***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * 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 ----------------------------------------------------------------------------- Created: Jun 02, 2016 at 09:37 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 02, 2016 at 09:37 by Martin Rubey