 2
[[.,[[[.,[.,[.,.]]],.],.]],.] => 2
[[.,[[[.,[[.,.],.]],.],.]],.] => 2
[[.,[[[[.,.],[.,.]],.],.]],.] => 2
[[.,[[[[.,[.,.]],.],.],.]],.] => 2
[[.,[[[[[.,.],.],.],.],.]],.] => 2
[[[.,.],[.,[.,[.,[.,.]]]]],.] => 3
[[[.,.],[.,[.,[[.,.],.]]]],.] => 3
[[[.,.],[.,[[.,.],[.,.]]]],.] => 3
[[[.,.],[.,[[.,[.,.]],.]]],.] => 3
[[[.,.],[.,[[[.,.],.],.]]],.] => 3
[[[.,.],[[.,.],[.,[.,.]]]],.] => 3
[[[.,.],[[.,.],[[.,.],.]]],.] => 3
[[[.,.],[[.,[.,.]],[.,.]]],.] => 3
[[[.,.],[[[.,.],.],[.,.]]],.] => 3
[[[.,.],[[.,[.,[.,.]]],.]],.] => 3
[[[.,.],[[.,[[.,.],.]],.]],.] => 3
[[[.,.],[[[.,.],[.,.]],.]],.] => 3
[[[.,.],[[[.,[.,.]],.],.]],.] => 3
[[[.,.],[[[[.,.],.],.],.]],.] => 3
[[[.,[.,.]],[.,[.,[.,.]]]],.] => 3
[[[.,[.,.]],[.,[[.,.],.]]],.] => 3
[[[.,[.,.]],[[.,.],[.,.]]],.] => 3
[[[.,[.,.]],[[.,[.,.]],.]],.] => 3
[[[.,[.,.]],[[[.,.],.],.]],.] => 3
[[[[.,.],.],[.,[.,[.,.]]]],.] => 4
[[[[.,.],.],[.,[[.,.],.]]],.] => 4
[[[[.,.],.],[[.,.],[.,.]]],.] => 4
[[[[.,.],.],[[.,[.,.]],.]],.] => 4
[[[[.,.],.],[[[.,.],.],.]],.] => 4
[[[.,[.,[.,.]]],[.,[.,.]]],.] => 3
[[[.,[.,[.,.]]],[[.,.],.]],.] => 3
[[[.,[[.,.],.]],[.,[.,.]]],.] => 3
[[[.,[[.,.],.]],[[.,.],.]],.] => 3
[[[[.,.],[.,.]],[.,[.,.]]],.] => 4
[[[[.,.],[.,.]],[[.,.],.]],.] => 4
[[[[.,[.,.]],.],[.,[.,.]]],.] => 4
[[[[.,[.,.]],.],[[.,.],.]],.] => 4
[[[[[.,.],.],.],[.,[.,.]]],.] => 5
[[[[[.,.],.],.],[[.,.],.]],.] => 5
[[[.,[.,[.,[.,.]]]],[.,.]],.] => 3
[[[.,[.,[[.,.],.]]],[.,.]],.] => 3
[[[.,[[.,.],[.,.]]],[.,.]],.] => 3
[[[.,[[.,[.,.]],.]],[.,.]],.] => 3
[[[.,[[[.,.],.],.]],[.,.]],.] => 3
[[[[.,.],[.,[.,.]]],[.,.]],.] => 4
[[[[.,.],[[.,.],.]],[.,.]],.] => 4
[[[[.,[.,.]],[.,.]],[.,.]],.] => 4
[[[[[.,.],.],[.,.]],[.,.]],.] => 5
[[[[.,[.,[.,.]]],.],[.,.]],.] => 4
[[[[.,[[.,.],.]],.],[.,.]],.] => 4
[[[[[.,.],[.,.]],.],[.,.]],.] => 5
[[[[[.,[.,.]],.],.],[.,.]],.] => 5
[[[[[[.,.],.],.],.],[.,.]],.] => 6
[[[.,[.,[.,[.,[.,.]]]]],.],.] => 3
[[[.,[.,[.,[[.,.],.]]]],.],.] => 3
[[[.,[.,[[.,.],[.,.]]]],.],.] => 3
[[[.,[.,[[.,[.,.]],.]]],.],.] => 3
[[[.,[.,[[[.,.],.],.]]],.],.] => 3
[[[.,[[.,.],[.,[.,.]]]],.],.] => 3
[[[.,[[.,.],[[.,.],.]]],.],.] => 3
[[[.,[[.,[.,.]],[.,.]]],.],.] => 3
[[[.,[[[.,.],.],[.,.]]],.],.] => 3
[[[.,[[.,[.,[.,.]]],.]],.],.] => 3
[[[.,[[.,[[.,.],.]],.]],.],.] => 3
[[[.,[[[.,.],[.,.]],.]],.],.] => 3
[[[.,[[[.,[.,.]],.],.]],.],.] => 3
[[[.,[[[[.,.],.],.],.]],.],.] => 3
[[[[.,.],[.,[.,[.,.]]]],.],.] => 4
[[[[.,.],[.,[[.,.],.]]],.],.] => 4
[[[[.,.],[[.,.],[.,.]]],.],.] => 4
[[[[.,.],[[.,[.,.]],.]],.],.] => 4
[[[[.,.],[[[.,.],.],.]],.],.] => 4
[[[[.,[.,.]],[.,[.,.]]],.],.] => 4
[[[[.,[.,.]],[[.,.],.]],.],.] => 4
[[[[[.,.],.],[.,[.,.]]],.],.] => 5
[[[[[.,.],.],[[.,.],.]],.],.] => 5
[[[[.,[.,[.,.]]],[.,.]],.],.] => 4
[[[[.,[[.,.],.]],[.,.]],.],.] => 4
[[[[[.,.],[.,.]],[.,.]],.],.] => 5
[[[[[.,[.,.]],.],[.,.]],.],.] => 5
[[[[[[.,.],.],.],[.,.]],.],.] => 6
[[[[.,[.,[.,[.,.]]]],.],.],.] => 4
[[[[.,[.,[[.,.],.]]],.],.],.] => 4
[[[[.,[[.,.],[.,.]]],.],.],.] => 4
[[[[.,[[.,[.,.]],.]],.],.],.] => 4
[[[[.,[[[.,.],.],.]],.],.],.] => 4
[[[[[.,.],[.,[.,.]]],.],.],.] => 5
[[[[[.,.],[[.,.],.]],.],.],.] => 5
[[[[[.,[.,.]],[.,.]],.],.],.] => 5
[[[[[[.,.],.],[.,.]],.],.],.] => 6
[[[[[.,[.,[.,.]]],.],.],.],.] => 5
[[[[[.,[[.,.],.]],.],.],.],.] => 5
[[[[[[.,.],[.,.]],.],.],.],.] => 6
[[[[[[.,[.,.]],.],.],.],.],.] => 6
[[[[[[[.,.],.],.],.],.],.],.] => 7
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => 5
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => 4
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => 3
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => 3
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => 3
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => 3
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => 3
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => 3
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => 2
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 2
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => 2
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 2
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => 2
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => 2
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 2
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => 2
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => 2
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => 2
[.,[[[[[[[.,.],.],.],.],.],.],.]] => 2
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 8
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 7
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 7
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 6
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 6
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 7
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 5
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 4
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => 4
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 5
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 5
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 4
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 5
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 4
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => 4
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 4
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 4
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 4
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 3
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 3
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 3
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 3
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 5
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 5
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 4
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => 5
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => 5
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => 4
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => 5
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => 4
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => 4
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => 4
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => 4
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => 3
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => 3
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => 3
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => 5
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => 5
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 4
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => 5
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => 4
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => 4
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => 4
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => 3
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => 3
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => 6
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => 6
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => 6
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => 6
[[[[.,.],.],.],[[[[.,.],.],.],.]] => 5
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 5
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => 4
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => 4
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => 3
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => 4
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => 3
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 6
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => 5
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => 4
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => 4
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => 4
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => 6
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => 6
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => 5
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => 6
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => 6
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => 5
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => 6
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => 6
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => 5
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => 3
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 6
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => 5
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => 5
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => 6
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => 5
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => 6
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 5
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => 6
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 5
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => 5
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 6
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 5
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 6
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => 5
[[[[[[.,.],.],.],.],.],[[.,.],.]] => 7
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 3
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => 4
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => 4
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => 5
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 5
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => 5
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => 5
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 5
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 5
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 4
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 5
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 5
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 5
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => 7
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 4
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => 7
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => 5
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => 7
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 6
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => 6
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => 7
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => 7
[[[[[[[.,.],.],.],.],.],.],[.,.]] => 8
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => 2
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => 2
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => 2
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => 2
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => 2
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => 2
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => 2
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => 2
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => 2
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => 2
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => 2
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => 4
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => 4
[[[[.,.],.],[[[[.,.],.],.],.]],.] => 4
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => 4
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => 4
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => 4
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => 4
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => 4
[[[[[[.,.],.],.],.],[[.,.],.]],.] => 6
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => 6
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => 6
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => 6
[[[[[[.,.],.],.],[[.,.],.]],.],.] => 6
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => 6
[[[[[[[[.,.],.],.],.],.],.],.],.] => 8
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 2
[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]] => 7
[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]] => 4
[[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 6
[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]] => 4
[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]] => 6
[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]] => 4
[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]] => 3
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => 2
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 9
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 8
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 2
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 8
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 7
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 2
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 2
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 9
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => 2
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 8
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => 2
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => 2
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 7
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 8
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 2
[[[[.,.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]] => 7
[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 4
[[[[[.,.],.],.],[.,.]],[[.,.],[.,[.,.]]]] => 8
[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]] => 4
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => 2
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 6
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 4
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 5
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 4
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 3
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => 3
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => 3
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => 3
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => 2
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.] => 2
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.] => 2
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.] => 2
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.] => 2
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => 2
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 2
[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 2
[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 2
[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 2
[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 3
[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 4
[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 4
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 3
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 3
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 3
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 3
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 3
[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]] => 3
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 5
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]] => 4
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => 4
[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.] => 2
[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.] => 2
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]] => 4
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]] => 4
[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.] => 2
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.] => 2
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] => 5
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]] => 4
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => 5
[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.] => 2
[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.] => 2
[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 2
[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.] => 2
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => 2
[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 5
[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 6
[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]] => 6
[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 7
[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]] => 4
[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]] => 4
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 5
[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]] => 5
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 10
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => 9
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 2
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 10
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => 2
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 9
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 2
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 2
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 2
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 2
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 2
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 2
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 2
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 2
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 2
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 2
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 3
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 3
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 3
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 3
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 4
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 4
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 3
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 4
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 4
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 5
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 3
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 4
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 4
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 5
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 4
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 4
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 5
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 5
[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]] => 7
[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]] => 4
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 11
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 2
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => 2
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 11
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => 7
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]] => 6
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => 6
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]] => 5
[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => 6
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]] => 5
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]] => 5
[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]] => 4
[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]] => 4
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => 6
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]] => 5
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => 5
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]] => 4
[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]] => 4
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => 5
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]] => 4
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] => 5
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]] => 4
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] => 4
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => 3
[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => 3
[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => 3
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => 3
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => 6
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => 5
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => 5
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => 4
[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => 4
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => 3
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => 3
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] => 4
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] => 5
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]] => 4
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] => 4
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] => 3
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] => 3
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] => 4
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] => 3
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => 3
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => 3
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => 3
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => 3
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] => 3
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] => 3
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] => 3
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] => 2
[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.] => 2
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.] => 2
[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.] => 2
[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.] => 2
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.] => 2
[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.] => 2
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.] => 2
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.] => 2
[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.] => 2
[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.] => 2
[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.] => 2
[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.] => 2
[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.] => 2
[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.] => 2
[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.] => 2
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.] => 2
[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.] => 2
[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.] => 2
[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.] => 2
[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.] => 2
[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.] => 2
[[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.] => 2
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => 2
[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],.]] => 2
[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]] => 2
[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]] => 2
[.,[[.,[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],.]] => 2
[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]] => 2
[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]] => 2
[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]] => 2
[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]] => 2
[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]] => 2
[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]] => 2
[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]] => 2
[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]] => 2
[.,[[[.,.],[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 3
[.,[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 3
[.,[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 2
[.,[[[.,.],[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 4
[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 4
[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => 3
[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]] => 4
[.,[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 3
[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 4
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => 4
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]] => 4
[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]] => 4
[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]] => 4
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]] => 4
[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]] => 3
[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]] => 3
[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]] => 3
[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => 3
[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]] => 3
[.,[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]] => 3
[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]] => 3
[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]] => 3
[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]] => 3
[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]] => 3
[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]] => 3
[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]] => 3
[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]] => 3
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => 3
[[.,[.,.]],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => 3
[[.,[.,.]],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => 3
[[.,[.,.]],[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => 3
[[.,[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]] => 4
[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] => 5
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => 5
[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] => 5
[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => 4
[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => 4
[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] => 4
[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => 4
[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => 4
[[.,[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.] => 2
[[.,[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]],.] => 2
[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 5
[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.] => 2
[[.,[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.] => 2
[[[.,[.,.]],[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]] => 4
[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] => 6
[[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]] => 4
[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => 4
[[.,[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.]],.] => 2
[[.,[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.] => 2
[[.,[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]],.] => 2
[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.] => 2
[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[.,.],[.,.]]],.]] => 4
[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]] => 5
[[[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]],.],[.,.]] => 4
[[[.,[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]] => 4
[[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]] => 5
[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] => 5
[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.] => 2
[[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.] => 2
[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.] => 2
[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.] => 2
[[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.] => 2
[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]] => 5
[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] => 5
[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]] => 5
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] => 6
[[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]] => 4
[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]] => 4
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] => 5
[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]] => 5
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => 6
[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.] => 2
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.] => 2
[[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.] => 2
[[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.] => 2
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.] => 2
[[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.] => 2
[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.] => 2
[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.] => 2
[[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.] => 2
[[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.] => 2
[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.] => 2
[[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.] => 2
[[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.] => 2
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => 2
[[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]] => 5
[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]] => 5
[[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.] => 3
[[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]] => 6
[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]] => 6
[[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]] => 5
[[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]] => 6
[[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]] => 6
[[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]] => 7
[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]] => 6
[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]] => 6
[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]] => 6
[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]] => 7
[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]] => 8
[[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]] => 4
[[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]] => 4
[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]] => 4
[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]] => 4
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]] => 4
[[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]] => 5
[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]] => 5
[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]] => 5
[[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]] => 6
[[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]] => 5
[[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]] => 5
[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]] => 6
[[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]] => 6
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 7
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => 2
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => 2
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => 2
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => 2
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => 2
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => 2
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => 2
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => 2
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => 2
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 2
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 2
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 2
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 2
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 2
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => 2
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => 2
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 2
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 2
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => 2
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => 2
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 2
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => 2
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 2
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => 2
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => 2
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => 2
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => 2
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 2
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => 2
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 2
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => 2
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => 2
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 2
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => 2
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => 2
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => 3
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => 3
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => 3
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => 3
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => 3
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => 3
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => 3
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => 3
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => 3
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => 3
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 3
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 3
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 3
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 3
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 3
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => 4
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => 4
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => 4
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => 4
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => 4
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => 3
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 3
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 3
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => 4
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => 4
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 4
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 4
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => 5
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => 5
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => 3
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => 3
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 3
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => 4
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => 4
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 4
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => 5
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => 4
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 4
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => 5
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 5
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => 6
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => 3
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => 3
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => 3
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 3
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => 3
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 3
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => 3
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => 3
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 3
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => 3
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => 3
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => 4
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => 4
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => 4
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 4
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 4
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => 5
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => 5
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => 4
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 4
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => 5
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 5
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => 6
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => 4
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => 4
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 4
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => 4
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => 4
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => 5
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => 5
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 5
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => 6
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 5
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 5
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 6
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 6
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Created: May 16, 2014 at 17:26 by Joseph Ching
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Last Updated: Jan 17, 2018 at 23:01 by Martin Rubey