*****************************************************************************
*       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: St000522

-----------------------------------------------------------------------------
Collection: Ordered trees

-----------------------------------------------------------------------------
Description: The number of 1-protected nodes of a rooted tree.

This is the number of nodes with minimal distance one to a leaf.

-----------------------------------------------------------------------------
References: [1] 1  Copenhaver, K. $k$-protected vertices in unlabeled rooted plane trees [[arXiv:1606.00083]]

-----------------------------------------------------------------------------
Code:
def protection_aux(T, k):
    """Return the number of nodes whose minimal distance to a leaf is k
    and the minimal distance of the root to a leaf.

    """
    children = [protection_aux(t, k) for t in T]
    if len(children) == 0:
        if k == 0:
            return (1, 0)
        else:
            return (0, 0)

    kids = sum(num for num, _ in children)
    root = 1 + min(p for _, p in children)
    if root == k:
        return (1 + kids, root)
    else:
        return (kids, root)

def statistic(T):
    """Return the number of nodes whose minimal distance to a leaf is k"""
    return protection_aux(T, 1)[0]


-----------------------------------------------------------------------------
Statistic values:

[[]]                      => 1
[[],[]]                   => 1
[[[]]]                    => 1
[[],[],[]]                => 1
[[],[[]]]                 => 2
[[[]],[]]                 => 2
[[[],[]]]                 => 1
[[[[]]]]                  => 1
[[],[],[],[]]             => 1
[[],[],[[]]]              => 2
[[],[[]],[]]              => 2
[[],[[],[]]]              => 2
[[],[[[]]]]               => 2
[[[]],[],[]]              => 2
[[[]],[[]]]               => 2
[[[],[]],[]]              => 2
[[[[]]],[]]               => 2
[[[],[],[]]]              => 1
[[[],[[]]]]               => 2
[[[[]],[]]]               => 2
[[[[],[]]]]               => 1
[[[[[]]]]]                => 1
[[],[],[],[],[]]          => 1
[[],[],[],[[]]]           => 2
[[],[],[[]],[]]           => 2
[[],[],[[],[]]]           => 2
[[],[],[[[]]]]            => 2
[[],[[]],[],[]]           => 2
[[],[[]],[[]]]            => 3
[[],[[],[]],[]]           => 2
[[],[[[]]],[]]            => 2
[[],[[],[],[]]]           => 2
[[],[[],[[]]]]            => 3
[[],[[[]],[]]]            => 3
[[],[[[],[]]]]            => 2
[[],[[[[]]]]]             => 2
[[[]],[],[],[]]           => 2
[[[]],[],[[]]]            => 3
[[[]],[[]],[]]            => 3
[[[]],[[],[]]]            => 2
[[[]],[[[]]]]             => 2
[[[],[]],[],[]]           => 2
[[[[]]],[],[]]            => 2
[[[],[]],[[]]]            => 2
[[[[]]],[[]]]             => 2
[[[],[],[]],[]]           => 2
[[[],[[]]],[]]            => 3
[[[[]],[]],[]]            => 3
[[[[],[]]],[]]            => 2
[[[[[]]]],[]]             => 2
[[[],[],[],[]]]           => 1
[[[],[],[[]]]]            => 2
[[[],[[]],[]]]            => 2
[[[],[[],[]]]]            => 2
[[[],[[[]]]]]             => 2
[[[[]],[],[]]]            => 2
[[[[]],[[]]]]             => 2
[[[[],[]],[]]]            => 2
[[[[[]]],[]]]             => 2
[[[[],[],[]]]]            => 1
[[[[],[[]]]]]             => 2
[[[[[]],[]]]]             => 2
[[[[[],[]]]]]             => 1
[[[[[[]]]]]]              => 1
[[],[],[],[],[],[]]       => 1
[[],[],[],[],[[]]]        => 2
[[],[],[],[[]],[]]        => 2
[[],[],[],[[],[]]]        => 2
[[],[],[],[[[]]]]         => 2
[[],[],[[]],[],[]]        => 2
[[],[],[[]],[[]]]         => 3
[[],[],[[],[]],[]]        => 2
[[],[],[[[]]],[]]         => 2
[[],[],[[],[],[]]]        => 2
[[],[],[[],[[]]]]         => 3
[[],[],[[[]],[]]]         => 3
[[],[],[[[],[]]]]         => 2
[[],[],[[[[]]]]]          => 2
[[],[[]],[],[],[]]        => 2
[[],[[]],[],[[]]]         => 3
[[],[[]],[[]],[]]         => 3
[[],[[]],[[],[]]]         => 3
[[],[[]],[[[]]]]          => 3
[[],[[],[]],[],[]]        => 2
[[],[[[]]],[],[]]         => 2
[[],[[],[]],[[]]]         => 3
[[],[[[]]],[[]]]          => 3
[[],[[],[],[]],[]]        => 2
[[],[[],[[]]],[]]         => 3
[[],[[[]],[]],[]]         => 3
[[],[[[],[]]],[]]         => 2
[[],[[[[]]]],[]]          => 2
[[],[[],[],[],[]]]        => 2
[[],[[],[],[[]]]]         => 3
[[],[[],[[]],[]]]         => 3
[[],[[],[[],[]]]]         => 3
[[],[[],[[[]]]]]          => 3
[[],[[[]],[],[]]]         => 3
[[],[[[]],[[]]]]          => 3
[[],[[[],[]],[]]]         => 3
[[],[[[[]]],[]]]          => 3
[[],[[[],[],[]]]]         => 2
[[],[[[],[[]]]]]          => 3
[[],[[[[]],[]]]]          => 3
[[],[[[[],[]]]]]          => 2
[[],[[[[[]]]]]]           => 2
[[[]],[],[],[],[]]        => 2
[[[]],[],[],[[]]]         => 3
[[[]],[],[[]],[]]         => 3
[[[]],[],[[],[]]]         => 3
[[[]],[],[[[]]]]          => 3
[[[]],[[]],[],[]]         => 3
[[[]],[[]],[[]]]          => 3
[[[]],[[],[]],[]]         => 3
[[[]],[[[]]],[]]          => 3
[[[]],[[],[],[]]]         => 2
[[[]],[[],[[]]]]          => 3
[[[]],[[[]],[]]]          => 3
[[[]],[[[],[]]]]          => 2
[[[]],[[[[]]]]]           => 2
[[[],[]],[],[],[]]        => 2
[[[[]]],[],[],[]]         => 2
[[[],[]],[],[[]]]         => 3
[[[[]]],[],[[]]]          => 3
[[[],[]],[[]],[]]         => 3
[[[[]]],[[]],[]]          => 3
[[[],[]],[[],[]]]         => 2
[[[],[]],[[[]]]]          => 2
[[[[]]],[[],[]]]          => 2
[[[[]]],[[[]]]]           => 2
[[[],[],[]],[],[]]        => 2
[[[],[[]]],[],[]]         => 3
[[[[]],[]],[],[]]         => 3
[[[[],[]]],[],[]]         => 2
[[[[[]]]],[],[]]          => 2
[[[],[],[]],[[]]]         => 2
[[[],[[]]],[[]]]          => 3
[[[[]],[]],[[]]]          => 3
[[[[],[]]],[[]]]          => 2
[[[[[]]]],[[]]]           => 2
[[[],[],[],[]],[]]        => 2
[[[],[],[[]]],[]]         => 3
[[[],[[]],[]],[]]         => 3
[[[],[[],[]]],[]]         => 3
[[[],[[[]]]],[]]          => 3
[[[[]],[],[]],[]]         => 3
[[[[]],[[]]],[]]          => 3
[[[[],[]],[]],[]]         => 3
[[[[[]]],[]],[]]          => 3
[[[[],[],[]]],[]]         => 2
[[[[],[[]]]],[]]          => 3
[[[[[]],[]]],[]]          => 3
[[[[[],[]]]],[]]          => 2
[[[[[[]]]]],[]]           => 2
[[[],[],[],[],[]]]        => 1
[[[],[],[],[[]]]]         => 2
[[[],[],[[]],[]]]         => 2
[[[],[],[[],[]]]]         => 2
[[[],[],[[[]]]]]          => 2
[[[],[[]],[],[]]]         => 2
[[[],[[]],[[]]]]          => 3
[[[],[[],[]],[]]]         => 2
[[[],[[[]]],[]]]          => 2
[[[],[[],[],[]]]]         => 2
[[[],[[],[[]]]]]          => 3
[[[],[[[]],[]]]]          => 3
[[[],[[[],[]]]]]          => 2
[[[],[[[[]]]]]]           => 2
[[[[]],[],[],[]]]         => 2
[[[[]],[],[[]]]]          => 3
[[[[]],[[]],[]]]          => 3
[[[[]],[[],[]]]]          => 2
[[[[]],[[[]]]]]           => 2
[[[[],[]],[],[]]]         => 2
[[[[[]]],[],[]]]          => 2
[[[[],[]],[[]]]]          => 2
[[[[[]]],[[]]]]           => 2
[[[[],[],[]],[]]]         => 2
[[[[],[[]]],[]]]          => 3
[[[[[]],[]],[]]]          => 3
[[[[[],[]]],[]]]          => 2
[[[[[[]]]],[]]]           => 2
[[[[],[],[],[]]]]         => 1
[[[[],[],[[]]]]]          => 2
[[[[],[[]],[]]]]          => 2
[[[[],[[],[]]]]]          => 2
[[[[],[[[]]]]]]           => 2
[[[[[]],[],[]]]]          => 2
[[[[[]],[[]]]]]           => 2
[[[[[],[]],[]]]]          => 2
[[[[[[]]],[]]]]           => 2
[[[[[],[],[]]]]]          => 1
[[[[[],[[]]]]]]           => 2
[[[[[[]],[]]]]]           => 2
[[[[[[],[]]]]]]           => 1
[[[[[[[]]]]]]]            => 1
[[],[],[],[],[],[],[]]    => 1
[[],[],[],[],[],[[]]]     => 2
[[],[],[],[],[[]],[]]     => 2
[[],[],[],[],[[],[]]]     => 2
[[],[],[],[],[[[]]]]      => 2
[[],[],[],[[]],[],[]]     => 2
[[],[],[],[[]],[[]]]      => 3
[[],[],[],[[],[]],[]]     => 2
[[],[],[],[[[]]],[]]      => 2
[[],[],[],[[],[],[]]]     => 2
[[],[],[],[[],[[]]]]      => 3
[[],[],[],[[[]],[]]]      => 3
[[],[],[],[[[],[]]]]      => 2
[[],[],[],[[[[]]]]]       => 2
[[],[],[[]],[],[],[]]     => 2
[[],[],[[]],[],[[]]]      => 3
[[],[],[[]],[[]],[]]      => 3
[[],[],[[]],[[],[]]]      => 3
[[],[],[[]],[[[]]]]       => 3
[[],[],[[],[]],[],[]]     => 2
[[],[],[[[]]],[],[]]      => 2
[[],[],[[],[]],[[]]]      => 3
[[],[],[[[]]],[[]]]       => 3
[[],[],[[],[],[]],[]]     => 2
[[],[],[[],[[]]],[]]      => 3
[[],[],[[[]],[]],[]]      => 3
[[],[],[[[],[]]],[]]      => 2
[[],[],[[[[]]]],[]]       => 2
[[],[],[[],[],[],[]]]     => 2
[[],[],[[],[],[[]]]]      => 3
[[],[],[[],[[]],[]]]      => 3
[[],[],[[],[[],[]]]]      => 3
[[],[],[[],[[[]]]]]       => 3
[[],[],[[[]],[],[]]]      => 3
[[],[],[[[]],[[]]]]       => 3
[[],[],[[[],[]],[]]]      => 3
[[],[],[[[[]]],[]]]       => 3
[[],[],[[[],[],[]]]]      => 2
[[],[],[[[],[[]]]]]       => 3
[[],[],[[[[]],[]]]]       => 3
[[],[],[[[[],[]]]]]       => 2
[[],[],[[[[[]]]]]]        => 2
[[],[[]],[],[],[],[]]     => 2
[[],[[]],[],[],[[]]]      => 3
[[],[[]],[],[[]],[]]      => 3
[[],[[]],[],[[],[]]]      => 3
[[],[[]],[],[[[]]]]       => 3
[[],[[]],[[]],[],[]]      => 3
[[],[[]],[[]],[[]]]       => 4
[[],[[]],[[],[]],[]]      => 3
[[],[[]],[[[]]],[]]       => 3
[[],[[]],[[],[],[]]]      => 3
[[],[[]],[[],[[]]]]       => 4
[[],[[]],[[[]],[]]]       => 4
[[],[[]],[[[],[]]]]       => 3
[[],[[]],[[[[]]]]]        => 3
[[],[[],[]],[],[],[]]     => 2
[[],[[[]]],[],[],[]]      => 2
[[],[[],[]],[],[[]]]      => 3
[[],[[[]]],[],[[]]]       => 3
[[],[[],[]],[[]],[]]      => 3
[[],[[[]]],[[]],[]]       => 3
[[],[[],[]],[[],[]]]      => 3
[[],[[],[]],[[[]]]]       => 3
[[],[[[]]],[[],[]]]       => 3
[[],[[[]]],[[[]]]]        => 3
[[],[[],[],[]],[],[]]     => 2
[[],[[],[[]]],[],[]]      => 3
[[],[[[]],[]],[],[]]      => 3
[[],[[[],[]]],[],[]]      => 2
[[],[[[[]]]],[],[]]       => 2
[[],[[],[],[]],[[]]]      => 3
[[],[[],[[]]],[[]]]       => 4
[[],[[[]],[]],[[]]]       => 4
[[],[[[],[]]],[[]]]       => 3
[[],[[[[]]]],[[]]]        => 3
[[],[[],[],[],[]],[]]     => 2
[[],[[],[],[[]]],[]]      => 3
[[],[[],[[]],[]],[]]      => 3
[[],[[],[[],[]]],[]]      => 3
[[],[[],[[[]]]],[]]       => 3
[[],[[[]],[],[]],[]]      => 3
[[],[[[]],[[]]],[]]       => 3
[[],[[[],[]],[]],[]]      => 3
[[],[[[[]]],[]],[]]       => 3
[[],[[[],[],[]]],[]]      => 2
[[],[[[],[[]]]],[]]       => 3
[[],[[[[]],[]]],[]]       => 3
[[],[[[[],[]]]],[]]       => 2
[[],[[[[[]]]]],[]]        => 2
[[],[[],[],[],[],[]]]     => 2
[[],[[],[],[],[[]]]]      => 3
[[],[[],[],[[]],[]]]      => 3
[[],[[],[],[[],[]]]]      => 3
[[],[[],[],[[[]]]]]       => 3
[[],[[],[[]],[],[]]]      => 3
[[],[[],[[]],[[]]]]       => 4
[[],[[],[[],[]],[]]]      => 3
[[],[[],[[[]]],[]]]       => 3
[[],[[],[[],[],[]]]]      => 3
[[],[[],[[],[[]]]]]       => 4
[[],[[],[[[]],[]]]]       => 4
[[],[[],[[[],[]]]]]       => 3
[[],[[],[[[[]]]]]]        => 3
[[],[[[]],[],[],[]]]      => 3
[[],[[[]],[],[[]]]]       => 4
[[],[[[]],[[]],[]]]       => 4
[[],[[[]],[[],[]]]]       => 3
[[],[[[]],[[[]]]]]        => 3
[[],[[[],[]],[],[]]]      => 3
[[],[[[[]]],[],[]]]       => 3
[[],[[[],[]],[[]]]]       => 3
[[],[[[[]]],[[]]]]        => 3
[[],[[[],[],[]],[]]]      => 3
[[],[[[],[[]]],[]]]       => 4
[[],[[[[]],[]],[]]]       => 4
[[],[[[[],[]]],[]]]       => 3
[[],[[[[[]]]],[]]]        => 3
[[],[[[],[],[],[]]]]      => 2
[[],[[[],[],[[]]]]]       => 3
[[],[[[],[[]],[]]]]       => 3
[[],[[[],[[],[]]]]]       => 3
[[],[[[],[[[]]]]]]        => 3
[[],[[[[]],[],[]]]]       => 3
[[],[[[[]],[[]]]]]        => 3
[[],[[[[],[]],[]]]]       => 3
[[],[[[[[]]],[]]]]        => 3
[[],[[[[],[],[]]]]]       => 2
[[],[[[[],[[]]]]]]        => 3
[[],[[[[[]],[]]]]]        => 3
[[],[[[[[],[]]]]]]        => 2
[[],[[[[[[]]]]]]]         => 2
[[[]],[],[],[],[],[]]     => 2
[[[]],[],[],[],[[]]]      => 3
[[[]],[],[],[[]],[]]      => 3
[[[]],[],[],[[],[]]]      => 3
[[[]],[],[],[[[]]]]       => 3
[[[]],[],[[]],[],[]]      => 3
[[[]],[],[[]],[[]]]       => 4
[[[]],[],[[],[]],[]]      => 3
[[[]],[],[[[]]],[]]       => 3
[[[]],[],[[],[],[]]]      => 3
[[[]],[],[[],[[]]]]       => 4
[[[]],[],[[[]],[]]]       => 4
[[[]],[],[[[],[]]]]       => 3
[[[]],[],[[[[]]]]]        => 3
[[[]],[[]],[],[],[]]      => 3
[[[]],[[]],[],[[]]]       => 4
[[[]],[[]],[[]],[]]       => 4
[[[]],[[]],[[],[]]]       => 3
[[[]],[[]],[[[]]]]        => 3
[[[]],[[],[]],[],[]]      => 3
[[[]],[[[]]],[],[]]       => 3
[[[]],[[],[]],[[]]]       => 3
[[[]],[[[]]],[[]]]        => 3
[[[]],[[],[],[]],[]]      => 3
[[[]],[[],[[]]],[]]       => 4
[[[]],[[[]],[]],[]]       => 4
[[[]],[[[],[]]],[]]       => 3
[[[]],[[[[]]]],[]]        => 3
[[[]],[[],[],[],[]]]      => 2
[[[]],[[],[],[[]]]]       => 3
[[[]],[[],[[]],[]]]       => 3
[[[]],[[],[[],[]]]]       => 3
[[[]],[[],[[[]]]]]        => 3
[[[]],[[[]],[],[]]]       => 3
[[[]],[[[]],[[]]]]        => 3
[[[]],[[[],[]],[]]]       => 3
[[[]],[[[[]]],[]]]        => 3
[[[]],[[[],[],[]]]]       => 2
[[[]],[[[],[[]]]]]        => 3
[[[]],[[[[]],[]]]]        => 3
[[[]],[[[[],[]]]]]        => 2
[[[]],[[[[[]]]]]]         => 2
[[[],[]],[],[],[],[]]     => 2
[[[[]]],[],[],[],[]]      => 2
[[[],[]],[],[],[[]]]      => 3
[[[[]]],[],[],[[]]]       => 3
[[[],[]],[],[[]],[]]      => 3
[[[[]]],[],[[]],[]]       => 3
[[[],[]],[],[[],[]]]      => 3
[[[],[]],[],[[[]]]]       => 3
[[[[]]],[],[[],[]]]       => 3
[[[[]]],[],[[[]]]]        => 3
[[[],[]],[[]],[],[]]      => 3
[[[[]]],[[]],[],[]]       => 3
[[[],[]],[[]],[[]]]       => 3
[[[[]]],[[]],[[]]]        => 3
[[[],[]],[[],[]],[]]      => 3
[[[],[]],[[[]]],[]]       => 3
[[[[]]],[[],[]],[]]       => 3
[[[[]]],[[[]]],[]]        => 3
[[[],[]],[[],[],[]]]      => 2
[[[],[]],[[],[[]]]]       => 3
[[[],[]],[[[]],[]]]       => 3
[[[],[]],[[[],[]]]]       => 2
[[[],[]],[[[[]]]]]        => 2
[[[[]]],[[],[],[]]]       => 2
[[[[]]],[[],[[]]]]        => 3
[[[[]]],[[[]],[]]]        => 3
[[[[]]],[[[],[]]]]        => 2
[[[[]]],[[[[]]]]]         => 2
[[[],[],[]],[],[],[]]     => 2
[[[],[[]]],[],[],[]]      => 3
[[[[]],[]],[],[],[]]      => 3
[[[[],[]]],[],[],[]]      => 2
[[[[[]]]],[],[],[]]       => 2
[[[],[],[]],[],[[]]]      => 3
[[[],[[]]],[],[[]]]       => 4
[[[[]],[]],[],[[]]]       => 4
[[[[],[]]],[],[[]]]       => 3
[[[[[]]]],[],[[]]]        => 3
[[[],[],[]],[[]],[]]      => 3
[[[],[[]]],[[]],[]]       => 4
[[[[]],[]],[[]],[]]       => 4
[[[[],[]]],[[]],[]]       => 3
[[[[[]]]],[[]],[]]        => 3
[[[],[],[]],[[],[]]]      => 2
[[[],[],[]],[[[]]]]       => 2
[[[],[[]]],[[],[]]]       => 3
[[[],[[]]],[[[]]]]        => 3
[[[[]],[]],[[],[]]]       => 3
[[[[]],[]],[[[]]]]        => 3
[[[[],[]]],[[],[]]]       => 2
[[[[],[]]],[[[]]]]        => 2
[[[[[]]]],[[],[]]]        => 2
[[[[[]]]],[[[]]]]         => 2
[[[],[],[],[]],[],[]]     => 2
[[[],[],[[]]],[],[]]      => 3
[[[],[[]],[]],[],[]]      => 3
[[[],[[],[]]],[],[]]      => 3
[[[],[[[]]]],[],[]]       => 3
[[[[]],[],[]],[],[]]      => 3
[[[[]],[[]]],[],[]]       => 3
[[[[],[]],[]],[],[]]      => 3
[[[[[]]],[]],[],[]]       => 3
[[[[],[],[]]],[],[]]      => 2
[[[[],[[]]]],[],[]]       => 3
[[[[[]],[]]],[],[]]       => 3
[[[[[],[]]]],[],[]]       => 2
[[[[[[]]]]],[],[]]        => 2
[[[],[],[],[]],[[]]]      => 2
[[[],[],[[]]],[[]]]       => 3
[[[],[[]],[]],[[]]]       => 3
[[[],[[],[]]],[[]]]       => 3
[[[],[[[]]]],[[]]]        => 3
[[[[]],[],[]],[[]]]       => 3
[[[[]],[[]]],[[]]]        => 3
[[[[],[]],[]],[[]]]       => 3
[[[[[]]],[]],[[]]]        => 3
[[[[],[],[]]],[[]]]       => 2
[[[[],[[]]]],[[]]]        => 3
[[[[[]],[]]],[[]]]        => 3
[[[[[],[]]]],[[]]]        => 2
[[[[[[]]]]],[[]]]         => 2
[[[],[],[],[],[]],[]]     => 2
[[[],[],[],[[]]],[]]      => 3
[[[],[],[[]],[]],[]]      => 3
[[[],[],[[],[]]],[]]      => 3
[[[],[],[[[]]]],[]]       => 3
[[[],[[]],[],[]],[]]      => 3
[[[],[[]],[[]]],[]]       => 4
[[[],[[],[]],[]],[]]      => 3
[[[],[[[]]],[]],[]]       => 3
[[[],[[],[],[]]],[]]      => 3
[[[],[[],[[]]]],[]]       => 4
[[[],[[[]],[]]],[]]       => 4
[[[],[[[],[]]]],[]]       => 3
[[[],[[[[]]]]],[]]        => 3
[[[[]],[],[],[]],[]]      => 3
[[[[]],[],[[]]],[]]       => 4
[[[[]],[[]],[]],[]]       => 4
[[[[]],[[],[]]],[]]       => 3
[[[[]],[[[]]]],[]]        => 3
[[[[],[]],[],[]],[]]      => 3
[[[[[]]],[],[]],[]]       => 3
[[[[],[]],[[]]],[]]       => 3
[[[[[]]],[[]]],[]]        => 3
[[[[],[],[]],[]],[]]      => 3
[[[[],[[]]],[]],[]]       => 4
[[[[[]],[]],[]],[]]       => 4
[[[[[],[]]],[]],[]]       => 3
[[[[[[]]]],[]],[]]        => 3
[[[[],[],[],[]]],[]]      => 2
[[[[],[],[[]]]],[]]       => 3
[[[[],[[]],[]]],[]]       => 3
[[[[],[[],[]]]],[]]       => 3
[[[[],[[[]]]]],[]]        => 3
[[[[[]],[],[]]],[]]       => 3
[[[[[]],[[]]]],[]]        => 3
[[[[[],[]],[]]],[]]       => 3
[[[[[[]]],[]]],[]]        => 3
[[[[[],[],[]]]],[]]       => 2
[[[[[],[[]]]]],[]]        => 3
[[[[[[]],[]]]],[]]        => 3
[[[[[[],[]]]]],[]]        => 2
[[[[[[[]]]]]],[]]         => 2
[[[],[],[],[],[],[]]]     => 1
[[[],[],[],[],[[]]]]      => 2
[[[],[],[],[[]],[]]]      => 2
[[[],[],[],[[],[]]]]      => 2
[[[],[],[],[[[]]]]]       => 2
[[[],[],[[]],[],[]]]      => 2
[[[],[],[[]],[[]]]]       => 3
[[[],[],[[],[]],[]]]      => 2
[[[],[],[[[]]],[]]]       => 2
[[[],[],[[],[],[]]]]      => 2
[[[],[],[[],[[]]]]]       => 3
[[[],[],[[[]],[]]]]       => 3
[[[],[],[[[],[]]]]]       => 2
[[[],[],[[[[]]]]]]        => 2
[[[],[[]],[],[],[]]]      => 2
[[[],[[]],[],[[]]]]       => 3
[[[],[[]],[[]],[]]]       => 3
[[[],[[]],[[],[]]]]       => 3
[[[],[[]],[[[]]]]]        => 3
[[[],[[],[]],[],[]]]      => 2
[[[],[[[]]],[],[]]]       => 2
[[[],[[],[]],[[]]]]       => 3
[[[],[[[]]],[[]]]]        => 3
[[[],[[],[],[]],[]]]      => 2
[[[],[[],[[]]],[]]]       => 3
[[[],[[[]],[]],[]]]       => 3
[[[],[[[],[]]],[]]]       => 2
[[[],[[[[]]]],[]]]        => 2
[[[],[[],[],[],[]]]]      => 2
[[[],[[],[],[[]]]]]       => 3
[[[],[[],[[]],[]]]]       => 3
[[[],[[],[[],[]]]]]       => 3
[[[],[[],[[[]]]]]]        => 3
[[[],[[[]],[],[]]]]       => 3
[[[],[[[]],[[]]]]]        => 3
[[[],[[[],[]],[]]]]       => 3
[[[],[[[[]]],[]]]]        => 3
[[[],[[[],[],[]]]]]       => 2
[[[],[[[],[[]]]]]]        => 3
[[[],[[[[]],[]]]]]        => 3
[[[],[[[[],[]]]]]]        => 2
[[[],[[[[[]]]]]]]         => 2
[[[[]],[],[],[],[]]]      => 2
[[[[]],[],[],[[]]]]       => 3
[[[[]],[],[[]],[]]]       => 3
[[[[]],[],[[],[]]]]       => 3
[[[[]],[],[[[]]]]]        => 3
[[[[]],[[]],[],[]]]       => 3
[[[[]],[[]],[[]]]]        => 3
[[[[]],[[],[]],[]]]       => 3
[[[[]],[[[]]],[]]]        => 3
[[[[]],[[],[],[]]]]       => 2
[[[[]],[[],[[]]]]]        => 3
[[[[]],[[[]],[]]]]        => 3
[[[[]],[[[],[]]]]]        => 2
[[[[]],[[[[]]]]]]         => 2
[[[[],[]],[],[],[]]]      => 2
[[[[[]]],[],[],[]]]       => 2
[[[[],[]],[],[[]]]]       => 3
[[[[[]]],[],[[]]]]        => 3
[[[[],[]],[[]],[]]]       => 3
[[[[[]]],[[]],[]]]        => 3
[[[[],[]],[[],[]]]]       => 2
[[[[],[]],[[[]]]]]        => 2
[[[[[]]],[[],[]]]]        => 2
[[[[[]]],[[[]]]]]         => 2
[[[[],[],[]],[],[]]]      => 2
[[[[],[[]]],[],[]]]       => 3
[[[[[]],[]],[],[]]]       => 3
[[[[[],[]]],[],[]]]       => 2
[[[[[[]]]],[],[]]]        => 2
[[[[],[],[]],[[]]]]       => 2
[[[[],[[]]],[[]]]]        => 3
[[[[[]],[]],[[]]]]        => 3
[[[[[],[]]],[[]]]]        => 2
[[[[[[]]]],[[]]]]         => 2
[[[[],[],[],[]],[]]]      => 2
[[[[],[],[[]]],[]]]       => 3
[[[[],[[]],[]],[]]]       => 3
[[[[],[[],[]]],[]]]       => 3
[[[[],[[[]]]],[]]]        => 3
[[[[[]],[],[]],[]]]       => 3
[[[[[]],[[]]],[]]]        => 3
[[[[[],[]],[]],[]]]       => 3
[[[[[[]]],[]],[]]]        => 3
[[[[[],[],[]]],[]]]       => 2
[[[[[],[[]]]],[]]]        => 3
[[[[[[]],[]]],[]]]        => 3
[[[[[[],[]]]],[]]]        => 2
[[[[[[[]]]]],[]]]         => 2
[[[[],[],[],[],[]]]]      => 1
[[[[],[],[],[[]]]]]       => 2
[[[[],[],[[]],[]]]]       => 2
[[[[],[],[[],[]]]]]       => 2
[[[[],[],[[[]]]]]]        => 2
[[[[],[[]],[],[]]]]       => 2
[[[[],[[]],[[]]]]]        => 3
[[[[],[[],[]],[]]]]       => 2
[[[[],[[[]]],[]]]]        => 2
[[[[],[[],[],[]]]]]       => 2
[[[[],[[],[[]]]]]]        => 3
[[[[],[[[]],[]]]]]        => 3
[[[[],[[[],[]]]]]]        => 2
[[[[],[[[[]]]]]]]         => 2
[[[[[]],[],[],[]]]]       => 2
[[[[[]],[],[[]]]]]        => 3
[[[[[]],[[]],[]]]]        => 3
[[[[[]],[[],[]]]]]        => 2
[[[[[]],[[[]]]]]]         => 2
[[[[[],[]],[],[]]]]       => 2
[[[[[[]]],[],[]]]]        => 2
[[[[[],[]],[[]]]]]        => 2
[[[[[[]]],[[]]]]]         => 2
[[[[[],[],[]],[]]]]       => 2
[[[[[],[[]]],[]]]]        => 3
[[[[[[]],[]],[]]]]        => 3
[[[[[[],[]]],[]]]]        => 2
[[[[[[[]]]],[]]]]         => 2
[[[[[],[],[],[]]]]]       => 1
[[[[[],[],[[]]]]]]        => 2
[[[[[],[[]],[]]]]]        => 2
[[[[[],[[],[]]]]]]        => 2
[[[[[],[[[]]]]]]]         => 2
[[[[[[]],[],[]]]]]        => 2
[[[[[[]],[[]]]]]]         => 2
[[[[[[],[]],[]]]]]        => 2
[[[[[[[]]],[]]]]]         => 2
[[[[[[],[],[]]]]]]        => 1
[[[[[[],[[]]]]]]]         => 2
[[[[[[[]],[]]]]]]         => 2
[[[[[[[],[]]]]]]]         => 1
[[[[[[[[]]]]]]]]          => 1
[[],[],[],[],[],[],[],[]] => 1
[[],[],[],[],[],[],[[]]]  => 2
[[],[],[],[],[],[[]],[]]  => 2
[[],[],[],[],[],[[],[]]]  => 2
[[],[],[],[],[],[[[]]]]   => 2
[[],[],[],[],[[]],[],[]]  => 2
[[],[],[],[],[[]],[[]]]   => 3
[[],[],[],[],[[],[]],[]]  => 2
[[],[],[],[],[[[]]],[]]   => 2
[[],[],[],[],[[],[],[]]]  => 2
[[],[],[],[],[[],[[]]]]   => 3
[[],[],[],[],[[[]],[]]]   => 3
[[],[],[],[],[[[],[]]]]   => 2
[[],[],[],[],[[[[]]]]]    => 2
[[],[],[],[[]],[],[],[]]  => 2
[[],[],[],[[]],[],[[]]]   => 3
[[],[],[],[[]],[[]],[]]   => 3
[[],[],[],[[]],[[],[]]]   => 3
[[],[],[],[[]],[[[]]]]    => 3
[[],[],[],[[],[]],[],[]]  => 2
[[],[],[],[[[]]],[],[]]   => 2
[[],[],[],[[],[]],[[]]]   => 3
[[],[],[],[[[]]],[[]]]    => 3
[[],[],[],[[],[],[]],[]]  => 2
[[],[],[],[[],[[]]],[]]   => 3
[[],[],[],[[[]],[]],[]]   => 3
[[],[],[],[[[],[]]],[]]   => 2
[[],[],[],[[[[]]]],[]]    => 2
[[],[],[],[[],[],[],[]]]  => 2
[[],[],[],[[],[],[[]]]]   => 3
[[],[],[],[[],[[]],[]]]   => 3
[[],[],[],[[],[[],[]]]]   => 3
[[],[],[],[[],[[[]]]]]    => 3
[[],[],[],[[[]],[],[]]]   => 3
[[],[],[],[[[]],[[]]]]    => 3
[[],[],[],[[[],[]],[]]]   => 3
[[],[],[],[[[[]]],[]]]    => 3
[[],[],[],[[[],[],[]]]]   => 2
[[],[],[],[[[],[[]]]]]    => 3
[[],[],[],[[[[]],[]]]]    => 3
[[],[],[],[[[[],[]]]]]    => 2
[[],[],[],[[[[[]]]]]]     => 2
[[],[],[[]],[],[],[],[]]  => 2
[[],[],[[]],[],[],[[]]]   => 3
[[],[],[[]],[],[[]],[]]   => 3
[[],[],[[]],[],[[],[]]]   => 3
[[],[],[[]],[],[[[]]]]    => 3
[[],[],[[]],[[]],[],[]]   => 3
[[],[],[[]],[[]],[[]]]    => 4
[[],[],[[]],[[],[]],[]]   => 3
[[],[],[[]],[[[]]],[]]    => 3
[[],[],[[]],[[],[],[]]]   => 3
[[],[],[[]],[[],[[]]]]    => 4
[[],[],[[]],[[[]],[]]]    => 4
[[],[],[[]],[[[],[]]]]    => 3
[[],[],[[]],[[[[]]]]]     => 3
[[],[],[[],[]],[],[],[]]  => 2
[[],[],[[[]]],[],[],[]]   => 2
[[],[],[[],[]],[],[[]]]   => 3
[[],[],[[[]]],[],[[]]]    => 3
[[],[],[[],[]],[[]],[]]   => 3
[[],[],[[[]]],[[]],[]]    => 3
[[],[],[[],[]],[[],[]]]   => 3
[[],[],[[],[]],[[[]]]]    => 3
[[],[],[[[]]],[[],[]]]    => 3
[[],[],[[[]]],[[[]]]]     => 3
[[],[],[[],[],[]],[],[]]  => 2
[[],[],[[],[[]]],[],[]]   => 3
[[],[],[[[]],[]],[],[]]   => 3
[[],[],[[[],[]]],[],[]]   => 2
[[],[],[[[[]]]],[],[]]    => 2
[[],[],[[],[],[]],[[]]]   => 3
[[],[],[[],[[]]],[[]]]    => 4
[[],[],[[[]],[]],[[]]]    => 4
[[],[],[[[],[]]],[[]]]    => 3
[[],[],[[[[]]]],[[]]]     => 3
[[],[],[[],[],[],[]],[]]  => 2
[[],[],[[],[],[[]]],[]]   => 3
[[],[],[[],[[]],[]],[]]   => 3
[[],[],[[],[[],[]]],[]]   => 3
[[],[],[[],[[[]]]],[]]    => 3
[[],[],[[[]],[],[]],[]]   => 3
[[],[],[[[]],[[]]],[]]    => 3
[[],[],[[[],[]],[]],[]]   => 3
[[],[],[[[[]]],[]],[]]    => 3
[[],[],[[[],[],[]]],[]]   => 2
[[],[],[[[],[[]]]],[]]    => 3
[[],[],[[[[]],[]]],[]]    => 3
[[],[],[[[[],[]]]],[]]    => 2
[[],[],[[[[[]]]]],[]]     => 2
[[],[],[[],[],[],[],[]]]  => 2
[[],[],[[],[],[],[[]]]]   => 3
[[],[],[[],[],[[]],[]]]   => 3
[[],[],[[],[],[[],[]]]]   => 3
[[],[],[[],[],[[[]]]]]    => 3
[[],[],[[],[[]],[],[]]]   => 3
[[],[],[[],[[]],[[]]]]    => 4
[[],[],[[],[[],[]],[]]]   => 3
[[],[],[[],[[[]]],[]]]    => 3
[[],[],[[],[[],[],[]]]]   => 3
[[],[],[[],[[],[[]]]]]    => 4
[[],[],[[],[[[]],[]]]]    => 4
[[],[],[[],[[[],[]]]]]    => 3
[[],[],[[],[[[[]]]]]]     => 3
[[],[],[[[]],[],[],[]]]   => 3
[[],[],[[[]],[],[[]]]]    => 4
[[],[],[[[]],[[]],[]]]    => 4
[[],[],[[[]],[[],[]]]]    => 3
[[],[],[[[]],[[[]]]]]     => 3
[[],[],[[[],[]],[],[]]]   => 3
[[],[],[[[[]]],[],[]]]    => 3
[[],[],[[[],[]],[[]]]]    => 3
[[],[],[[[[]]],[[]]]]     => 3
[[],[],[[[],[],[]],[]]]   => 3
[[],[],[[[],[[]]],[]]]    => 4
[[],[],[[[[]],[]],[]]]    => 4
[[],[],[[[[],[]]],[]]]    => 3
[[],[],[[[[[]]]],[]]]     => 3
[[],[],[[[],[],[],[]]]]   => 2
[[],[],[[[],[],[[]]]]]    => 3
[[],[],[[[],[[]],[]]]]    => 3
[[],[],[[[],[[],[]]]]]    => 3
[[],[],[[[],[[[]]]]]]     => 3
[[],[],[[[[]],[],[]]]]    => 3
[[],[],[[[[]],[[]]]]]     => 3
[[],[],[[[[],[]],[]]]]    => 3
[[],[],[[[[[]]],[]]]]     => 3
[[],[],[[[[],[],[]]]]]    => 2
[[],[],[[[[],[[]]]]]]     => 3
[[],[],[[[[[]],[]]]]]     => 3
[[],[],[[[[[],[]]]]]]     => 2
[[],[],[[[[[[]]]]]]]      => 2
[[],[[]],[],[],[],[],[]]  => 2
[[],[[]],[],[],[],[[]]]   => 3
[[],[[]],[],[],[[]],[]]   => 3
[[],[[]],[],[],[[],[]]]   => 3
[[],[[]],[],[],[[[]]]]    => 3
[[],[[]],[],[[]],[],[]]   => 3
[[],[[]],[],[[]],[[]]]    => 4
[[],[[]],[],[[],[]],[]]   => 3
[[],[[]],[],[[[]]],[]]    => 3
[[],[[]],[],[[],[],[]]]   => 3
[[],[[]],[],[[],[[]]]]    => 4
[[],[[]],[],[[[]],[]]]    => 4
[[],[[]],[],[[[],[]]]]    => 3
[[],[[]],[],[[[[]]]]]     => 3
[[],[[]],[[]],[],[],[]]   => 3
[[],[[]],[[]],[],[[]]]    => 4
[[],[[]],[[]],[[]],[]]    => 4
[[],[[]],[[]],[[],[]]]    => 4
[[],[[]],[[]],[[[]]]]     => 4
[[],[[]],[[],[]],[],[]]   => 3
[[],[[]],[[[]]],[],[]]    => 3
[[],[[]],[[],[]],[[]]]    => 4
[[],[[]],[[[]]],[[]]]     => 4
[[],[[]],[[],[],[]],[]]   => 3
[[],[[]],[[],[[]]],[]]    => 4
[[],[[]],[[[]],[]],[]]    => 4
[[],[[]],[[[],[]]],[]]    => 3
[[],[[]],[[[[]]]],[]]     => 3
[[],[[]],[[],[],[],[]]]   => 3
[[],[[]],[[],[],[[]]]]    => 4
[[],[[]],[[],[[]],[]]]    => 4
[[],[[]],[[],[[],[]]]]    => 4
[[],[[]],[[],[[[]]]]]     => 4
[[],[[]],[[[]],[],[]]]    => 4
[[],[[]],[[[]],[[]]]]     => 4
[[],[[]],[[[],[]],[]]]    => 4
[[],[[]],[[[[]]],[]]]     => 4
[[],[[]],[[[],[],[]]]]    => 3
[[],[[]],[[[],[[]]]]]     => 4
[[],[[]],[[[[]],[]]]]     => 4
[[],[[]],[[[[],[]]]]]     => 3
[[],[[]],[[[[[]]]]]]      => 3
[[],[[],[]],[],[],[],[]]  => 2
[[],[[[]]],[],[],[],[]]   => 2
[[],[[],[]],[],[],[[]]]   => 3
[[],[[[]]],[],[],[[]]]    => 3
[[],[[],[]],[],[[]],[]]   => 3
[[],[[[]]],[],[[]],[]]    => 3
[[],[[],[]],[],[[],[]]]   => 3
[[],[[],[]],[],[[[]]]]    => 3
[[],[[[]]],[],[[],[]]]    => 3
[[],[[[]]],[],[[[]]]]     => 3
[[],[[],[]],[[]],[],[]]   => 3
[[],[[[]]],[[]],[],[]]    => 3
[[],[[],[]],[[]],[[]]]    => 4
[[],[[[]]],[[]],[[]]]     => 4
[[],[[],[]],[[],[]],[]]   => 3
[[],[[],[]],[[[]]],[]]    => 3
[[],[[[]]],[[],[]],[]]    => 3
[[],[[[]]],[[[]]],[]]     => 3
[[],[[],[]],[[],[],[]]]   => 3
[[],[[],[]],[[],[[]]]]    => 4
[[],[[],[]],[[[]],[]]]    => 4
[[],[[],[]],[[[],[]]]]    => 3
[[],[[],[]],[[[[]]]]]     => 3
[[],[[[]]],[[],[],[]]]    => 3
[[],[[[]]],[[],[[]]]]     => 4
[[],[[[]]],[[[]],[]]]     => 4
[[],[[[]]],[[[],[]]]]     => 3
[[],[[[]]],[[[[]]]]]      => 3
[[],[[],[],[]],[],[],[]]  => 2
[[],[[],[[]]],[],[],[]]   => 3
[[],[[[]],[]],[],[],[]]   => 3
[[],[[[],[]]],[],[],[]]   => 2
[[],[[[[]]]],[],[],[]]    => 2
[[],[[],[],[]],[],[[]]]   => 3
[[],[[],[[]]],[],[[]]]    => 4
[[],[[[]],[]],[],[[]]]    => 4
[[],[[[],[]]],[],[[]]]    => 3
[[],[[[[]]]],[],[[]]]     => 3
[[],[[],[],[]],[[]],[]]   => 3
[[],[[],[[]]],[[]],[]]    => 4
[[],[[[]],[]],[[]],[]]    => 4
[[],[[[],[]]],[[]],[]]    => 3
[[],[[[[]]]],[[]],[]]     => 3
[[],[[],[],[]],[[],[]]]   => 3
[[],[[],[],[]],[[[]]]]    => 3
[[],[[],[[]]],[[],[]]]    => 4
[[],[[],[[]]],[[[]]]]     => 4
[[],[[[]],[]],[[],[]]]    => 4
[[],[[[]],[]],[[[]]]]     => 4
[[],[[[],[]]],[[],[]]]    => 3
[[],[[[],[]]],[[[]]]]     => 3
[[],[[[[]]]],[[],[]]]     => 3
[[],[[[[]]]],[[[]]]]      => 3
[[],[[],[],[],[]],[],[]]  => 2
[[],[[],[],[[]]],[],[]]   => 3
[[],[[],[[]],[]],[],[]]   => 3
[[],[[],[[],[]]],[],[]]   => 3
[[],[[],[[[]]]],[],[]]    => 3
[[],[[[]],[],[]],[],[]]   => 3
[[],[[[]],[[]]],[],[]]    => 3
[[],[[[],[]],[]],[],[]]   => 3
[[],[[[[]]],[]],[],[]]    => 3
[[],[[[],[],[]]],[],[]]   => 2
[[],[[[],[[]]]],[],[]]    => 3
[[],[[[[]],[]]],[],[]]    => 3
[[],[[[[],[]]]],[],[]]    => 2
[[],[[[[[]]]]],[],[]]     => 2
[[],[[],[],[],[]],[[]]]   => 3
[[],[[],[],[[]]],[[]]]    => 4
[[],[[],[[]],[]],[[]]]    => 4
[[],[[],[[],[]]],[[]]]    => 4
[[],[[],[[[]]]],[[]]]     => 4
[[],[[[]],[],[]],[[]]]    => 4
[[],[[[]],[[]]],[[]]]     => 4
[[],[[[],[]],[]],[[]]]    => 4
[[],[[[[]]],[]],[[]]]     => 4
[[],[[[],[],[]]],[[]]]    => 3
[[],[[[],[[]]]],[[]]]     => 4
[[],[[[[]],[]]],[[]]]     => 4
[[],[[[[],[]]]],[[]]]     => 3
[[],[[[[[]]]]],[[]]]      => 3
[[],[[],[],[],[],[]],[]]  => 2
[[],[[],[],[],[[]]],[]]   => 3
[[],[[],[],[[]],[]],[]]   => 3
[[],[[],[],[[],[]]],[]]   => 3
[[],[[],[],[[[]]]],[]]    => 3
[[],[[],[[]],[],[]],[]]   => 3
[[],[[],[[]],[[]]],[]]    => 4
[[],[[],[[],[]],[]],[]]   => 3
[[],[[],[[[]]],[]],[]]    => 3
[[],[[],[[],[],[]]],[]]   => 3
[[],[[],[[],[[]]]],[]]    => 4
[[],[[],[[[]],[]]],[]]    => 4
[[],[[],[[[],[]]]],[]]    => 3
[[],[[],[[[[]]]]],[]]     => 3
[[],[[[]],[],[],[]],[]]   => 3
[[],[[[]],[],[[]]],[]]    => 4
[[],[[[]],[[]],[]],[]]    => 4
[[],[[[]],[[],[]]],[]]    => 3
[[],[[[]],[[[]]]],[]]     => 3
[[],[[[],[]],[],[]],[]]   => 3
[[],[[[[]]],[],[]],[]]    => 3
[[],[[[],[]],[[]]],[]]    => 3
[[],[[[[]]],[[]]],[]]     => 3
[[],[[[],[],[]],[]],[]]   => 3
[[],[[[],[[]]],[]],[]]    => 4
[[],[[[[]],[]],[]],[]]    => 4
[[],[[[[],[]]],[]],[]]    => 3
[[],[[[[[]]]],[]],[]]     => 3
[[],[[[],[],[],[]]],[]]   => 2
[[],[[[],[],[[]]]],[]]    => 3
[[],[[[],[[]],[]]],[]]    => 3
[[],[[[],[[],[]]]],[]]    => 3
[[],[[[],[[[]]]]],[]]     => 3
[[],[[[[]],[],[]]],[]]    => 3
[[],[[[[]],[[]]]],[]]     => 3
[[],[[[[],[]],[]]],[]]    => 3
[[],[[[[[]]],[]]],[]]     => 3
[[],[[[[],[],[]]]],[]]    => 2
[[],[[[[],[[]]]]],[]]     => 3
[[],[[[[[]],[]]]],[]]     => 3
[[],[[[[[],[]]]]],[]]     => 2
[[],[[[[[[]]]]]],[]]      => 2
[[],[[],[],[],[],[],[]]]  => 2
[[],[[],[],[],[],[[]]]]   => 3
[[],[[],[],[],[[]],[]]]   => 3
[[],[[],[],[],[[],[]]]]   => 3
[[],[[],[],[],[[[]]]]]    => 3
[[],[[],[],[[]],[],[]]]   => 3
[[],[[],[],[[]],[[]]]]    => 4
[[],[[],[],[[],[]],[]]]   => 3
[[],[[],[],[[[]]],[]]]    => 3
[[],[[],[],[[],[],[]]]]   => 3
[[],[[],[],[[],[[]]]]]    => 4
[[],[[],[],[[[]],[]]]]    => 4
[[],[[],[],[[[],[]]]]]    => 3
[[],[[],[],[[[[]]]]]]     => 3
[[],[[],[[]],[],[],[]]]   => 3
[[],[[],[[]],[],[[]]]]    => 4
[[],[[],[[]],[[]],[]]]    => 4
[[],[[],[[]],[[],[]]]]    => 4
[[],[[],[[]],[[[]]]]]     => 4
[[],[[],[[],[]],[],[]]]   => 3
[[],[[],[[[]]],[],[]]]    => 3
[[],[[],[[],[]],[[]]]]    => 4
[[],[[],[[[]]],[[]]]]     => 4
[[],[[],[[],[],[]],[]]]   => 3
[[],[[],[[],[[]]],[]]]    => 4
[[],[[],[[[]],[]],[]]]    => 4
[[],[[],[[[],[]]],[]]]    => 3
[[],[[],[[[[]]]],[]]]     => 3
[[],[[],[[],[],[],[]]]]   => 3
[[],[[],[[],[],[[]]]]]    => 4
[[],[[],[[],[[]],[]]]]    => 4
[[],[[],[[],[[],[]]]]]    => 4
[[],[[],[[],[[[]]]]]]     => 4
[[],[[],[[[]],[],[]]]]    => 4
[[],[[],[[[]],[[]]]]]     => 4
[[],[[],[[[],[]],[]]]]    => 4
[[],[[],[[[[]]],[]]]]     => 4
[[],[[],[[[],[],[]]]]]    => 3
[[],[[],[[[],[[]]]]]]     => 4
[[],[[],[[[[]],[]]]]]     => 4
[[],[[],[[[[],[]]]]]]     => 3
[[],[[],[[[[[]]]]]]]      => 3
[[],[[[]],[],[],[],[]]]   => 3
[[],[[[]],[],[],[[]]]]    => 4
[[],[[[]],[],[[]],[]]]    => 4
[[],[[[]],[],[[],[]]]]    => 4
[[],[[[]],[],[[[]]]]]     => 4
[[],[[[]],[[]],[],[]]]    => 4
[[],[[[]],[[]],[[]]]]     => 4
[[],[[[]],[[],[]],[]]]    => 4
[[],[[[]],[[[]]],[]]]     => 4
[[],[[[]],[[],[],[]]]]    => 3
[[],[[[]],[[],[[]]]]]     => 4
[[],[[[]],[[[]],[]]]]     => 4
[[],[[[]],[[[],[]]]]]     => 3
[[],[[[]],[[[[]]]]]]      => 3
[[],[[[],[]],[],[],[]]]   => 3
[[],[[[[]]],[],[],[]]]    => 3
[[],[[[],[]],[],[[]]]]    => 4
[[],[[[[]]],[],[[]]]]     => 4
[[],[[[],[]],[[]],[]]]    => 4
[[],[[[[]]],[[]],[]]]     => 4
[[],[[[],[]],[[],[]]]]    => 3
[[],[[[],[]],[[[]]]]]     => 3
[[],[[[[]]],[[],[]]]]     => 3
[[],[[[[]]],[[[]]]]]      => 3
[[],[[[],[],[]],[],[]]]   => 3
[[],[[[],[[]]],[],[]]]    => 4
[[],[[[[]],[]],[],[]]]    => 4
[[],[[[[],[]]],[],[]]]    => 3
[[],[[[[[]]]],[],[]]]     => 3
[[],[[[],[],[]],[[]]]]    => 3
[[],[[[],[[]]],[[]]]]     => 4
[[],[[[[]],[]],[[]]]]     => 4
[[],[[[[],[]]],[[]]]]     => 3
[[],[[[[[]]]],[[]]]]      => 3
[[],[[[],[],[],[]],[]]]   => 3
[[],[[[],[],[[]]],[]]]    => 4
[[],[[[],[[]],[]],[]]]    => 4
[[],[[[],[[],[]]],[]]]    => 4
[[],[[[],[[[]]]],[]]]     => 4
[[],[[[[]],[],[]],[]]]    => 4
[[],[[[[]],[[]]],[]]]     => 4
[[],[[[[],[]],[]],[]]]    => 4
[[],[[[[[]]],[]],[]]]     => 4
[[],[[[[],[],[]]],[]]]    => 3
[[],[[[[],[[]]]],[]]]     => 4
[[],[[[[[]],[]]],[]]]     => 4
[[],[[[[[],[]]]],[]]]     => 3
[[],[[[[[[]]]]],[]]]      => 3
[[],[[[],[],[],[],[]]]]   => 2
[[],[[[],[],[],[[]]]]]    => 3
[[],[[[],[],[[]],[]]]]    => 3
[[],[[[],[],[[],[]]]]]    => 3
[[],[[[],[],[[[]]]]]]     => 3
[[],[[[],[[]],[],[]]]]    => 3
[[],[[[],[[]],[[]]]]]     => 4
[[],[[[],[[],[]],[]]]]    => 3
[[],[[[],[[[]]],[]]]]     => 3
[[],[[[],[[],[],[]]]]]    => 3
[[],[[[],[[],[[]]]]]]     => 4
[[],[[[],[[[]],[]]]]]     => 4
[[],[[[],[[[],[]]]]]]     => 3
[[],[[[],[[[[]]]]]]]      => 3
[[],[[[[]],[],[],[]]]]    => 3
[[],[[[[]],[],[[]]]]]     => 4
[[],[[[[]],[[]],[]]]]     => 4
[[],[[[[]],[[],[]]]]]     => 3
[[],[[[[]],[[[]]]]]]      => 3
[[],[[[[],[]],[],[]]]]    => 3
[[],[[[[[]]],[],[]]]]     => 3
[[],[[[[],[]],[[]]]]]     => 3
[[],[[[[[]]],[[]]]]]      => 3
[[],[[[[],[],[]],[]]]]    => 3
[[],[[[[],[[]]],[]]]]     => 4
[[],[[[[[]],[]],[]]]]     => 4
[[],[[[[[],[]]],[]]]]     => 3
[[],[[[[[[]]]],[]]]]      => 3
[[],[[[[],[],[],[]]]]]    => 2
[[],[[[[],[],[[]]]]]]     => 3
[[],[[[[],[[]],[]]]]]     => 3
[[],[[[[],[[],[]]]]]]     => 3
[[],[[[[],[[[]]]]]]]      => 3
[[],[[[[[]],[],[]]]]]     => 3
[[],[[[[[]],[[]]]]]]      => 3
[[],[[[[[],[]],[]]]]]     => 3
[[],[[[[[[]]],[]]]]]      => 3
[[],[[[[[],[],[]]]]]]     => 2
[[],[[[[[],[[]]]]]]]      => 3
[[],[[[[[[]],[]]]]]]      => 3
[[],[[[[[[],[]]]]]]]      => 2
[[],[[[[[[[]]]]]]]]       => 2
[[[]],[],[],[],[],[],[]]  => 2
[[[]],[],[],[],[],[[]]]   => 3
[[[]],[],[],[],[[]],[]]   => 3
[[[]],[],[],[],[[],[]]]   => 3
[[[]],[],[],[],[[[]]]]    => 3
[[[]],[],[],[[]],[],[]]   => 3
[[[]],[],[],[[]],[[]]]    => 4
[[[]],[],[],[[],[]],[]]   => 3
[[[]],[],[],[[[]]],[]]    => 3
[[[]],[],[],[[],[],[]]]   => 3
[[[]],[],[],[[],[[]]]]    => 4
[[[]],[],[],[[[]],[]]]    => 4
[[[]],[],[],[[[],[]]]]    => 3
[[[]],[],[],[[[[]]]]]     => 3
[[[]],[],[[]],[],[],[]]   => 3
[[[]],[],[[]],[],[[]]]    => 4
[[[]],[],[[]],[[]],[]]    => 4
[[[]],[],[[]],[[],[]]]    => 4
[[[]],[],[[]],[[[]]]]     => 4
[[[]],[],[[],[]],[],[]]   => 3
[[[]],[],[[[]]],[],[]]    => 3
[[[]],[],[[],[]],[[]]]    => 4
[[[]],[],[[[]]],[[]]]     => 4
[[[]],[],[[],[],[]],[]]   => 3
[[[]],[],[[],[[]]],[]]    => 4
[[[]],[],[[[]],[]],[]]    => 4
[[[]],[],[[[],[]]],[]]    => 3
[[[]],[],[[[[]]]],[]]     => 3
[[[]],[],[[],[],[],[]]]   => 3
[[[]],[],[[],[],[[]]]]    => 4
[[[]],[],[[],[[]],[]]]    => 4
[[[]],[],[[],[[],[]]]]    => 4
[[[]],[],[[],[[[]]]]]     => 4
[[[]],[],[[[]],[],[]]]    => 4
[[[]],[],[[[]],[[]]]]     => 4
[[[]],[],[[[],[]],[]]]    => 4
[[[]],[],[[[[]]],[]]]     => 4
[[[]],[],[[[],[],[]]]]    => 3
[[[]],[],[[[],[[]]]]]     => 4
[[[]],[],[[[[]],[]]]]     => 4
[[[]],[],[[[[],[]]]]]     => 3
[[[]],[],[[[[[]]]]]]      => 3
[[[]],[[]],[],[],[],[]]   => 3
[[[]],[[]],[],[],[[]]]    => 4
[[[]],[[]],[],[[]],[]]    => 4
[[[]],[[]],[],[[],[]]]    => 4
[[[]],[[]],[],[[[]]]]     => 4
[[[]],[[]],[[]],[],[]]    => 4
[[[]],[[]],[[]],[[]]]     => 4
[[[]],[[]],[[],[]],[]]    => 4
[[[]],[[]],[[[]]],[]]     => 4
[[[]],[[]],[[],[],[]]]    => 3
[[[]],[[]],[[],[[]]]]     => 4
[[[]],[[]],[[[]],[]]]     => 4
[[[]],[[]],[[[],[]]]]     => 3
[[[]],[[]],[[[[]]]]]      => 3
[[[]],[[],[]],[],[],[]]   => 3
[[[]],[[[]]],[],[],[]]    => 3
[[[]],[[],[]],[],[[]]]    => 4
[[[]],[[[]]],[],[[]]]     => 4
[[[]],[[],[]],[[]],[]]    => 4
[[[]],[[[]]],[[]],[]]     => 4
[[[]],[[],[]],[[],[]]]    => 3
[[[]],[[],[]],[[[]]]]     => 3
[[[]],[[[]]],[[],[]]]     => 3
[[[]],[[[]]],[[[]]]]      => 3
[[[]],[[],[],[]],[],[]]   => 3
[[[]],[[],[[]]],[],[]]    => 4
[[[]],[[[]],[]],[],[]]    => 4
[[[]],[[[],[]]],[],[]]    => 3
[[[]],[[[[]]]],[],[]]     => 3
[[[]],[[],[],[]],[[]]]    => 3
[[[]],[[],[[]]],[[]]]     => 4
[[[]],[[[]],[]],[[]]]     => 4
[[[]],[[[],[]]],[[]]]     => 3
[[[]],[[[[]]]],[[]]]      => 3
[[[]],[[],[],[],[]],[]]   => 3
[[[]],[[],[],[[]]],[]]    => 4
[[[]],[[],[[]],[]],[]]    => 4
[[[]],[[],[[],[]]],[]]    => 4
[[[]],[[],[[[]]]],[]]     => 4
[[[]],[[[]],[],[]],[]]    => 4
[[[]],[[[]],[[]]],[]]     => 4
[[[]],[[[],[]],[]],[]]    => 4
[[[]],[[[[]]],[]],[]]     => 4
[[[]],[[[],[],[]]],[]]    => 3
[[[]],[[[],[[]]]],[]]     => 4
[[[]],[[[[]],[]]],[]]     => 4
[[[]],[[[[],[]]]],[]]     => 3
[[[]],[[[[[]]]]],[]]      => 3
[[[]],[[],[],[],[],[]]]   => 2
[[[]],[[],[],[],[[]]]]    => 3
[[[]],[[],[],[[]],[]]]    => 3
[[[]],[[],[],[[],[]]]]    => 3
[[[]],[[],[],[[[]]]]]     => 3
[[[]],[[],[[]],[],[]]]    => 3
[[[]],[[],[[]],[[]]]]     => 4
[[[]],[[],[[],[]],[]]]    => 3
[[[]],[[],[[[]]],[]]]     => 3
[[[]],[[],[[],[],[]]]]    => 3
[[[]],[[],[[],[[]]]]]     => 4
[[[]],[[],[[[]],[]]]]     => 4
[[[]],[[],[[[],[]]]]]     => 3
[[[]],[[],[[[[]]]]]]      => 3
[[[]],[[[]],[],[],[]]]    => 3
[[[]],[[[]],[],[[]]]]     => 4
[[[]],[[[]],[[]],[]]]     => 4
[[[]],[[[]],[[],[]]]]     => 3
[[[]],[[[]],[[[]]]]]      => 3
[[[]],[[[],[]],[],[]]]    => 3
[[[]],[[[[]]],[],[]]]     => 3
[[[]],[[[],[]],[[]]]]     => 3
[[[]],[[[[]]],[[]]]]      => 3
[[[]],[[[],[],[]],[]]]    => 3
[[[]],[[[],[[]]],[]]]     => 4
[[[]],[[[[]],[]],[]]]     => 4
[[[]],[[[[],[]]],[]]]     => 3
[[[]],[[[[[]]]],[]]]      => 3
[[[]],[[[],[],[],[]]]]    => 2
[[[]],[[[],[],[[]]]]]     => 3
[[[]],[[[],[[]],[]]]]     => 3
[[[]],[[[],[[],[]]]]]     => 3
[[[]],[[[],[[[]]]]]]      => 3
[[[]],[[[[]],[],[]]]]     => 3
[[[]],[[[[]],[[]]]]]      => 3
[[[]],[[[[],[]],[]]]]     => 3
[[[]],[[[[[]]],[]]]]      => 3
[[[]],[[[[],[],[]]]]]     => 2
[[[]],[[[[],[[]]]]]]      => 3
[[[]],[[[[[]],[]]]]]      => 3
[[[]],[[[[[],[]]]]]]      => 2
[[[]],[[[[[[]]]]]]]       => 2
[[[],[]],[],[],[],[],[]]  => 2
[[[[]]],[],[],[],[],[]]   => 2
[[[],[]],[],[],[],[[]]]   => 3
[[[[]]],[],[],[],[[]]]    => 3
[[[],[]],[],[],[[]],[]]   => 3
[[[[]]],[],[],[[]],[]]    => 3
[[[],[]],[],[],[[],[]]]   => 3
[[[],[]],[],[],[[[]]]]    => 3
[[[[]]],[],[],[[],[]]]    => 3
[[[[]]],[],[],[[[]]]]     => 3
[[[],[]],[],[[]],[],[]]   => 3
[[[[]]],[],[[]],[],[]]    => 3
[[[],[]],[],[[]],[[]]]    => 4
[[[[]]],[],[[]],[[]]]     => 4

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Created: Jun 02, 2016 at 09:37 by Martin Rubey

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Last Updated: Jun 02, 2016 at 09:37 by Martin Rubey