*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000679
-----------------------------------------------------------------------------
Collection: Ordered trees
-----------------------------------------------------------------------------
Description: The pruning number of an ordered tree.
A hanging branch of an ordered tree is a proper factor of the form $[^r]^r$ for some $r\geq 1$. A hanging branch is a maximal hanging branch if it is not a proper factor of another hanging branch.
A pruning of an ordered tree is the act of deleting all its maximal hanging branches. The pruning order of an ordered tree is the number of prunings required to reduce it to $[]$.
-----------------------------------------------------------------------------
References: [1] Zeilberger, D. A bijection from ordered trees to binary trees that sends the pruning order to the Strahler number [[MathSciNet:1058712]]
-----------------------------------------------------------------------------
Code:
def prune(t):
"""
sage: prune([[]])
[]
sage: prune([[[],[[],[]]],[[],[],[[]]]])
[[[]], []]
"""
def is_branch(b):
n = len(b)
return n == 0 or (n == 1 and is_branch(b[0]))
if len(t) == 0:
return []
else:
return [prune(b) for b in t if not is_branch(b)]
def statistic(t):
"""
sage: statistic([[[],[[],[]]],[[],[],[[]]]])
2
"""
o = 0
while len(t) > 0:
t = prune(t)
o += 1
return o
-----------------------------------------------------------------------------
Statistic values:
[[]] => 1
[[],[]] => 1
[[[]]] => 1
[[],[],[]] => 1
[[],[[]]] => 1
[[[]],[]] => 1
[[[],[]]] => 2
[[[[]]]] => 1
[[],[],[],[]] => 1
[[],[],[[]]] => 1
[[],[[]],[]] => 1
[[],[[],[]]] => 2
[[],[[[]]]] => 1
[[[]],[],[]] => 1
[[[]],[[]]] => 1
[[[],[]],[]] => 2
[[[[]]],[]] => 1
[[[],[],[]]] => 2
[[[],[[]]]] => 2
[[[[]],[]]] => 2
[[[[],[]]]] => 2
[[[[[]]]]] => 1
[[],[],[],[],[]] => 1
[[],[],[],[[]]] => 1
[[],[],[[]],[]] => 1
[[],[],[[],[]]] => 2
[[],[],[[[]]]] => 1
[[],[[]],[],[]] => 1
[[],[[]],[[]]] => 1
[[],[[],[]],[]] => 2
[[],[[[]]],[]] => 1
[[],[[],[],[]]] => 2
[[],[[],[[]]]] => 2
[[],[[[]],[]]] => 2
[[],[[[],[]]]] => 2
[[],[[[[]]]]] => 1
[[[]],[],[],[]] => 1
[[[]],[],[[]]] => 1
[[[]],[[]],[]] => 1
[[[]],[[],[]]] => 2
[[[]],[[[]]]] => 1
[[[],[]],[],[]] => 2
[[[[]]],[],[]] => 1
[[[],[]],[[]]] => 2
[[[[]]],[[]]] => 1
[[[],[],[]],[]] => 2
[[[],[[]]],[]] => 2
[[[[]],[]],[]] => 2
[[[[],[]]],[]] => 2
[[[[[]]]],[]] => 1
[[[],[],[],[]]] => 2
[[[],[],[[]]]] => 2
[[[],[[]],[]]] => 2
[[[],[[],[]]]] => 2
[[[],[[[]]]]] => 2
[[[[]],[],[]]] => 2
[[[[]],[[]]]] => 2
[[[[],[]],[]]] => 2
[[[[[]]],[]]] => 2
[[[[],[],[]]]] => 2
[[[[],[[]]]]] => 2
[[[[[]],[]]]] => 2
[[[[[],[]]]]] => 2
[[[[[[]]]]]] => 1
[[],[],[],[],[],[]] => 1
[[],[],[],[],[[]]] => 1
[[],[],[],[[]],[]] => 1
[[],[],[],[[],[]]] => 2
[[],[],[],[[[]]]] => 1
[[],[],[[]],[],[]] => 1
[[],[],[[]],[[]]] => 1
[[],[],[[],[]],[]] => 2
[[],[],[[[]]],[]] => 1
[[],[],[[],[],[]]] => 2
[[],[],[[],[[]]]] => 2
[[],[],[[[]],[]]] => 2
[[],[],[[[],[]]]] => 2
[[],[],[[[[]]]]] => 1
[[],[[]],[],[],[]] => 1
[[],[[]],[],[[]]] => 1
[[],[[]],[[]],[]] => 1
[[],[[]],[[],[]]] => 2
[[],[[]],[[[]]]] => 1
[[],[[],[]],[],[]] => 2
[[],[[[]]],[],[]] => 1
[[],[[],[]],[[]]] => 2
[[],[[[]]],[[]]] => 1
[[],[[],[],[]],[]] => 2
[[],[[],[[]]],[]] => 2
[[],[[[]],[]],[]] => 2
[[],[[[],[]]],[]] => 2
[[],[[[[]]]],[]] => 1
[[],[[],[],[],[]]] => 2
[[],[[],[],[[]]]] => 2
[[],[[],[[]],[]]] => 2
[[],[[],[[],[]]]] => 2
[[],[[],[[[]]]]] => 2
[[],[[[]],[],[]]] => 2
[[],[[[]],[[]]]] => 2
[[],[[[],[]],[]]] => 2
[[],[[[[]]],[]]] => 2
[[],[[[],[],[]]]] => 2
[[],[[[],[[]]]]] => 2
[[],[[[[]],[]]]] => 2
[[],[[[[],[]]]]] => 2
[[],[[[[[]]]]]] => 1
[[[]],[],[],[],[]] => 1
[[[]],[],[],[[]]] => 1
[[[]],[],[[]],[]] => 1
[[[]],[],[[],[]]] => 2
[[[]],[],[[[]]]] => 1
[[[]],[[]],[],[]] => 1
[[[]],[[]],[[]]] => 1
[[[]],[[],[]],[]] => 2
[[[]],[[[]]],[]] => 1
[[[]],[[],[],[]]] => 2
[[[]],[[],[[]]]] => 2
[[[]],[[[]],[]]] => 2
[[[]],[[[],[]]]] => 2
[[[]],[[[[]]]]] => 1
[[[],[]],[],[],[]] => 2
[[[[]]],[],[],[]] => 1
[[[],[]],[],[[]]] => 2
[[[[]]],[],[[]]] => 1
[[[],[]],[[]],[]] => 2
[[[[]]],[[]],[]] => 1
[[[],[]],[[],[]]] => 2
[[[],[]],[[[]]]] => 2
[[[[]]],[[],[]]] => 2
[[[[]]],[[[]]]] => 1
[[[],[],[]],[],[]] => 2
[[[],[[]]],[],[]] => 2
[[[[]],[]],[],[]] => 2
[[[[],[]]],[],[]] => 2
[[[[[]]]],[],[]] => 1
[[[],[],[]],[[]]] => 2
[[[],[[]]],[[]]] => 2
[[[[]],[]],[[]]] => 2
[[[[],[]]],[[]]] => 2
[[[[[]]]],[[]]] => 1
[[[],[],[],[]],[]] => 2
[[[],[],[[]]],[]] => 2
[[[],[[]],[]],[]] => 2
[[[],[[],[]]],[]] => 2
[[[],[[[]]]],[]] => 2
[[[[]],[],[]],[]] => 2
[[[[]],[[]]],[]] => 2
[[[[],[]],[]],[]] => 2
[[[[[]]],[]],[]] => 2
[[[[],[],[]]],[]] => 2
[[[[],[[]]]],[]] => 2
[[[[[]],[]]],[]] => 2
[[[[[],[]]]],[]] => 2
[[[[[[]]]]],[]] => 1
[[[],[],[],[],[]]] => 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
[[[[[[[]]]]]]] => 1
[[],[],[],[],[],[],[]] => 1
[[],[],[],[],[],[[]]] => 1
[[],[],[],[],[[]],[]] => 1
[[],[],[],[],[[],[]]] => 2
[[],[],[],[],[[[]]]] => 1
[[],[],[],[[]],[],[]] => 1
[[],[],[],[[]],[[]]] => 1
[[],[],[],[[],[]],[]] => 2
[[],[],[],[[[]]],[]] => 1
[[],[],[],[[],[],[]]] => 2
[[],[],[],[[],[[]]]] => 2
[[],[],[],[[[]],[]]] => 2
[[],[],[],[[[],[]]]] => 2
[[],[],[],[[[[]]]]] => 1
[[],[],[[]],[],[],[]] => 1
[[],[],[[]],[],[[]]] => 1
[[],[],[[]],[[]],[]] => 1
[[],[],[[]],[[],[]]] => 2
[[],[],[[]],[[[]]]] => 1
[[],[],[[],[]],[],[]] => 2
[[],[],[[[]]],[],[]] => 1
[[],[],[[],[]],[[]]] => 2
[[],[],[[[]]],[[]]] => 1
[[],[],[[],[],[]],[]] => 2
[[],[],[[],[[]]],[]] => 2
[[],[],[[[]],[]],[]] => 2
[[],[],[[[],[]]],[]] => 2
[[],[],[[[[]]]],[]] => 1
[[],[],[[],[],[],[]]] => 2
[[],[],[[],[],[[]]]] => 2
[[],[],[[],[[]],[]]] => 2
[[],[],[[],[[],[]]]] => 2
[[],[],[[],[[[]]]]] => 2
[[],[],[[[]],[],[]]] => 2
[[],[],[[[]],[[]]]] => 2
[[],[],[[[],[]],[]]] => 2
[[],[],[[[[]]],[]]] => 2
[[],[],[[[],[],[]]]] => 2
[[],[],[[[],[[]]]]] => 2
[[],[],[[[[]],[]]]] => 2
[[],[],[[[[],[]]]]] => 2
[[],[],[[[[[]]]]]] => 1
[[],[[]],[],[],[],[]] => 1
[[],[[]],[],[],[[]]] => 1
[[],[[]],[],[[]],[]] => 1
[[],[[]],[],[[],[]]] => 2
[[],[[]],[],[[[]]]] => 1
[[],[[]],[[]],[],[]] => 1
[[],[[]],[[]],[[]]] => 1
[[],[[]],[[],[]],[]] => 2
[[],[[]],[[[]]],[]] => 1
[[],[[]],[[],[],[]]] => 2
[[],[[]],[[],[[]]]] => 2
[[],[[]],[[[]],[]]] => 2
[[],[[]],[[[],[]]]] => 2
[[],[[]],[[[[]]]]] => 1
[[],[[],[]],[],[],[]] => 2
[[],[[[]]],[],[],[]] => 1
[[],[[],[]],[],[[]]] => 2
[[],[[[]]],[],[[]]] => 1
[[],[[],[]],[[]],[]] => 2
[[],[[[]]],[[]],[]] => 1
[[],[[],[]],[[],[]]] => 2
[[],[[],[]],[[[]]]] => 2
[[],[[[]]],[[],[]]] => 2
[[],[[[]]],[[[]]]] => 1
[[],[[],[],[]],[],[]] => 2
[[],[[],[[]]],[],[]] => 2
[[],[[[]],[]],[],[]] => 2
[[],[[[],[]]],[],[]] => 2
[[],[[[[]]]],[],[]] => 1
[[],[[],[],[]],[[]]] => 2
[[],[[],[[]]],[[]]] => 2
[[],[[[]],[]],[[]]] => 2
[[],[[[],[]]],[[]]] => 2
[[],[[[[]]]],[[]]] => 1
[[],[[],[],[],[]],[]] => 2
[[],[[],[],[[]]],[]] => 2
[[],[[],[[]],[]],[]] => 2
[[],[[],[[],[]]],[]] => 2
[[],[[],[[[]]]],[]] => 2
[[],[[[]],[],[]],[]] => 2
[[],[[[]],[[]]],[]] => 2
[[],[[[],[]],[]],[]] => 2
[[],[[[[]]],[]],[]] => 2
[[],[[[],[],[]]],[]] => 2
[[],[[[],[[]]]],[]] => 2
[[],[[[[]],[]]],[]] => 2
[[],[[[[],[]]]],[]] => 2
[[],[[[[[]]]]],[]] => 1
[[],[[],[],[],[],[]]] => 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
[[],[[[[[[]]]]]]] => 1
[[[]],[],[],[],[],[]] => 1
[[[]],[],[],[],[[]]] => 1
[[[]],[],[],[[]],[]] => 1
[[[]],[],[],[[],[]]] => 2
[[[]],[],[],[[[]]]] => 1
[[[]],[],[[]],[],[]] => 1
[[[]],[],[[]],[[]]] => 1
[[[]],[],[[],[]],[]] => 2
[[[]],[],[[[]]],[]] => 1
[[[]],[],[[],[],[]]] => 2
[[[]],[],[[],[[]]]] => 2
[[[]],[],[[[]],[]]] => 2
[[[]],[],[[[],[]]]] => 2
[[[]],[],[[[[]]]]] => 1
[[[]],[[]],[],[],[]] => 1
[[[]],[[]],[],[[]]] => 1
[[[]],[[]],[[]],[]] => 1
[[[]],[[]],[[],[]]] => 2
[[[]],[[]],[[[]]]] => 1
[[[]],[[],[]],[],[]] => 2
[[[]],[[[]]],[],[]] => 1
[[[]],[[],[]],[[]]] => 2
[[[]],[[[]]],[[]]] => 1
[[[]],[[],[],[]],[]] => 2
[[[]],[[],[[]]],[]] => 2
[[[]],[[[]],[]],[]] => 2
[[[]],[[[],[]]],[]] => 2
[[[]],[[[[]]]],[]] => 1
[[[]],[[],[],[],[]]] => 2
[[[]],[[],[],[[]]]] => 2
[[[]],[[],[[]],[]]] => 2
[[[]],[[],[[],[]]]] => 2
[[[]],[[],[[[]]]]] => 2
[[[]],[[[]],[],[]]] => 2
[[[]],[[[]],[[]]]] => 2
[[[]],[[[],[]],[]]] => 2
[[[]],[[[[]]],[]]] => 2
[[[]],[[[],[],[]]]] => 2
[[[]],[[[],[[]]]]] => 2
[[[]],[[[[]],[]]]] => 2
[[[]],[[[[],[]]]]] => 2
[[[]],[[[[[]]]]]] => 1
[[[],[]],[],[],[],[]] => 2
[[[[]]],[],[],[],[]] => 1
[[[],[]],[],[],[[]]] => 2
[[[[]]],[],[],[[]]] => 1
[[[],[]],[],[[]],[]] => 2
[[[[]]],[],[[]],[]] => 1
[[[],[]],[],[[],[]]] => 2
[[[],[]],[],[[[]]]] => 2
[[[[]]],[],[[],[]]] => 2
[[[[]]],[],[[[]]]] => 1
[[[],[]],[[]],[],[]] => 2
[[[[]]],[[]],[],[]] => 1
[[[],[]],[[]],[[]]] => 2
[[[[]]],[[]],[[]]] => 1
[[[],[]],[[],[]],[]] => 2
[[[],[]],[[[]]],[]] => 2
[[[[]]],[[],[]],[]] => 2
[[[[]]],[[[]]],[]] => 1
[[[],[]],[[],[],[]]] => 2
[[[],[]],[[],[[]]]] => 2
[[[],[]],[[[]],[]]] => 2
[[[],[]],[[[],[]]]] => 2
[[[],[]],[[[[]]]]] => 2
[[[[]]],[[],[],[]]] => 2
[[[[]]],[[],[[]]]] => 2
[[[[]]],[[[]],[]]] => 2
[[[[]]],[[[],[]]]] => 2
[[[[]]],[[[[]]]]] => 1
[[[],[],[]],[],[],[]] => 2
[[[],[[]]],[],[],[]] => 2
[[[[]],[]],[],[],[]] => 2
[[[[],[]]],[],[],[]] => 2
[[[[[]]]],[],[],[]] => 1
[[[],[],[]],[],[[]]] => 2
[[[],[[]]],[],[[]]] => 2
[[[[]],[]],[],[[]]] => 2
[[[[],[]]],[],[[]]] => 2
[[[[[]]]],[],[[]]] => 1
[[[],[],[]],[[]],[]] => 2
[[[],[[]]],[[]],[]] => 2
[[[[]],[]],[[]],[]] => 2
[[[[],[]]],[[]],[]] => 2
[[[[[]]]],[[]],[]] => 1
[[[],[],[]],[[],[]]] => 2
[[[],[],[]],[[[]]]] => 2
[[[],[[]]],[[],[]]] => 2
[[[],[[]]],[[[]]]] => 2
[[[[]],[]],[[],[]]] => 2
[[[[]],[]],[[[]]]] => 2
[[[[],[]]],[[],[]]] => 2
[[[[],[]]],[[[]]]] => 2
[[[[[]]]],[[],[]]] => 2
[[[[[]]]],[[[]]]] => 1
[[[],[],[],[]],[],[]] => 2
[[[],[],[[]]],[],[]] => 2
[[[],[[]],[]],[],[]] => 2
[[[],[[],[]]],[],[]] => 2
[[[],[[[]]]],[],[]] => 2
[[[[]],[],[]],[],[]] => 2
[[[[]],[[]]],[],[]] => 2
[[[[],[]],[]],[],[]] => 2
[[[[[]]],[]],[],[]] => 2
[[[[],[],[]]],[],[]] => 2
[[[[],[[]]]],[],[]] => 2
[[[[[]],[]]],[],[]] => 2
[[[[[],[]]]],[],[]] => 2
[[[[[[]]]]],[],[]] => 1
[[[],[],[],[]],[[]]] => 2
[[[],[],[[]]],[[]]] => 2
[[[],[[]],[]],[[]]] => 2
[[[],[[],[]]],[[]]] => 2
[[[],[[[]]]],[[]]] => 2
[[[[]],[],[]],[[]]] => 2
[[[[]],[[]]],[[]]] => 2
[[[[],[]],[]],[[]]] => 2
[[[[[]]],[]],[[]]] => 2
[[[[],[],[]]],[[]]] => 2
[[[[],[[]]]],[[]]] => 2
[[[[[]],[]]],[[]]] => 2
[[[[[],[]]]],[[]]] => 2
[[[[[[]]]]],[[]]] => 1
[[[],[],[],[],[]],[]] => 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
[[[[[[[]]]]]],[]] => 1
[[[],[],[],[],[],[]]] => 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
[[[[],[]],[],[],[]]] => 2
[[[[[]]],[],[],[]]] => 2
[[[[],[]],[],[[]]]] => 2
[[[[[]]],[],[[]]]] => 2
[[[[],[]],[[]],[]]] => 2
[[[[[]]],[[]],[]]] => 2
[[[[],[]],[[],[]]]] => 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
[[[[[],[],[[]]]]]] => 2
[[[[[],[[]],[]]]]] => 2
[[[[[],[[],[]]]]]] => 2
[[[[[],[[[]]]]]]] => 2
[[[[[[]],[],[]]]]] => 2
[[[[[[]],[[]]]]]] => 2
[[[[[[],[]],[]]]]] => 2
[[[[[[[]]],[]]]]] => 2
[[[[[[],[],[]]]]]] => 2
[[[[[[],[[]]]]]]] => 2
[[[[[[[]],[]]]]]] => 2
[[[[[[[],[]]]]]]] => 2
[[[[[[[[]]]]]]]] => 1
[[],[],[],[],[],[],[],[]] => 1
[[],[],[],[],[],[],[[]]] => 1
[[],[],[],[],[],[[]],[]] => 1
[[],[],[],[],[],[[],[]]] => 2
[[],[],[],[],[],[[[]]]] => 1
[[],[],[],[],[[]],[],[]] => 1
[[],[],[],[],[[]],[[]]] => 1
[[],[],[],[],[[],[]],[]] => 2
[[],[],[],[],[[[]]],[]] => 1
[[],[],[],[],[[],[],[]]] => 2
[[],[],[],[],[[],[[]]]] => 2
[[],[],[],[],[[[]],[]]] => 2
[[],[],[],[],[[[],[]]]] => 2
[[],[],[],[],[[[[]]]]] => 1
[[],[],[],[[]],[],[],[]] => 1
[[],[],[],[[]],[],[[]]] => 1
[[],[],[],[[]],[[]],[]] => 1
[[],[],[],[[]],[[],[]]] => 2
[[],[],[],[[]],[[[]]]] => 1
[[],[],[],[[],[]],[],[]] => 2
[[],[],[],[[[]]],[],[]] => 1
[[],[],[],[[],[]],[[]]] => 2
[[],[],[],[[[]]],[[]]] => 1
[[],[],[],[[],[],[]],[]] => 2
[[],[],[],[[],[[]]],[]] => 2
[[],[],[],[[[]],[]],[]] => 2
[[],[],[],[[[],[]]],[]] => 2
[[],[],[],[[[[]]]],[]] => 1
[[],[],[],[[],[],[],[]]] => 2
[[],[],[],[[],[],[[]]]] => 2
[[],[],[],[[],[[]],[]]] => 2
[[],[],[],[[],[[],[]]]] => 2
[[],[],[],[[],[[[]]]]] => 2
[[],[],[],[[[]],[],[]]] => 2
[[],[],[],[[[]],[[]]]] => 2
[[],[],[],[[[],[]],[]]] => 2
[[],[],[],[[[[]]],[]]] => 2
[[],[],[],[[[],[],[]]]] => 2
[[],[],[],[[[],[[]]]]] => 2
[[],[],[],[[[[]],[]]]] => 2
[[],[],[],[[[[],[]]]]] => 2
[[],[],[],[[[[[]]]]]] => 1
[[],[],[[]],[],[],[],[]] => 1
[[],[],[[]],[],[],[[]]] => 1
[[],[],[[]],[],[[]],[]] => 1
[[],[],[[]],[],[[],[]]] => 2
[[],[],[[]],[],[[[]]]] => 1
[[],[],[[]],[[]],[],[]] => 1
[[],[],[[]],[[]],[[]]] => 1
[[],[],[[]],[[],[]],[]] => 2
[[],[],[[]],[[[]]],[]] => 1
[[],[],[[]],[[],[],[]]] => 2
[[],[],[[]],[[],[[]]]] => 2
[[],[],[[]],[[[]],[]]] => 2
[[],[],[[]],[[[],[]]]] => 2
[[],[],[[]],[[[[]]]]] => 1
[[],[],[[],[]],[],[],[]] => 2
[[],[],[[[]]],[],[],[]] => 1
[[],[],[[],[]],[],[[]]] => 2
[[],[],[[[]]],[],[[]]] => 1
[[],[],[[],[]],[[]],[]] => 2
[[],[],[[[]]],[[]],[]] => 1
[[],[],[[],[]],[[],[]]] => 2
[[],[],[[],[]],[[[]]]] => 2
[[],[],[[[]]],[[],[]]] => 2
[[],[],[[[]]],[[[]]]] => 1
[[],[],[[],[],[]],[],[]] => 2
[[],[],[[],[[]]],[],[]] => 2
[[],[],[[[]],[]],[],[]] => 2
[[],[],[[[],[]]],[],[]] => 2
[[],[],[[[[]]]],[],[]] => 1
[[],[],[[],[],[]],[[]]] => 2
[[],[],[[],[[]]],[[]]] => 2
[[],[],[[[]],[]],[[]]] => 2
[[],[],[[[],[]]],[[]]] => 2
[[],[],[[[[]]]],[[]]] => 1
[[],[],[[],[],[],[]],[]] => 2
[[],[],[[],[],[[]]],[]] => 2
[[],[],[[],[[]],[]],[]] => 2
[[],[],[[],[[],[]]],[]] => 2
[[],[],[[],[[[]]]],[]] => 2
[[],[],[[[]],[],[]],[]] => 2
[[],[],[[[]],[[]]],[]] => 2
[[],[],[[[],[]],[]],[]] => 2
[[],[],[[[[]]],[]],[]] => 2
[[],[],[[[],[],[]]],[]] => 2
[[],[],[[[],[[]]]],[]] => 2
[[],[],[[[[]],[]]],[]] => 2
[[],[],[[[[],[]]]],[]] => 2
[[],[],[[[[[]]]]],[]] => 1
[[],[],[[],[],[],[],[]]] => 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
[[],[],[[[[[[]]]]]]] => 1
[[],[[]],[],[],[],[],[]] => 1
[[],[[]],[],[],[],[[]]] => 1
[[],[[]],[],[],[[]],[]] => 1
[[],[[]],[],[],[[],[]]] => 2
[[],[[]],[],[],[[[]]]] => 1
[[],[[]],[],[[]],[],[]] => 1
[[],[[]],[],[[]],[[]]] => 1
[[],[[]],[],[[],[]],[]] => 2
[[],[[]],[],[[[]]],[]] => 1
[[],[[]],[],[[],[],[]]] => 2
[[],[[]],[],[[],[[]]]] => 2
[[],[[]],[],[[[]],[]]] => 2
[[],[[]],[],[[[],[]]]] => 2
[[],[[]],[],[[[[]]]]] => 1
[[],[[]],[[]],[],[],[]] => 1
[[],[[]],[[]],[],[[]]] => 1
[[],[[]],[[]],[[]],[]] => 1
[[],[[]],[[]],[[],[]]] => 2
[[],[[]],[[]],[[[]]]] => 1
[[],[[]],[[],[]],[],[]] => 2
[[],[[]],[[[]]],[],[]] => 1
[[],[[]],[[],[]],[[]]] => 2
[[],[[]],[[[]]],[[]]] => 1
[[],[[]],[[],[],[]],[]] => 2
[[],[[]],[[],[[]]],[]] => 2
[[],[[]],[[[]],[]],[]] => 2
[[],[[]],[[[],[]]],[]] => 2
[[],[[]],[[[[]]]],[]] => 1
[[],[[]],[[],[],[],[]]] => 2
[[],[[]],[[],[],[[]]]] => 2
[[],[[]],[[],[[]],[]]] => 2
[[],[[]],[[],[[],[]]]] => 2
[[],[[]],[[],[[[]]]]] => 2
[[],[[]],[[[]],[],[]]] => 2
[[],[[]],[[[]],[[]]]] => 2
[[],[[]],[[[],[]],[]]] => 2
[[],[[]],[[[[]]],[]]] => 2
[[],[[]],[[[],[],[]]]] => 2
[[],[[]],[[[],[[]]]]] => 2
[[],[[]],[[[[]],[]]]] => 2
[[],[[]],[[[[],[]]]]] => 2
[[],[[]],[[[[[]]]]]] => 1
[[],[[],[]],[],[],[],[]] => 2
[[],[[[]]],[],[],[],[]] => 1
[[],[[],[]],[],[],[[]]] => 2
[[],[[[]]],[],[],[[]]] => 1
[[],[[],[]],[],[[]],[]] => 2
[[],[[[]]],[],[[]],[]] => 1
[[],[[],[]],[],[[],[]]] => 2
[[],[[],[]],[],[[[]]]] => 2
[[],[[[]]],[],[[],[]]] => 2
[[],[[[]]],[],[[[]]]] => 1
[[],[[],[]],[[]],[],[]] => 2
[[],[[[]]],[[]],[],[]] => 1
[[],[[],[]],[[]],[[]]] => 2
[[],[[[]]],[[]],[[]]] => 1
[[],[[],[]],[[],[]],[]] => 2
[[],[[],[]],[[[]]],[]] => 2
[[],[[[]]],[[],[]],[]] => 2
[[],[[[]]],[[[]]],[]] => 1
[[],[[],[]],[[],[],[]]] => 2
[[],[[],[]],[[],[[]]]] => 2
[[],[[],[]],[[[]],[]]] => 2
[[],[[],[]],[[[],[]]]] => 2
[[],[[],[]],[[[[]]]]] => 2
[[],[[[]]],[[],[],[]]] => 2
[[],[[[]]],[[],[[]]]] => 2
[[],[[[]]],[[[]],[]]] => 2
[[],[[[]]],[[[],[]]]] => 2
[[],[[[]]],[[[[]]]]] => 1
[[],[[],[],[]],[],[],[]] => 2
[[],[[],[[]]],[],[],[]] => 2
[[],[[[]],[]],[],[],[]] => 2
[[],[[[],[]]],[],[],[]] => 2
[[],[[[[]]]],[],[],[]] => 1
[[],[[],[],[]],[],[[]]] => 2
[[],[[],[[]]],[],[[]]] => 2
[[],[[[]],[]],[],[[]]] => 2
[[],[[[],[]]],[],[[]]] => 2
[[],[[[[]]]],[],[[]]] => 1
[[],[[],[],[]],[[]],[]] => 2
[[],[[],[[]]],[[]],[]] => 2
[[],[[[]],[]],[[]],[]] => 2
[[],[[[],[]]],[[]],[]] => 2
[[],[[[[]]]],[[]],[]] => 1
[[],[[],[],[]],[[],[]]] => 2
[[],[[],[],[]],[[[]]]] => 2
[[],[[],[[]]],[[],[]]] => 2
[[],[[],[[]]],[[[]]]] => 2
[[],[[[]],[]],[[],[]]] => 2
[[],[[[]],[]],[[[]]]] => 2
[[],[[[],[]]],[[],[]]] => 2
[[],[[[],[]]],[[[]]]] => 2
[[],[[[[]]]],[[],[]]] => 2
[[],[[[[]]]],[[[]]]] => 1
[[],[[],[],[],[]],[],[]] => 2
[[],[[],[],[[]]],[],[]] => 2
[[],[[],[[]],[]],[],[]] => 2
[[],[[],[[],[]]],[],[]] => 2
[[],[[],[[[]]]],[],[]] => 2
[[],[[[]],[],[]],[],[]] => 2
[[],[[[]],[[]]],[],[]] => 2
[[],[[[],[]],[]],[],[]] => 2
[[],[[[[]]],[]],[],[]] => 2
[[],[[[],[],[]]],[],[]] => 2
[[],[[[],[[]]]],[],[]] => 2
[[],[[[[]],[]]],[],[]] => 2
[[],[[[[],[]]]],[],[]] => 2
[[],[[[[[]]]]],[],[]] => 1
[[],[[],[],[],[]],[[]]] => 2
[[],[[],[],[[]]],[[]]] => 2
[[],[[],[[]],[]],[[]]] => 2
[[],[[],[[],[]]],[[]]] => 2
[[],[[],[[[]]]],[[]]] => 2
[[],[[[]],[],[]],[[]]] => 2
[[],[[[]],[[]]],[[]]] => 2
[[],[[[],[]],[]],[[]]] => 2
[[],[[[[]]],[]],[[]]] => 2
[[],[[[],[],[]]],[[]]] => 2
[[],[[[],[[]]]],[[]]] => 2
[[],[[[[]],[]]],[[]]] => 2
[[],[[[[],[]]]],[[]]] => 2
[[],[[[[[]]]]],[[]]] => 1
[[],[[],[],[],[],[]],[]] => 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
[[],[[[[[[]]]]]],[]] => 1
[[],[[],[],[],[],[],[]]] => 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
[[],[[[],[]],[],[],[]]] => 2
[[],[[[[]]],[],[],[]]] => 2
[[],[[[],[]],[],[[]]]] => 2
[[],[[[[]]],[],[[]]]] => 2
[[],[[[],[]],[[]],[]]] => 2
[[],[[[[]]],[[]],[]]] => 2
[[],[[[],[]],[[],[]]]] => 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
[[],[[[[],[],[[]]]]]] => 2
[[],[[[[],[[]],[]]]]] => 2
[[],[[[[],[[],[]]]]]] => 2
[[],[[[[],[[[]]]]]]] => 2
[[],[[[[[]],[],[]]]]] => 2
[[],[[[[[]],[[]]]]]] => 2
[[],[[[[[],[]],[]]]]] => 2
[[],[[[[[[]]],[]]]]] => 2
[[],[[[[[],[],[]]]]]] => 2
[[],[[[[[],[[]]]]]]] => 2
[[],[[[[[[]],[]]]]]] => 2
[[],[[[[[[],[]]]]]]] => 2
[[],[[[[[[[]]]]]]]] => 1
[[[]],[],[],[],[],[],[]] => 1
[[[]],[],[],[],[],[[]]] => 1
[[[]],[],[],[],[[]],[]] => 1
[[[]],[],[],[],[[],[]]] => 2
[[[]],[],[],[],[[[]]]] => 1
[[[]],[],[],[[]],[],[]] => 1
[[[]],[],[],[[]],[[]]] => 1
[[[]],[],[],[[],[]],[]] => 2
[[[]],[],[],[[[]]],[]] => 1
[[[]],[],[],[[],[],[]]] => 2
[[[]],[],[],[[],[[]]]] => 2
[[[]],[],[],[[[]],[]]] => 2
[[[]],[],[],[[[],[]]]] => 2
[[[]],[],[],[[[[]]]]] => 1
[[[]],[],[[]],[],[],[]] => 1
[[[]],[],[[]],[],[[]]] => 1
[[[]],[],[[]],[[]],[]] => 1
[[[]],[],[[]],[[],[]]] => 2
[[[]],[],[[]],[[[]]]] => 1
[[[]],[],[[],[]],[],[]] => 2
[[[]],[],[[[]]],[],[]] => 1
[[[]],[],[[],[]],[[]]] => 2
[[[]],[],[[[]]],[[]]] => 1
[[[]],[],[[],[],[]],[]] => 2
[[[]],[],[[],[[]]],[]] => 2
[[[]],[],[[[]],[]],[]] => 2
[[[]],[],[[[],[]]],[]] => 2
[[[]],[],[[[[]]]],[]] => 1
[[[]],[],[[],[],[],[]]] => 2
[[[]],[],[[],[],[[]]]] => 2
[[[]],[],[[],[[]],[]]] => 2
[[[]],[],[[],[[],[]]]] => 2
[[[]],[],[[],[[[]]]]] => 2
[[[]],[],[[[]],[],[]]] => 2
[[[]],[],[[[]],[[]]]] => 2
[[[]],[],[[[],[]],[]]] => 2
[[[]],[],[[[[]]],[]]] => 2
[[[]],[],[[[],[],[]]]] => 2
[[[]],[],[[[],[[]]]]] => 2
[[[]],[],[[[[]],[]]]] => 2
[[[]],[],[[[[],[]]]]] => 2
[[[]],[],[[[[[]]]]]] => 1
[[[]],[[]],[],[],[],[]] => 1
[[[]],[[]],[],[],[[]]] => 1
[[[]],[[]],[],[[]],[]] => 1
[[[]],[[]],[],[[],[]]] => 2
[[[]],[[]],[],[[[]]]] => 1
[[[]],[[]],[[]],[],[]] => 1
[[[]],[[]],[[]],[[]]] => 1
[[[]],[[]],[[],[]],[]] => 2
[[[]],[[]],[[[]]],[]] => 1
[[[]],[[]],[[],[],[]]] => 2
[[[]],[[]],[[],[[]]]] => 2
[[[]],[[]],[[[]],[]]] => 2
[[[]],[[]],[[[],[]]]] => 2
[[[]],[[]],[[[[]]]]] => 1
[[[]],[[],[]],[],[],[]] => 2
[[[]],[[[]]],[],[],[]] => 1
[[[]],[[],[]],[],[[]]] => 2
[[[]],[[[]]],[],[[]]] => 1
[[[]],[[],[]],[[]],[]] => 2
[[[]],[[[]]],[[]],[]] => 1
[[[]],[[],[]],[[],[]]] => 2
[[[]],[[],[]],[[[]]]] => 2
[[[]],[[[]]],[[],[]]] => 2
[[[]],[[[]]],[[[]]]] => 1
[[[]],[[],[],[]],[],[]] => 2
[[[]],[[],[[]]],[],[]] => 2
[[[]],[[[]],[]],[],[]] => 2
[[[]],[[[],[]]],[],[]] => 2
[[[]],[[[[]]]],[],[]] => 1
[[[]],[[],[],[]],[[]]] => 2
[[[]],[[],[[]]],[[]]] => 2
[[[]],[[[]],[]],[[]]] => 2
[[[]],[[[],[]]],[[]]] => 2
[[[]],[[[[]]]],[[]]] => 1
[[[]],[[],[],[],[]],[]] => 2
[[[]],[[],[],[[]]],[]] => 2
[[[]],[[],[[]],[]],[]] => 2
[[[]],[[],[[],[]]],[]] => 2
[[[]],[[],[[[]]]],[]] => 2
[[[]],[[[]],[],[]],[]] => 2
[[[]],[[[]],[[]]],[]] => 2
[[[]],[[[],[]],[]],[]] => 2
[[[]],[[[[]]],[]],[]] => 2
[[[]],[[[],[],[]]],[]] => 2
[[[]],[[[],[[]]]],[]] => 2
[[[]],[[[[]],[]]],[]] => 2
[[[]],[[[[],[]]]],[]] => 2
[[[]],[[[[[]]]]],[]] => 1
[[[]],[[],[],[],[],[]]] => 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
[[[]],[[[[[[]]]]]]] => 1
[[[],[]],[],[],[],[],[]] => 2
[[[[]]],[],[],[],[],[]] => 1
[[[],[]],[],[],[],[[]]] => 2
[[[[]]],[],[],[],[[]]] => 1
[[[],[]],[],[],[[]],[]] => 2
[[[[]]],[],[],[[]],[]] => 1
[[[],[]],[],[],[[],[]]] => 2
[[[],[]],[],[],[[[]]]] => 2
[[[[]]],[],[],[[],[]]] => 2
[[[[]]],[],[],[[[]]]] => 1
[[[],[]],[],[[]],[],[]] => 2
[[[[]]],[],[[]],[],[]] => 1
[[[],[]],[],[[]],[[]]] => 2
[[[[]]],[],[[]],[[]]] => 1
-----------------------------------------------------------------------------
Created: Jan 03, 2017 at 00:09 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Jan 03, 2017 at 00:09 by Martin Rubey