***************************************************************************** * 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: St000521 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The number of distinct subtrees of an ordered tree. A subtree is specified by a node of the tree. Thus, the tree consisting of a single path has as many subtrees as nodes, whereas the tree of height two, having all leaves attached to the root, has only two distinct subtrees. Because we consider ordered trees, the tree $[[[[]], []], [[], [[]]]]$ on nine nodes has five distinct subtrees. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(T): return len(set(T.subtrees())) ----------------------------------------------------------------------------- Statistic values: [[]] => 2 [[],[]] => 2 [[[]]] => 3 [[],[],[]] => 2 [[],[[]]] => 3 [[[]],[]] => 3 [[[],[]]] => 3 [[[[]]]] => 4 [[],[],[],[]] => 2 [[],[],[[]]] => 3 [[],[[]],[]] => 3 [[],[[],[]]] => 3 [[],[[[]]]] => 4 [[[]],[],[]] => 3 [[[]],[[]]] => 3 [[[],[]],[]] => 3 [[[[]]],[]] => 4 [[[],[],[]]] => 3 [[[],[[]]]] => 4 [[[[]],[]]] => 4 [[[[],[]]]] => 4 [[[[[]]]]] => 5 [[],[],[],[],[]] => 2 [[],[],[],[[]]] => 3 [[],[],[[]],[]] => 3 [[],[],[[],[]]] => 3 [[],[],[[[]]]] => 4 [[],[[]],[],[]] => 3 [[],[[]],[[]]] => 3 [[],[[],[]],[]] => 3 [[],[[[]]],[]] => 4 [[],[[],[],[]]] => 3 [[],[[],[[]]]] => 4 [[],[[[]],[]]] => 4 [[],[[[],[]]]] => 4 [[],[[[[]]]]] => 5 [[[]],[],[],[]] => 3 [[[]],[],[[]]] => 3 [[[]],[[]],[]] => 3 [[[]],[[],[]]] => 4 [[[]],[[[]]]] => 4 [[[],[]],[],[]] => 3 [[[[]]],[],[]] => 4 [[[],[]],[[]]] => 4 [[[[]]],[[]]] => 4 [[[],[],[]],[]] => 3 [[[],[[]]],[]] => 4 [[[[]],[]],[]] => 4 [[[[],[]]],[]] => 4 [[[[[]]]],[]] => 5 [[[],[],[],[]]] => 3 [[[],[],[[]]]] => 4 [[[],[[]],[]]] => 4 [[[],[[],[]]]] => 4 [[[],[[[]]]]] => 5 [[[[]],[],[]]] => 4 [[[[]],[[]]]] => 4 [[[[],[]],[]]] => 4 [[[[[]]],[]]] => 5 [[[[],[],[]]]] => 4 [[[[],[[]]]]] => 5 [[[[[]],[]]]] => 5 [[[[[],[]]]]] => 5 [[[[[[]]]]]] => 6 [[],[],[],[],[],[]] => 2 [[],[],[],[],[[]]] => 3 [[],[],[],[[]],[]] => 3 [[],[],[],[[],[]]] => 3 [[],[],[],[[[]]]] => 4 [[],[],[[]],[],[]] => 3 [[],[],[[]],[[]]] => 3 [[],[],[[],[]],[]] => 3 [[],[],[[[]]],[]] => 4 [[],[],[[],[],[]]] => 3 [[],[],[[],[[]]]] => 4 [[],[],[[[]],[]]] => 4 [[],[],[[[],[]]]] => 4 [[],[],[[[[]]]]] => 5 [[],[[]],[],[],[]] => 3 [[],[[]],[],[[]]] => 3 [[],[[]],[[]],[]] => 3 [[],[[]],[[],[]]] => 4 [[],[[]],[[[]]]] => 4 [[],[[],[]],[],[]] => 3 [[],[[[]]],[],[]] => 4 [[],[[],[]],[[]]] => 4 [[],[[[]]],[[]]] => 4 [[],[[],[],[]],[]] => 3 [[],[[],[[]]],[]] => 4 [[],[[[]],[]],[]] => 4 [[],[[[],[]]],[]] => 4 [[],[[[[]]]],[]] => 5 [[],[[],[],[],[]]] => 3 [[],[[],[],[[]]]] => 4 [[],[[],[[]],[]]] => 4 [[],[[],[[],[]]]] => 4 [[],[[],[[[]]]]] => 5 [[],[[[]],[],[]]] => 4 [[],[[[]],[[]]]] => 4 [[],[[[],[]],[]]] => 4 [[],[[[[]]],[]]] => 5 [[],[[[],[],[]]]] => 4 [[],[[[],[[]]]]] => 5 [[],[[[[]],[]]]] => 5 [[],[[[[],[]]]]] => 5 [[],[[[[[]]]]]] => 6 [[[]],[],[],[],[]] => 3 [[[]],[],[],[[]]] => 3 [[[]],[],[[]],[]] => 3 [[[]],[],[[],[]]] => 4 [[[]],[],[[[]]]] => 4 [[[]],[[]],[],[]] => 3 [[[]],[[]],[[]]] => 3 [[[]],[[],[]],[]] => 4 [[[]],[[[]]],[]] => 4 [[[]],[[],[],[]]] => 4 [[[]],[[],[[]]]] => 4 [[[]],[[[]],[]]] => 4 [[[]],[[[],[]]]] => 5 [[[]],[[[[]]]]] => 5 [[[],[]],[],[],[]] => 3 [[[[]]],[],[],[]] => 4 [[[],[]],[],[[]]] => 4 [[[[]]],[],[[]]] => 4 [[[],[]],[[]],[]] => 4 [[[[]]],[[]],[]] => 4 [[[],[]],[[],[]]] => 3 [[[],[]],[[[]]]] => 5 [[[[]]],[[],[]]] => 5 [[[[]]],[[[]]]] => 4 [[[],[],[]],[],[]] => 3 [[[],[[]]],[],[]] => 4 [[[[]],[]],[],[]] => 4 [[[[],[]]],[],[]] => 4 [[[[[]]]],[],[]] => 5 [[[],[],[]],[[]]] => 4 [[[],[[]]],[[]]] => 4 [[[[]],[]],[[]]] => 4 [[[[],[]]],[[]]] => 5 [[[[[]]]],[[]]] => 5 [[[],[],[],[]],[]] => 3 [[[],[],[[]]],[]] => 4 [[[],[[]],[]],[]] => 4 [[[],[[],[]]],[]] => 4 [[[],[[[]]]],[]] => 5 [[[[]],[],[]],[]] => 4 [[[[]],[[]]],[]] => 4 [[[[],[]],[]],[]] => 4 [[[[[]]],[]],[]] => 5 [[[[],[],[]]],[]] => 4 [[[[],[[]]]],[]] => 5 [[[[[]],[]]],[]] => 5 [[[[[],[]]]],[]] => 5 [[[[[[]]]]],[]] => 6 [[[],[],[],[],[]]] => 3 [[[],[],[],[[]]]] => 4 [[[],[],[[]],[]]] => 4 [[[],[],[[],[]]]] => 4 [[[],[],[[[]]]]] => 5 [[[],[[]],[],[]]] => 4 [[[],[[]],[[]]]] => 4 [[[],[[],[]],[]]] => 4 [[[],[[[]]],[]]] => 5 [[[],[[],[],[]]]] => 4 [[[],[[],[[]]]]] => 5 [[[],[[[]],[]]]] => 5 [[[],[[[],[]]]]] => 5 [[[],[[[[]]]]]] => 6 [[[[]],[],[],[]]] => 4 [[[[]],[],[[]]]] => 4 [[[[]],[[]],[]]] => 4 [[[[]],[[],[]]]] => 5 [[[[]],[[[]]]]] => 5 [[[[],[]],[],[]]] => 4 [[[[[]]],[],[]]] => 5 [[[[],[]],[[]]]] => 5 [[[[[]]],[[]]]] => 5 [[[[],[],[]],[]]] => 4 [[[[],[[]]],[]]] => 5 [[[[[]],[]],[]]] => 5 [[[[[],[]]],[]]] => 5 [[[[[[]]]],[]]] => 6 [[[[],[],[],[]]]] => 4 [[[[],[],[[]]]]] => 5 [[[[],[[]],[]]]] => 5 [[[[],[[],[]]]]] => 5 [[[[],[[[]]]]]] => 6 [[[[[]],[],[]]]] => 5 [[[[[]],[[]]]]] => 5 [[[[[],[]],[]]]] => 5 [[[[[[]]],[]]]] => 6 [[[[[],[],[]]]]] => 5 [[[[[],[[]]]]]] => 6 [[[[[[]],[]]]]] => 6 [[[[[[],[]]]]]] => 6 [[[[[[[]]]]]]] => 7 [[],[],[],[],[],[],[]] => 2 [[],[],[],[],[],[[]]] => 3 [[],[],[],[],[[]],[]] => 3 [[],[],[],[],[[],[]]] => 3 [[],[],[],[],[[[]]]] => 4 [[],[],[],[[]],[],[]] => 3 [[],[],[],[[]],[[]]] => 3 [[],[],[],[[],[]],[]] => 3 [[],[],[],[[[]]],[]] => 4 [[],[],[],[[],[],[]]] => 3 [[],[],[],[[],[[]]]] => 4 [[],[],[],[[[]],[]]] => 4 [[],[],[],[[[],[]]]] => 4 [[],[],[],[[[[]]]]] => 5 [[],[],[[]],[],[],[]] => 3 [[],[],[[]],[],[[]]] => 3 [[],[],[[]],[[]],[]] => 3 [[],[],[[]],[[],[]]] => 4 [[],[],[[]],[[[]]]] => 4 [[],[],[[],[]],[],[]] => 3 [[],[],[[[]]],[],[]] => 4 [[],[],[[],[]],[[]]] => 4 [[],[],[[[]]],[[]]] => 4 [[],[],[[],[],[]],[]] => 3 [[],[],[[],[[]]],[]] => 4 [[],[],[[[]],[]],[]] => 4 [[],[],[[[],[]]],[]] => 4 [[],[],[[[[]]]],[]] => 5 [[],[],[[],[],[],[]]] => 3 [[],[],[[],[],[[]]]] => 4 [[],[],[[],[[]],[]]] => 4 [[],[],[[],[[],[]]]] => 4 [[],[],[[],[[[]]]]] => 5 [[],[],[[[]],[],[]]] => 4 [[],[],[[[]],[[]]]] => 4 [[],[],[[[],[]],[]]] => 4 [[],[],[[[[]]],[]]] => 5 [[],[],[[[],[],[]]]] => 4 [[],[],[[[],[[]]]]] => 5 [[],[],[[[[]],[]]]] => 5 [[],[],[[[[],[]]]]] => 5 [[],[],[[[[[]]]]]] => 6 [[],[[]],[],[],[],[]] => 3 [[],[[]],[],[],[[]]] => 3 [[],[[]],[],[[]],[]] => 3 [[],[[]],[],[[],[]]] => 4 [[],[[]],[],[[[]]]] => 4 [[],[[]],[[]],[],[]] => 3 [[],[[]],[[]],[[]]] => 3 [[],[[]],[[],[]],[]] => 4 [[],[[]],[[[]]],[]] => 4 [[],[[]],[[],[],[]]] => 4 [[],[[]],[[],[[]]]] => 4 [[],[[]],[[[]],[]]] => 4 [[],[[]],[[[],[]]]] => 5 [[],[[]],[[[[]]]]] => 5 [[],[[],[]],[],[],[]] => 3 [[],[[[]]],[],[],[]] => 4 [[],[[],[]],[],[[]]] => 4 [[],[[[]]],[],[[]]] => 4 [[],[[],[]],[[]],[]] => 4 [[],[[[]]],[[]],[]] => 4 [[],[[],[]],[[],[]]] => 3 [[],[[],[]],[[[]]]] => 5 [[],[[[]]],[[],[]]] => 5 [[],[[[]]],[[[]]]] => 4 [[],[[],[],[]],[],[]] => 3 [[],[[],[[]]],[],[]] => 4 [[],[[[]],[]],[],[]] => 4 [[],[[[],[]]],[],[]] => 4 [[],[[[[]]]],[],[]] => 5 [[],[[],[],[]],[[]]] => 4 [[],[[],[[]]],[[]]] => 4 [[],[[[]],[]],[[]]] => 4 [[],[[[],[]]],[[]]] => 5 [[],[[[[]]]],[[]]] => 5 [[],[[],[],[],[]],[]] => 3 [[],[[],[],[[]]],[]] => 4 [[],[[],[[]],[]],[]] => 4 [[],[[],[[],[]]],[]] => 4 [[],[[],[[[]]]],[]] => 5 [[],[[[]],[],[]],[]] => 4 [[],[[[]],[[]]],[]] => 4 [[],[[[],[]],[]],[]] => 4 [[],[[[[]]],[]],[]] => 5 [[],[[[],[],[]]],[]] => 4 [[],[[[],[[]]]],[]] => 5 [[],[[[[]],[]]],[]] => 5 [[],[[[[],[]]]],[]] => 5 [[],[[[[[]]]]],[]] => 6 [[],[[],[],[],[],[]]] => 3 [[],[[],[],[],[[]]]] => 4 [[],[[],[],[[]],[]]] => 4 [[],[[],[],[[],[]]]] => 4 [[],[[],[],[[[]]]]] => 5 [[],[[],[[]],[],[]]] => 4 [[],[[],[[]],[[]]]] => 4 [[],[[],[[],[]],[]]] => 4 [[],[[],[[[]]],[]]] => 5 [[],[[],[[],[],[]]]] => 4 [[],[[],[[],[[]]]]] => 5 [[],[[],[[[]],[]]]] => 5 [[],[[],[[[],[]]]]] => 5 [[],[[],[[[[]]]]]] => 6 [[],[[[]],[],[],[]]] => 4 [[],[[[]],[],[[]]]] => 4 [[],[[[]],[[]],[]]] => 4 [[],[[[]],[[],[]]]] => 5 [[],[[[]],[[[]]]]] => 5 [[],[[[],[]],[],[]]] => 4 [[],[[[[]]],[],[]]] => 5 [[],[[[],[]],[[]]]] => 5 [[],[[[[]]],[[]]]] => 5 [[],[[[],[],[]],[]]] => 4 [[],[[[],[[]]],[]]] => 5 [[],[[[[]],[]],[]]] => 5 [[],[[[[],[]]],[]]] => 5 [[],[[[[[]]]],[]]] => 6 [[],[[[],[],[],[]]]] => 4 [[],[[[],[],[[]]]]] => 5 [[],[[[],[[]],[]]]] => 5 [[],[[[],[[],[]]]]] => 5 [[],[[[],[[[]]]]]] => 6 [[],[[[[]],[],[]]]] => 5 [[],[[[[]],[[]]]]] => 5 [[],[[[[],[]],[]]]] => 5 [[],[[[[[]]],[]]]] => 6 [[],[[[[],[],[]]]]] => 5 [[],[[[[],[[]]]]]] => 6 [[],[[[[[]],[]]]]] => 6 [[],[[[[[],[]]]]]] => 6 [[],[[[[[[]]]]]]] => 7 [[[]],[],[],[],[],[]] => 3 [[[]],[],[],[],[[]]] => 3 [[[]],[],[],[[]],[]] => 3 [[[]],[],[],[[],[]]] => 4 [[[]],[],[],[[[]]]] => 4 [[[]],[],[[]],[],[]] => 3 [[[]],[],[[]],[[]]] => 3 [[[]],[],[[],[]],[]] => 4 [[[]],[],[[[]]],[]] => 4 [[[]],[],[[],[],[]]] => 4 [[[]],[],[[],[[]]]] => 4 [[[]],[],[[[]],[]]] => 4 [[[]],[],[[[],[]]]] => 5 [[[]],[],[[[[]]]]] => 5 [[[]],[[]],[],[],[]] => 3 [[[]],[[]],[],[[]]] => 3 [[[]],[[]],[[]],[]] => 3 [[[]],[[]],[[],[]]] => 4 [[[]],[[]],[[[]]]] => 4 [[[]],[[],[]],[],[]] => 4 [[[]],[[[]]],[],[]] => 4 [[[]],[[],[]],[[]]] => 4 [[[]],[[[]]],[[]]] => 4 [[[]],[[],[],[]],[]] => 4 [[[]],[[],[[]]],[]] => 4 [[[]],[[[]],[]],[]] => 4 [[[]],[[[],[]]],[]] => 5 [[[]],[[[[]]]],[]] => 5 [[[]],[[],[],[],[]]] => 4 [[[]],[[],[],[[]]]] => 4 [[[]],[[],[[]],[]]] => 4 [[[]],[[],[[],[]]]] => 5 [[[]],[[],[[[]]]]] => 5 [[[]],[[[]],[],[]]] => 4 [[[]],[[[]],[[]]]] => 4 [[[]],[[[],[]],[]]] => 5 [[[]],[[[[]]],[]]] => 5 [[[]],[[[],[],[]]]] => 5 [[[]],[[[],[[]]]]] => 5 [[[]],[[[[]],[]]]] => 5 [[[]],[[[[],[]]]]] => 6 [[[]],[[[[[]]]]]] => 6 [[[],[]],[],[],[],[]] => 3 [[[[]]],[],[],[],[]] => 4 [[[],[]],[],[],[[]]] => 4 [[[[]]],[],[],[[]]] => 4 [[[],[]],[],[[]],[]] => 4 [[[[]]],[],[[]],[]] => 4 [[[],[]],[],[[],[]]] => 3 [[[],[]],[],[[[]]]] => 5 [[[[]]],[],[[],[]]] => 5 [[[[]]],[],[[[]]]] => 4 [[[],[]],[[]],[],[]] => 4 [[[[]]],[[]],[],[]] => 4 [[[],[]],[[]],[[]]] => 4 [[[[]]],[[]],[[]]] => 4 [[[],[]],[[],[]],[]] => 3 [[[],[]],[[[]]],[]] => 5 [[[[]]],[[],[]],[]] => 5 [[[[]]],[[[]]],[]] => 4 [[[],[]],[[],[],[]]] => 4 [[[],[]],[[],[[]]]] => 5 [[[],[]],[[[]],[]]] => 5 [[[],[]],[[[],[]]]] => 4 [[[],[]],[[[[]]]]] => 6 [[[[]]],[[],[],[]]] => 5 [[[[]]],[[],[[]]]] => 5 [[[[]]],[[[]],[]]] => 5 [[[[]]],[[[],[]]]] => 6 [[[[]]],[[[[]]]]] => 5 [[[],[],[]],[],[],[]] => 3 [[[],[[]]],[],[],[]] => 4 [[[[]],[]],[],[],[]] => 4 [[[[],[]]],[],[],[]] => 4 [[[[[]]]],[],[],[]] => 5 [[[],[],[]],[],[[]]] => 4 [[[],[[]]],[],[[]]] => 4 [[[[]],[]],[],[[]]] => 4 [[[[],[]]],[],[[]]] => 5 [[[[[]]]],[],[[]]] => 5 [[[],[],[]],[[]],[]] => 4 [[[],[[]]],[[]],[]] => 4 [[[[]],[]],[[]],[]] => 4 [[[[],[]]],[[]],[]] => 5 [[[[[]]]],[[]],[]] => 5 [[[],[],[]],[[],[]]] => 4 [[[],[],[]],[[[]]]] => 5 [[[],[[]]],[[],[]]] => 5 [[[],[[]]],[[[]]]] => 5 [[[[]],[]],[[],[]]] => 5 [[[[]],[]],[[[]]]] => 5 [[[[],[]]],[[],[]]] => 4 [[[[],[]]],[[[]]]] => 6 [[[[[]]]],[[],[]]] => 6 [[[[[]]]],[[[]]]] => 5 [[[],[],[],[]],[],[]] => 3 [[[],[],[[]]],[],[]] => 4 [[[],[[]],[]],[],[]] => 4 [[[],[[],[]]],[],[]] => 4 [[[],[[[]]]],[],[]] => 5 [[[[]],[],[]],[],[]] => 4 [[[[]],[[]]],[],[]] => 4 [[[[],[]],[]],[],[]] => 4 [[[[[]]],[]],[],[]] => 5 [[[[],[],[]]],[],[]] => 4 [[[[],[[]]]],[],[]] => 5 [[[[[]],[]]],[],[]] => 5 [[[[[],[]]]],[],[]] => 5 [[[[[[]]]]],[],[]] => 6 [[[],[],[],[]],[[]]] => 4 [[[],[],[[]]],[[]]] => 4 [[[],[[]],[]],[[]]] => 4 [[[],[[],[]]],[[]]] => 5 [[[],[[[]]]],[[]]] => 5 [[[[]],[],[]],[[]]] => 4 [[[[]],[[]]],[[]]] => 4 [[[[],[]],[]],[[]]] => 5 [[[[[]]],[]],[[]]] => 5 [[[[],[],[]]],[[]]] => 5 [[[[],[[]]]],[[]]] => 5 [[[[[]],[]]],[[]]] => 5 [[[[[],[]]]],[[]]] => 6 [[[[[[]]]]],[[]]] => 6 [[[],[],[],[],[]],[]] => 3 [[[],[],[],[[]]],[]] => 4 [[[],[],[[]],[]],[]] => 4 [[[],[],[[],[]]],[]] => 4 [[[],[],[[[]]]],[]] => 5 [[[],[[]],[],[]],[]] => 4 [[[],[[]],[[]]],[]] => 4 [[[],[[],[]],[]],[]] => 4 [[[],[[[]]],[]],[]] => 5 [[[],[[],[],[]]],[]] => 4 [[[],[[],[[]]]],[]] => 5 [[[],[[[]],[]]],[]] => 5 [[[],[[[],[]]]],[]] => 5 [[[],[[[[]]]]],[]] => 6 [[[[]],[],[],[]],[]] => 4 [[[[]],[],[[]]],[]] => 4 [[[[]],[[]],[]],[]] => 4 [[[[]],[[],[]]],[]] => 5 [[[[]],[[[]]]],[]] => 5 [[[[],[]],[],[]],[]] => 4 [[[[[]]],[],[]],[]] => 5 [[[[],[]],[[]]],[]] => 5 [[[[[]]],[[]]],[]] => 5 [[[[],[],[]],[]],[]] => 4 [[[[],[[]]],[]],[]] => 5 [[[[[]],[]],[]],[]] => 5 [[[[[],[]]],[]],[]] => 5 [[[[[[]]]],[]],[]] => 6 [[[[],[],[],[]]],[]] => 4 [[[[],[],[[]]]],[]] => 5 [[[[],[[]],[]]],[]] => 5 [[[[],[[],[]]]],[]] => 5 [[[[],[[[]]]]],[]] => 6 [[[[[]],[],[]]],[]] => 5 [[[[[]],[[]]]],[]] => 5 [[[[[],[]],[]]],[]] => 5 [[[[[[]]],[]]],[]] => 6 [[[[[],[],[]]]],[]] => 5 [[[[[],[[]]]]],[]] => 6 [[[[[[]],[]]]],[]] => 6 [[[[[[],[]]]]],[]] => 6 [[[[[[[]]]]]],[]] => 7 [[[],[],[],[],[],[]]] => 3 [[[],[],[],[],[[]]]] => 4 [[[],[],[],[[]],[]]] => 4 [[[],[],[],[[],[]]]] => 4 [[[],[],[],[[[]]]]] => 5 [[[],[],[[]],[],[]]] => 4 [[[],[],[[]],[[]]]] => 4 [[[],[],[[],[]],[]]] => 4 [[[],[],[[[]]],[]]] => 5 [[[],[],[[],[],[]]]] => 4 [[[],[],[[],[[]]]]] => 5 [[[],[],[[[]],[]]]] => 5 [[[],[],[[[],[]]]]] => 5 [[[],[],[[[[]]]]]] => 6 [[[],[[]],[],[],[]]] => 4 [[[],[[]],[],[[]]]] => 4 [[[],[[]],[[]],[]]] => 4 [[[],[[]],[[],[]]]] => 5 [[[],[[]],[[[]]]]] => 5 [[[],[[],[]],[],[]]] => 4 [[[],[[[]]],[],[]]] => 5 [[[],[[],[]],[[]]]] => 5 [[[],[[[]]],[[]]]] => 5 [[[],[[],[],[]],[]]] => 4 [[[],[[],[[]]],[]]] => 5 [[[],[[[]],[]],[]]] => 5 [[[],[[[],[]]],[]]] => 5 [[[],[[[[]]]],[]]] => 6 [[[],[[],[],[],[]]]] => 4 [[[],[[],[],[[]]]]] => 5 [[[],[[],[[]],[]]]] => 5 [[[],[[],[[],[]]]]] => 5 [[[],[[],[[[]]]]]] => 6 [[[],[[[]],[],[]]]] => 5 [[[],[[[]],[[]]]]] => 5 [[[],[[[],[]],[]]]] => 5 [[[],[[[[]]],[]]]] => 6 [[[],[[[],[],[]]]]] => 5 [[[],[[[],[[]]]]]] => 6 [[[],[[[[]],[]]]]] => 6 [[[],[[[[],[]]]]]] => 6 [[[],[[[[[]]]]]]] => 7 [[[[]],[],[],[],[]]] => 4 [[[[]],[],[],[[]]]] => 4 [[[[]],[],[[]],[]]] => 4 [[[[]],[],[[],[]]]] => 5 [[[[]],[],[[[]]]]] => 5 [[[[]],[[]],[],[]]] => 4 [[[[]],[[]],[[]]]] => 4 [[[[]],[[],[]],[]]] => 5 [[[[]],[[[]]],[]]] => 5 [[[[]],[[],[],[]]]] => 5 [[[[]],[[],[[]]]]] => 5 [[[[]],[[[]],[]]]] => 5 [[[[]],[[[],[]]]]] => 6 [[[[]],[[[[]]]]]] => 6 [[[[],[]],[],[],[]]] => 4 [[[[[]]],[],[],[]]] => 5 [[[[],[]],[],[[]]]] => 5 [[[[[]]],[],[[]]]] => 5 [[[[],[]],[[]],[]]] => 5 [[[[[]]],[[]],[]]] => 5 [[[[],[]],[[],[]]]] => 4 [[[[],[]],[[[]]]]] => 6 [[[[[]]],[[],[]]]] => 6 [[[[[]]],[[[]]]]] => 5 [[[[],[],[]],[],[]]] => 4 [[[[],[[]]],[],[]]] => 5 [[[[[]],[]],[],[]]] => 5 [[[[[],[]]],[],[]]] => 5 [[[[[[]]]],[],[]]] => 6 [[[[],[],[]],[[]]]] => 5 [[[[],[[]]],[[]]]] => 5 [[[[[]],[]],[[]]]] => 5 [[[[[],[]]],[[]]]] => 6 [[[[[[]]]],[[]]]] => 6 [[[[],[],[],[]],[]]] => 4 [[[[],[],[[]]],[]]] => 5 [[[[],[[]],[]],[]]] => 5 [[[[],[[],[]]],[]]] => 5 [[[[],[[[]]]],[]]] => 6 [[[[[]],[],[]],[]]] => 5 [[[[[]],[[]]],[]]] => 5 [[[[[],[]],[]],[]]] => 5 [[[[[[]]],[]],[]]] => 6 [[[[[],[],[]]],[]]] => 5 [[[[[],[[]]]],[]]] => 6 [[[[[[]],[]]],[]]] => 6 [[[[[[],[]]]],[]]] => 6 [[[[[[[]]]]],[]]] => 7 [[[[],[],[],[],[]]]] => 4 [[[[],[],[],[[]]]]] => 5 [[[[],[],[[]],[]]]] => 5 [[[[],[],[[],[]]]]] => 5 [[[[],[],[[[]]]]]] => 6 [[[[],[[]],[],[]]]] => 5 [[[[],[[]],[[]]]]] => 5 [[[[],[[],[]],[]]]] => 5 [[[[],[[[]]],[]]]] => 6 [[[[],[[],[],[]]]]] => 5 [[[[],[[],[[]]]]]] => 6 [[[[],[[[]],[]]]]] => 6 [[[[],[[[],[]]]]]] => 6 [[[[],[[[[]]]]]]] => 7 [[[[[]],[],[],[]]]] => 5 [[[[[]],[],[[]]]]] => 5 [[[[[]],[[]],[]]]] => 5 [[[[[]],[[],[]]]]] => 6 [[[[[]],[[[]]]]]] => 6 [[[[[],[]],[],[]]]] => 5 [[[[[[]]],[],[]]]] => 6 [[[[[],[]],[[]]]]] => 6 [[[[[[]]],[[]]]]] => 6 [[[[[],[],[]],[]]]] => 5 [[[[[],[[]]],[]]]] => 6 [[[[[[]],[]],[]]]] => 6 [[[[[[],[]]],[]]]] => 6 [[[[[[[]]]],[]]]] => 7 [[[[[],[],[],[]]]]] => 5 [[[[[],[],[[]]]]]] => 6 [[[[[],[[]],[]]]]] => 6 [[[[[],[[],[]]]]]] => 6 [[[[[],[[[]]]]]]] => 7 [[[[[[]],[],[]]]]] => 6 [[[[[[]],[[]]]]]] => 6 [[[[[[],[]],[]]]]] => 6 [[[[[[[]]],[]]]]] => 7 [[[[[[],[],[]]]]]] => 6 [[[[[[],[[]]]]]]] => 7 [[[[[[[]],[]]]]]] => 7 [[[[[[[],[]]]]]]] => 7 [[[[[[[[]]]]]]]] => 8 [[],[],[],[],[],[],[],[]] => 2 [[],[],[],[],[],[],[[]]] => 3 [[],[],[],[],[],[[]],[]] => 3 [[],[],[],[],[],[[],[]]] => 3 [[],[],[],[],[],[[[]]]] => 4 [[],[],[],[],[[]],[],[]] => 3 [[],[],[],[],[[]],[[]]] => 3 [[],[],[],[],[[],[]],[]] => 3 [[],[],[],[],[[[]]],[]] => 4 [[],[],[],[],[[],[],[]]] => 3 [[],[],[],[],[[],[[]]]] => 4 [[],[],[],[],[[[]],[]]] => 4 [[],[],[],[],[[[],[]]]] => 4 [[],[],[],[],[[[[]]]]] => 5 [[],[],[],[[]],[],[],[]] => 3 [[],[],[],[[]],[],[[]]] => 3 [[],[],[],[[]],[[]],[]] => 3 [[],[],[],[[]],[[],[]]] => 4 [[],[],[],[[]],[[[]]]] => 4 [[],[],[],[[],[]],[],[]] => 3 [[],[],[],[[[]]],[],[]] => 4 [[],[],[],[[],[]],[[]]] => 4 [[],[],[],[[[]]],[[]]] => 4 [[],[],[],[[],[],[]],[]] => 3 [[],[],[],[[],[[]]],[]] => 4 [[],[],[],[[[]],[]],[]] => 4 [[],[],[],[[[],[]]],[]] => 4 [[],[],[],[[[[]]]],[]] => 5 [[],[],[],[[],[],[],[]]] => 3 [[],[],[],[[],[],[[]]]] => 4 [[],[],[],[[],[[]],[]]] => 4 [[],[],[],[[],[[],[]]]] => 4 [[],[],[],[[],[[[]]]]] => 5 [[],[],[],[[[]],[],[]]] => 4 [[],[],[],[[[]],[[]]]] => 4 [[],[],[],[[[],[]],[]]] => 4 [[],[],[],[[[[]]],[]]] => 5 [[],[],[],[[[],[],[]]]] => 4 [[],[],[],[[[],[[]]]]] => 5 [[],[],[],[[[[]],[]]]] => 5 [[],[],[],[[[[],[]]]]] => 5 [[],[],[],[[[[[]]]]]] => 6 [[],[],[[]],[],[],[],[]] => 3 [[],[],[[]],[],[],[[]]] => 3 [[],[],[[]],[],[[]],[]] => 3 [[],[],[[]],[],[[],[]]] => 4 [[],[],[[]],[],[[[]]]] => 4 [[],[],[[]],[[]],[],[]] => 3 [[],[],[[]],[[]],[[]]] => 3 [[],[],[[]],[[],[]],[]] => 4 [[],[],[[]],[[[]]],[]] => 4 [[],[],[[]],[[],[],[]]] => 4 [[],[],[[]],[[],[[]]]] => 4 [[],[],[[]],[[[]],[]]] => 4 [[],[],[[]],[[[],[]]]] => 5 [[],[],[[]],[[[[]]]]] => 5 [[],[],[[],[]],[],[],[]] => 3 [[],[],[[[]]],[],[],[]] => 4 [[],[],[[],[]],[],[[]]] => 4 [[],[],[[[]]],[],[[]]] => 4 [[],[],[[],[]],[[]],[]] => 4 [[],[],[[[]]],[[]],[]] => 4 [[],[],[[],[]],[[],[]]] => 3 [[],[],[[],[]],[[[]]]] => 5 [[],[],[[[]]],[[],[]]] => 5 [[],[],[[[]]],[[[]]]] => 4 [[],[],[[],[],[]],[],[]] => 3 [[],[],[[],[[]]],[],[]] => 4 [[],[],[[[]],[]],[],[]] => 4 [[],[],[[[],[]]],[],[]] => 4 [[],[],[[[[]]]],[],[]] => 5 [[],[],[[],[],[]],[[]]] => 4 [[],[],[[],[[]]],[[]]] => 4 [[],[],[[[]],[]],[[]]] => 4 [[],[],[[[],[]]],[[]]] => 5 [[],[],[[[[]]]],[[]]] => 5 [[],[],[[],[],[],[]],[]] => 3 [[],[],[[],[],[[]]],[]] => 4 [[],[],[[],[[]],[]],[]] => 4 [[],[],[[],[[],[]]],[]] => 4 [[],[],[[],[[[]]]],[]] => 5 [[],[],[[[]],[],[]],[]] => 4 [[],[],[[[]],[[]]],[]] => 4 [[],[],[[[],[]],[]],[]] => 4 [[],[],[[[[]]],[]],[]] => 5 [[],[],[[[],[],[]]],[]] => 4 [[],[],[[[],[[]]]],[]] => 5 [[],[],[[[[]],[]]],[]] => 5 [[],[],[[[[],[]]]],[]] => 5 [[],[],[[[[[]]]]],[]] => 6 [[],[],[[],[],[],[],[]]] => 3 [[],[],[[],[],[],[[]]]] => 4 [[],[],[[],[],[[]],[]]] => 4 [[],[],[[],[],[[],[]]]] => 4 [[],[],[[],[],[[[]]]]] => 5 [[],[],[[],[[]],[],[]]] => 4 [[],[],[[],[[]],[[]]]] => 4 [[],[],[[],[[],[]],[]]] => 4 [[],[],[[],[[[]]],[]]] => 5 [[],[],[[],[[],[],[]]]] => 4 [[],[],[[],[[],[[]]]]] => 5 [[],[],[[],[[[]],[]]]] => 5 [[],[],[[],[[[],[]]]]] => 5 [[],[],[[],[[[[]]]]]] => 6 [[],[],[[[]],[],[],[]]] => 4 [[],[],[[[]],[],[[]]]] => 4 [[],[],[[[]],[[]],[]]] => 4 [[],[],[[[]],[[],[]]]] => 5 [[],[],[[[]],[[[]]]]] => 5 [[],[],[[[],[]],[],[]]] => 4 [[],[],[[[[]]],[],[]]] => 5 [[],[],[[[],[]],[[]]]] => 5 [[],[],[[[[]]],[[]]]] => 5 [[],[],[[[],[],[]],[]]] => 4 [[],[],[[[],[[]]],[]]] => 5 [[],[],[[[[]],[]],[]]] => 5 [[],[],[[[[],[]]],[]]] => 5 [[],[],[[[[[]]]],[]]] => 6 [[],[],[[[],[],[],[]]]] => 4 [[],[],[[[],[],[[]]]]] => 5 [[],[],[[[],[[]],[]]]] => 5 [[],[],[[[],[[],[]]]]] => 5 [[],[],[[[],[[[]]]]]] => 6 [[],[],[[[[]],[],[]]]] => 5 [[],[],[[[[]],[[]]]]] => 5 [[],[],[[[[],[]],[]]]] => 5 [[],[],[[[[[]]],[]]]] => 6 [[],[],[[[[],[],[]]]]] => 5 [[],[],[[[[],[[]]]]]] => 6 [[],[],[[[[[]],[]]]]] => 6 [[],[],[[[[[],[]]]]]] => 6 [[],[],[[[[[[]]]]]]] => 7 [[],[[]],[],[],[],[],[]] => 3 [[],[[]],[],[],[],[[]]] => 3 [[],[[]],[],[],[[]],[]] => 3 [[],[[]],[],[],[[],[]]] => 4 [[],[[]],[],[],[[[]]]] => 4 [[],[[]],[],[[]],[],[]] => 3 [[],[[]],[],[[]],[[]]] => 3 [[],[[]],[],[[],[]],[]] => 4 [[],[[]],[],[[[]]],[]] => 4 [[],[[]],[],[[],[],[]]] => 4 [[],[[]],[],[[],[[]]]] => 4 [[],[[]],[],[[[]],[]]] => 4 [[],[[]],[],[[[],[]]]] => 5 [[],[[]],[],[[[[]]]]] => 5 [[],[[]],[[]],[],[],[]] => 3 [[],[[]],[[]],[],[[]]] => 3 [[],[[]],[[]],[[]],[]] => 3 [[],[[]],[[]],[[],[]]] => 4 [[],[[]],[[]],[[[]]]] => 4 [[],[[]],[[],[]],[],[]] => 4 [[],[[]],[[[]]],[],[]] => 4 [[],[[]],[[],[]],[[]]] => 4 [[],[[]],[[[]]],[[]]] => 4 [[],[[]],[[],[],[]],[]] => 4 [[],[[]],[[],[[]]],[]] => 4 [[],[[]],[[[]],[]],[]] => 4 [[],[[]],[[[],[]]],[]] => 5 [[],[[]],[[[[]]]],[]] => 5 [[],[[]],[[],[],[],[]]] => 4 [[],[[]],[[],[],[[]]]] => 4 [[],[[]],[[],[[]],[]]] => 4 [[],[[]],[[],[[],[]]]] => 5 [[],[[]],[[],[[[]]]]] => 5 [[],[[]],[[[]],[],[]]] => 4 [[],[[]],[[[]],[[]]]] => 4 [[],[[]],[[[],[]],[]]] => 5 [[],[[]],[[[[]]],[]]] => 5 [[],[[]],[[[],[],[]]]] => 5 [[],[[]],[[[],[[]]]]] => 5 [[],[[]],[[[[]],[]]]] => 5 [[],[[]],[[[[],[]]]]] => 6 [[],[[]],[[[[[]]]]]] => 6 [[],[[],[]],[],[],[],[]] => 3 [[],[[[]]],[],[],[],[]] => 4 [[],[[],[]],[],[],[[]]] => 4 [[],[[[]]],[],[],[[]]] => 4 [[],[[],[]],[],[[]],[]] => 4 [[],[[[]]],[],[[]],[]] => 4 [[],[[],[]],[],[[],[]]] => 3 [[],[[],[]],[],[[[]]]] => 5 [[],[[[]]],[],[[],[]]] => 5 [[],[[[]]],[],[[[]]]] => 4 [[],[[],[]],[[]],[],[]] => 4 [[],[[[]]],[[]],[],[]] => 4 [[],[[],[]],[[]],[[]]] => 4 [[],[[[]]],[[]],[[]]] => 4 [[],[[],[]],[[],[]],[]] => 3 [[],[[],[]],[[[]]],[]] => 5 [[],[[[]]],[[],[]],[]] => 5 [[],[[[]]],[[[]]],[]] => 4 [[],[[],[]],[[],[],[]]] => 4 [[],[[],[]],[[],[[]]]] => 5 [[],[[],[]],[[[]],[]]] => 5 [[],[[],[]],[[[],[]]]] => 4 [[],[[],[]],[[[[]]]]] => 6 [[],[[[]]],[[],[],[]]] => 5 [[],[[[]]],[[],[[]]]] => 5 [[],[[[]]],[[[]],[]]] => 5 [[],[[[]]],[[[],[]]]] => 6 [[],[[[]]],[[[[]]]]] => 5 [[],[[],[],[]],[],[],[]] => 3 [[],[[],[[]]],[],[],[]] => 4 [[],[[[]],[]],[],[],[]] => 4 [[],[[[],[]]],[],[],[]] => 4 [[],[[[[]]]],[],[],[]] => 5 [[],[[],[],[]],[],[[]]] => 4 [[],[[],[[]]],[],[[]]] => 4 [[],[[[]],[]],[],[[]]] => 4 [[],[[[],[]]],[],[[]]] => 5 [[],[[[[]]]],[],[[]]] => 5 [[],[[],[],[]],[[]],[]] => 4 [[],[[],[[]]],[[]],[]] => 4 [[],[[[]],[]],[[]],[]] => 4 [[],[[[],[]]],[[]],[]] => 5 [[],[[[[]]]],[[]],[]] => 5 [[],[[],[],[]],[[],[]]] => 4 [[],[[],[],[]],[[[]]]] => 5 [[],[[],[[]]],[[],[]]] => 5 [[],[[],[[]]],[[[]]]] => 5 [[],[[[]],[]],[[],[]]] => 5 [[],[[[]],[]],[[[]]]] => 5 [[],[[[],[]]],[[],[]]] => 4 [[],[[[],[]]],[[[]]]] => 6 [[],[[[[]]]],[[],[]]] => 6 [[],[[[[]]]],[[[]]]] => 5 [[],[[],[],[],[]],[],[]] => 3 [[],[[],[],[[]]],[],[]] => 4 [[],[[],[[]],[]],[],[]] => 4 [[],[[],[[],[]]],[],[]] => 4 [[],[[],[[[]]]],[],[]] => 5 [[],[[[]],[],[]],[],[]] => 4 [[],[[[]],[[]]],[],[]] => 4 [[],[[[],[]],[]],[],[]] => 4 [[],[[[[]]],[]],[],[]] => 5 [[],[[[],[],[]]],[],[]] => 4 [[],[[[],[[]]]],[],[]] => 5 [[],[[[[]],[]]],[],[]] => 5 [[],[[[[],[]]]],[],[]] => 5 [[],[[[[[]]]]],[],[]] => 6 [[],[[],[],[],[]],[[]]] => 4 [[],[[],[],[[]]],[[]]] => 4 [[],[[],[[]],[]],[[]]] => 4 [[],[[],[[],[]]],[[]]] => 5 [[],[[],[[[]]]],[[]]] => 5 [[],[[[]],[],[]],[[]]] => 4 [[],[[[]],[[]]],[[]]] => 4 [[],[[[],[]],[]],[[]]] => 5 [[],[[[[]]],[]],[[]]] => 5 [[],[[[],[],[]]],[[]]] => 5 [[],[[[],[[]]]],[[]]] => 5 [[],[[[[]],[]]],[[]]] => 5 [[],[[[[],[]]]],[[]]] => 6 [[],[[[[[]]]]],[[]]] => 6 [[],[[],[],[],[],[]],[]] => 3 [[],[[],[],[],[[]]],[]] => 4 [[],[[],[],[[]],[]],[]] => 4 [[],[[],[],[[],[]]],[]] => 4 [[],[[],[],[[[]]]],[]] => 5 [[],[[],[[]],[],[]],[]] => 4 [[],[[],[[]],[[]]],[]] => 4 [[],[[],[[],[]],[]],[]] => 4 [[],[[],[[[]]],[]],[]] => 5 [[],[[],[[],[],[]]],[]] => 4 [[],[[],[[],[[]]]],[]] => 5 [[],[[],[[[]],[]]],[]] => 5 [[],[[],[[[],[]]]],[]] => 5 [[],[[],[[[[]]]]],[]] => 6 [[],[[[]],[],[],[]],[]] => 4 [[],[[[]],[],[[]]],[]] => 4 [[],[[[]],[[]],[]],[]] => 4 [[],[[[]],[[],[]]],[]] => 5 [[],[[[]],[[[]]]],[]] => 5 [[],[[[],[]],[],[]],[]] => 4 [[],[[[[]]],[],[]],[]] => 5 [[],[[[],[]],[[]]],[]] => 5 [[],[[[[]]],[[]]],[]] => 5 [[],[[[],[],[]],[]],[]] => 4 [[],[[[],[[]]],[]],[]] => 5 [[],[[[[]],[]],[]],[]] => 5 [[],[[[[],[]]],[]],[]] => 5 [[],[[[[[]]]],[]],[]] => 6 [[],[[[],[],[],[]]],[]] => 4 [[],[[[],[],[[]]]],[]] => 5 [[],[[[],[[]],[]]],[]] => 5 [[],[[[],[[],[]]]],[]] => 5 [[],[[[],[[[]]]]],[]] => 6 [[],[[[[]],[],[]]],[]] => 5 [[],[[[[]],[[]]]],[]] => 5 [[],[[[[],[]],[]]],[]] => 5 [[],[[[[[]]],[]]],[]] => 6 [[],[[[[],[],[]]]],[]] => 5 [[],[[[[],[[]]]]],[]] => 6 [[],[[[[[]],[]]]],[]] => 6 [[],[[[[[],[]]]]],[]] => 6 [[],[[[[[[]]]]]],[]] => 7 [[],[[],[],[],[],[],[]]] => 3 [[],[[],[],[],[],[[]]]] => 4 [[],[[],[],[],[[]],[]]] => 4 [[],[[],[],[],[[],[]]]] => 4 [[],[[],[],[],[[[]]]]] => 5 [[],[[],[],[[]],[],[]]] => 4 [[],[[],[],[[]],[[]]]] => 4 [[],[[],[],[[],[]],[]]] => 4 [[],[[],[],[[[]]],[]]] => 5 [[],[[],[],[[],[],[]]]] => 4 [[],[[],[],[[],[[]]]]] => 5 [[],[[],[],[[[]],[]]]] => 5 [[],[[],[],[[[],[]]]]] => 5 [[],[[],[],[[[[]]]]]] => 6 [[],[[],[[]],[],[],[]]] => 4 [[],[[],[[]],[],[[]]]] => 4 [[],[[],[[]],[[]],[]]] => 4 [[],[[],[[]],[[],[]]]] => 5 [[],[[],[[]],[[[]]]]] => 5 [[],[[],[[],[]],[],[]]] => 4 [[],[[],[[[]]],[],[]]] => 5 [[],[[],[[],[]],[[]]]] => 5 [[],[[],[[[]]],[[]]]] => 5 [[],[[],[[],[],[]],[]]] => 4 [[],[[],[[],[[]]],[]]] => 5 [[],[[],[[[]],[]],[]]] => 5 [[],[[],[[[],[]]],[]]] => 5 [[],[[],[[[[]]]],[]]] => 6 [[],[[],[[],[],[],[]]]] => 4 [[],[[],[[],[],[[]]]]] => 5 [[],[[],[[],[[]],[]]]] => 5 [[],[[],[[],[[],[]]]]] => 5 [[],[[],[[],[[[]]]]]] => 6 [[],[[],[[[]],[],[]]]] => 5 [[],[[],[[[]],[[]]]]] => 5 [[],[[],[[[],[]],[]]]] => 5 [[],[[],[[[[]]],[]]]] => 6 [[],[[],[[[],[],[]]]]] => 5 [[],[[],[[[],[[]]]]]] => 6 [[],[[],[[[[]],[]]]]] => 6 [[],[[],[[[[],[]]]]]] => 6 [[],[[],[[[[[]]]]]]] => 7 [[],[[[]],[],[],[],[]]] => 4 [[],[[[]],[],[],[[]]]] => 4 [[],[[[]],[],[[]],[]]] => 4 [[],[[[]],[],[[],[]]]] => 5 [[],[[[]],[],[[[]]]]] => 5 [[],[[[]],[[]],[],[]]] => 4 [[],[[[]],[[]],[[]]]] => 4 [[],[[[]],[[],[]],[]]] => 5 [[],[[[]],[[[]]],[]]] => 5 [[],[[[]],[[],[],[]]]] => 5 [[],[[[]],[[],[[]]]]] => 5 [[],[[[]],[[[]],[]]]] => 5 [[],[[[]],[[[],[]]]]] => 6 [[],[[[]],[[[[]]]]]] => 6 [[],[[[],[]],[],[],[]]] => 4 [[],[[[[]]],[],[],[]]] => 5 [[],[[[],[]],[],[[]]]] => 5 [[],[[[[]]],[],[[]]]] => 5 [[],[[[],[]],[[]],[]]] => 5 [[],[[[[]]],[[]],[]]] => 5 [[],[[[],[]],[[],[]]]] => 4 [[],[[[],[]],[[[]]]]] => 6 [[],[[[[]]],[[],[]]]] => 6 [[],[[[[]]],[[[]]]]] => 5 [[],[[[],[],[]],[],[]]] => 4 [[],[[[],[[]]],[],[]]] => 5 [[],[[[[]],[]],[],[]]] => 5 [[],[[[[],[]]],[],[]]] => 5 [[],[[[[[]]]],[],[]]] => 6 [[],[[[],[],[]],[[]]]] => 5 [[],[[[],[[]]],[[]]]] => 5 [[],[[[[]],[]],[[]]]] => 5 [[],[[[[],[]]],[[]]]] => 6 [[],[[[[[]]]],[[]]]] => 6 [[],[[[],[],[],[]],[]]] => 4 [[],[[[],[],[[]]],[]]] => 5 [[],[[[],[[]],[]],[]]] => 5 [[],[[[],[[],[]]],[]]] => 5 [[],[[[],[[[]]]],[]]] => 6 [[],[[[[]],[],[]],[]]] => 5 [[],[[[[]],[[]]],[]]] => 5 [[],[[[[],[]],[]],[]]] => 5 [[],[[[[[]]],[]],[]]] => 6 [[],[[[[],[],[]]],[]]] => 5 [[],[[[[],[[]]]],[]]] => 6 [[],[[[[[]],[]]],[]]] => 6 [[],[[[[[],[]]]],[]]] => 6 [[],[[[[[[]]]]],[]]] => 7 [[],[[[],[],[],[],[]]]] => 4 [[],[[[],[],[],[[]]]]] => 5 [[],[[[],[],[[]],[]]]] => 5 [[],[[[],[],[[],[]]]]] => 5 [[],[[[],[],[[[]]]]]] => 6 [[],[[[],[[]],[],[]]]] => 5 [[],[[[],[[]],[[]]]]] => 5 [[],[[[],[[],[]],[]]]] => 5 [[],[[[],[[[]]],[]]]] => 6 [[],[[[],[[],[],[]]]]] => 5 [[],[[[],[[],[[]]]]]] => 6 [[],[[[],[[[]],[]]]]] => 6 [[],[[[],[[[],[]]]]]] => 6 [[],[[[],[[[[]]]]]]] => 7 [[],[[[[]],[],[],[]]]] => 5 [[],[[[[]],[],[[]]]]] => 5 [[],[[[[]],[[]],[]]]] => 5 [[],[[[[]],[[],[]]]]] => 6 [[],[[[[]],[[[]]]]]] => 6 [[],[[[[],[]],[],[]]]] => 5 [[],[[[[[]]],[],[]]]] => 6 [[],[[[[],[]],[[]]]]] => 6 [[],[[[[[]]],[[]]]]] => 6 [[],[[[[],[],[]],[]]]] => 5 [[],[[[[],[[]]],[]]]] => 6 [[],[[[[[]],[]],[]]]] => 6 [[],[[[[[],[]]],[]]]] => 6 [[],[[[[[[]]]],[]]]] => 7 [[],[[[[],[],[],[]]]]] => 5 [[],[[[[],[],[[]]]]]] => 6 [[],[[[[],[[]],[]]]]] => 6 [[],[[[[],[[],[]]]]]] => 6 [[],[[[[],[[[]]]]]]] => 7 [[],[[[[[]],[],[]]]]] => 6 [[],[[[[[]],[[]]]]]] => 6 [[],[[[[[],[]],[]]]]] => 6 [[],[[[[[[]]],[]]]]] => 7 [[],[[[[[],[],[]]]]]] => 6 [[],[[[[[],[[]]]]]]] => 7 [[],[[[[[[]],[]]]]]] => 7 [[],[[[[[[],[]]]]]]] => 7 [[],[[[[[[[]]]]]]]] => 8 [[[]],[],[],[],[],[],[]] => 3 [[[]],[],[],[],[],[[]]] => 3 [[[]],[],[],[],[[]],[]] => 3 [[[]],[],[],[],[[],[]]] => 4 [[[]],[],[],[],[[[]]]] => 4 [[[]],[],[],[[]],[],[]] => 3 [[[]],[],[],[[]],[[]]] => 3 [[[]],[],[],[[],[]],[]] => 4 [[[]],[],[],[[[]]],[]] => 4 [[[]],[],[],[[],[],[]]] => 4 [[[]],[],[],[[],[[]]]] => 4 [[[]],[],[],[[[]],[]]] => 4 [[[]],[],[],[[[],[]]]] => 5 [[[]],[],[],[[[[]]]]] => 5 [[[]],[],[[]],[],[],[]] => 3 [[[]],[],[[]],[],[[]]] => 3 [[[]],[],[[]],[[]],[]] => 3 [[[]],[],[[]],[[],[]]] => 4 [[[]],[],[[]],[[[]]]] => 4 [[[]],[],[[],[]],[],[]] => 4 [[[]],[],[[[]]],[],[]] => 4 [[[]],[],[[],[]],[[]]] => 4 [[[]],[],[[[]]],[[]]] => 4 [[[]],[],[[],[],[]],[]] => 4 [[[]],[],[[],[[]]],[]] => 4 [[[]],[],[[[]],[]],[]] => 4 [[[]],[],[[[],[]]],[]] => 5 [[[]],[],[[[[]]]],[]] => 5 [[[]],[],[[],[],[],[]]] => 4 [[[]],[],[[],[],[[]]]] => 4 [[[]],[],[[],[[]],[]]] => 4 [[[]],[],[[],[[],[]]]] => 5 [[[]],[],[[],[[[]]]]] => 5 [[[]],[],[[[]],[],[]]] => 4 [[[]],[],[[[]],[[]]]] => 4 [[[]],[],[[[],[]],[]]] => 5 [[[]],[],[[[[]]],[]]] => 5 [[[]],[],[[[],[],[]]]] => 5 [[[]],[],[[[],[[]]]]] => 5 [[[]],[],[[[[]],[]]]] => 5 [[[]],[],[[[[],[]]]]] => 6 [[[]],[],[[[[[]]]]]] => 6 [[[]],[[]],[],[],[],[]] => 3 [[[]],[[]],[],[],[[]]] => 3 [[[]],[[]],[],[[]],[]] => 3 [[[]],[[]],[],[[],[]]] => 4 [[[]],[[]],[],[[[]]]] => 4 [[[]],[[]],[[]],[],[]] => 3 [[[]],[[]],[[]],[[]]] => 3 [[[]],[[]],[[],[]],[]] => 4 [[[]],[[]],[[[]]],[]] => 4 [[[]],[[]],[[],[],[]]] => 4 [[[]],[[]],[[],[[]]]] => 4 [[[]],[[]],[[[]],[]]] => 4 [[[]],[[]],[[[],[]]]] => 5 [[[]],[[]],[[[[]]]]] => 5 [[[]],[[],[]],[],[],[]] => 4 [[[]],[[[]]],[],[],[]] => 4 [[[]],[[],[]],[],[[]]] => 4 [[[]],[[[]]],[],[[]]] => 4 [[[]],[[],[]],[[]],[]] => 4 [[[]],[[[]]],[[]],[]] => 4 [[[]],[[],[]],[[],[]]] => 4 [[[]],[[],[]],[[[]]]] => 5 [[[]],[[[]]],[[],[]]] => 5 [[[]],[[[]]],[[[]]]] => 4 [[[]],[[],[],[]],[],[]] => 4 [[[]],[[],[[]]],[],[]] => 4 [[[]],[[[]],[]],[],[]] => 4 [[[]],[[[],[]]],[],[]] => 5 [[[]],[[[[]]]],[],[]] => 5 [[[]],[[],[],[]],[[]]] => 4 [[[]],[[],[[]]],[[]]] => 4 [[[]],[[[]],[]],[[]]] => 4 [[[]],[[[],[]]],[[]]] => 5 [[[]],[[[[]]]],[[]]] => 5 [[[]],[[],[],[],[]],[]] => 4 [[[]],[[],[],[[]]],[]] => 4 [[[]],[[],[[]],[]],[]] => 4 [[[]],[[],[[],[]]],[]] => 5 [[[]],[[],[[[]]]],[]] => 5 [[[]],[[[]],[],[]],[]] => 4 [[[]],[[[]],[[]]],[]] => 4 [[[]],[[[],[]],[]],[]] => 5 [[[]],[[[[]]],[]],[]] => 5 [[[]],[[[],[],[]]],[]] => 5 [[[]],[[[],[[]]]],[]] => 5 [[[]],[[[[]],[]]],[]] => 5 [[[]],[[[[],[]]]],[]] => 6 [[[]],[[[[[]]]]],[]] => 6 [[[]],[[],[],[],[],[]]] => 4 [[[]],[[],[],[],[[]]]] => 4 [[[]],[[],[],[[]],[]]] => 4 [[[]],[[],[],[[],[]]]] => 5 [[[]],[[],[],[[[]]]]] => 5 [[[]],[[],[[]],[],[]]] => 4 [[[]],[[],[[]],[[]]]] => 4 [[[]],[[],[[],[]],[]]] => 5 [[[]],[[],[[[]]],[]]] => 5 [[[]],[[],[[],[],[]]]] => 5 [[[]],[[],[[],[[]]]]] => 5 [[[]],[[],[[[]],[]]]] => 5 [[[]],[[],[[[],[]]]]] => 6 [[[]],[[],[[[[]]]]]] => 6 [[[]],[[[]],[],[],[]]] => 4 [[[]],[[[]],[],[[]]]] => 4 [[[]],[[[]],[[]],[]]] => 4 [[[]],[[[]],[[],[]]]] => 5 [[[]],[[[]],[[[]]]]] => 5 [[[]],[[[],[]],[],[]]] => 5 [[[]],[[[[]]],[],[]]] => 5 [[[]],[[[],[]],[[]]]] => 5 [[[]],[[[[]]],[[]]]] => 5 [[[]],[[[],[],[]],[]]] => 5 [[[]],[[[],[[]]],[]]] => 5 [[[]],[[[[]],[]],[]]] => 5 [[[]],[[[[],[]]],[]]] => 6 [[[]],[[[[[]]]],[]]] => 6 [[[]],[[[],[],[],[]]]] => 5 [[[]],[[[],[],[[]]]]] => 5 [[[]],[[[],[[]],[]]]] => 5 [[[]],[[[],[[],[]]]]] => 6 [[[]],[[[],[[[]]]]]] => 6 [[[]],[[[[]],[],[]]]] => 5 [[[]],[[[[]],[[]]]]] => 5 [[[]],[[[[],[]],[]]]] => 6 [[[]],[[[[[]]],[]]]] => 6 [[[]],[[[[],[],[]]]]] => 6 [[[]],[[[[],[[]]]]]] => 6 [[[]],[[[[[]],[]]]]] => 6 [[[]],[[[[[],[]]]]]] => 7 [[[]],[[[[[[]]]]]]] => 7 [[[],[]],[],[],[],[],[]] => 3 [[[[]]],[],[],[],[],[]] => 4 [[[],[]],[],[],[],[[]]] => 4 [[[[]]],[],[],[],[[]]] => 4 [[[],[]],[],[],[[]],[]] => 4 [[[[]]],[],[],[[]],[]] => 4 [[[],[]],[],[],[[],[]]] => 3 [[[],[]],[],[],[[[]]]] => 5 [[[[]]],[],[],[[],[]]] => 5 [[[[]]],[],[],[[[]]]] => 4 [[[],[]],[],[[]],[],[]] => 4 [[[[]]],[],[[]],[],[]] => 4 [[[],[]],[],[[]],[[]]] => 4 [[[[]]],[],[[]],[[]]] => 4 ----------------------------------------------------------------------------- Created: Jun 02, 2016 at 08:53 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 02, 2016 at 08:53 by Martin Rubey