***************************************************************************** * 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: St000700 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The protection number of an ordered tree. This is the minimal distance from the root to a leaf. ----------------------------------------------------------------------------- References: [1] Heuberger, C., Prodinger, H. Protection Number in Plane Trees [[arXiv:1702.06816]] ----------------------------------------------------------------------------- Code: def statistic(T): if len(T) == 0: return 0 else: return 1+min(statistic(S) for S in T) ----------------------------------------------------------------------------- Statistic values: [[]] => 1 [[],[]] => 1 [[[]]] => 2 [[],[],[]] => 1 [[],[[]]] => 1 [[[]],[]] => 1 [[[],[]]] => 2 [[[[]]]] => 3 [[],[],[],[]] => 1 [[],[],[[]]] => 1 [[],[[]],[]] => 1 [[],[[],[]]] => 1 [[],[[[]]]] => 1 [[[]],[],[]] => 1 [[[]],[[]]] => 2 [[[],[]],[]] => 1 [[[[]]],[]] => 1 [[[],[],[]]] => 2 [[[],[[]]]] => 2 [[[[]],[]]] => 2 [[[[],[]]]] => 3 [[[[[]]]]] => 4 [[],[],[],[],[]] => 1 [[],[],[],[[]]] => 1 [[],[],[[]],[]] => 1 [[],[],[[],[]]] => 1 [[],[],[[[]]]] => 1 [[],[[]],[],[]] => 1 [[],[[]],[[]]] => 1 [[],[[],[]],[]] => 1 [[],[[[]]],[]] => 1 [[],[[],[],[]]] => 1 [[],[[],[[]]]] => 1 [[],[[[]],[]]] => 1 [[],[[[],[]]]] => 1 [[],[[[[]]]]] => 1 [[[]],[],[],[]] => 1 [[[]],[],[[]]] => 1 [[[]],[[]],[]] => 1 [[[]],[[],[]]] => 2 [[[]],[[[]]]] => 2 [[[],[]],[],[]] => 1 [[[[]]],[],[]] => 1 [[[],[]],[[]]] => 2 [[[[]]],[[]]] => 2 [[[],[],[]],[]] => 1 [[[],[[]]],[]] => 1 [[[[]],[]],[]] => 1 [[[[],[]]],[]] => 1 [[[[[]]]],[]] => 1 [[[],[],[],[]]] => 2 [[[],[],[[]]]] => 2 [[[],[[]],[]]] => 2 [[[],[[],[]]]] => 2 [[[],[[[]]]]] => 2 [[[[]],[],[]]] => 2 [[[[]],[[]]]] => 3 [[[[],[]],[]]] => 2 [[[[[]]],[]]] => 2 [[[[],[],[]]]] => 3 [[[[],[[]]]]] => 3 [[[[[]],[]]]] => 3 [[[[[],[]]]]] => 4 [[[[[[]]]]]] => 5 [[],[],[],[],[],[]] => 1 [[],[],[],[],[[]]] => 1 [[],[],[],[[]],[]] => 1 [[],[],[],[[],[]]] => 1 [[],[],[],[[[]]]] => 1 [[],[],[[]],[],[]] => 1 [[],[],[[]],[[]]] => 1 [[],[],[[],[]],[]] => 1 [[],[],[[[]]],[]] => 1 [[],[],[[],[],[]]] => 1 [[],[],[[],[[]]]] => 1 [[],[],[[[]],[]]] => 1 [[],[],[[[],[]]]] => 1 [[],[],[[[[]]]]] => 1 [[],[[]],[],[],[]] => 1 [[],[[]],[],[[]]] => 1 [[],[[]],[[]],[]] => 1 [[],[[]],[[],[]]] => 1 [[],[[]],[[[]]]] => 1 [[],[[],[]],[],[]] => 1 [[],[[[]]],[],[]] => 1 [[],[[],[]],[[]]] => 1 [[],[[[]]],[[]]] => 1 [[],[[],[],[]],[]] => 1 [[],[[],[[]]],[]] => 1 [[],[[[]],[]],[]] => 1 [[],[[[],[]]],[]] => 1 [[],[[[[]]]],[]] => 1 [[],[[],[],[],[]]] => 1 [[],[[],[],[[]]]] => 1 [[],[[],[[]],[]]] => 1 [[],[[],[[],[]]]] => 1 [[],[[],[[[]]]]] => 1 [[],[[[]],[],[]]] => 1 [[],[[[]],[[]]]] => 1 [[],[[[],[]],[]]] => 1 [[],[[[[]]],[]]] => 1 [[],[[[],[],[]]]] => 1 [[],[[[],[[]]]]] => 1 [[],[[[[]],[]]]] => 1 [[],[[[[],[]]]]] => 1 [[],[[[[[]]]]]] => 1 [[[]],[],[],[],[]] => 1 [[[]],[],[],[[]]] => 1 [[[]],[],[[]],[]] => 1 [[[]],[],[[],[]]] => 1 [[[]],[],[[[]]]] => 1 [[[]],[[]],[],[]] => 1 [[[]],[[]],[[]]] => 2 [[[]],[[],[]],[]] => 1 [[[]],[[[]]],[]] => 1 [[[]],[[],[],[]]] => 2 [[[]],[[],[[]]]] => 2 [[[]],[[[]],[]]] => 2 [[[]],[[[],[]]]] => 2 [[[]],[[[[]]]]] => 2 [[[],[]],[],[],[]] => 1 [[[[]]],[],[],[]] => 1 [[[],[]],[],[[]]] => 1 [[[[]]],[],[[]]] => 1 [[[],[]],[[]],[]] => 1 [[[[]]],[[]],[]] => 1 [[[],[]],[[],[]]] => 2 [[[],[]],[[[]]]] => 2 [[[[]]],[[],[]]] => 2 [[[[]]],[[[]]]] => 3 [[[],[],[]],[],[]] => 1 [[[],[[]]],[],[]] => 1 [[[[]],[]],[],[]] => 1 [[[[],[]]],[],[]] => 1 [[[[[]]]],[],[]] => 1 [[[],[],[]],[[]]] => 2 [[[],[[]]],[[]]] => 2 [[[[]],[]],[[]]] => 2 [[[[],[]]],[[]]] => 2 [[[[[]]]],[[]]] => 2 [[[],[],[],[]],[]] => 1 [[[],[],[[]]],[]] => 1 [[[],[[]],[]],[]] => 1 [[[],[[],[]]],[]] => 1 [[[],[[[]]]],[]] => 1 [[[[]],[],[]],[]] => 1 [[[[]],[[]]],[]] => 1 [[[[],[]],[]],[]] => 1 [[[[[]]],[]],[]] => 1 [[[[],[],[]]],[]] => 1 [[[[],[[]]]],[]] => 1 [[[[[]],[]]],[]] => 1 [[[[[],[]]]],[]] => 1 [[[[[[]]]]],[]] => 1 [[[],[],[],[],[]]] => 2 [[[],[],[],[[]]]] => 2 [[[],[],[[]],[]]] => 2 [[[],[],[[],[]]]] => 2 [[[],[],[[[]]]]] => 2 [[[],[[]],[],[]]] => 2 [[[],[[]],[[]]]] => 2 [[[],[[],[]],[]]] => 2 [[[],[[[]]],[]]] => 2 [[[],[[],[],[]]]] => 2 [[[],[[],[[]]]]] => 2 [[[],[[[]],[]]]] => 2 [[[],[[[],[]]]]] => 2 [[[],[[[[]]]]]] => 2 [[[[]],[],[],[]]] => 2 [[[[]],[],[[]]]] => 2 [[[[]],[[]],[]]] => 2 [[[[]],[[],[]]]] => 3 [[[[]],[[[]]]]] => 3 [[[[],[]],[],[]]] => 2 [[[[[]]],[],[]]] => 2 [[[[],[]],[[]]]] => 3 [[[[[]]],[[]]]] => 3 [[[[],[],[]],[]]] => 2 [[[[],[[]]],[]]] => 2 [[[[[]],[]],[]]] => 2 [[[[[],[]]],[]]] => 2 [[[[[[]]]],[]]] => 2 [[[[],[],[],[]]]] => 3 [[[[],[],[[]]]]] => 3 [[[[],[[]],[]]]] => 3 [[[[],[[],[]]]]] => 3 [[[[],[[[]]]]]] => 3 [[[[[]],[],[]]]] => 3 [[[[[]],[[]]]]] => 4 [[[[[],[]],[]]]] => 3 [[[[[[]]],[]]]] => 3 [[[[[],[],[]]]]] => 4 [[[[[],[[]]]]]] => 4 [[[[[[]],[]]]]] => 4 [[[[[[],[]]]]]] => 5 [[[[[[[]]]]]]] => 6 [[],[],[],[],[],[],[]] => 1 [[],[],[],[],[],[[]]] => 1 [[],[],[],[],[[]],[]] => 1 [[],[],[],[],[[],[]]] => 1 [[],[],[],[],[[[]]]] => 1 [[],[],[],[[]],[],[]] => 1 [[],[],[],[[]],[[]]] => 1 [[],[],[],[[],[]],[]] => 1 [[],[],[],[[[]]],[]] => 1 [[],[],[],[[],[],[]]] => 1 [[],[],[],[[],[[]]]] => 1 [[],[],[],[[[]],[]]] => 1 [[],[],[],[[[],[]]]] => 1 [[],[],[],[[[[]]]]] => 1 [[],[],[[]],[],[],[]] => 1 [[],[],[[]],[],[[]]] => 1 [[],[],[[]],[[]],[]] => 1 [[],[],[[]],[[],[]]] => 1 [[],[],[[]],[[[]]]] => 1 [[],[],[[],[]],[],[]] => 1 [[],[],[[[]]],[],[]] => 1 [[],[],[[],[]],[[]]] => 1 [[],[],[[[]]],[[]]] => 1 [[],[],[[],[],[]],[]] => 1 [[],[],[[],[[]]],[]] => 1 [[],[],[[[]],[]],[]] => 1 [[],[],[[[],[]]],[]] => 1 [[],[],[[[[]]]],[]] => 1 [[],[],[[],[],[],[]]] => 1 [[],[],[[],[],[[]]]] => 1 [[],[],[[],[[]],[]]] => 1 [[],[],[[],[[],[]]]] => 1 [[],[],[[],[[[]]]]] => 1 [[],[],[[[]],[],[]]] => 1 [[],[],[[[]],[[]]]] => 1 [[],[],[[[],[]],[]]] => 1 [[],[],[[[[]]],[]]] => 1 [[],[],[[[],[],[]]]] => 1 [[],[],[[[],[[]]]]] => 1 [[],[],[[[[]],[]]]] => 1 [[],[],[[[[],[]]]]] => 1 [[],[],[[[[[]]]]]] => 1 [[],[[]],[],[],[],[]] => 1 [[],[[]],[],[],[[]]] => 1 [[],[[]],[],[[]],[]] => 1 [[],[[]],[],[[],[]]] => 1 [[],[[]],[],[[[]]]] => 1 [[],[[]],[[]],[],[]] => 1 [[],[[]],[[]],[[]]] => 1 [[],[[]],[[],[]],[]] => 1 [[],[[]],[[[]]],[]] => 1 [[],[[]],[[],[],[]]] => 1 [[],[[]],[[],[[]]]] => 1 [[],[[]],[[[]],[]]] => 1 [[],[[]],[[[],[]]]] => 1 [[],[[]],[[[[]]]]] => 1 [[],[[],[]],[],[],[]] => 1 [[],[[[]]],[],[],[]] => 1 [[],[[],[]],[],[[]]] => 1 [[],[[[]]],[],[[]]] => 1 [[],[[],[]],[[]],[]] => 1 [[],[[[]]],[[]],[]] => 1 [[],[[],[]],[[],[]]] => 1 [[],[[],[]],[[[]]]] => 1 [[],[[[]]],[[],[]]] => 1 [[],[[[]]],[[[]]]] => 1 [[],[[],[],[]],[],[]] => 1 [[],[[],[[]]],[],[]] => 1 [[],[[[]],[]],[],[]] => 1 [[],[[[],[]]],[],[]] => 1 [[],[[[[]]]],[],[]] => 1 [[],[[],[],[]],[[]]] => 1 [[],[[],[[]]],[[]]] => 1 [[],[[[]],[]],[[]]] => 1 [[],[[[],[]]],[[]]] => 1 [[],[[[[]]]],[[]]] => 1 [[],[[],[],[],[]],[]] => 1 [[],[[],[],[[]]],[]] => 1 [[],[[],[[]],[]],[]] => 1 [[],[[],[[],[]]],[]] => 1 [[],[[],[[[]]]],[]] => 1 [[],[[[]],[],[]],[]] => 1 [[],[[[]],[[]]],[]] => 1 [[],[[[],[]],[]],[]] => 1 [[],[[[[]]],[]],[]] => 1 [[],[[[],[],[]]],[]] => 1 [[],[[[],[[]]]],[]] => 1 [[],[[[[]],[]]],[]] => 1 [[],[[[[],[]]]],[]] => 1 [[],[[[[[]]]]],[]] => 1 [[],[[],[],[],[],[]]] => 1 [[],[[],[],[],[[]]]] => 1 [[],[[],[],[[]],[]]] => 1 [[],[[],[],[[],[]]]] => 1 [[],[[],[],[[[]]]]] => 1 [[],[[],[[]],[],[]]] => 1 [[],[[],[[]],[[]]]] => 1 [[],[[],[[],[]],[]]] => 1 [[],[[],[[[]]],[]]] => 1 [[],[[],[[],[],[]]]] => 1 [[],[[],[[],[[]]]]] => 1 [[],[[],[[[]],[]]]] => 1 [[],[[],[[[],[]]]]] => 1 [[],[[],[[[[]]]]]] => 1 [[],[[[]],[],[],[]]] => 1 [[],[[[]],[],[[]]]] => 1 [[],[[[]],[[]],[]]] => 1 [[],[[[]],[[],[]]]] => 1 [[],[[[]],[[[]]]]] => 1 [[],[[[],[]],[],[]]] => 1 [[],[[[[]]],[],[]]] => 1 [[],[[[],[]],[[]]]] => 1 [[],[[[[]]],[[]]]] => 1 [[],[[[],[],[]],[]]] => 1 [[],[[[],[[]]],[]]] => 1 [[],[[[[]],[]],[]]] => 1 [[],[[[[],[]]],[]]] => 1 [[],[[[[[]]]],[]]] => 1 [[],[[[],[],[],[]]]] => 1 [[],[[[],[],[[]]]]] => 1 [[],[[[],[[]],[]]]] => 1 [[],[[[],[[],[]]]]] => 1 [[],[[[],[[[]]]]]] => 1 [[],[[[[]],[],[]]]] => 1 [[],[[[[]],[[]]]]] => 1 [[],[[[[],[]],[]]]] => 1 [[],[[[[[]]],[]]]] => 1 [[],[[[[],[],[]]]]] => 1 [[],[[[[],[[]]]]]] => 1 [[],[[[[[]],[]]]]] => 1 [[],[[[[[],[]]]]]] => 1 [[],[[[[[[]]]]]]] => 1 [[[]],[],[],[],[],[]] => 1 [[[]],[],[],[],[[]]] => 1 [[[]],[],[],[[]],[]] => 1 [[[]],[],[],[[],[]]] => 1 [[[]],[],[],[[[]]]] => 1 [[[]],[],[[]],[],[]] => 1 [[[]],[],[[]],[[]]] => 1 [[[]],[],[[],[]],[]] => 1 [[[]],[],[[[]]],[]] => 1 [[[]],[],[[],[],[]]] => 1 [[[]],[],[[],[[]]]] => 1 [[[]],[],[[[]],[]]] => 1 [[[]],[],[[[],[]]]] => 1 [[[]],[],[[[[]]]]] => 1 [[[]],[[]],[],[],[]] => 1 [[[]],[[]],[],[[]]] => 1 [[[]],[[]],[[]],[]] => 1 [[[]],[[]],[[],[]]] => 2 [[[]],[[]],[[[]]]] => 2 [[[]],[[],[]],[],[]] => 1 [[[]],[[[]]],[],[]] => 1 [[[]],[[],[]],[[]]] => 2 [[[]],[[[]]],[[]]] => 2 [[[]],[[],[],[]],[]] => 1 [[[]],[[],[[]]],[]] => 1 [[[]],[[[]],[]],[]] => 1 [[[]],[[[],[]]],[]] => 1 [[[]],[[[[]]]],[]] => 1 [[[]],[[],[],[],[]]] => 2 [[[]],[[],[],[[]]]] => 2 [[[]],[[],[[]],[]]] => 2 [[[]],[[],[[],[]]]] => 2 [[[]],[[],[[[]]]]] => 2 [[[]],[[[]],[],[]]] => 2 [[[]],[[[]],[[]]]] => 2 [[[]],[[[],[]],[]]] => 2 [[[]],[[[[]]],[]]] => 2 [[[]],[[[],[],[]]]] => 2 [[[]],[[[],[[]]]]] => 2 [[[]],[[[[]],[]]]] => 2 [[[]],[[[[],[]]]]] => 2 [[[]],[[[[[]]]]]] => 2 [[[],[]],[],[],[],[]] => 1 [[[[]]],[],[],[],[]] => 1 [[[],[]],[],[],[[]]] => 1 [[[[]]],[],[],[[]]] => 1 [[[],[]],[],[[]],[]] => 1 [[[[]]],[],[[]],[]] => 1 [[[],[]],[],[[],[]]] => 1 [[[],[]],[],[[[]]]] => 1 [[[[]]],[],[[],[]]] => 1 [[[[]]],[],[[[]]]] => 1 [[[],[]],[[]],[],[]] => 1 [[[[]]],[[]],[],[]] => 1 [[[],[]],[[]],[[]]] => 2 [[[[]]],[[]],[[]]] => 2 [[[],[]],[[],[]],[]] => 1 [[[],[]],[[[]]],[]] => 1 [[[[]]],[[],[]],[]] => 1 [[[[]]],[[[]]],[]] => 1 [[[],[]],[[],[],[]]] => 2 [[[],[]],[[],[[]]]] => 2 [[[],[]],[[[]],[]]] => 2 [[[],[]],[[[],[]]]] => 2 [[[],[]],[[[[]]]]] => 2 [[[[]]],[[],[],[]]] => 2 [[[[]]],[[],[[]]]] => 2 [[[[]]],[[[]],[]]] => 2 [[[[]]],[[[],[]]]] => 3 [[[[]]],[[[[]]]]] => 3 [[[],[],[]],[],[],[]] => 1 [[[],[[]]],[],[],[]] => 1 [[[[]],[]],[],[],[]] => 1 [[[[],[]]],[],[],[]] => 1 [[[[[]]]],[],[],[]] => 1 [[[],[],[]],[],[[]]] => 1 [[[],[[]]],[],[[]]] => 1 [[[[]],[]],[],[[]]] => 1 [[[[],[]]],[],[[]]] => 1 [[[[[]]]],[],[[]]] => 1 [[[],[],[]],[[]],[]] => 1 [[[],[[]]],[[]],[]] => 1 [[[[]],[]],[[]],[]] => 1 [[[[],[]]],[[]],[]] => 1 [[[[[]]]],[[]],[]] => 1 [[[],[],[]],[[],[]]] => 2 [[[],[],[]],[[[]]]] => 2 [[[],[[]]],[[],[]]] => 2 [[[],[[]]],[[[]]]] => 2 [[[[]],[]],[[],[]]] => 2 [[[[]],[]],[[[]]]] => 2 [[[[],[]]],[[],[]]] => 2 [[[[],[]]],[[[]]]] => 3 [[[[[]]]],[[],[]]] => 2 [[[[[]]]],[[[]]]] => 3 [[[],[],[],[]],[],[]] => 1 [[[],[],[[]]],[],[]] => 1 [[[],[[]],[]],[],[]] => 1 [[[],[[],[]]],[],[]] => 1 [[[],[[[]]]],[],[]] => 1 [[[[]],[],[]],[],[]] => 1 [[[[]],[[]]],[],[]] => 1 [[[[],[]],[]],[],[]] => 1 [[[[[]]],[]],[],[]] => 1 [[[[],[],[]]],[],[]] => 1 [[[[],[[]]]],[],[]] => 1 [[[[[]],[]]],[],[]] => 1 [[[[[],[]]]],[],[]] => 1 [[[[[[]]]]],[],[]] => 1 [[[],[],[],[]],[[]]] => 2 [[[],[],[[]]],[[]]] => 2 [[[],[[]],[]],[[]]] => 2 [[[],[[],[]]],[[]]] => 2 [[[],[[[]]]],[[]]] => 2 [[[[]],[],[]],[[]]] => 2 [[[[]],[[]]],[[]]] => 2 [[[[],[]],[]],[[]]] => 2 [[[[[]]],[]],[[]]] => 2 [[[[],[],[]]],[[]]] => 2 [[[[],[[]]]],[[]]] => 2 [[[[[]],[]]],[[]]] => 2 [[[[[],[]]]],[[]]] => 2 [[[[[[]]]]],[[]]] => 2 [[[],[],[],[],[]],[]] => 1 [[[],[],[],[[]]],[]] => 1 [[[],[],[[]],[]],[]] => 1 [[[],[],[[],[]]],[]] => 1 [[[],[],[[[]]]],[]] => 1 [[[],[[]],[],[]],[]] => 1 [[[],[[]],[[]]],[]] => 1 [[[],[[],[]],[]],[]] => 1 [[[],[[[]]],[]],[]] => 1 [[[],[[],[],[]]],[]] => 1 [[[],[[],[[]]]],[]] => 1 [[[],[[[]],[]]],[]] => 1 [[[],[[[],[]]]],[]] => 1 [[[],[[[[]]]]],[]] => 1 [[[[]],[],[],[]],[]] => 1 [[[[]],[],[[]]],[]] => 1 [[[[]],[[]],[]],[]] => 1 [[[[]],[[],[]]],[]] => 1 [[[[]],[[[]]]],[]] => 1 [[[[],[]],[],[]],[]] => 1 [[[[[]]],[],[]],[]] => 1 [[[[],[]],[[]]],[]] => 1 [[[[[]]],[[]]],[]] => 1 [[[[],[],[]],[]],[]] => 1 [[[[],[[]]],[]],[]] => 1 [[[[[]],[]],[]],[]] => 1 [[[[[],[]]],[]],[]] => 1 [[[[[[]]]],[]],[]] => 1 [[[[],[],[],[]]],[]] => 1 [[[[],[],[[]]]],[]] => 1 [[[[],[[]],[]]],[]] => 1 [[[[],[[],[]]]],[]] => 1 [[[[],[[[]]]]],[]] => 1 [[[[[]],[],[]]],[]] => 1 [[[[[]],[[]]]],[]] => 1 [[[[[],[]],[]]],[]] => 1 [[[[[[]]],[]]],[]] => 1 [[[[[],[],[]]]],[]] => 1 [[[[[],[[]]]]],[]] => 1 [[[[[[]],[]]]],[]] => 1 [[[[[[],[]]]]],[]] => 1 [[[[[[[]]]]]],[]] => 1 [[[],[],[],[],[],[]]] => 2 [[[],[],[],[],[[]]]] => 2 [[[],[],[],[[]],[]]] => 2 [[[],[],[],[[],[]]]] => 2 [[[],[],[],[[[]]]]] => 2 [[[],[],[[]],[],[]]] => 2 [[[],[],[[]],[[]]]] => 2 [[[],[],[[],[]],[]]] => 2 [[[],[],[[[]]],[]]] => 2 [[[],[],[[],[],[]]]] => 2 [[[],[],[[],[[]]]]] => 2 [[[],[],[[[]],[]]]] => 2 [[[],[],[[[],[]]]]] => 2 [[[],[],[[[[]]]]]] => 2 [[[],[[]],[],[],[]]] => 2 [[[],[[]],[],[[]]]] => 2 [[[],[[]],[[]],[]]] => 2 [[[],[[]],[[],[]]]] => 2 [[[],[[]],[[[]]]]] => 2 [[[],[[],[]],[],[]]] => 2 [[[],[[[]]],[],[]]] => 2 [[[],[[],[]],[[]]]] => 2 [[[],[[[]]],[[]]]] => 2 [[[],[[],[],[]],[]]] => 2 [[[],[[],[[]]],[]]] => 2 [[[],[[[]],[]],[]]] => 2 [[[],[[[],[]]],[]]] => 2 [[[],[[[[]]]],[]]] => 2 [[[],[[],[],[],[]]]] => 2 [[[],[[],[],[[]]]]] => 2 [[[],[[],[[]],[]]]] => 2 [[[],[[],[[],[]]]]] => 2 [[[],[[],[[[]]]]]] => 2 [[[],[[[]],[],[]]]] => 2 [[[],[[[]],[[]]]]] => 2 [[[],[[[],[]],[]]]] => 2 [[[],[[[[]]],[]]]] => 2 [[[],[[[],[],[]]]]] => 2 [[[],[[[],[[]]]]]] => 2 [[[],[[[[]],[]]]]] => 2 [[[],[[[[],[]]]]]] => 2 [[[],[[[[[]]]]]]] => 2 [[[[]],[],[],[],[]]] => 2 [[[[]],[],[],[[]]]] => 2 [[[[]],[],[[]],[]]] => 2 [[[[]],[],[[],[]]]] => 2 [[[[]],[],[[[]]]]] => 2 [[[[]],[[]],[],[]]] => 2 [[[[]],[[]],[[]]]] => 3 [[[[]],[[],[]],[]]] => 2 [[[[]],[[[]]],[]]] => 2 [[[[]],[[],[],[]]]] => 3 [[[[]],[[],[[]]]]] => 3 [[[[]],[[[]],[]]]] => 3 [[[[]],[[[],[]]]]] => 3 [[[[]],[[[[]]]]]] => 3 [[[[],[]],[],[],[]]] => 2 [[[[[]]],[],[],[]]] => 2 [[[[],[]],[],[[]]]] => 2 [[[[[]]],[],[[]]]] => 2 [[[[],[]],[[]],[]]] => 2 [[[[[]]],[[]],[]]] => 2 [[[[],[]],[[],[]]]] => 3 [[[[],[]],[[[]]]]] => 3 [[[[[]]],[[],[]]]] => 3 [[[[[]]],[[[]]]]] => 4 [[[[],[],[]],[],[]]] => 2 [[[[],[[]]],[],[]]] => 2 [[[[[]],[]],[],[]]] => 2 [[[[[],[]]],[],[]]] => 2 [[[[[[]]]],[],[]]] => 2 [[[[],[],[]],[[]]]] => 3 [[[[],[[]]],[[]]]] => 3 [[[[[]],[]],[[]]]] => 3 [[[[[],[]]],[[]]]] => 3 [[[[[[]]]],[[]]]] => 3 [[[[],[],[],[]],[]]] => 2 [[[[],[],[[]]],[]]] => 2 [[[[],[[]],[]],[]]] => 2 [[[[],[[],[]]],[]]] => 2 [[[[],[[[]]]],[]]] => 2 [[[[[]],[],[]],[]]] => 2 [[[[[]],[[]]],[]]] => 2 [[[[[],[]],[]],[]]] => 2 [[[[[[]]],[]],[]]] => 2 [[[[[],[],[]]],[]]] => 2 [[[[[],[[]]]],[]]] => 2 [[[[[[]],[]]],[]]] => 2 [[[[[[],[]]]],[]]] => 2 [[[[[[[]]]]],[]]] => 2 [[[[],[],[],[],[]]]] => 3 [[[[],[],[],[[]]]]] => 3 [[[[],[],[[]],[]]]] => 3 [[[[],[],[[],[]]]]] => 3 [[[[],[],[[[]]]]]] => 3 [[[[],[[]],[],[]]]] => 3 [[[[],[[]],[[]]]]] => 3 [[[[],[[],[]],[]]]] => 3 [[[[],[[[]]],[]]]] => 3 [[[[],[[],[],[]]]]] => 3 [[[[],[[],[[]]]]]] => 3 [[[[],[[[]],[]]]]] => 3 [[[[],[[[],[]]]]]] => 3 [[[[],[[[[]]]]]]] => 3 [[[[[]],[],[],[]]]] => 3 [[[[[]],[],[[]]]]] => 3 [[[[[]],[[]],[]]]] => 3 [[[[[]],[[],[]]]]] => 4 [[[[[]],[[[]]]]]] => 4 [[[[[],[]],[],[]]]] => 3 [[[[[[]]],[],[]]]] => 3 [[[[[],[]],[[]]]]] => 4 [[[[[[]]],[[]]]]] => 4 [[[[[],[],[]],[]]]] => 3 [[[[[],[[]]],[]]]] => 3 [[[[[[]],[]],[]]]] => 3 [[[[[[],[]]],[]]]] => 3 [[[[[[[]]]],[]]]] => 3 [[[[[],[],[],[]]]]] => 4 [[[[[],[],[[]]]]]] => 4 [[[[[],[[]],[]]]]] => 4 [[[[[],[[],[]]]]]] => 4 [[[[[],[[[]]]]]]] => 4 [[[[[[]],[],[]]]]] => 4 [[[[[[]],[[]]]]]] => 5 [[[[[[],[]],[]]]]] => 4 [[[[[[[]]],[]]]]] => 4 [[[[[[],[],[]]]]]] => 5 [[[[[[],[[]]]]]]] => 5 [[[[[[[]],[]]]]]] => 5 [[[[[[[],[]]]]]]] => 6 [[[[[[[[]]]]]]]] => 7 [[],[],[],[],[],[],[],[]] => 1 [[],[],[],[],[],[],[[]]] => 1 [[],[],[],[],[],[[]],[]] => 1 [[],[],[],[],[],[[],[]]] => 1 [[],[],[],[],[],[[[]]]] => 1 [[],[],[],[],[[]],[],[]] => 1 [[],[],[],[],[[]],[[]]] => 1 [[],[],[],[],[[],[]],[]] => 1 [[],[],[],[],[[[]]],[]] => 1 [[],[],[],[],[[],[],[]]] => 1 [[],[],[],[],[[],[[]]]] => 1 [[],[],[],[],[[[]],[]]] => 1 [[],[],[],[],[[[],[]]]] => 1 [[],[],[],[],[[[[]]]]] => 1 [[],[],[],[[]],[],[],[]] => 1 [[],[],[],[[]],[],[[]]] => 1 [[],[],[],[[]],[[]],[]] => 1 [[],[],[],[[]],[[],[]]] => 1 [[],[],[],[[]],[[[]]]] => 1 [[],[],[],[[],[]],[],[]] => 1 [[],[],[],[[[]]],[],[]] => 1 [[],[],[],[[],[]],[[]]] => 1 [[],[],[],[[[]]],[[]]] => 1 [[],[],[],[[],[],[]],[]] => 1 [[],[],[],[[],[[]]],[]] => 1 [[],[],[],[[[]],[]],[]] => 1 [[],[],[],[[[],[]]],[]] => 1 [[],[],[],[[[[]]]],[]] => 1 [[],[],[],[[],[],[],[]]] => 1 [[],[],[],[[],[],[[]]]] => 1 [[],[],[],[[],[[]],[]]] => 1 [[],[],[],[[],[[],[]]]] => 1 [[],[],[],[[],[[[]]]]] => 1 [[],[],[],[[[]],[],[]]] => 1 [[],[],[],[[[]],[[]]]] => 1 [[],[],[],[[[],[]],[]]] => 1 [[],[],[],[[[[]]],[]]] => 1 [[],[],[],[[[],[],[]]]] => 1 [[],[],[],[[[],[[]]]]] => 1 [[],[],[],[[[[]],[]]]] => 1 [[],[],[],[[[[],[]]]]] => 1 [[],[],[],[[[[[]]]]]] => 1 [[],[],[[]],[],[],[],[]] => 1 [[],[],[[]],[],[],[[]]] => 1 [[],[],[[]],[],[[]],[]] => 1 [[],[],[[]],[],[[],[]]] => 1 [[],[],[[]],[],[[[]]]] => 1 [[],[],[[]],[[]],[],[]] => 1 [[],[],[[]],[[]],[[]]] => 1 [[],[],[[]],[[],[]],[]] => 1 [[],[],[[]],[[[]]],[]] => 1 [[],[],[[]],[[],[],[]]] => 1 [[],[],[[]],[[],[[]]]] => 1 [[],[],[[]],[[[]],[]]] => 1 [[],[],[[]],[[[],[]]]] => 1 [[],[],[[]],[[[[]]]]] => 1 [[],[],[[],[]],[],[],[]] => 1 [[],[],[[[]]],[],[],[]] => 1 [[],[],[[],[]],[],[[]]] => 1 [[],[],[[[]]],[],[[]]] => 1 [[],[],[[],[]],[[]],[]] => 1 [[],[],[[[]]],[[]],[]] => 1 [[],[],[[],[]],[[],[]]] => 1 [[],[],[[],[]],[[[]]]] => 1 [[],[],[[[]]],[[],[]]] => 1 [[],[],[[[]]],[[[]]]] => 1 [[],[],[[],[],[]],[],[]] => 1 [[],[],[[],[[]]],[],[]] => 1 [[],[],[[[]],[]],[],[]] => 1 [[],[],[[[],[]]],[],[]] => 1 [[],[],[[[[]]]],[],[]] => 1 [[],[],[[],[],[]],[[]]] => 1 [[],[],[[],[[]]],[[]]] => 1 [[],[],[[[]],[]],[[]]] => 1 [[],[],[[[],[]]],[[]]] => 1 [[],[],[[[[]]]],[[]]] => 1 [[],[],[[],[],[],[]],[]] => 1 [[],[],[[],[],[[]]],[]] => 1 [[],[],[[],[[]],[]],[]] => 1 [[],[],[[],[[],[]]],[]] => 1 [[],[],[[],[[[]]]],[]] => 1 [[],[],[[[]],[],[]],[]] => 1 [[],[],[[[]],[[]]],[]] => 1 [[],[],[[[],[]],[]],[]] => 1 [[],[],[[[[]]],[]],[]] => 1 [[],[],[[[],[],[]]],[]] => 1 [[],[],[[[],[[]]]],[]] => 1 [[],[],[[[[]],[]]],[]] => 1 [[],[],[[[[],[]]]],[]] => 1 [[],[],[[[[[]]]]],[]] => 1 [[],[],[[],[],[],[],[]]] => 1 [[],[],[[],[],[],[[]]]] => 1 [[],[],[[],[],[[]],[]]] => 1 [[],[],[[],[],[[],[]]]] => 1 [[],[],[[],[],[[[]]]]] => 1 [[],[],[[],[[]],[],[]]] => 1 [[],[],[[],[[]],[[]]]] => 1 [[],[],[[],[[],[]],[]]] => 1 [[],[],[[],[[[]]],[]]] => 1 [[],[],[[],[[],[],[]]]] => 1 [[],[],[[],[[],[[]]]]] => 1 [[],[],[[],[[[]],[]]]] => 1 [[],[],[[],[[[],[]]]]] => 1 [[],[],[[],[[[[]]]]]] => 1 [[],[],[[[]],[],[],[]]] => 1 [[],[],[[[]],[],[[]]]] => 1 [[],[],[[[]],[[]],[]]] => 1 [[],[],[[[]],[[],[]]]] => 1 [[],[],[[[]],[[[]]]]] => 1 [[],[],[[[],[]],[],[]]] => 1 [[],[],[[[[]]],[],[]]] => 1 [[],[],[[[],[]],[[]]]] => 1 [[],[],[[[[]]],[[]]]] => 1 [[],[],[[[],[],[]],[]]] => 1 [[],[],[[[],[[]]],[]]] => 1 [[],[],[[[[]],[]],[]]] => 1 [[],[],[[[[],[]]],[]]] => 1 [[],[],[[[[[]]]],[]]] => 1 [[],[],[[[],[],[],[]]]] => 1 [[],[],[[[],[],[[]]]]] => 1 [[],[],[[[],[[]],[]]]] => 1 [[],[],[[[],[[],[]]]]] => 1 [[],[],[[[],[[[]]]]]] => 1 [[],[],[[[[]],[],[]]]] => 1 [[],[],[[[[]],[[]]]]] => 1 [[],[],[[[[],[]],[]]]] => 1 [[],[],[[[[[]]],[]]]] => 1 [[],[],[[[[],[],[]]]]] => 1 [[],[],[[[[],[[]]]]]] => 1 [[],[],[[[[[]],[]]]]] => 1 [[],[],[[[[[],[]]]]]] => 1 [[],[],[[[[[[]]]]]]] => 1 [[],[[]],[],[],[],[],[]] => 1 [[],[[]],[],[],[],[[]]] => 1 [[],[[]],[],[],[[]],[]] => 1 [[],[[]],[],[],[[],[]]] => 1 [[],[[]],[],[],[[[]]]] => 1 [[],[[]],[],[[]],[],[]] => 1 [[],[[]],[],[[]],[[]]] => 1 [[],[[]],[],[[],[]],[]] => 1 [[],[[]],[],[[[]]],[]] => 1 [[],[[]],[],[[],[],[]]] => 1 [[],[[]],[],[[],[[]]]] => 1 [[],[[]],[],[[[]],[]]] => 1 [[],[[]],[],[[[],[]]]] => 1 [[],[[]],[],[[[[]]]]] => 1 [[],[[]],[[]],[],[],[]] => 1 [[],[[]],[[]],[],[[]]] => 1 [[],[[]],[[]],[[]],[]] => 1 [[],[[]],[[]],[[],[]]] => 1 [[],[[]],[[]],[[[]]]] => 1 [[],[[]],[[],[]],[],[]] => 1 [[],[[]],[[[]]],[],[]] => 1 [[],[[]],[[],[]],[[]]] => 1 [[],[[]],[[[]]],[[]]] => 1 [[],[[]],[[],[],[]],[]] => 1 [[],[[]],[[],[[]]],[]] => 1 [[],[[]],[[[]],[]],[]] => 1 [[],[[]],[[[],[]]],[]] => 1 [[],[[]],[[[[]]]],[]] => 1 [[],[[]],[[],[],[],[]]] => 1 [[],[[]],[[],[],[[]]]] => 1 [[],[[]],[[],[[]],[]]] => 1 [[],[[]],[[],[[],[]]]] => 1 [[],[[]],[[],[[[]]]]] => 1 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1 [[],[[[]]],[[[[]]]]] => 1 [[],[[],[],[]],[],[],[]] => 1 [[],[[],[[]]],[],[],[]] => 1 [[],[[[]],[]],[],[],[]] => 1 [[],[[[],[]]],[],[],[]] => 1 [[],[[[[]]]],[],[],[]] => 1 [[],[[],[],[]],[],[[]]] => 1 [[],[[],[[]]],[],[[]]] => 1 [[],[[[]],[]],[],[[]]] => 1 [[],[[[],[]]],[],[[]]] => 1 [[],[[[[]]]],[],[[]]] => 1 [[],[[],[],[]],[[]],[]] => 1 [[],[[],[[]]],[[]],[]] => 1 [[],[[[]],[]],[[]],[]] => 1 [[],[[[],[]]],[[]],[]] => 1 [[],[[[[]]]],[[]],[]] => 1 [[],[[],[],[]],[[],[]]] => 1 [[],[[],[],[]],[[[]]]] => 1 [[],[[],[[]]],[[],[]]] => 1 [[],[[],[[]]],[[[]]]] => 1 [[],[[[]],[]],[[],[]]] => 1 [[],[[[]],[]],[[[]]]] => 1 [[],[[[],[]]],[[],[]]] => 1 [[],[[[],[]]],[[[]]]] => 1 [[],[[[[]]]],[[],[]]] => 1 [[],[[[[]]]],[[[]]]] => 1 [[],[[],[],[],[]],[],[]] => 1 [[],[[],[],[[]]],[],[]] => 1 [[],[[],[[]],[]],[],[]] => 1 [[],[[],[[],[]]],[],[]] => 1 [[],[[],[[[]]]],[],[]] => 1 [[],[[[]],[],[]],[],[]] => 1 [[],[[[]],[[]]],[],[]] => 1 [[],[[[],[]],[]],[],[]] => 1 [[],[[[[]]],[]],[],[]] => 1 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1 [[],[[[]],[],[[],[]]]] => 1 [[],[[[]],[],[[[]]]]] => 1 [[],[[[]],[[]],[],[]]] => 1 [[],[[[]],[[]],[[]]]] => 1 [[],[[[]],[[],[]],[]]] => 1 [[],[[[]],[[[]]],[]]] => 1 [[],[[[]],[[],[],[]]]] => 1 [[],[[[]],[[],[[]]]]] => 1 [[],[[[]],[[[]],[]]]] => 1 [[],[[[]],[[[],[]]]]] => 1 [[],[[[]],[[[[]]]]]] => 1 [[],[[[],[]],[],[],[]]] => 1 [[],[[[[]]],[],[],[]]] => 1 [[],[[[],[]],[],[[]]]] => 1 [[],[[[[]]],[],[[]]]] => 1 [[],[[[],[]],[[]],[]]] => 1 [[],[[[[]]],[[]],[]]] => 1 [[],[[[],[]],[[],[]]]] => 1 [[],[[[],[]],[[[]]]]] => 1 [[],[[[[]]],[[],[]]]] => 1 [[],[[[[]]],[[[]]]]] => 1 [[],[[[],[],[]],[],[]]] => 1 [[],[[[],[[]]],[],[]]] => 1 [[],[[[[]],[]],[],[]]] => 1 [[],[[[[],[]]],[],[]]] => 1 [[],[[[[[]]]],[],[]]] => 1 [[],[[[],[],[]],[[]]]] => 1 [[],[[[],[[]]],[[]]]] => 1 [[],[[[[]],[]],[[]]]] => 1 [[],[[[[],[]]],[[]]]] => 1 [[],[[[[[]]]],[[]]]] => 1 [[],[[[],[],[],[]],[]]] => 1 [[],[[[],[],[[]]],[]]] => 1 [[],[[[],[[]],[]],[]]] => 1 [[],[[[],[[],[]]],[]]] => 1 [[],[[[],[[[]]]],[]]] => 1 [[],[[[[]],[],[]],[]]] => 1 [[],[[[[]],[[]]],[]]] => 1 [[],[[[[],[]],[]],[]]] => 1 [[],[[[[[]]],[]],[]]] => 1 [[],[[[[],[],[]]],[]]] => 1 [[],[[[[],[[]]]],[]]] => 1 [[],[[[[[]],[]]],[]]] => 1 [[],[[[[[],[]]]],[]]] => 1 [[],[[[[[[]]]]],[]]] => 1 [[],[[[],[],[],[],[]]]] => 1 [[],[[[],[],[],[[]]]]] => 1 [[],[[[],[],[[]],[]]]] => 1 [[],[[[],[],[[],[]]]]] => 1 [[],[[[],[],[[[]]]]]] => 1 [[],[[[],[[]],[],[]]]] => 1 [[],[[[],[[]],[[]]]]] => 1 [[],[[[],[[],[]],[]]]] => 1 [[],[[[],[[[]]],[]]]] => 1 [[],[[[],[[],[],[]]]]] => 1 [[],[[[],[[],[[]]]]]] => 1 [[],[[[],[[[]],[]]]]] => 1 [[],[[[],[[[],[]]]]]] => 1 [[],[[[],[[[[]]]]]]] => 1 [[],[[[[]],[],[],[]]]] => 1 [[],[[[[]],[],[[]]]]] => 1 [[],[[[[]],[[]],[]]]] => 1 [[],[[[[]],[[],[]]]]] => 1 [[],[[[[]],[[[]]]]]] => 1 [[],[[[[],[]],[],[]]]] => 1 [[],[[[[[]]],[],[]]]] => 1 [[],[[[[],[]],[[]]]]] => 1 [[],[[[[[]]],[[]]]]] => 1 [[],[[[[],[],[]],[]]]] => 1 [[],[[[[],[[]]],[]]]] => 1 [[],[[[[[]],[]],[]]]] => 1 [[],[[[[[],[]]],[]]]] => 1 [[],[[[[[[]]]],[]]]] => 1 [[],[[[[],[],[],[]]]]] => 1 [[],[[[[],[],[[]]]]]] => 1 [[],[[[[],[[]],[]]]]] => 1 [[],[[[[],[[],[]]]]]] => 1 [[],[[[[],[[[]]]]]]] => 1 [[],[[[[[]],[],[]]]]] => 1 [[],[[[[[]],[[]]]]]] => 1 [[],[[[[[],[]],[]]]]] => 1 [[],[[[[[[]]],[]]]]] => 1 [[],[[[[[],[],[]]]]]] => 1 [[],[[[[[],[[]]]]]]] => 1 [[],[[[[[[]],[]]]]]] => 1 [[],[[[[[[],[]]]]]]] => 1 [[],[[[[[[[]]]]]]]] => 1 [[[]],[],[],[],[],[],[]] => 1 [[[]],[],[],[],[],[[]]] => 1 [[[]],[],[],[],[[]],[]] => 1 [[[]],[],[],[],[[],[]]] => 1 [[[]],[],[],[],[[[]]]] => 1 [[[]],[],[],[[]],[],[]] => 1 [[[]],[],[],[[]],[[]]] => 1 [[[]],[],[],[[],[]],[]] => 1 [[[]],[],[],[[[]]],[]] => 1 [[[]],[],[],[[],[],[]]] => 1 [[[]],[],[],[[],[[]]]] => 1 [[[]],[],[],[[[]],[]]] => 1 [[[]],[],[],[[[],[]]]] => 1 [[[]],[],[],[[[[]]]]] => 1 [[[]],[],[[]],[],[],[]] => 1 [[[]],[],[[]],[],[[]]] => 1 [[[]],[],[[]],[[]],[]] => 1 [[[]],[],[[]],[[],[]]] => 1 [[[]],[],[[]],[[[]]]] => 1 [[[]],[],[[],[]],[],[]] => 1 [[[]],[],[[[]]],[],[]] => 1 [[[]],[],[[],[]],[[]]] => 1 [[[]],[],[[[]]],[[]]] => 1 [[[]],[],[[],[],[]],[]] => 1 [[[]],[],[[],[[]]],[]] => 1 [[[]],[],[[[]],[]],[]] => 1 [[[]],[],[[[],[]]],[]] => 1 [[[]],[],[[[[]]]],[]] => 1 [[[]],[],[[],[],[],[]]] => 1 [[[]],[],[[],[],[[]]]] => 1 [[[]],[],[[],[[]],[]]] => 1 [[[]],[],[[],[[],[]]]] => 1 [[[]],[],[[],[[[]]]]] => 1 [[[]],[],[[[]],[],[]]] => 1 [[[]],[],[[[]],[[]]]] => 1 [[[]],[],[[[],[]],[]]] => 1 [[[]],[],[[[[]]],[]]] => 1 [[[]],[],[[[],[],[]]]] => 1 [[[]],[],[[[],[[]]]]] => 1 [[[]],[],[[[[]],[]]]] => 1 [[[]],[],[[[[],[]]]]] => 1 [[[]],[],[[[[[]]]]]] => 1 [[[]],[[]],[],[],[],[]] => 1 [[[]],[[]],[],[],[[]]] => 1 [[[]],[[]],[],[[]],[]] => 1 [[[]],[[]],[],[[],[]]] => 1 [[[]],[[]],[],[[[]]]] => 1 [[[]],[[]],[[]],[],[]] => 1 [[[]],[[]],[[]],[[]]] => 2 [[[]],[[]],[[],[]],[]] => 1 [[[]],[[]],[[[]]],[]] => 1 [[[]],[[]],[[],[],[]]] => 2 [[[]],[[]],[[],[[]]]] => 2 [[[]],[[]],[[[]],[]]] => 2 [[[]],[[]],[[[],[]]]] => 2 [[[]],[[]],[[[[]]]]] => 2 [[[]],[[],[]],[],[],[]] => 1 [[[]],[[[]]],[],[],[]] => 1 [[[]],[[],[]],[],[[]]] => 1 [[[]],[[[]]],[],[[]]] => 1 [[[]],[[],[]],[[]],[]] => 1 [[[]],[[[]]],[[]],[]] => 1 [[[]],[[],[]],[[],[]]] => 2 [[[]],[[],[]],[[[]]]] => 2 [[[]],[[[]]],[[],[]]] => 2 [[[]],[[[]]],[[[]]]] => 2 [[[]],[[],[],[]],[],[]] => 1 [[[]],[[],[[]]],[],[]] => 1 [[[]],[[[]],[]],[],[]] => 1 [[[]],[[[],[]]],[],[]] => 1 [[[]],[[[[]]]],[],[]] => 1 [[[]],[[],[],[]],[[]]] => 2 [[[]],[[],[[]]],[[]]] => 2 [[[]],[[[]],[]],[[]]] => 2 [[[]],[[[],[]]],[[]]] => 2 [[[]],[[[[]]]],[[]]] => 2 [[[]],[[],[],[],[]],[]] => 1 [[[]],[[],[],[[]]],[]] => 1 [[[]],[[],[[]],[]],[]] => 1 [[[]],[[],[[],[]]],[]] => 1 [[[]],[[],[[[]]]],[]] => 1 [[[]],[[[]],[],[]],[]] => 1 [[[]],[[[]],[[]]],[]] => 1 [[[]],[[[],[]],[]],[]] => 1 [[[]],[[[[]]],[]],[]] => 1 [[[]],[[[],[],[]]],[]] => 1 [[[]],[[[],[[]]]],[]] => 1 [[[]],[[[[]],[]]],[]] => 1 [[[]],[[[[],[]]]],[]] => 1 [[[]],[[[[[]]]]],[]] => 1 [[[]],[[],[],[],[],[]]] => 2 [[[]],[[],[],[],[[]]]] => 2 [[[]],[[],[],[[]],[]]] => 2 [[[]],[[],[],[[],[]]]] => 2 [[[]],[[],[],[[[]]]]] => 2 [[[]],[[],[[]],[],[]]] => 2 [[[]],[[],[[]],[[]]]] => 2 [[[]],[[],[[],[]],[]]] => 2 [[[]],[[],[[[]]],[]]] => 2 [[[]],[[],[[],[],[]]]] => 2 [[[]],[[],[[],[[]]]]] => 2 [[[]],[[],[[[]],[]]]] => 2 [[[]],[[],[[[],[]]]]] => 2 [[[]],[[],[[[[]]]]]] => 2 [[[]],[[[]],[],[],[]]] => 2 [[[]],[[[]],[],[[]]]] => 2 [[[]],[[[]],[[]],[]]] => 2 [[[]],[[[]],[[],[]]]] => 2 [[[]],[[[]],[[[]]]]] => 2 [[[]],[[[],[]],[],[]]] => 2 [[[]],[[[[]]],[],[]]] => 2 [[[]],[[[],[]],[[]]]] => 2 [[[]],[[[[]]],[[]]]] => 2 [[[]],[[[],[],[]],[]]] => 2 [[[]],[[[],[[]]],[]]] => 2 [[[]],[[[[]],[]],[]]] => 2 [[[]],[[[[],[]]],[]]] => 2 [[[]],[[[[[]]]],[]]] => 2 [[[]],[[[],[],[],[]]]] => 2 [[[]],[[[],[],[[]]]]] => 2 [[[]],[[[],[[]],[]]]] => 2 [[[]],[[[],[[],[]]]]] => 2 [[[]],[[[],[[[]]]]]] => 2 [[[]],[[[[]],[],[]]]] => 2 [[[]],[[[[]],[[]]]]] => 2 [[[]],[[[[],[]],[]]]] => 2 [[[]],[[[[[]]],[]]]] => 2 [[[]],[[[[],[],[]]]]] => 2 [[[]],[[[[],[[]]]]]] => 2 [[[]],[[[[[]],[]]]]] => 2 [[[]],[[[[[],[]]]]]] => 2 [[[]],[[[[[[]]]]]]] => 2 [[[],[]],[],[],[],[],[]] => 1 [[[[]]],[],[],[],[],[]] => 1 [[[],[]],[],[],[],[[]]] => 1 [[[[]]],[],[],[],[[]]] => 1 [[[],[]],[],[],[[]],[]] => 1 [[[[]]],[],[],[[]],[]] => 1 [[[],[]],[],[],[[],[]]] => 1 [[[],[]],[],[],[[[]]]] => 1 [[[[]]],[],[],[[],[]]] => 1 [[[[]]],[],[],[[[]]]] => 1 [[[],[]],[],[[]],[],[]] => 1 [[[[]]],[],[[]],[],[]] => 1 [[[],[]],[],[[]],[[]]] => 1 [[[[]]],[],[[]],[[]]] => 1 [[[],[]],[[],[[],[]]]] => 2 [[[],[]],[[[],[]],[]]] => 2 [[[],[[],[]]],[[],[]]] => 2 [[[[],[]],[]],[[],[]]] => 2 [[[],[[],[[],[]]]],[]] => 1 [[[],[[[],[]],[]]],[]] => 1 [[[[],[]],[[],[]]],[]] => 1 [[[[],[[],[]]],[]],[]] => 1 [[[[[],[]],[]],[]],[]] => 1 [[[[[],[[[]]]]]],[]] => 1 [[[[[[[]]],[]]]],[]] => 1 [[[[[[],[],[]]]]],[]] => 1 [[[[[[],[[]]]]]],[]] => 1 [[[[[[[]],[]]]]],[]] => 1 [[[[[[[],[]]]]]],[]] => 1 [[[[[[[[]]]]]]],[]] => 1 [[[[[[[[[]]]]]]]],[]] => 1 [[],[[[[[[[[]]]]]]]]] => 1 [[[[[[[[],[]]]]]]],[]] => 1 [[],[[[[[[[],[]]]]]]]] => 1 [[[[[[[[]],[]]]]]],[]] => 1 [[[[[[[],[[]]]]]]],[]] => 1 [[],[[[[[[[]],[]]]]]]] => 1 [[],[[[[[[],[[]]]]]]]] => 1 [[],[[],[[],[[],[[],[]]]]]] => 1 [[],[[],[[],[[[],[]],[]]]]] => 1 [[],[[],[[[],[]],[[],[]]]]] => 1 [[],[[],[[[],[[],[]]],[]]]] => 1 [[],[[],[[[[],[]],[]],[]]]] => 1 [[],[[[],[]],[[],[[],[]]]]] => 1 [[],[[[],[]],[[[],[]],[]]]] => 1 [[],[[[],[[],[]]],[[],[]]]] => 1 [[],[[[[],[]],[]],[[],[]]]] => 1 [[],[[[],[[],[[],[]]]],[]]] => 1 [[],[[[],[[[],[]],[]]],[]]] => 1 [[],[[[[],[]],[[],[]]],[]]] => 1 [[],[[[[],[[],[]]],[]],[]]] => 1 [[],[[[[[],[]],[]],[]],[]]] => 1 [[[],[]],[[],[[],[[],[]]]]] => 2 [[[],[]],[[],[[[],[]],[]]]] => 2 [[[],[]],[[[],[]],[[],[]]]] => 2 [[[],[]],[[[],[[],[]]],[]]] => 2 [[[],[]],[[[[],[]],[]],[]]] => 2 [[[],[[],[]]],[[],[[],[]]]] => 2 [[[],[[],[]]],[[[],[]],[]]] => 2 [[[[],[]],[]],[[],[[],[]]]] => 2 [[[[],[]],[]],[[[],[]],[]]] => 2 [[[],[[],[[],[]]]],[[],[]]] => 2 [[[],[[[],[]],[]]],[[],[]]] => 2 [[[[],[]],[[],[]]],[[],[]]] => 2 [[[[],[[],[]]],[]],[[],[]]] => 2 [[[[[],[]],[]],[]],[[],[]]] => 2 [[[],[[],[[],[[],[]]]]],[]] => 1 [[[],[[],[[[],[]],[]]]],[]] => 1 [[[],[[[],[]],[[],[]]]],[]] => 1 [[[],[[[],[[],[]]],[]]],[]] => 1 [[[],[[[[],[]],[]],[]]],[]] => 1 [[[[],[]],[[],[[],[]]]],[]] => 1 [[[[],[]],[[[],[]],[]]],[]] => 1 [[[[],[[],[]]],[[],[]]],[]] => 1 [[[[[],[]],[]],[[],[]]],[]] => 1 [[[[],[[],[[],[]]]],[]],[]] => 1 [[[[],[[[],[]],[]]],[]],[]] => 1 [[[[[],[]],[[],[]]],[]],[]] => 1 [[[[[],[[],[]]],[]],[]],[]] => 1 [[[[[[],[]],[]],[]],[]],[]] => 1 [[[[[[[[[[]]]]]]]]],[]] => 1 [[],[[[[[[[[[]]]]]]]]]] => 1 [[[[[[[[[],[]]]]]]]],[]] => 1 [[],[[[[[[[[],[]]]]]]]]] => 1 [[[[[[[[[[[]]]]]]]]]],[]] => 1 [[],[[[[[[[[[[]]]]]]]]]]] => 1 [[],[[],[[],[[],[[],[[],[]]]]]]] => 1 [[],[[],[[],[[],[[[],[]],[]]]]]] => 1 [[],[[],[[],[[[],[]],[[],[]]]]]] => 1 [[],[[],[[],[[[],[[],[]]],[]]]]] => 1 [[],[[],[[],[[[[],[]],[]],[]]]]] => 1 [[],[[],[[[],[]],[[],[[],[]]]]]] => 1 [[],[[],[[[],[]],[[[],[]],[]]]]] => 1 [[],[[],[[[],[[],[]]],[[],[]]]]] => 1 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[[[[],[[[],[]],[]]],[]],[[],[]]] => 2 [[[[[],[]],[[],[]]],[]],[[],[]]] => 2 [[[[[],[[],[]]],[]],[]],[[],[]]] => 2 [[[[[[],[]],[]],[]],[]],[[],[]]] => 2 [[[],[[],[[],[[],[[],[]]]]]],[]] => 1 [[[],[[],[[],[[[],[]],[]]]]],[]] => 1 [[[],[[],[[[],[]],[[],[]]]]],[]] => 1 [[[],[[],[[[],[[],[]]],[]]]],[]] => 1 [[[],[[],[[[[],[]],[]],[]]]],[]] => 1 [[[],[[[],[]],[[],[[],[]]]]],[]] => 1 [[[],[[[],[]],[[[],[]],[]]]],[]] => 1 [[[],[[[],[[],[]]],[[],[]]]],[]] => 1 [[[],[[[[],[]],[]],[[],[]]]],[]] => 1 [[[],[[[],[[],[[],[]]]],[]]],[]] => 1 [[[],[[[],[[[],[]],[]]],[]]],[]] => 1 [[[],[[[[],[]],[[],[]]],[]]],[]] => 1 [[[],[[[[],[[],[]]],[]],[]]],[]] => 1 [[[],[[[[[],[]],[]],[]],[]]],[]] => 1 [[[[],[]],[[],[[],[[],[]]]]],[]] => 1 [[[[],[]],[[],[[[],[]],[]]]],[]] => 1 [[[[],[]],[[[],[]],[[],[]]]],[]] => 1 [[[[],[]],[[[],[[],[]]],[]]],[]] => 1 [[[[],[]],[[[[],[]],[]],[]]],[]] => 1 [[[[],[[],[]]],[[],[[],[]]]],[]] => 1 [[[[],[[],[]]],[[[],[]],[]]],[]] => 1 [[[[[],[]],[]],[[],[[],[]]]],[]] => 1 [[[[[],[]],[]],[[[],[]],[]]],[]] => 1 [[[[],[[],[[],[]]]],[[],[]]],[]] => 1 [[[[],[[[],[]],[]]],[[],[]]],[]] => 1 [[[[[],[]],[[],[]]],[[],[]]],[]] => 1 [[[[[],[[],[]]],[]],[[],[]]],[]] => 1 [[[[[[],[]],[]],[]],[[],[]]],[]] => 1 [[[[],[[],[[],[[],[]]]]],[]],[]] => 1 [[[[],[[],[[[],[]],[]]]],[]],[]] => 1 [[[[],[[[],[]],[[],[]]]],[]],[]] => 1 [[[[],[[[],[[],[]]],[]]],[]],[]] => 1 [[[[],[[[[],[]],[]],[]]],[]],[]] => 1 [[[[[],[]],[[],[[],[]]]],[]],[]] => 1 [[[[[],[]],[[[],[]],[]]],[]],[]] => 1 [[[[[],[[],[]]],[[],[]]],[]],[]] => 1 [[[[[[],[]],[]],[[],[]]],[]],[]] => 1 [[[[[],[[],[[],[]]]],[]],[]],[]] => 1 [[[[[],[[[],[]],[]]],[]],[]],[]] => 1 [[[[[[],[]],[[],[]]],[]],[]],[]] => 1 [[[[[[],[[],[]]],[]],[]],[]],[]] => 1 [[[[[[[],[]],[]],[]],[]],[]],[]] => 1 ----------------------------------------------------------------------------- Created: Feb 23, 2017 at 20:14 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 26, 2017 at 12:32 by Martin Rubey