***************************************************************************** * 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: St001058 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The breadth of the ordered tree. This is the maximal number of nodes having the same depth. ----------------------------------------------------------------------------- References: [1] koalo Term for the maximum number of vertices per depth of a rooted tree [[MathOverflow:287474]] ----------------------------------------------------------------------------- Code: def statistic(T): return max(T.node_number_at_depth(i) for i in range(T.depth())) ----------------------------------------------------------------------------- Statistic values: [[]] => 1 [[],[]] => 2 [[[]]] => 1 [[],[],[]] => 3 [[],[[]]] => 2 [[[]],[]] => 2 [[[],[]]] => 2 [[[[]]]] => 1 [[],[],[],[]] => 4 [[],[],[[]]] => 3 [[],[[]],[]] => 3 [[],[[],[]]] => 2 [[],[[[]]]] => 2 [[[]],[],[]] => 3 [[[]],[[]]] => 2 [[[],[]],[]] => 2 [[[[]]],[]] => 2 [[[],[],[]]] => 3 [[[],[[]]]] => 2 [[[[]],[]]] => 2 [[[[],[]]]] => 2 [[[[[]]]]] => 1 [[],[],[],[],[]] => 5 [[],[],[],[[]]] => 4 [[],[],[[]],[]] => 4 [[],[],[[],[]]] => 3 [[],[],[[[]]]] => 3 [[],[[]],[],[]] => 4 [[],[[]],[[]]] => 3 [[],[[],[]],[]] => 3 [[],[[[]]],[]] => 3 [[],[[],[],[]]] => 3 [[],[[],[[]]]] => 2 [[],[[[]],[]]] => 2 [[],[[[],[]]]] => 2 [[],[[[[]]]]] => 2 [[[]],[],[],[]] => 4 [[[]],[],[[]]] => 3 [[[]],[[]],[]] => 3 [[[]],[[],[]]] => 3 [[[]],[[[]]]] => 2 [[[],[]],[],[]] => 3 [[[[]]],[],[]] => 3 [[[],[]],[[]]] => 3 [[[[]]],[[]]] => 2 [[[],[],[]],[]] => 3 [[[],[[]]],[]] => 2 [[[[]],[]],[]] => 2 [[[[],[]]],[]] => 2 [[[[[]]]],[]] => 2 [[[],[],[],[]]] => 4 [[[],[],[[]]]] => 3 [[[],[[]],[]]] => 3 [[[],[[],[]]]] => 2 [[[],[[[]]]]] => 2 [[[[]],[],[]]] => 3 [[[[]],[[]]]] => 2 [[[[],[]],[]]] => 2 [[[[[]]],[]]] => 2 [[[[],[],[]]]] => 3 [[[[],[[]]]]] => 2 [[[[[]],[]]]] => 2 [[[[[],[]]]]] => 2 [[[[[[]]]]]] => 1 [[],[],[],[],[],[]] => 6 [[],[],[],[],[[]]] => 5 [[],[],[],[[]],[]] => 5 [[],[],[],[[],[]]] => 4 [[],[],[],[[[]]]] => 4 [[],[],[[]],[],[]] => 5 [[],[],[[]],[[]]] => 4 [[],[],[[],[]],[]] => 4 [[],[],[[[]]],[]] => 4 [[],[],[[],[],[]]] => 3 [[],[],[[],[[]]]] => 3 [[],[],[[[]],[]]] => 3 [[],[],[[[],[]]]] => 3 [[],[],[[[[]]]]] => 3 [[],[[]],[],[],[]] => 5 [[],[[]],[],[[]]] => 4 [[],[[]],[[]],[]] => 4 [[],[[]],[[],[]]] => 3 [[],[[]],[[[]]]] => 3 [[],[[],[]],[],[]] => 4 [[],[[[]]],[],[]] => 4 [[],[[],[]],[[]]] => 3 [[],[[[]]],[[]]] => 3 [[],[[],[],[]],[]] => 3 [[],[[],[[]]],[]] => 3 [[],[[[]],[]],[]] => 3 [[],[[[],[]]],[]] => 3 [[],[[[[]]]],[]] => 3 [[],[[],[],[],[]]] => 4 [[],[[],[],[[]]]] => 3 [[],[[],[[]],[]]] => 3 [[],[[],[[],[]]]] => 2 [[],[[],[[[]]]]] => 2 [[],[[[]],[],[]]] => 3 [[],[[[]],[[]]]] => 2 [[],[[[],[]],[]]] => 2 [[],[[[[]]],[]]] => 2 [[],[[[],[],[]]]] => 3 [[],[[[],[[]]]]] => 2 [[],[[[[]],[]]]] => 2 [[],[[[[],[]]]]] => 2 [[],[[[[[]]]]]] => 2 [[[]],[],[],[],[]] => 5 [[[]],[],[],[[]]] => 4 [[[]],[],[[]],[]] => 4 [[[]],[],[[],[]]] => 3 [[[]],[],[[[]]]] => 3 [[[]],[[]],[],[]] => 4 [[[]],[[]],[[]]] => 3 [[[]],[[],[]],[]] => 3 [[[]],[[[]]],[]] => 3 [[[]],[[],[],[]]] => 4 [[[]],[[],[[]]]] => 3 [[[]],[[[]],[]]] => 3 [[[]],[[[],[]]]] => 2 [[[]],[[[[]]]]] => 2 [[[],[]],[],[],[]] => 4 [[[[]]],[],[],[]] => 4 [[[],[]],[],[[]]] => 3 [[[[]]],[],[[]]] => 3 [[[],[]],[[]],[]] => 3 [[[[]]],[[]],[]] => 3 [[[],[]],[[],[]]] => 4 [[[],[]],[[[]]]] => 3 [[[[]]],[[],[]]] => 3 [[[[]]],[[[]]]] => 2 [[[],[],[]],[],[]] => 3 [[[],[[]]],[],[]] => 3 [[[[]],[]],[],[]] => 3 [[[[],[]]],[],[]] => 3 [[[[[]]]],[],[]] => 3 [[[],[],[]],[[]]] => 4 [[[],[[]]],[[]]] => 3 [[[[]],[]],[[]]] => 3 [[[[],[]]],[[]]] => 2 [[[[[]]]],[[]]] => 2 [[[],[],[],[]],[]] => 4 [[[],[],[[]]],[]] => 3 [[[],[[]],[]],[]] => 3 [[[],[[],[]]],[]] => 2 [[[],[[[]]]],[]] => 2 [[[[]],[],[]],[]] => 3 [[[[]],[[]]],[]] => 2 [[[[],[]],[]],[]] => 2 [[[[[]]],[]],[]] => 2 [[[[],[],[]]],[]] => 3 [[[[],[[]]]],[]] => 2 [[[[[]],[]]],[]] => 2 [[[[[],[]]]],[]] => 2 [[[[[[]]]]],[]] => 2 [[[],[],[],[],[]]] => 5 [[[],[],[],[[]]]] => 4 [[[],[],[[]],[]]] => 4 [[[],[],[[],[]]]] => 3 [[[],[],[[[]]]]] => 3 [[[],[[]],[],[]]] => 4 [[[],[[]],[[]]]] => 3 [[[],[[],[]],[]]] => 3 [[[],[[[]]],[]]] => 3 [[[],[[],[],[]]]] => 3 [[[],[[],[[]]]]] => 2 [[[],[[[]],[]]]] => 2 [[[],[[[],[]]]]] => 2 [[[],[[[[]]]]]] => 2 [[[[]],[],[],[]]] => 4 [[[[]],[],[[]]]] => 3 [[[[]],[[]],[]]] => 3 [[[[]],[[],[]]]] => 3 [[[[]],[[[]]]]] => 2 [[[[],[]],[],[]]] => 3 [[[[[]]],[],[]]] => 3 [[[[],[]],[[]]]] => 3 [[[[[]]],[[]]]] => 2 [[[[],[],[]],[]]] => 3 [[[[],[[]]],[]]] => 2 [[[[[]],[]],[]]] => 2 [[[[[],[]]],[]]] => 2 [[[[[[]]]],[]]] => 2 [[[[],[],[],[]]]] => 4 [[[[],[],[[]]]]] => 3 [[[[],[[]],[]]]] => 3 [[[[],[[],[]]]]] => 2 [[[[],[[[]]]]]] => 2 [[[[[]],[],[]]]] => 3 [[[[[]],[[]]]]] => 2 [[[[[],[]],[]]]] => 2 [[[[[[]]],[]]]] => 2 [[[[[],[],[]]]]] => 3 [[[[[],[[]]]]]] => 2 [[[[[[]],[]]]]] => 2 [[[[[[],[]]]]]] => 2 [[[[[[[]]]]]]] => 1 [[],[],[],[],[],[],[]] => 7 [[],[],[],[],[],[[]]] => 6 [[],[],[],[],[[]],[]] => 6 [[],[],[],[],[[],[]]] => 5 [[],[],[],[],[[[]]]] => 5 [[],[],[],[[]],[],[]] => 6 [[],[],[],[[]],[[]]] => 5 [[],[],[],[[],[]],[]] => 5 [[],[],[],[[[]]],[]] => 5 [[],[],[],[[],[],[]]] => 4 [[],[],[],[[],[[]]]] => 4 [[],[],[],[[[]],[]]] => 4 [[],[],[],[[[],[]]]] => 4 [[],[],[],[[[[]]]]] => 4 [[],[],[[]],[],[],[]] => 6 [[],[],[[]],[],[[]]] => 5 [[],[],[[]],[[]],[]] => 5 [[],[],[[]],[[],[]]] => 4 [[],[],[[]],[[[]]]] => 4 [[],[],[[],[]],[],[]] => 5 [[],[],[[[]]],[],[]] => 5 [[],[],[[],[]],[[]]] => 4 [[],[],[[[]]],[[]]] => 4 [[],[],[[],[],[]],[]] => 4 [[],[],[[],[[]]],[]] => 4 [[],[],[[[]],[]],[]] => 4 [[],[],[[[],[]]],[]] => 4 [[],[],[[[[]]]],[]] => 4 [[],[],[[],[],[],[]]] => 4 [[],[],[[],[],[[]]]] => 3 [[],[],[[],[[]],[]]] => 3 [[],[],[[],[[],[]]]] => 3 [[],[],[[],[[[]]]]] => 3 [[],[],[[[]],[],[]]] => 3 [[],[],[[[]],[[]]]] => 3 [[],[],[[[],[]],[]]] => 3 [[],[],[[[[]]],[]]] => 3 [[],[],[[[],[],[]]]] => 3 [[],[],[[[],[[]]]]] => 3 [[],[],[[[[]],[]]]] => 3 [[],[],[[[[],[]]]]] => 3 [[],[],[[[[[]]]]]] => 3 [[],[[]],[],[],[],[]] => 6 [[],[[]],[],[],[[]]] => 5 [[],[[]],[],[[]],[]] => 5 [[],[[]],[],[[],[]]] => 4 [[],[[]],[],[[[]]]] => 4 [[],[[]],[[]],[],[]] => 5 [[],[[]],[[]],[[]]] => 4 [[],[[]],[[],[]],[]] => 4 [[],[[]],[[[]]],[]] => 4 [[],[[]],[[],[],[]]] => 4 [[],[[]],[[],[[]]]] => 3 [[],[[]],[[[]],[]]] => 3 [[],[[]],[[[],[]]]] => 3 [[],[[]],[[[[]]]]] => 3 [[],[[],[]],[],[],[]] => 5 [[],[[[]]],[],[],[]] => 5 [[],[[],[]],[],[[]]] => 4 [[],[[[]]],[],[[]]] => 4 [[],[[],[]],[[]],[]] => 4 [[],[[[]]],[[]],[]] => 4 [[],[[],[]],[[],[]]] => 4 [[],[[],[]],[[[]]]] => 3 [[],[[[]]],[[],[]]] => 3 [[],[[[]]],[[[]]]] => 3 [[],[[],[],[]],[],[]] => 4 [[],[[],[[]]],[],[]] => 4 [[],[[[]],[]],[],[]] => 4 [[],[[[],[]]],[],[]] => 4 [[],[[[[]]]],[],[]] => 4 [[],[[],[],[]],[[]]] => 4 [[],[[],[[]]],[[]]] => 3 [[],[[[]],[]],[[]]] => 3 [[],[[[],[]]],[[]]] => 3 [[],[[[[]]]],[[]]] => 3 [[],[[],[],[],[]],[]] => 4 [[],[[],[],[[]]],[]] => 3 [[],[[],[[]],[]],[]] => 3 [[],[[],[[],[]]],[]] => 3 [[],[[],[[[]]]],[]] => 3 [[],[[[]],[],[]],[]] => 3 [[],[[[]],[[]]],[]] => 3 [[],[[[],[]],[]],[]] => 3 [[],[[[[]]],[]],[]] => 3 [[],[[[],[],[]]],[]] => 3 [[],[[[],[[]]]],[]] => 3 [[],[[[[]],[]]],[]] => 3 [[],[[[[],[]]]],[]] => 3 [[],[[[[[]]]]],[]] => 3 [[],[[],[],[],[],[]]] => 5 [[],[[],[],[],[[]]]] => 4 [[],[[],[],[[]],[]]] => 4 [[],[[],[],[[],[]]]] => 3 [[],[[],[],[[[]]]]] => 3 [[],[[],[[]],[],[]]] => 4 [[],[[],[[]],[[]]]] => 3 [[],[[],[[],[]],[]]] => 3 [[],[[],[[[]]],[]]] => 3 [[],[[],[[],[],[]]]] => 3 [[],[[],[[],[[]]]]] => 2 [[],[[],[[[]],[]]]] => 2 [[],[[],[[[],[]]]]] => 2 [[],[[],[[[[]]]]]] => 2 [[],[[[]],[],[],[]]] => 4 [[],[[[]],[],[[]]]] => 3 [[],[[[]],[[]],[]]] => 3 [[],[[[]],[[],[]]]] => 3 [[],[[[]],[[[]]]]] => 2 [[],[[[],[]],[],[]]] => 3 [[],[[[[]]],[],[]]] => 3 [[],[[[],[]],[[]]]] => 3 [[],[[[[]]],[[]]]] => 2 [[],[[[],[],[]],[]]] => 3 [[],[[[],[[]]],[]]] => 2 [[],[[[[]],[]],[]]] => 2 [[],[[[[],[]]],[]]] => 2 [[],[[[[[]]]],[]]] => 2 [[],[[[],[],[],[]]]] => 4 [[],[[[],[],[[]]]]] => 3 [[],[[[],[[]],[]]]] => 3 [[],[[[],[[],[]]]]] => 2 [[],[[[],[[[]]]]]] => 2 [[],[[[[]],[],[]]]] => 3 [[],[[[[]],[[]]]]] => 2 [[],[[[[],[]],[]]]] => 2 [[],[[[[[]]],[]]]] => 2 [[],[[[[],[],[]]]]] => 3 [[],[[[[],[[]]]]]] => 2 [[],[[[[[]],[]]]]] => 2 [[],[[[[[],[]]]]]] => 2 [[],[[[[[[]]]]]]] => 2 [[[]],[],[],[],[],[]] => 6 [[[]],[],[],[],[[]]] => 5 [[[]],[],[],[[]],[]] => 5 [[[]],[],[],[[],[]]] => 4 [[[]],[],[],[[[]]]] => 4 [[[]],[],[[]],[],[]] => 5 [[[]],[],[[]],[[]]] => 4 [[[]],[],[[],[]],[]] => 4 [[[]],[],[[[]]],[]] => 4 [[[]],[],[[],[],[]]] => 4 [[[]],[],[[],[[]]]] => 3 [[[]],[],[[[]],[]]] => 3 [[[]],[],[[[],[]]]] => 3 [[[]],[],[[[[]]]]] => 3 [[[]],[[]],[],[],[]] => 5 [[[]],[[]],[],[[]]] => 4 [[[]],[[]],[[]],[]] => 4 [[[]],[[]],[[],[]]] => 4 [[[]],[[]],[[[]]]] => 3 [[[]],[[],[]],[],[]] => 4 [[[]],[[[]]],[],[]] => 4 [[[]],[[],[]],[[]]] => 4 [[[]],[[[]]],[[]]] => 3 [[[]],[[],[],[]],[]] => 4 [[[]],[[],[[]]],[]] => 3 [[[]],[[[]],[]],[]] => 3 [[[]],[[[],[]]],[]] => 3 [[[]],[[[[]]]],[]] => 3 [[[]],[[],[],[],[]]] => 5 [[[]],[[],[],[[]]]] => 4 [[[]],[[],[[]],[]]] => 4 [[[]],[[],[[],[]]]] => 3 [[[]],[[],[[[]]]]] => 3 [[[]],[[[]],[],[]]] => 4 [[[]],[[[]],[[]]]] => 3 [[[]],[[[],[]],[]]] => 3 [[[]],[[[[]]],[]]] => 3 [[[]],[[[],[],[]]]] => 3 [[[]],[[[],[[]]]]] => 2 [[[]],[[[[]],[]]]] => 2 [[[]],[[[[],[]]]]] => 2 [[[]],[[[[[]]]]]] => 2 [[[],[]],[],[],[],[]] => 5 [[[[]]],[],[],[],[]] => 5 [[[],[]],[],[],[[]]] => 4 [[[[]]],[],[],[[]]] => 4 [[[],[]],[],[[]],[]] => 4 [[[[]]],[],[[]],[]] => 4 [[[],[]],[],[[],[]]] => 4 [[[],[]],[],[[[]]]] => 3 [[[[]]],[],[[],[]]] => 3 [[[[]]],[],[[[]]]] => 3 [[[],[]],[[]],[],[]] => 4 [[[[]]],[[]],[],[]] => 4 [[[],[]],[[]],[[]]] => 4 [[[[]]],[[]],[[]]] => 3 [[[],[]],[[],[]],[]] => 4 [[[],[]],[[[]]],[]] => 3 [[[[]]],[[],[]],[]] => 3 [[[[]]],[[[]]],[]] => 3 [[[],[]],[[],[],[]]] => 5 [[[],[]],[[],[[]]]] => 4 [[[],[]],[[[]],[]]] => 4 [[[],[]],[[[],[]]]] => 3 [[[],[]],[[[[]]]]] => 3 [[[[]]],[[],[],[]]] => 4 [[[[]]],[[],[[]]]] => 3 [[[[]]],[[[]],[]]] => 3 [[[[]]],[[[],[]]]] => 3 [[[[]]],[[[[]]]]] => 2 [[[],[],[]],[],[],[]] => 4 [[[],[[]]],[],[],[]] => 4 [[[[]],[]],[],[],[]] => 4 [[[[],[]]],[],[],[]] => 4 [[[[[]]]],[],[],[]] => 4 [[[],[],[]],[],[[]]] => 4 [[[],[[]]],[],[[]]] => 3 [[[[]],[]],[],[[]]] => 3 [[[[],[]]],[],[[]]] => 3 [[[[[]]]],[],[[]]] => 3 [[[],[],[]],[[]],[]] => 4 [[[],[[]]],[[]],[]] => 3 [[[[]],[]],[[]],[]] => 3 [[[[],[]]],[[]],[]] => 3 [[[[[]]]],[[]],[]] => 3 [[[],[],[]],[[],[]]] => 5 [[[],[],[]],[[[]]]] => 4 [[[],[[]]],[[],[]]] => 4 [[[],[[]]],[[[]]]] => 3 [[[[]],[]],[[],[]]] => 4 [[[[]],[]],[[[]]]] => 3 [[[[],[]]],[[],[]]] => 3 [[[[],[]]],[[[]]]] => 3 [[[[[]]]],[[],[]]] => 3 [[[[[]]]],[[[]]]] => 2 [[[],[],[],[]],[],[]] => 4 [[[],[],[[]]],[],[]] => 3 [[[],[[]],[]],[],[]] => 3 [[[],[[],[]]],[],[]] => 3 [[[],[[[]]]],[],[]] => 3 [[[[]],[],[]],[],[]] => 3 [[[[]],[[]]],[],[]] => 3 [[[[],[]],[]],[],[]] => 3 [[[[[]]],[]],[],[]] => 3 [[[[],[],[]]],[],[]] => 3 [[[[],[[]]]],[],[]] => 3 [[[[[]],[]]],[],[]] => 3 [[[[[],[]]]],[],[]] => 3 [[[[[[]]]]],[],[]] => 3 [[[],[],[],[]],[[]]] => 5 [[[],[],[[]]],[[]]] => 4 [[[],[[]],[]],[[]]] => 4 [[[],[[],[]]],[[]]] => 3 [[[],[[[]]]],[[]]] => 3 [[[[]],[],[]],[[]]] => 4 [[[[]],[[]]],[[]]] => 3 [[[[],[]],[]],[[]]] => 3 [[[[[]]],[]],[[]]] => 3 [[[[],[],[]]],[[]]] => 3 [[[[],[[]]]],[[]]] => 2 [[[[[]],[]]],[[]]] => 2 [[[[[],[]]]],[[]]] => 2 [[[[[[]]]]],[[]]] => 2 [[[],[],[],[],[]],[]] => 5 [[[],[],[],[[]]],[]] => 4 [[[],[],[[]],[]],[]] => 4 [[[],[],[[],[]]],[]] => 3 [[[],[],[[[]]]],[]] => 3 [[[],[[]],[],[]],[]] => 4 [[[],[[]],[[]]],[]] => 3 [[[],[[],[]],[]],[]] => 3 [[[],[[[]]],[]],[]] => 3 [[[],[[],[],[]]],[]] => 3 [[[],[[],[[]]]],[]] => 2 [[[],[[[]],[]]],[]] => 2 [[[],[[[],[]]]],[]] => 2 [[[],[[[[]]]]],[]] => 2 [[[[]],[],[],[]],[]] => 4 [[[[]],[],[[]]],[]] => 3 [[[[]],[[]],[]],[]] => 3 [[[[]],[[],[]]],[]] => 3 [[[[]],[[[]]]],[]] => 2 [[[[],[]],[],[]],[]] => 3 [[[[[]]],[],[]],[]] => 3 [[[[],[]],[[]]],[]] => 3 [[[[[]]],[[]]],[]] => 2 [[[[],[],[]],[]],[]] => 3 [[[[],[[]]],[]],[]] => 2 [[[[[]],[]],[]],[]] => 2 [[[[[],[]]],[]],[]] => 2 [[[[[[]]]],[]],[]] => 2 [[[[],[],[],[]]],[]] => 4 [[[[],[],[[]]]],[]] => 3 [[[[],[[]],[]]],[]] => 3 [[[[],[[],[]]]],[]] => 2 [[[[],[[[]]]]],[]] => 2 [[[[[]],[],[]]],[]] => 3 [[[[[]],[[]]]],[]] => 2 [[[[[],[]],[]]],[]] => 2 [[[[[[]]],[]]],[]] => 2 [[[[[],[],[]]]],[]] => 3 [[[[[],[[]]]]],[]] => 2 [[[[[[]],[]]]],[]] => 2 [[[[[[],[]]]]],[]] => 2 [[[[[[[]]]]]],[]] => 2 [[[],[],[],[],[],[]]] => 6 [[[],[],[],[],[[]]]] => 5 [[[],[],[],[[]],[]]] => 5 [[[],[],[],[[],[]]]] => 4 [[[],[],[],[[[]]]]] => 4 [[[],[],[[]],[],[]]] => 5 [[[],[],[[]],[[]]]] => 4 [[[],[],[[],[]],[]]] => 4 [[[],[],[[[]]],[]]] => 4 [[[],[],[[],[],[]]]] => 3 [[[],[],[[],[[]]]]] => 3 [[[],[],[[[]],[]]]] => 3 [[[],[],[[[],[]]]]] => 3 [[[],[],[[[[]]]]]] => 3 [[[],[[]],[],[],[]]] => 5 [[[],[[]],[],[[]]]] => 4 [[[],[[]],[[]],[]]] => 4 [[[],[[]],[[],[]]]] => 3 [[[],[[]],[[[]]]]] => 3 [[[],[[],[]],[],[]]] => 4 [[[],[[[]]],[],[]]] => 4 [[[],[[],[]],[[]]]] => 3 [[[],[[[]]],[[]]]] => 3 [[[],[[],[],[]],[]]] => 3 [[[],[[],[[]]],[]]] => 3 [[[],[[[]],[]],[]]] => 3 [[[],[[[],[]]],[]]] => 3 [[[],[[[[]]]],[]]] => 3 [[[],[[],[],[],[]]]] => 4 [[[],[[],[],[[]]]]] => 3 [[[],[[],[[]],[]]]] => 3 [[[],[[],[[],[]]]]] => 2 [[[],[[],[[[]]]]]] => 2 [[[],[[[]],[],[]]]] => 3 [[[],[[[]],[[]]]]] => 2 [[[],[[[],[]],[]]]] => 2 [[[],[[[[]]],[]]]] => 2 [[[],[[[],[],[]]]]] => 3 [[[],[[[],[[]]]]]] => 2 [[[],[[[[]],[]]]]] => 2 [[[],[[[[],[]]]]]] => 2 [[[],[[[[[]]]]]]] => 2 [[[[]],[],[],[],[]]] => 5 [[[[]],[],[],[[]]]] => 4 [[[[]],[],[[]],[]]] => 4 [[[[]],[],[[],[]]]] => 3 [[[[]],[],[[[]]]]] => 3 [[[[]],[[]],[],[]]] => 4 [[[[]],[[]],[[]]]] => 3 [[[[]],[[],[]],[]]] => 3 [[[[]],[[[]]],[]]] => 3 [[[[]],[[],[],[]]]] => 4 [[[[]],[[],[[]]]]] => 3 [[[[]],[[[]],[]]]] => 3 [[[[]],[[[],[]]]]] => 2 [[[[]],[[[[]]]]]] => 2 [[[[],[]],[],[],[]]] => 4 [[[[[]]],[],[],[]]] => 4 [[[[],[]],[],[[]]]] => 3 [[[[[]]],[],[[]]]] => 3 [[[[],[]],[[]],[]]] => 3 [[[[[]]],[[]],[]]] => 3 [[[[],[]],[[],[]]]] => 4 [[[[],[]],[[[]]]]] => 3 [[[[[]]],[[],[]]]] => 3 [[[[[]]],[[[]]]]] => 2 [[[[],[],[]],[],[]]] => 3 [[[[],[[]]],[],[]]] => 3 [[[[[]],[]],[],[]]] => 3 [[[[[],[]]],[],[]]] => 3 [[[[[[]]]],[],[]]] => 3 [[[[],[],[]],[[]]]] => 4 [[[[],[[]]],[[]]]] => 3 [[[[[]],[]],[[]]]] => 3 [[[[[],[]]],[[]]]] => 2 [[[[[[]]]],[[]]]] => 2 [[[[],[],[],[]],[]]] => 4 [[[[],[],[[]]],[]]] => 3 [[[[],[[]],[]],[]]] => 3 [[[[],[[],[]]],[]]] => 2 [[[[],[[[]]]],[]]] => 2 [[[[[]],[],[]],[]]] => 3 [[[[[]],[[]]],[]]] => 2 [[[[[],[]],[]],[]]] => 2 [[[[[[]]],[]],[]]] => 2 [[[[[],[],[]]],[]]] => 3 [[[[[],[[]]]],[]]] => 2 [[[[[[]],[]]],[]]] => 2 [[[[[[],[]]]],[]]] => 2 [[[[[[[]]]]],[]]] => 2 [[[[],[],[],[],[]]]] => 5 [[[[],[],[],[[]]]]] => 4 [[[[],[],[[]],[]]]] => 4 [[[[],[],[[],[]]]]] => 3 [[[[],[],[[[]]]]]] => 3 [[[[],[[]],[],[]]]] => 4 [[[[],[[]],[[]]]]] => 3 [[[[],[[],[]],[]]]] => 3 [[[[],[[[]]],[]]]] => 3 [[[[],[[],[],[]]]]] => 3 [[[[],[[],[[]]]]]] => 2 [[[[],[[[]],[]]]]] => 2 [[[[],[[[],[]]]]]] => 2 [[[[],[[[[]]]]]]] => 2 [[[[[]],[],[],[]]]] => 4 [[[[[]],[],[[]]]]] => 3 [[[[[]],[[]],[]]]] => 3 [[[[[]],[[],[]]]]] => 3 [[[[[]],[[[]]]]]] => 2 [[[[[],[]],[],[]]]] => 3 [[[[[[]]],[],[]]]] => 3 [[[[[],[]],[[]]]]] => 3 [[[[[[]]],[[]]]]] => 2 [[[[[],[],[]],[]]]] => 3 [[[[[],[[]]],[]]]] => 2 [[[[[[]],[]],[]]]] => 2 [[[[[[],[]]],[]]]] => 2 [[[[[[[]]]],[]]]] => 2 [[[[[],[],[],[]]]]] => 4 [[[[[],[],[[]]]]]] => 3 [[[[[],[[]],[]]]]] => 3 [[[[[],[[],[]]]]]] => 2 [[[[[],[[[]]]]]]] => 2 [[[[[[]],[],[]]]]] => 3 [[[[[[]],[[]]]]]] => 2 [[[[[[],[]],[]]]]] => 2 [[[[[[[]]],[]]]]] => 2 [[[[[[],[],[]]]]]] => 3 [[[[[[],[[]]]]]]] => 2 [[[[[[[]],[]]]]]] => 2 [[[[[[[],[]]]]]]] => 2 [[[[[[[[]]]]]]]] => 1 [[],[],[],[],[],[],[],[]] => 8 [[],[],[],[],[],[],[[]]] => 7 [[],[],[],[],[],[[]],[]] => 7 [[],[],[],[],[],[[],[]]] => 6 [[],[],[],[],[],[[[]]]] => 6 [[],[],[],[],[[]],[],[]] => 7 [[],[],[],[],[[]],[[]]] => 6 [[],[],[],[],[[],[]],[]] => 6 [[],[],[],[],[[[]]],[]] => 6 [[],[],[],[],[[],[],[]]] => 5 [[],[],[],[],[[],[[]]]] => 5 [[],[],[],[],[[[]],[]]] => 5 [[],[],[],[],[[[],[]]]] => 5 [[],[],[],[],[[[[]]]]] => 5 [[],[],[],[[]],[],[],[]] => 7 [[],[],[],[[]],[],[[]]] => 6 [[],[],[],[[]],[[]],[]] => 6 [[],[],[],[[]],[[],[]]] => 5 [[],[],[],[[]],[[[]]]] => 5 [[],[],[],[[],[]],[],[]] => 6 [[],[],[],[[[]]],[],[]] => 6 [[],[],[],[[],[]],[[]]] => 5 [[],[],[],[[[]]],[[]]] => 5 [[],[],[],[[],[],[]],[]] => 5 [[],[],[],[[],[[]]],[]] => 5 [[],[],[],[[[]],[]],[]] => 5 [[],[],[],[[[],[]]],[]] => 5 [[],[],[],[[[[]]]],[]] => 5 [[],[],[],[[],[],[],[]]] => 4 [[],[],[],[[],[],[[]]]] => 4 [[],[],[],[[],[[]],[]]] => 4 [[],[],[],[[],[[],[]]]] => 4 [[],[],[],[[],[[[]]]]] => 4 [[],[],[],[[[]],[],[]]] => 4 [[],[],[],[[[]],[[]]]] => 4 [[],[],[],[[[],[]],[]]] => 4 [[],[],[],[[[[]]],[]]] => 4 [[],[],[],[[[],[],[]]]] => 4 [[],[],[],[[[],[[]]]]] => 4 [[],[],[],[[[[]],[]]]] => 4 [[],[],[],[[[[],[]]]]] => 4 [[],[],[],[[[[[]]]]]] => 4 [[],[],[[]],[],[],[],[]] => 7 [[],[],[[]],[],[],[[]]] => 6 [[],[],[[]],[],[[]],[]] => 6 [[],[],[[]],[],[[],[]]] => 5 [[],[],[[]],[],[[[]]]] => 5 [[],[],[[]],[[]],[],[]] => 6 [[],[],[[]],[[]],[[]]] => 5 [[],[],[[]],[[],[]],[]] => 5 [[],[],[[]],[[[]]],[]] => 5 [[],[],[[]],[[],[],[]]] => 4 [[],[],[[]],[[],[[]]]] => 4 [[],[],[[]],[[[]],[]]] => 4 [[],[],[[]],[[[],[]]]] => 4 [[],[],[[]],[[[[]]]]] => 4 [[],[],[[],[]],[],[],[]] => 6 [[],[],[[[]]],[],[],[]] => 6 [[],[],[[],[]],[],[[]]] => 5 [[],[],[[[]]],[],[[]]] => 5 [[],[],[[],[]],[[]],[]] => 5 [[],[],[[[]]],[[]],[]] => 5 [[],[],[[],[]],[[],[]]] => 4 [[],[],[[],[]],[[[]]]] => 4 [[],[],[[[]]],[[],[]]] => 4 [[],[],[[[]]],[[[]]]] => 4 [[],[],[[],[],[]],[],[]] => 5 [[],[],[[],[[]]],[],[]] => 5 [[],[],[[[]],[]],[],[]] => 5 [[],[],[[[],[]]],[],[]] => 5 [[],[],[[[[]]]],[],[]] => 5 [[],[],[[],[],[]],[[]]] => 4 [[],[],[[],[[]]],[[]]] => 4 [[],[],[[[]],[]],[[]]] => 4 [[],[],[[[],[]]],[[]]] => 4 [[],[],[[[[]]]],[[]]] => 4 [[],[],[[],[],[],[]],[]] => 4 [[],[],[[],[],[[]]],[]] => 4 [[],[],[[],[[]],[]],[]] => 4 [[],[],[[],[[],[]]],[]] => 4 [[],[],[[],[[[]]]],[]] => 4 [[],[],[[[]],[],[]],[]] => 4 [[],[],[[[]],[[]]],[]] => 4 [[],[],[[[],[]],[]],[]] => 4 [[],[],[[[[]]],[]],[]] => 4 [[],[],[[[],[],[]]],[]] => 4 [[],[],[[[],[[]]]],[]] => 4 [[],[],[[[[]],[]]],[]] => 4 [[],[],[[[[],[]]]],[]] => 4 [[],[],[[[[[]]]]],[]] => 4 [[],[],[[],[],[],[],[]]] => 5 [[],[],[[],[],[],[[]]]] => 4 [[],[],[[],[],[[]],[]]] => 4 [[],[],[[],[],[[],[]]]] => 3 [[],[],[[],[],[[[]]]]] => 3 [[],[],[[],[[]],[],[]]] => 4 [[],[],[[],[[]],[[]]]] => 3 [[],[],[[],[[],[]],[]]] => 3 [[],[],[[],[[[]]],[]]] => 3 [[],[],[[],[[],[],[]]]] => 3 [[],[],[[],[[],[[]]]]] => 3 [[],[],[[],[[[]],[]]]] => 3 [[],[],[[],[[[],[]]]]] => 3 [[],[],[[],[[[[]]]]]] => 3 [[],[],[[[]],[],[],[]]] => 4 [[],[],[[[]],[],[[]]]] => 3 [[],[],[[[]],[[]],[]]] => 3 [[],[],[[[]],[[],[]]]] => 3 [[],[],[[[]],[[[]]]]] => 3 [[],[],[[[],[]],[],[]]] => 3 [[],[],[[[[]]],[],[]]] => 3 [[],[],[[[],[]],[[]]]] => 3 [[],[],[[[[]]],[[]]]] => 3 [[],[],[[[],[],[]],[]]] => 3 [[],[],[[[],[[]]],[]]] => 3 [[],[],[[[[]],[]],[]]] => 3 [[],[],[[[[],[]]],[]]] => 3 [[],[],[[[[[]]]],[]]] => 3 [[],[],[[[],[],[],[]]]] => 4 [[],[],[[[],[],[[]]]]] => 3 [[],[],[[[],[[]],[]]]] => 3 [[],[],[[[],[[],[]]]]] => 3 [[],[],[[[],[[[]]]]]] => 3 [[],[],[[[[]],[],[]]]] => 3 [[],[],[[[[]],[[]]]]] => 3 [[],[],[[[[],[]],[]]]] => 3 [[],[],[[[[[]]],[]]]] => 3 [[],[],[[[[],[],[]]]]] => 3 [[],[],[[[[],[[]]]]]] => 3 [[],[],[[[[[]],[]]]]] => 3 [[],[],[[[[[],[]]]]]] => 3 [[],[],[[[[[[]]]]]]] => 3 [[],[[]],[],[],[],[],[]] => 7 [[],[[]],[],[],[],[[]]] => 6 [[],[[]],[],[],[[]],[]] => 6 [[],[[]],[],[],[[],[]]] => 5 [[],[[]],[],[],[[[]]]] => 5 [[],[[]],[],[[]],[],[]] => 6 [[],[[]],[],[[]],[[]]] => 5 [[],[[]],[],[[],[]],[]] => 5 [[],[[]],[],[[[]]],[]] => 5 [[],[[]],[],[[],[],[]]] => 4 [[],[[]],[],[[],[[]]]] => 4 [[],[[]],[],[[[]],[]]] => 4 [[],[[]],[],[[[],[]]]] => 4 [[],[[]],[],[[[[]]]]] => 4 [[],[[]],[[]],[],[],[]] => 6 [[],[[]],[[]],[],[[]]] => 5 [[],[[]],[[]],[[]],[]] => 5 [[],[[]],[[]],[[],[]]] => 4 [[],[[]],[[]],[[[]]]] => 4 [[],[[]],[[],[]],[],[]] => 5 [[],[[]],[[[]]],[],[]] => 5 [[],[[]],[[],[]],[[]]] => 4 [[],[[]],[[[]]],[[]]] => 4 [[],[[]],[[],[],[]],[]] => 4 [[],[[]],[[],[[]]],[]] => 4 [[],[[]],[[[]],[]],[]] => 4 [[],[[]],[[[],[]]],[]] => 4 [[],[[]],[[[[]]]],[]] => 4 [[],[[]],[[],[],[],[]]] => 5 [[],[[]],[[],[],[[]]]] => 4 [[],[[]],[[],[[]],[]]] => 4 [[],[[]],[[],[[],[]]]] => 3 [[],[[]],[[],[[[]]]]] => 3 [[],[[]],[[[]],[],[]]] => 4 [[],[[]],[[[]],[[]]]] => 3 [[],[[]],[[[],[]],[]]] => 3 [[],[[]],[[[[]]],[]]] => 3 [[],[[]],[[[],[],[]]]] => 3 [[],[[]],[[[],[[]]]]] => 3 [[],[[]],[[[[]],[]]]] => 3 [[],[[]],[[[[],[]]]]] => 3 [[],[[]],[[[[[]]]]]] => 3 [[],[[],[]],[],[],[],[]] => 6 [[],[[[]]],[],[],[],[]] => 6 [[],[[],[]],[],[],[[]]] => 5 [[],[[[]]],[],[],[[]]] => 5 [[],[[],[]],[],[[]],[]] => 5 [[],[[[]]],[],[[]],[]] => 5 [[],[[],[]],[],[[],[]]] => 4 [[],[[],[]],[],[[[]]]] => 4 [[],[[[]]],[],[[],[]]] => 4 [[],[[[]]],[],[[[]]]] => 4 [[],[[],[]],[[]],[],[]] => 5 [[],[[[]]],[[]],[],[]] => 5 [[],[[],[]],[[]],[[]]] => 4 [[],[[[]]],[[]],[[]]] => 4 [[],[[],[]],[[],[]],[]] => 4 [[],[[],[]],[[[]]],[]] => 4 [[],[[[]]],[[],[]],[]] => 4 [[],[[[]]],[[[]]],[]] => 4 [[],[[],[]],[[],[],[]]] => 5 [[],[[],[]],[[],[[]]]] => 4 [[],[[],[]],[[[]],[]]] => 4 [[],[[],[]],[[[],[]]]] => 3 [[],[[],[]],[[[[]]]]] => 3 [[],[[[]]],[[],[],[]]] => 4 [[],[[[]]],[[],[[]]]] => 3 [[],[[[]]],[[[]],[]]] => 3 [[],[[[]]],[[[],[]]]] => 3 [[],[[[]]],[[[[]]]]] => 3 [[],[[],[],[]],[],[],[]] => 5 [[],[[],[[]]],[],[],[]] => 5 [[],[[[]],[]],[],[],[]] => 5 [[],[[[],[]]],[],[],[]] => 5 [[],[[[[]]]],[],[],[]] => 5 [[],[[],[],[]],[],[[]]] => 4 [[],[[],[[]]],[],[[]]] => 4 [[],[[[]],[]],[],[[]]] => 4 [[],[[[],[]]],[],[[]]] => 4 [[],[[[[]]]],[],[[]]] => 4 [[],[[],[],[]],[[]],[]] => 4 [[],[[],[[]]],[[]],[]] => 4 [[],[[[]],[]],[[]],[]] => 4 [[],[[[],[]]],[[]],[]] => 4 [[],[[[[]]]],[[]],[]] => 4 [[],[[],[],[]],[[],[]]] => 5 [[],[[],[],[]],[[[]]]] => 4 [[],[[],[[]]],[[],[]]] => 4 [[],[[],[[]]],[[[]]]] => 3 [[],[[[]],[]],[[],[]]] => 4 [[],[[[]],[]],[[[]]]] => 3 [[],[[[],[]]],[[],[]]] => 3 [[],[[[],[]]],[[[]]]] => 3 [[],[[[[]]]],[[],[]]] => 3 [[],[[[[]]]],[[[]]]] => 3 [[],[[],[],[],[]],[],[]] => 4 [[],[[],[],[[]]],[],[]] => 4 [[],[[],[[]],[]],[],[]] => 4 [[],[[],[[],[]]],[],[]] => 4 [[],[[],[[[]]]],[],[]] => 4 [[],[[[]],[],[]],[],[]] => 4 [[],[[[]],[[]]],[],[]] => 4 [[],[[[],[]],[]],[],[]] => 4 [[],[[[[]]],[]],[],[]] => 4 [[],[[[],[],[]]],[],[]] => 4 [[],[[[],[[]]]],[],[]] => 4 [[],[[[[]],[]]],[],[]] => 4 [[],[[[[],[]]]],[],[]] => 4 [[],[[[[[]]]]],[],[]] => 4 [[],[[],[],[],[]],[[]]] => 5 [[],[[],[],[[]]],[[]]] => 4 [[],[[],[[]],[]],[[]]] => 4 [[],[[],[[],[]]],[[]]] => 3 [[],[[],[[[]]]],[[]]] => 3 [[],[[[]],[],[]],[[]]] => 4 [[],[[[]],[[]]],[[]]] => 3 [[],[[[],[]],[]],[[]]] => 3 [[],[[[[]]],[]],[[]]] => 3 [[],[[[],[],[]]],[[]]] => 3 [[],[[[],[[]]]],[[]]] => 3 [[],[[[[]],[]]],[[]]] => 3 [[],[[[[],[]]]],[[]]] => 3 [[],[[[[[]]]]],[[]]] => 3 [[],[[],[],[],[],[]],[]] => 5 [[],[[],[],[],[[]]],[]] => 4 [[],[[],[],[[]],[]],[]] => 4 [[],[[],[],[[],[]]],[]] => 3 [[],[[],[],[[[]]]],[]] => 3 [[],[[],[[]],[],[]],[]] => 4 [[],[[],[[]],[[]]],[]] => 3 [[],[[],[[],[]],[]],[]] => 3 [[],[[],[[[]]],[]],[]] => 3 [[],[[],[[],[],[]]],[]] => 3 [[],[[],[[],[[]]]],[]] => 3 [[],[[],[[[]],[]]],[]] => 3 [[],[[],[[[],[]]]],[]] => 3 [[],[[],[[[[]]]]],[]] => 3 [[],[[[]],[],[],[]],[]] => 4 [[],[[[]],[],[[]]],[]] => 3 [[],[[[]],[[]],[]],[]] => 3 [[],[[[]],[[],[]]],[]] => 3 [[],[[[]],[[[]]]],[]] => 3 [[],[[[],[]],[],[]],[]] => 3 [[],[[[[]]],[],[]],[]] => 3 [[],[[[],[]],[[]]],[]] => 3 [[],[[[[]]],[[]]],[]] => 3 [[],[[[],[],[]],[]],[]] => 3 [[],[[[],[[]]],[]],[]] => 3 [[],[[[[]],[]],[]],[]] => 3 [[],[[[[],[]]],[]],[]] => 3 [[],[[[[[]]]],[]],[]] => 3 [[],[[[],[],[],[]]],[]] => 4 [[],[[[],[],[[]]]],[]] => 3 [[],[[[],[[]],[]]],[]] => 3 [[],[[[],[[],[]]]],[]] => 3 [[],[[[],[[[]]]]],[]] => 3 [[],[[[[]],[],[]]],[]] => 3 [[],[[[[]],[[]]]],[]] => 3 [[],[[[[],[]],[]]],[]] => 3 [[],[[[[[]]],[]]],[]] => 3 [[],[[[[],[],[]]]],[]] => 3 [[],[[[[],[[]]]]],[]] => 3 [[],[[[[[]],[]]]],[]] => 3 [[],[[[[[],[]]]]],[]] => 3 [[],[[[[[[]]]]]],[]] => 3 [[],[[],[],[],[],[],[]]] => 6 [[],[[],[],[],[],[[]]]] => 5 [[],[[],[],[],[[]],[]]] => 5 [[],[[],[],[],[[],[]]]] => 4 [[],[[],[],[],[[[]]]]] => 4 [[],[[],[],[[]],[],[]]] => 5 [[],[[],[],[[]],[[]]]] => 4 [[],[[],[],[[],[]],[]]] => 4 [[],[[],[],[[[]]],[]]] => 4 [[],[[],[],[[],[],[]]]] => 3 [[],[[],[],[[],[[]]]]] => 3 [[],[[],[],[[[]],[]]]] => 3 [[],[[],[],[[[],[]]]]] => 3 [[],[[],[],[[[[]]]]]] => 3 [[],[[],[[]],[],[],[]]] => 5 [[],[[],[[]],[],[[]]]] => 4 [[],[[],[[]],[[]],[]]] => 4 [[],[[],[[]],[[],[]]]] => 3 [[],[[],[[]],[[[]]]]] => 3 [[],[[],[[],[]],[],[]]] => 4 [[],[[],[[[]]],[],[]]] => 4 [[],[[],[[],[]],[[]]]] => 3 [[],[[],[[[]]],[[]]]] => 3 [[],[[],[[],[],[]],[]]] => 3 [[],[[],[[],[[]]],[]]] => 3 [[],[[],[[[]],[]],[]]] => 3 [[],[[],[[[],[]]],[]]] => 3 [[],[[],[[[[]]]],[]]] => 3 [[],[[],[[],[],[],[]]]] => 4 [[],[[],[[],[],[[]]]]] => 3 [[],[[],[[],[[]],[]]]] => 3 [[],[[],[[],[[],[]]]]] => 2 [[],[[],[[],[[[]]]]]] => 2 [[],[[],[[[]],[],[]]]] => 3 [[],[[],[[[]],[[]]]]] => 2 [[],[[],[[[],[]],[]]]] => 2 [[],[[],[[[[]]],[]]]] => 2 [[],[[],[[[],[],[]]]]] => 3 [[],[[],[[[],[[]]]]]] => 2 [[],[[],[[[[]],[]]]]] => 2 [[],[[],[[[[],[]]]]]] => 2 [[],[[],[[[[[]]]]]]] => 2 [[],[[[]],[],[],[],[]]] => 5 [[],[[[]],[],[],[[]]]] => 4 [[],[[[]],[],[[]],[]]] => 4 [[],[[[]],[],[[],[]]]] => 3 [[],[[[]],[],[[[]]]]] => 3 [[],[[[]],[[]],[],[]]] => 4 [[],[[[]],[[]],[[]]]] => 3 [[],[[[]],[[],[]],[]]] => 3 [[],[[[]],[[[]]],[]]] => 3 [[],[[[]],[[],[],[]]]] => 4 [[],[[[]],[[],[[]]]]] => 3 [[],[[[]],[[[]],[]]]] => 3 [[],[[[]],[[[],[]]]]] => 2 [[],[[[]],[[[[]]]]]] => 2 [[],[[[],[]],[],[],[]]] => 4 [[],[[[[]]],[],[],[]]] => 4 [[],[[[],[]],[],[[]]]] => 3 [[],[[[[]]],[],[[]]]] => 3 [[],[[[],[]],[[]],[]]] => 3 [[],[[[[]]],[[]],[]]] => 3 [[],[[[],[]],[[],[]]]] => 4 [[],[[[],[]],[[[]]]]] => 3 [[],[[[[]]],[[],[]]]] => 3 [[],[[[[]]],[[[]]]]] => 2 [[],[[[],[],[]],[],[]]] => 3 [[],[[[],[[]]],[],[]]] => 3 [[],[[[[]],[]],[],[]]] => 3 [[],[[[[],[]]],[],[]]] => 3 [[],[[[[[]]]],[],[]]] => 3 [[],[[[],[],[]],[[]]]] => 4 [[],[[[],[[]]],[[]]]] => 3 [[],[[[[]],[]],[[]]]] => 3 [[],[[[[],[]]],[[]]]] => 2 [[],[[[[[]]]],[[]]]] => 2 [[],[[[],[],[],[]],[]]] => 4 [[],[[[],[],[[]]],[]]] => 3 [[],[[[],[[]],[]],[]]] => 3 [[],[[[],[[],[]]],[]]] => 2 [[],[[[],[[[]]]],[]]] => 2 [[],[[[[]],[],[]],[]]] => 3 [[],[[[[]],[[]]],[]]] => 2 [[],[[[[],[]],[]],[]]] => 2 [[],[[[[[]]],[]],[]]] => 2 [[],[[[[],[],[]]],[]]] => 3 [[],[[[[],[[]]]],[]]] => 2 [[],[[[[[]],[]]],[]]] => 2 [[],[[[[[],[]]]],[]]] => 2 [[],[[[[[[]]]]],[]]] => 2 [[],[[[],[],[],[],[]]]] => 5 [[],[[[],[],[],[[]]]]] => 4 [[],[[[],[],[[]],[]]]] => 4 [[],[[[],[],[[],[]]]]] => 3 [[],[[[],[],[[[]]]]]] => 3 [[],[[[],[[]],[],[]]]] => 4 [[],[[[],[[]],[[]]]]] => 3 [[],[[[],[[],[]],[]]]] => 3 [[],[[[],[[[]]],[]]]] => 3 [[],[[[],[[],[],[]]]]] => 3 [[],[[[],[[],[[]]]]]] => 2 [[],[[[],[[[]],[]]]]] => 2 [[],[[[],[[[],[]]]]]] => 2 [[],[[[],[[[[]]]]]]] => 2 [[],[[[[]],[],[],[]]]] => 4 [[],[[[[]],[],[[]]]]] => 3 [[],[[[[]],[[]],[]]]] => 3 [[],[[[[]],[[],[]]]]] => 3 [[],[[[[]],[[[]]]]]] => 2 [[],[[[[],[]],[],[]]]] => 3 [[],[[[[[]]],[],[]]]] => 3 [[],[[[[],[]],[[]]]]] => 3 [[],[[[[[]]],[[]]]]] => 2 [[],[[[[],[],[]],[]]]] => 3 [[],[[[[],[[]]],[]]]] => 2 [[],[[[[[]],[]],[]]]] => 2 [[],[[[[[],[]]],[]]]] => 2 [[],[[[[[[]]]],[]]]] => 2 [[],[[[[],[],[],[]]]]] => 4 [[],[[[[],[],[[]]]]]] => 3 [[],[[[[],[[]],[]]]]] => 3 [[],[[[[],[[],[]]]]]] => 2 [[],[[[[],[[[]]]]]]] => 2 [[],[[[[[]],[],[]]]]] => 3 [[],[[[[[]],[[]]]]]] => 2 [[],[[[[[],[]],[]]]]] => 2 [[],[[[[[[]]],[]]]]] => 2 [[],[[[[[],[],[]]]]]] => 3 [[],[[[[[],[[]]]]]]] => 2 [[],[[[[[[]],[]]]]]] => 2 [[],[[[[[[],[]]]]]]] => 2 [[],[[[[[[[]]]]]]]] => 2 [[[]],[],[],[],[],[],[]] => 7 [[[]],[],[],[],[],[[]]] => 6 [[[]],[],[],[],[[]],[]] => 6 [[[]],[],[],[],[[],[]]] => 5 [[[]],[],[],[],[[[]]]] => 5 [[[]],[],[],[[]],[],[]] => 6 [[[]],[],[],[[]],[[]]] => 5 [[[]],[],[],[[],[]],[]] => 5 [[[]],[],[],[[[]]],[]] => 5 [[[]],[],[],[[],[],[]]] => 4 [[[]],[],[],[[],[[]]]] => 4 [[[]],[],[],[[[]],[]]] => 4 [[[]],[],[],[[[],[]]]] => 4 [[[]],[],[],[[[[]]]]] => 4 [[[]],[],[[]],[],[],[]] => 6 [[[]],[],[[]],[],[[]]] => 5 [[[]],[],[[]],[[]],[]] => 5 [[[]],[],[[]],[[],[]]] => 4 [[[]],[],[[]],[[[]]]] => 4 [[[]],[],[[],[]],[],[]] => 5 [[[]],[],[[[]]],[],[]] => 5 [[[]],[],[[],[]],[[]]] => 4 [[[]],[],[[[]]],[[]]] => 4 [[[]],[],[[],[],[]],[]] => 4 [[[]],[],[[],[[]]],[]] => 4 [[[]],[],[[[]],[]],[]] => 4 [[[]],[],[[[],[]]],[]] => 4 [[[]],[],[[[[]]]],[]] => 4 [[[]],[],[[],[],[],[]]] => 5 [[[]],[],[[],[],[[]]]] => 4 [[[]],[],[[],[[]],[]]] => 4 [[[]],[],[[],[[],[]]]] => 3 [[[]],[],[[],[[[]]]]] => 3 [[[]],[],[[[]],[],[]]] => 4 [[[]],[],[[[]],[[]]]] => 3 [[[]],[],[[[],[]],[]]] => 3 [[[]],[],[[[[]]],[]]] => 3 [[[]],[],[[[],[],[]]]] => 3 [[[]],[],[[[],[[]]]]] => 3 [[[]],[],[[[[]],[]]]] => 3 [[[]],[],[[[[],[]]]]] => 3 [[[]],[],[[[[[]]]]]] => 3 [[[]],[[]],[],[],[],[]] => 6 [[[]],[[]],[],[],[[]]] => 5 [[[]],[[]],[],[[]],[]] => 5 [[[]],[[]],[],[[],[]]] => 4 [[[]],[[]],[],[[[]]]] => 4 [[[]],[[]],[[]],[],[]] => 5 [[[]],[[]],[[]],[[]]] => 4 [[[]],[[]],[[],[]],[]] => 4 [[[]],[[]],[[[]]],[]] => 4 [[[]],[[]],[[],[],[]]] => 5 [[[]],[[]],[[],[[]]]] => 4 [[[]],[[]],[[[]],[]]] => 4 [[[]],[[]],[[[],[]]]] => 3 [[[]],[[]],[[[[]]]]] => 3 [[[]],[[],[]],[],[],[]] => 5 [[[]],[[[]]],[],[],[]] => 5 [[[]],[[],[]],[],[[]]] => 4 [[[]],[[[]]],[],[[]]] => 4 [[[]],[[],[]],[[]],[]] => 4 [[[]],[[[]]],[[]],[]] => 4 [[[]],[[],[]],[[],[]]] => 5 [[[]],[[],[]],[[[]]]] => 4 [[[]],[[[]]],[[],[]]] => 4 [[[]],[[[]]],[[[]]]] => 3 [[[]],[[],[],[]],[],[]] => 4 [[[]],[[],[[]]],[],[]] => 4 [[[]],[[[]],[]],[],[]] => 4 [[[]],[[[],[]]],[],[]] => 4 [[[]],[[[[]]]],[],[]] => 4 [[[]],[[],[],[]],[[]]] => 5 [[[]],[[],[[]]],[[]]] => 4 [[[]],[[[]],[]],[[]]] => 4 [[[]],[[[],[]]],[[]]] => 3 [[[]],[[[[]]]],[[]]] => 3 [[[]],[[],[],[],[]],[]] => 5 [[[]],[[],[],[[]]],[]] => 4 [[[]],[[],[[]],[]],[]] => 4 [[[]],[[],[[],[]]],[]] => 3 [[[]],[[],[[[]]]],[]] => 3 [[[]],[[[]],[],[]],[]] => 4 [[[]],[[[]],[[]]],[]] => 3 [[[]],[[[],[]],[]],[]] => 3 [[[]],[[[[]]],[]],[]] => 3 [[[]],[[[],[],[]]],[]] => 3 [[[]],[[[],[[]]]],[]] => 3 [[[]],[[[[]],[]]],[]] => 3 [[[]],[[[[],[]]]],[]] => 3 [[[]],[[[[[]]]]],[]] => 3 [[[]],[[],[],[],[],[]]] => 6 [[[]],[[],[],[],[[]]]] => 5 [[[]],[[],[],[[]],[]]] => 5 [[[]],[[],[],[[],[]]]] => 4 [[[]],[[],[],[[[]]]]] => 4 [[[]],[[],[[]],[],[]]] => 5 [[[]],[[],[[]],[[]]]] => 4 [[[]],[[],[[],[]],[]]] => 4 [[[]],[[],[[[]]],[]]] => 4 [[[]],[[],[[],[],[]]]] => 3 [[[]],[[],[[],[[]]]]] => 3 [[[]],[[],[[[]],[]]]] => 3 [[[]],[[],[[[],[]]]]] => 3 [[[]],[[],[[[[]]]]]] => 3 [[[]],[[[]],[],[],[]]] => 5 [[[]],[[[]],[],[[]]]] => 4 [[[]],[[[]],[[]],[]]] => 4 [[[]],[[[]],[[],[]]]] => 3 [[[]],[[[]],[[[]]]]] => 3 [[[]],[[[],[]],[],[]]] => 4 [[[]],[[[[]]],[],[]]] => 4 [[[]],[[[],[]],[[]]]] => 3 [[[]],[[[[]]],[[]]]] => 3 [[[]],[[[],[],[]],[]]] => 3 [[[]],[[[],[[]]],[]]] => 3 [[[]],[[[[]],[]],[]]] => 3 [[[]],[[[[],[]]],[]]] => 3 [[[]],[[[[[]]]],[]]] => 3 [[[]],[[[],[],[],[]]]] => 4 [[[]],[[[],[],[[]]]]] => 3 [[[]],[[[],[[]],[]]]] => 3 [[[]],[[[],[[],[]]]]] => 2 [[[]],[[[],[[[]]]]]] => 2 [[[]],[[[[]],[],[]]]] => 3 [[[]],[[[[]],[[]]]]] => 2 [[[]],[[[[],[]],[]]]] => 2 [[[]],[[[[[]]],[]]]] => 2 [[[]],[[[[],[],[]]]]] => 3 [[[]],[[[[],[[]]]]]] => 2 [[[]],[[[[[]],[]]]]] => 2 [[[]],[[[[[],[]]]]]] => 2 [[[]],[[[[[[]]]]]]] => 2 [[[],[]],[],[],[],[],[]] => 6 [[[[]]],[],[],[],[],[]] => 6 [[[],[]],[],[],[],[[]]] => 5 [[[[]]],[],[],[],[[]]] => 5 [[[],[]],[],[],[[]],[]] => 5 [[[[]]],[],[],[[]],[]] => 5 [[[],[]],[],[],[[],[]]] => 4 [[[],[]],[],[],[[[]]]] => 4 [[[[]]],[],[],[[],[]]] => 4 [[[[]]],[],[],[[[]]]] => 4 [[[],[]],[],[[]],[],[]] => 5 [[[[]]],[],[[]],[],[]] => 5 [[[],[]],[],[[]],[[]]] => 4 [[[[]]],[],[[]],[[]]] => 4 ----------------------------------------------------------------------------- Created: Dec 01, 2017 at 19:26 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 04, 2017 at 18:38 by Martin Rubey