***************************************************************************** * 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: St000400 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The path length of an ordered tree. This is the sum of the lengths of all paths from the root to a node, see Section 2.3.4.5 of [1]. ----------------------------------------------------------------------------- References: [1] Knuth, D. E. The art of computer programming. Vol. 1 [[MathSciNet:3077152]] ----------------------------------------------------------------------------- Code: def statistic(T): return path_length_aux(T, 0) def path_length_aux(T, n): return n+sum(path_length_aux(S, n+1) for S in T if not S.is_empty()) ----------------------------------------------------------------------------- Statistic values: [[]] => 1 [[],[]] => 2 [[[]]] => 3 [[],[],[]] => 3 [[],[[]]] => 4 [[[]],[]] => 4 [[[],[]]] => 5 [[[[]]]] => 6 [[],[],[],[]] => 4 [[],[],[[]]] => 5 [[],[[]],[]] => 5 [[],[[],[]]] => 6 [[],[[[]]]] => 7 [[[]],[],[]] => 5 [[[]],[[]]] => 6 [[[],[]],[]] => 6 [[[[]]],[]] => 7 [[[],[],[]]] => 7 [[[],[[]]]] => 8 [[[[]],[]]] => 8 [[[[],[]]]] => 9 [[[[[]]]]] => 10 [[],[],[],[],[]] => 5 [[],[],[],[[]]] => 6 [[],[],[[]],[]] => 6 [[],[],[[],[]]] => 7 [[],[],[[[]]]] => 8 [[],[[]],[],[]] => 6 [[],[[]],[[]]] => 7 [[],[[],[]],[]] => 7 [[],[[[]]],[]] => 8 [[],[[],[],[]]] => 8 [[],[[],[[]]]] => 9 [[],[[[]],[]]] => 9 [[],[[[],[]]]] => 10 [[],[[[[]]]]] => 11 [[[]],[],[],[]] => 6 [[[]],[],[[]]] => 7 [[[]],[[]],[]] => 7 [[[]],[[],[]]] => 8 [[[]],[[[]]]] => 9 [[[],[]],[],[]] => 7 [[[[]]],[],[]] => 8 [[[],[]],[[]]] => 8 [[[[]]],[[]]] => 9 [[[],[],[]],[]] => 8 [[[],[[]]],[]] => 9 [[[[]],[]],[]] => 9 [[[[],[]]],[]] => 10 [[[[[]]]],[]] => 11 [[[],[],[],[]]] => 9 [[[],[],[[]]]] => 10 [[[],[[]],[]]] => 10 [[[],[[],[]]]] => 11 [[[],[[[]]]]] => 12 [[[[]],[],[]]] => 10 [[[[]],[[]]]] => 11 [[[[],[]],[]]] => 11 [[[[[]]],[]]] => 12 [[[[],[],[]]]] => 12 [[[[],[[]]]]] => 13 [[[[[]],[]]]] => 13 [[[[[],[]]]]] => 14 [[[[[[]]]]]] => 15 [[],[],[],[],[],[]] => 6 [[],[],[],[],[[]]] => 7 [[],[],[],[[]],[]] => 7 [[],[],[],[[],[]]] => 8 [[],[],[],[[[]]]] => 9 [[],[],[[]],[],[]] => 7 [[],[],[[]],[[]]] => 8 [[],[],[[],[]],[]] => 8 [[],[],[[[]]],[]] => 9 [[],[],[[],[],[]]] => 9 [[],[],[[],[[]]]] => 10 [[],[],[[[]],[]]] => 10 [[],[],[[[],[]]]] => 11 [[],[],[[[[]]]]] => 12 [[],[[]],[],[],[]] => 7 [[],[[]],[],[[]]] => 8 [[],[[]],[[]],[]] => 8 [[],[[]],[[],[]]] => 9 [[],[[]],[[[]]]] => 10 [[],[[],[]],[],[]] => 8 [[],[[[]]],[],[]] => 9 [[],[[],[]],[[]]] => 9 [[],[[[]]],[[]]] => 10 [[],[[],[],[]],[]] => 9 [[],[[],[[]]],[]] => 10 [[],[[[]],[]],[]] => 10 [[],[[[],[]]],[]] => 11 [[],[[[[]]]],[]] => 12 [[],[[],[],[],[]]] => 10 [[],[[],[],[[]]]] => 11 [[],[[],[[]],[]]] => 11 [[],[[],[[],[]]]] => 12 [[],[[],[[[]]]]] => 13 [[],[[[]],[],[]]] => 11 [[],[[[]],[[]]]] => 12 [[],[[[],[]],[]]] => 12 [[],[[[[]]],[]]] => 13 [[],[[[],[],[]]]] => 13 [[],[[[],[[]]]]] => 14 [[],[[[[]],[]]]] => 14 [[],[[[[],[]]]]] => 15 [[],[[[[[]]]]]] => 16 [[[]],[],[],[],[]] => 7 [[[]],[],[],[[]]] => 8 [[[]],[],[[]],[]] => 8 [[[]],[],[[],[]]] => 9 [[[]],[],[[[]]]] => 10 [[[]],[[]],[],[]] => 8 [[[]],[[]],[[]]] => 9 [[[]],[[],[]],[]] => 9 [[[]],[[[]]],[]] => 10 [[[]],[[],[],[]]] => 10 [[[]],[[],[[]]]] => 11 [[[]],[[[]],[]]] => 11 [[[]],[[[],[]]]] => 12 [[[]],[[[[]]]]] => 13 [[[],[]],[],[],[]] => 8 [[[[]]],[],[],[]] => 9 [[[],[]],[],[[]]] => 9 [[[[]]],[],[[]]] => 10 [[[],[]],[[]],[]] => 9 [[[[]]],[[]],[]] => 10 [[[],[]],[[],[]]] => 10 [[[],[]],[[[]]]] => 11 [[[[]]],[[],[]]] => 11 [[[[]]],[[[]]]] => 12 [[[],[],[]],[],[]] => 9 [[[],[[]]],[],[]] => 10 [[[[]],[]],[],[]] => 10 [[[[],[]]],[],[]] => 11 [[[[[]]]],[],[]] => 12 [[[],[],[]],[[]]] => 10 [[[],[[]]],[[]]] => 11 [[[[]],[]],[[]]] => 11 [[[[],[]]],[[]]] => 12 [[[[[]]]],[[]]] => 13 [[[],[],[],[]],[]] => 10 [[[],[],[[]]],[]] => 11 [[[],[[]],[]],[]] => 11 [[[],[[],[]]],[]] => 12 [[[],[[[]]]],[]] => 13 [[[[]],[],[]],[]] => 11 [[[[]],[[]]],[]] => 12 [[[[],[]],[]],[]] => 12 [[[[[]]],[]],[]] => 13 [[[[],[],[]]],[]] => 13 [[[[],[[]]]],[]] => 14 [[[[[]],[]]],[]] => 14 [[[[[],[]]]],[]] => 15 [[[[[[]]]]],[]] => 16 [[[],[],[],[],[]]] => 11 [[[],[],[],[[]]]] => 12 [[[],[],[[]],[]]] => 12 [[[],[],[[],[]]]] => 13 [[[],[],[[[]]]]] => 14 [[[],[[]],[],[]]] => 12 [[[],[[]],[[]]]] => 13 [[[],[[],[]],[]]] => 13 [[[],[[[]]],[]]] => 14 [[[],[[],[],[]]]] => 14 [[[],[[],[[]]]]] => 15 [[[],[[[]],[]]]] => 15 [[[],[[[],[]]]]] => 16 [[[],[[[[]]]]]] => 17 [[[[]],[],[],[]]] => 12 [[[[]],[],[[]]]] => 13 [[[[]],[[]],[]]] => 13 [[[[]],[[],[]]]] => 14 [[[[]],[[[]]]]] => 15 [[[[],[]],[],[]]] => 13 [[[[[]]],[],[]]] => 14 [[[[],[]],[[]]]] => 14 [[[[[]]],[[]]]] => 15 [[[[],[],[]],[]]] => 14 [[[[],[[]]],[]]] => 15 [[[[[]],[]],[]]] => 15 [[[[[],[]]],[]]] => 16 [[[[[[]]]],[]]] => 17 [[[[],[],[],[]]]] => 15 [[[[],[],[[]]]]] => 16 [[[[],[[]],[]]]] => 16 [[[[],[[],[]]]]] => 17 [[[[],[[[]]]]]] => 18 [[[[[]],[],[]]]] => 16 [[[[[]],[[]]]]] => 17 [[[[[],[]],[]]]] => 17 [[[[[[]]],[]]]] => 18 [[[[[],[],[]]]]] => 18 [[[[[],[[]]]]]] => 19 [[[[[[]],[]]]]] => 19 [[[[[[],[]]]]]] => 20 [[[[[[[]]]]]]] => 21 [[],[],[],[],[],[],[]] => 7 [[],[],[],[],[],[[]]] => 8 [[],[],[],[],[[]],[]] => 8 [[],[],[],[],[[],[]]] => 9 [[],[],[],[],[[[]]]] => 10 [[],[],[],[[]],[],[]] => 8 [[],[],[],[[]],[[]]] => 9 [[],[],[],[[],[]],[]] => 9 [[],[],[],[[[]]],[]] => 10 [[],[],[],[[],[],[]]] => 10 [[],[],[],[[],[[]]]] => 11 [[],[],[],[[[]],[]]] => 11 [[],[],[],[[[],[]]]] => 12 [[],[],[],[[[[]]]]] => 13 [[],[],[[]],[],[],[]] => 8 [[],[],[[]],[],[[]]] => 9 [[],[],[[]],[[]],[]] => 9 [[],[],[[]],[[],[]]] => 10 [[],[],[[]],[[[]]]] => 11 [[],[],[[],[]],[],[]] => 9 [[],[],[[[]]],[],[]] => 10 [[],[],[[],[]],[[]]] => 10 [[],[],[[[]]],[[]]] => 11 [[],[],[[],[],[]],[]] => 10 [[],[],[[],[[]]],[]] => 11 [[],[],[[[]],[]],[]] => 11 [[],[],[[[],[]]],[]] => 12 [[],[],[[[[]]]],[]] => 13 [[],[],[[],[],[],[]]] => 11 [[],[],[[],[],[[]]]] => 12 [[],[],[[],[[]],[]]] => 12 [[],[],[[],[[],[]]]] => 13 [[],[],[[],[[[]]]]] => 14 [[],[],[[[]],[],[]]] => 12 [[],[],[[[]],[[]]]] => 13 [[],[],[[[],[]],[]]] => 13 [[],[],[[[[]]],[]]] => 14 [[],[],[[[],[],[]]]] => 14 [[],[],[[[],[[]]]]] => 15 [[],[],[[[[]],[]]]] => 15 [[],[],[[[[],[]]]]] => 16 [[],[],[[[[[]]]]]] => 17 [[],[[]],[],[],[],[]] => 8 [[],[[]],[],[],[[]]] => 9 [[],[[]],[],[[]],[]] => 9 [[],[[]],[],[[],[]]] => 10 [[],[[]],[],[[[]]]] => 11 [[],[[]],[[]],[],[]] => 9 [[],[[]],[[]],[[]]] => 10 [[],[[]],[[],[]],[]] => 10 [[],[[]],[[[]]],[]] => 11 [[],[[]],[[],[],[]]] => 11 [[],[[]],[[],[[]]]] => 12 [[],[[]],[[[]],[]]] => 12 [[],[[]],[[[],[]]]] => 13 [[],[[]],[[[[]]]]] => 14 [[],[[],[]],[],[],[]] => 9 [[],[[[]]],[],[],[]] => 10 [[],[[],[]],[],[[]]] => 10 [[],[[[]]],[],[[]]] => 11 [[],[[],[]],[[]],[]] => 10 [[],[[[]]],[[]],[]] => 11 [[],[[],[]],[[],[]]] => 11 [[],[[],[]],[[[]]]] => 12 [[],[[[]]],[[],[]]] => 12 [[],[[[]]],[[[]]]] => 13 [[],[[],[],[]],[],[]] => 10 [[],[[],[[]]],[],[]] => 11 [[],[[[]],[]],[],[]] => 11 [[],[[[],[]]],[],[]] => 12 [[],[[[[]]]],[],[]] => 13 [[],[[],[],[]],[[]]] => 11 [[],[[],[[]]],[[]]] => 12 [[],[[[]],[]],[[]]] => 12 [[],[[[],[]]],[[]]] => 13 [[],[[[[]]]],[[]]] => 14 [[],[[],[],[],[]],[]] => 11 [[],[[],[],[[]]],[]] => 12 [[],[[],[[]],[]],[]] => 12 [[],[[],[[],[]]],[]] => 13 [[],[[],[[[]]]],[]] => 14 [[],[[[]],[],[]],[]] => 12 [[],[[[]],[[]]],[]] => 13 [[],[[[],[]],[]],[]] => 13 [[],[[[[]]],[]],[]] => 14 [[],[[[],[],[]]],[]] => 14 [[],[[[],[[]]]],[]] => 15 [[],[[[[]],[]]],[]] => 15 [[],[[[[],[]]]],[]] => 16 [[],[[[[[]]]]],[]] => 17 [[],[[],[],[],[],[]]] => 12 [[],[[],[],[],[[]]]] => 13 [[],[[],[],[[]],[]]] => 13 [[],[[],[],[[],[]]]] => 14 [[],[[],[],[[[]]]]] => 15 [[],[[],[[]],[],[]]] => 13 [[],[[],[[]],[[]]]] => 14 [[],[[],[[],[]],[]]] => 14 [[],[[],[[[]]],[]]] => 15 [[],[[],[[],[],[]]]] => 15 [[],[[],[[],[[]]]]] => 16 [[],[[],[[[]],[]]]] => 16 [[],[[],[[[],[]]]]] => 17 [[],[[],[[[[]]]]]] => 18 [[],[[[]],[],[],[]]] => 13 [[],[[[]],[],[[]]]] => 14 [[],[[[]],[[]],[]]] => 14 [[],[[[]],[[],[]]]] => 15 [[],[[[]],[[[]]]]] => 16 [[],[[[],[]],[],[]]] => 14 [[],[[[[]]],[],[]]] => 15 [[],[[[],[]],[[]]]] => 15 [[],[[[[]]],[[]]]] => 16 [[],[[[],[],[]],[]]] => 15 [[],[[[],[[]]],[]]] => 16 [[],[[[[]],[]],[]]] => 16 [[],[[[[],[]]],[]]] => 17 [[],[[[[[]]]],[]]] => 18 [[],[[[],[],[],[]]]] => 16 [[],[[[],[],[[]]]]] => 17 [[],[[[],[[]],[]]]] => 17 [[],[[[],[[],[]]]]] => 18 [[],[[[],[[[]]]]]] => 19 [[],[[[[]],[],[]]]] => 17 [[],[[[[]],[[]]]]] => 18 [[],[[[[],[]],[]]]] => 18 [[],[[[[[]]],[]]]] => 19 [[],[[[[],[],[]]]]] => 19 [[],[[[[],[[]]]]]] => 20 [[],[[[[[]],[]]]]] => 20 [[],[[[[[],[]]]]]] => 21 [[],[[[[[[]]]]]]] => 22 [[[]],[],[],[],[],[]] => 8 [[[]],[],[],[],[[]]] => 9 [[[]],[],[],[[]],[]] => 9 [[[]],[],[],[[],[]]] => 10 [[[]],[],[],[[[]]]] => 11 [[[]],[],[[]],[],[]] => 9 [[[]],[],[[]],[[]]] => 10 [[[]],[],[[],[]],[]] => 10 [[[]],[],[[[]]],[]] => 11 [[[]],[],[[],[],[]]] => 11 [[[]],[],[[],[[]]]] => 12 [[[]],[],[[[]],[]]] => 12 [[[]],[],[[[],[]]]] => 13 [[[]],[],[[[[]]]]] => 14 [[[]],[[]],[],[],[]] => 9 [[[]],[[]],[],[[]]] => 10 [[[]],[[]],[[]],[]] => 10 [[[]],[[]],[[],[]]] => 11 [[[]],[[]],[[[]]]] => 12 [[[]],[[],[]],[],[]] => 10 [[[]],[[[]]],[],[]] => 11 [[[]],[[],[]],[[]]] => 11 [[[]],[[[]]],[[]]] => 12 [[[]],[[],[],[]],[]] => 11 [[[]],[[],[[]]],[]] => 12 [[[]],[[[]],[]],[]] => 12 [[[]],[[[],[]]],[]] => 13 [[[]],[[[[]]]],[]] => 14 [[[]],[[],[],[],[]]] => 12 [[[]],[[],[],[[]]]] => 13 [[[]],[[],[[]],[]]] => 13 [[[]],[[],[[],[]]]] => 14 [[[]],[[],[[[]]]]] => 15 [[[]],[[[]],[],[]]] => 13 [[[]],[[[]],[[]]]] => 14 [[[]],[[[],[]],[]]] => 14 [[[]],[[[[]]],[]]] => 15 [[[]],[[[],[],[]]]] => 15 [[[]],[[[],[[]]]]] => 16 [[[]],[[[[]],[]]]] => 16 [[[]],[[[[],[]]]]] => 17 [[[]],[[[[[]]]]]] => 18 [[[],[]],[],[],[],[]] => 9 [[[[]]],[],[],[],[]] => 10 [[[],[]],[],[],[[]]] => 10 [[[[]]],[],[],[[]]] => 11 [[[],[]],[],[[]],[]] => 10 [[[[]]],[],[[]],[]] => 11 [[[],[]],[],[[],[]]] => 11 [[[],[]],[],[[[]]]] => 12 [[[[]]],[],[[],[]]] => 12 [[[[]]],[],[[[]]]] => 13 [[[],[]],[[]],[],[]] => 10 [[[[]]],[[]],[],[]] => 11 [[[],[]],[[]],[[]]] => 11 [[[[]]],[[]],[[]]] => 12 [[[],[]],[[],[]],[]] => 11 [[[],[]],[[[]]],[]] => 12 [[[[]]],[[],[]],[]] => 12 [[[[]]],[[[]]],[]] => 13 [[[],[]],[[],[],[]]] => 12 [[[],[]],[[],[[]]]] => 13 [[[],[]],[[[]],[]]] => 13 [[[],[]],[[[],[]]]] => 14 [[[],[]],[[[[]]]]] => 15 [[[[]]],[[],[],[]]] => 13 [[[[]]],[[],[[]]]] => 14 [[[[]]],[[[]],[]]] => 14 [[[[]]],[[[],[]]]] => 15 [[[[]]],[[[[]]]]] => 16 [[[],[],[]],[],[],[]] => 10 [[[],[[]]],[],[],[]] => 11 [[[[]],[]],[],[],[]] => 11 [[[[],[]]],[],[],[]] => 12 [[[[[]]]],[],[],[]] => 13 [[[],[],[]],[],[[]]] => 11 [[[],[[]]],[],[[]]] => 12 [[[[]],[]],[],[[]]] => 12 [[[[],[]]],[],[[]]] => 13 [[[[[]]]],[],[[]]] => 14 [[[],[],[]],[[]],[]] => 11 [[[],[[]]],[[]],[]] => 12 [[[[]],[]],[[]],[]] => 12 [[[[],[]]],[[]],[]] => 13 [[[[[]]]],[[]],[]] => 14 [[[],[],[]],[[],[]]] => 12 [[[],[],[]],[[[]]]] => 13 [[[],[[]]],[[],[]]] => 13 [[[],[[]]],[[[]]]] => 14 [[[[]],[]],[[],[]]] => 13 [[[[]],[]],[[[]]]] => 14 [[[[],[]]],[[],[]]] => 14 [[[[],[]]],[[[]]]] => 15 [[[[[]]]],[[],[]]] => 15 [[[[[]]]],[[[]]]] => 16 [[[],[],[],[]],[],[]] => 11 [[[],[],[[]]],[],[]] => 12 [[[],[[]],[]],[],[]] => 12 [[[],[[],[]]],[],[]] => 13 [[[],[[[]]]],[],[]] => 14 [[[[]],[],[]],[],[]] => 12 [[[[]],[[]]],[],[]] => 13 [[[[],[]],[]],[],[]] => 13 [[[[[]]],[]],[],[]] => 14 [[[[],[],[]]],[],[]] => 14 [[[[],[[]]]],[],[]] => 15 [[[[[]],[]]],[],[]] => 15 [[[[[],[]]]],[],[]] => 16 [[[[[[]]]]],[],[]] => 17 [[[],[],[],[]],[[]]] => 12 [[[],[],[[]]],[[]]] => 13 [[[],[[]],[]],[[]]] => 13 [[[],[[],[]]],[[]]] => 14 [[[],[[[]]]],[[]]] => 15 [[[[]],[],[]],[[]]] => 13 [[[[]],[[]]],[[]]] => 14 [[[[],[]],[]],[[]]] => 14 [[[[[]]],[]],[[]]] => 15 [[[[],[],[]]],[[]]] => 15 [[[[],[[]]]],[[]]] => 16 [[[[[]],[]]],[[]]] => 16 [[[[[],[]]]],[[]]] => 17 [[[[[[]]]]],[[]]] => 18 [[[],[],[],[],[]],[]] => 12 [[[],[],[],[[]]],[]] => 13 [[[],[],[[]],[]],[]] => 13 [[[],[],[[],[]]],[]] => 14 [[[],[],[[[]]]],[]] => 15 [[[],[[]],[],[]],[]] => 13 [[[],[[]],[[]]],[]] => 14 [[[],[[],[]],[]],[]] => 14 [[[],[[[]]],[]],[]] => 15 [[[],[[],[],[]]],[]] => 15 [[[],[[],[[]]]],[]] => 16 [[[],[[[]],[]]],[]] => 16 [[[],[[[],[]]]],[]] => 17 [[[],[[[[]]]]],[]] => 18 [[[[]],[],[],[]],[]] => 13 [[[[]],[],[[]]],[]] => 14 [[[[]],[[]],[]],[]] => 14 [[[[]],[[],[]]],[]] => 15 [[[[]],[[[]]]],[]] => 16 [[[[],[]],[],[]],[]] => 14 [[[[[]]],[],[]],[]] => 15 [[[[],[]],[[]]],[]] => 15 [[[[[]]],[[]]],[]] => 16 [[[[],[],[]],[]],[]] => 15 [[[[],[[]]],[]],[]] => 16 [[[[[]],[]],[]],[]] => 16 [[[[[],[]]],[]],[]] => 17 [[[[[[]]]],[]],[]] => 18 [[[[],[],[],[]]],[]] => 16 [[[[],[],[[]]]],[]] => 17 [[[[],[[]],[]]],[]] => 17 [[[[],[[],[]]]],[]] => 18 [[[[],[[[]]]]],[]] => 19 [[[[[]],[],[]]],[]] => 17 [[[[[]],[[]]]],[]] => 18 [[[[[],[]],[]]],[]] => 18 [[[[[[]]],[]]],[]] => 19 [[[[[],[],[]]]],[]] => 19 [[[[[],[[]]]]],[]] => 20 [[[[[[]],[]]]],[]] => 20 [[[[[[],[]]]]],[]] => 21 [[[[[[[]]]]]],[]] => 22 [[[],[],[],[],[],[]]] => 13 [[[],[],[],[],[[]]]] => 14 [[[],[],[],[[]],[]]] => 14 [[[],[],[],[[],[]]]] => 15 [[[],[],[],[[[]]]]] => 16 [[[],[],[[]],[],[]]] => 14 [[[],[],[[]],[[]]]] => 15 [[[],[],[[],[]],[]]] => 15 [[[],[],[[[]]],[]]] => 16 [[[],[],[[],[],[]]]] => 16 [[[],[],[[],[[]]]]] => 17 [[[],[],[[[]],[]]]] => 17 [[[],[],[[[],[]]]]] => 18 [[[],[],[[[[]]]]]] => 19 [[[],[[]],[],[],[]]] => 14 [[[],[[]],[],[[]]]] => 15 [[[],[[]],[[]],[]]] => 15 [[[],[[]],[[],[]]]] => 16 [[[],[[]],[[[]]]]] => 17 [[[],[[],[]],[],[]]] => 15 [[[],[[[]]],[],[]]] => 16 [[[],[[],[]],[[]]]] => 16 [[[],[[[]]],[[]]]] => 17 [[[],[[],[],[]],[]]] => 16 [[[],[[],[[]]],[]]] => 17 [[[],[[[]],[]],[]]] => 17 [[[],[[[],[]]],[]]] => 18 [[[],[[[[]]]],[]]] => 19 [[[],[[],[],[],[]]]] => 17 [[[],[[],[],[[]]]]] => 18 [[[],[[],[[]],[]]]] => 18 [[[],[[],[[],[]]]]] => 19 [[[],[[],[[[]]]]]] => 20 [[[],[[[]],[],[]]]] => 18 [[[],[[[]],[[]]]]] => 19 [[[],[[[],[]],[]]]] => 19 [[[],[[[[]]],[]]]] => 20 [[[],[[[],[],[]]]]] => 20 [[[],[[[],[[]]]]]] => 21 [[[],[[[[]],[]]]]] => 21 [[[],[[[[],[]]]]]] => 22 [[[],[[[[[]]]]]]] => 23 [[[[]],[],[],[],[]]] => 14 [[[[]],[],[],[[]]]] => 15 [[[[]],[],[[]],[]]] => 15 [[[[]],[],[[],[]]]] => 16 [[[[]],[],[[[]]]]] => 17 [[[[]],[[]],[],[]]] => 15 [[[[]],[[]],[[]]]] => 16 [[[[]],[[],[]],[]]] => 16 [[[[]],[[[]]],[]]] => 17 [[[[]],[[],[],[]]]] => 17 [[[[]],[[],[[]]]]] => 18 [[[[]],[[[]],[]]]] => 18 [[[[]],[[[],[]]]]] => 19 [[[[]],[[[[]]]]]] => 20 [[[[],[]],[],[],[]]] => 15 [[[[[]]],[],[],[]]] => 16 [[[[],[]],[],[[]]]] => 16 [[[[[]]],[],[[]]]] => 17 [[[[],[]],[[]],[]]] => 16 [[[[[]]],[[]],[]]] => 17 [[[[],[]],[[],[]]]] => 17 [[[[],[]],[[[]]]]] => 18 [[[[[]]],[[],[]]]] => 18 [[[[[]]],[[[]]]]] => 19 [[[[],[],[]],[],[]]] => 16 [[[[],[[]]],[],[]]] => 17 [[[[[]],[]],[],[]]] => 17 [[[[[],[]]],[],[]]] => 18 [[[[[[]]]],[],[]]] => 19 [[[[],[],[]],[[]]]] => 17 [[[[],[[]]],[[]]]] => 18 [[[[[]],[]],[[]]]] => 18 [[[[[],[]]],[[]]]] => 19 [[[[[[]]]],[[]]]] => 20 [[[[],[],[],[]],[]]] => 17 [[[[],[],[[]]],[]]] => 18 [[[[],[[]],[]],[]]] => 18 [[[[],[[],[]]],[]]] => 19 [[[[],[[[]]]],[]]] => 20 [[[[[]],[],[]],[]]] => 18 [[[[[]],[[]]],[]]] => 19 [[[[[],[]],[]],[]]] => 19 [[[[[[]]],[]],[]]] => 20 [[[[[],[],[]]],[]]] => 20 [[[[[],[[]]]],[]]] => 21 [[[[[[]],[]]],[]]] => 21 [[[[[[],[]]]],[]]] => 22 [[[[[[[]]]]],[]]] => 23 [[[[],[],[],[],[]]]] => 18 [[[[],[],[],[[]]]]] => 19 [[[[],[],[[]],[]]]] => 19 [[[[],[],[[],[]]]]] => 20 [[[[],[],[[[]]]]]] => 21 [[[[],[[]],[],[]]]] => 19 [[[[],[[]],[[]]]]] => 20 [[[[],[[],[]],[]]]] => 20 [[[[],[[[]]],[]]]] => 21 [[[[],[[],[],[]]]]] => 21 [[[[],[[],[[]]]]]] => 22 [[[[],[[[]],[]]]]] => 22 [[[[],[[[],[]]]]]] => 23 [[[[],[[[[]]]]]]] => 24 [[[[[]],[],[],[]]]] => 19 [[[[[]],[],[[]]]]] => 20 [[[[[]],[[]],[]]]] => 20 [[[[[]],[[],[]]]]] => 21 [[[[[]],[[[]]]]]] => 22 [[[[[],[]],[],[]]]] => 20 [[[[[[]]],[],[]]]] => 21 [[[[[],[]],[[]]]]] => 21 [[[[[[]]],[[]]]]] => 22 [[[[[],[],[]],[]]]] => 21 [[[[[],[[]]],[]]]] => 22 [[[[[[]],[]],[]]]] => 22 [[[[[[],[]]],[]]]] => 23 [[[[[[[]]]],[]]]] => 24 [[[[[],[],[],[]]]]] => 22 [[[[[],[],[[]]]]]] => 23 [[[[[],[[]],[]]]]] => 23 [[[[[],[[],[]]]]]] => 24 [[[[[],[[[]]]]]]] => 25 [[[[[[]],[],[]]]]] => 23 [[[[[[]],[[]]]]]] => 24 [[[[[[],[]],[]]]]] => 24 [[[[[[[]]],[]]]]] => 25 [[[[[[],[],[]]]]]] => 25 [[[[[[],[[]]]]]]] => 26 [[[[[[[]],[]]]]]] => 26 [[[[[[[],[]]]]]]] => 27 [[[[[[[[]]]]]]]] => 28 [[],[],[],[],[],[],[],[]] => 8 [[],[],[],[],[],[],[[]]] => 9 [[],[],[],[],[],[[]],[]] => 9 [[],[],[],[],[],[[],[]]] => 10 [[],[],[],[],[],[[[]]]] => 11 [[],[],[],[],[[]],[],[]] => 9 [[],[],[],[],[[]],[[]]] => 10 [[],[],[],[],[[],[]],[]] => 10 [[],[],[],[],[[[]]],[]] => 11 [[],[],[],[],[[],[],[]]] => 11 [[],[],[],[],[[],[[]]]] => 12 [[],[],[],[],[[[]],[]]] => 12 [[],[],[],[],[[[],[]]]] => 13 [[],[],[],[],[[[[]]]]] => 14 [[],[],[],[[]],[],[],[]] => 9 [[],[],[],[[]],[],[[]]] => 10 [[],[],[],[[]],[[]],[]] => 10 [[],[],[],[[]],[[],[]]] => 11 [[],[],[],[[]],[[[]]]] => 12 [[],[],[],[[],[]],[],[]] => 10 [[],[],[],[[[]]],[],[]] => 11 [[],[],[],[[],[]],[[]]] => 11 [[],[],[],[[[]]],[[]]] => 12 [[],[],[],[[],[],[]],[]] => 11 [[],[],[],[[],[[]]],[]] => 12 [[],[],[],[[[]],[]],[]] => 12 [[],[],[],[[[],[]]],[]] => 13 [[],[],[],[[[[]]]],[]] => 14 [[],[],[],[[],[],[],[]]] => 12 [[],[],[],[[],[],[[]]]] => 13 [[],[],[],[[],[[]],[]]] => 13 [[],[],[],[[],[[],[]]]] => 14 [[],[],[],[[],[[[]]]]] => 15 [[],[],[],[[[]],[],[]]] => 13 [[],[],[],[[[]],[[]]]] => 14 [[],[],[],[[[],[]],[]]] => 14 [[],[],[],[[[[]]],[]]] => 15 [[],[],[],[[[],[],[]]]] => 15 [[],[],[],[[[],[[]]]]] => 16 [[],[],[],[[[[]],[]]]] => 16 [[],[],[],[[[[],[]]]]] => 17 [[],[],[],[[[[[]]]]]] => 18 [[],[],[[]],[],[],[],[]] => 9 [[],[],[[]],[],[],[[]]] => 10 [[],[],[[]],[],[[]],[]] => 10 [[],[],[[]],[],[[],[]]] => 11 [[],[],[[]],[],[[[]]]] => 12 [[],[],[[]],[[]],[],[]] => 10 [[],[],[[]],[[]],[[]]] => 11 [[],[],[[]],[[],[]],[]] => 11 [[],[],[[]],[[[]]],[]] => 12 [[],[],[[]],[[],[],[]]] => 12 [[],[],[[]],[[],[[]]]] => 13 [[],[],[[]],[[[]],[]]] => 13 [[],[],[[]],[[[],[]]]] => 14 [[],[],[[]],[[[[]]]]] => 15 [[],[],[[],[]],[],[],[]] => 10 [[],[],[[[]]],[],[],[]] => 11 [[],[],[[],[]],[],[[]]] => 11 [[],[],[[[]]],[],[[]]] => 12 [[],[],[[],[]],[[]],[]] => 11 [[],[],[[[]]],[[]],[]] => 12 [[],[],[[],[]],[[],[]]] => 12 [[],[],[[],[]],[[[]]]] => 13 [[],[],[[[]]],[[],[]]] => 13 [[],[],[[[]]],[[[]]]] => 14 [[],[],[[],[],[]],[],[]] => 11 [[],[],[[],[[]]],[],[]] => 12 [[],[],[[[]],[]],[],[]] => 12 [[],[],[[[],[]]],[],[]] => 13 [[],[],[[[[]]]],[],[]] => 14 [[],[],[[],[],[]],[[]]] => 12 [[],[],[[],[[]]],[[]]] => 13 [[],[],[[[]],[]],[[]]] => 13 [[],[],[[[],[]]],[[]]] => 14 [[],[],[[[[]]]],[[]]] => 15 [[],[],[[],[],[],[]],[]] => 12 [[],[],[[],[],[[]]],[]] => 13 [[],[],[[],[[]],[]],[]] => 13 [[],[],[[],[[],[]]],[]] => 14 [[],[],[[],[[[]]]],[]] => 15 [[],[],[[[]],[],[]],[]] => 13 [[],[],[[[]],[[]]],[]] => 14 [[],[],[[[],[]],[]],[]] => 14 [[],[],[[[[]]],[]],[]] => 15 [[],[],[[[],[],[]]],[]] => 15 [[],[],[[[],[[]]]],[]] => 16 [[],[],[[[[]],[]]],[]] => 16 [[],[],[[[[],[]]]],[]] => 17 [[],[],[[[[[]]]]],[]] => 18 [[],[],[[],[],[],[],[]]] => 13 [[],[],[[],[],[],[[]]]] => 14 [[],[],[[],[],[[]],[]]] => 14 [[],[],[[],[],[[],[]]]] => 15 [[],[],[[],[],[[[]]]]] => 16 [[],[],[[],[[]],[],[]]] => 14 [[],[],[[],[[]],[[]]]] => 15 [[],[],[[],[[],[]],[]]] => 15 [[],[],[[],[[[]]],[]]] => 16 [[],[],[[],[[],[],[]]]] => 16 [[],[],[[],[[],[[]]]]] => 17 [[],[],[[],[[[]],[]]]] => 17 [[],[],[[],[[[],[]]]]] => 18 [[],[],[[],[[[[]]]]]] => 19 [[],[],[[[]],[],[],[]]] => 14 [[],[],[[[]],[],[[]]]] => 15 [[],[],[[[]],[[]],[]]] => 15 [[],[],[[[]],[[],[]]]] => 16 [[],[],[[[]],[[[]]]]] => 17 [[],[],[[[],[]],[],[]]] => 15 [[],[],[[[[]]],[],[]]] => 16 [[],[],[[[],[]],[[]]]] => 16 [[],[],[[[[]]],[[]]]] => 17 [[],[],[[[],[],[]],[]]] => 16 [[],[],[[[],[[]]],[]]] => 17 [[],[],[[[[]],[]],[]]] => 17 [[],[],[[[[],[]]],[]]] => 18 [[],[],[[[[[]]]],[]]] => 19 [[],[],[[[],[],[],[]]]] => 17 [[],[],[[[],[],[[]]]]] => 18 [[],[],[[[],[[]],[]]]] => 18 [[],[],[[[],[[],[]]]]] => 19 [[],[],[[[],[[[]]]]]] => 20 [[],[],[[[[]],[],[]]]] => 18 [[],[],[[[[]],[[]]]]] => 19 [[],[],[[[[],[]],[]]]] => 19 [[],[],[[[[[]]],[]]]] => 20 [[],[],[[[[],[],[]]]]] => 20 [[],[],[[[[],[[]]]]]] => 21 [[],[],[[[[[]],[]]]]] => 21 [[],[],[[[[[],[]]]]]] => 22 [[],[],[[[[[[]]]]]]] => 23 [[],[[]],[],[],[],[],[]] => 9 [[],[[]],[],[],[],[[]]] => 10 [[],[[]],[],[],[[]],[]] => 10 [[],[[]],[],[],[[],[]]] => 11 [[],[[]],[],[],[[[]]]] => 12 [[],[[]],[],[[]],[],[]] => 10 [[],[[]],[],[[]],[[]]] => 11 [[],[[]],[],[[],[]],[]] => 11 [[],[[]],[],[[[]]],[]] => 12 [[],[[]],[],[[],[],[]]] => 12 [[],[[]],[],[[],[[]]]] => 13 [[],[[]],[],[[[]],[]]] => 13 [[],[[]],[],[[[],[]]]] => 14 [[],[[]],[],[[[[]]]]] => 15 [[],[[]],[[]],[],[],[]] => 10 [[],[[]],[[]],[],[[]]] => 11 [[],[[]],[[]],[[]],[]] => 11 [[],[[]],[[]],[[],[]]] => 12 [[],[[]],[[]],[[[]]]] => 13 [[],[[]],[[],[]],[],[]] => 11 [[],[[]],[[[]]],[],[]] => 12 [[],[[]],[[],[]],[[]]] => 12 [[],[[]],[[[]]],[[]]] => 13 [[],[[]],[[],[],[]],[]] => 12 [[],[[]],[[],[[]]],[]] => 13 [[],[[]],[[[]],[]],[]] => 13 [[],[[]],[[[],[]]],[]] => 14 [[],[[]],[[[[]]]],[]] => 15 [[],[[]],[[],[],[],[]]] => 13 [[],[[]],[[],[],[[]]]] => 14 [[],[[]],[[],[[]],[]]] => 14 [[],[[]],[[],[[],[]]]] => 15 [[],[[]],[[],[[[]]]]] => 16 [[],[[]],[[[]],[],[]]] => 14 [[],[[]],[[[]],[[]]]] => 15 [[],[[]],[[[],[]],[]]] => 15 [[],[[]],[[[[]]],[]]] => 16 [[],[[]],[[[],[],[]]]] => 16 [[],[[]],[[[],[[]]]]] => 17 [[],[[]],[[[[]],[]]]] => 17 [[],[[]],[[[[],[]]]]] => 18 [[],[[]],[[[[[]]]]]] => 19 [[],[[],[]],[],[],[],[]] => 10 [[],[[[]]],[],[],[],[]] => 11 [[],[[],[]],[],[],[[]]] => 11 [[],[[[]]],[],[],[[]]] => 12 [[],[[],[]],[],[[]],[]] => 11 [[],[[[]]],[],[[]],[]] => 12 [[],[[],[]],[],[[],[]]] => 12 [[],[[],[]],[],[[[]]]] => 13 [[],[[[]]],[],[[],[]]] => 13 [[],[[[]]],[],[[[]]]] => 14 [[],[[],[]],[[]],[],[]] => 11 [[],[[[]]],[[]],[],[]] => 12 [[],[[],[]],[[]],[[]]] => 12 [[],[[[]]],[[]],[[]]] => 13 [[],[[],[]],[[],[]],[]] => 12 [[],[[],[]],[[[]]],[]] => 13 [[],[[[]]],[[],[]],[]] => 13 [[],[[[]]],[[[]]],[]] => 14 [[],[[],[]],[[],[],[]]] => 13 [[],[[],[]],[[],[[]]]] => 14 [[],[[],[]],[[[]],[]]] => 14 [[],[[],[]],[[[],[]]]] => 15 [[],[[],[]],[[[[]]]]] => 16 [[],[[[]]],[[],[],[]]] => 14 [[],[[[]]],[[],[[]]]] => 15 [[],[[[]]],[[[]],[]]] => 15 [[],[[[]]],[[[],[]]]] => 16 [[],[[[]]],[[[[]]]]] => 17 [[],[[],[],[]],[],[],[]] => 11 [[],[[],[[]]],[],[],[]] => 12 [[],[[[]],[]],[],[],[]] => 12 [[],[[[],[]]],[],[],[]] => 13 [[],[[[[]]]],[],[],[]] => 14 [[],[[],[],[]],[],[[]]] => 12 [[],[[],[[]]],[],[[]]] => 13 [[],[[[]],[]],[],[[]]] => 13 [[],[[[],[]]],[],[[]]] => 14 [[],[[[[]]]],[],[[]]] => 15 [[],[[],[],[]],[[]],[]] => 12 [[],[[],[[]]],[[]],[]] => 13 [[],[[[]],[]],[[]],[]] => 13 [[],[[[],[]]],[[]],[]] => 14 [[],[[[[]]]],[[]],[]] => 15 [[],[[],[],[]],[[],[]]] => 13 [[],[[],[],[]],[[[]]]] => 14 [[],[[],[[]]],[[],[]]] => 14 [[],[[],[[]]],[[[]]]] => 15 [[],[[[]],[]],[[],[]]] => 14 [[],[[[]],[]],[[[]]]] => 15 [[],[[[],[]]],[[],[]]] => 15 [[],[[[],[]]],[[[]]]] => 16 [[],[[[[]]]],[[],[]]] => 16 [[],[[[[]]]],[[[]]]] => 17 [[],[[],[],[],[]],[],[]] => 12 [[],[[],[],[[]]],[],[]] => 13 [[],[[],[[]],[]],[],[]] => 13 [[],[[],[[],[]]],[],[]] => 14 [[],[[],[[[]]]],[],[]] => 15 [[],[[[]],[],[]],[],[]] => 13 [[],[[[]],[[]]],[],[]] => 14 [[],[[[],[]],[]],[],[]] => 14 [[],[[[[]]],[]],[],[]] => 15 [[],[[[],[],[]]],[],[]] => 15 [[],[[[],[[]]]],[],[]] => 16 [[],[[[[]],[]]],[],[]] => 16 [[],[[[[],[]]]],[],[]] => 17 [[],[[[[[]]]]],[],[]] => 18 [[],[[],[],[],[]],[[]]] => 13 [[],[[],[],[[]]],[[]]] => 14 [[],[[],[[]],[]],[[]]] => 14 [[],[[],[[],[]]],[[]]] => 15 [[],[[],[[[]]]],[[]]] => 16 [[],[[[]],[],[]],[[]]] => 14 [[],[[[]],[[]]],[[]]] => 15 [[],[[[],[]],[]],[[]]] => 15 [[],[[[[]]],[]],[[]]] => 16 [[],[[[],[],[]]],[[]]] => 16 [[],[[[],[[]]]],[[]]] => 17 [[],[[[[]],[]]],[[]]] => 17 [[],[[[[],[]]]],[[]]] => 18 [[],[[[[[]]]]],[[]]] => 19 [[],[[],[],[],[],[]],[]] => 13 [[],[[],[],[],[[]]],[]] => 14 [[],[[],[],[[]],[]],[]] => 14 [[],[[],[],[[],[]]],[]] => 15 [[],[[],[],[[[]]]],[]] => 16 [[],[[],[[]],[],[]],[]] => 14 [[],[[],[[]],[[]]],[]] => 15 [[],[[],[[],[]],[]],[]] => 15 [[],[[],[[[]]],[]],[]] => 16 [[],[[],[[],[],[]]],[]] => 16 [[],[[],[[],[[]]]],[]] => 17 [[],[[],[[[]],[]]],[]] => 17 [[],[[],[[[],[]]]],[]] => 18 [[],[[],[[[[]]]]],[]] => 19 [[],[[[]],[],[],[]],[]] => 14 [[],[[[]],[],[[]]],[]] => 15 [[],[[[]],[[]],[]],[]] => 15 [[],[[[]],[[],[]]],[]] => 16 [[],[[[]],[[[]]]],[]] => 17 [[],[[[],[]],[],[]],[]] => 15 [[],[[[[]]],[],[]],[]] => 16 [[],[[[],[]],[[]]],[]] => 16 [[],[[[[]]],[[]]],[]] => 17 [[],[[[],[],[]],[]],[]] => 16 [[],[[[],[[]]],[]],[]] => 17 [[],[[[[]],[]],[]],[]] => 17 [[],[[[[],[]]],[]],[]] => 18 [[],[[[[[]]]],[]],[]] => 19 [[],[[[],[],[],[]]],[]] => 17 [[],[[[],[],[[]]]],[]] => 18 [[],[[[],[[]],[]]],[]] => 18 [[],[[[],[[],[]]]],[]] => 19 [[],[[[],[[[]]]]],[]] => 20 [[],[[[[]],[],[]]],[]] => 18 [[],[[[[]],[[]]]],[]] => 19 [[],[[[[],[]],[]]],[]] => 19 [[],[[[[[]]],[]]],[]] => 20 [[],[[[[],[],[]]]],[]] => 20 [[],[[[[],[[]]]]],[]] => 21 [[],[[[[[]],[]]]],[]] => 21 [[],[[[[[],[]]]]],[]] => 22 [[],[[[[[[]]]]]],[]] => 23 [[],[[],[],[],[],[],[]]] => 14 [[],[[],[],[],[],[[]]]] => 15 [[],[[],[],[],[[]],[]]] => 15 [[],[[],[],[],[[],[]]]] => 16 [[],[[],[],[],[[[]]]]] => 17 [[],[[],[],[[]],[],[]]] => 15 [[],[[],[],[[]],[[]]]] => 16 [[],[[],[],[[],[]],[]]] => 16 [[],[[],[],[[[]]],[]]] => 17 [[],[[],[],[[],[],[]]]] => 17 [[],[[],[],[[],[[]]]]] => 18 [[],[[],[],[[[]],[]]]] => 18 [[],[[],[],[[[],[]]]]] => 19 [[],[[],[],[[[[]]]]]] => 20 [[],[[],[[]],[],[],[]]] => 15 [[],[[],[[]],[],[[]]]] => 16 [[],[[],[[]],[[]],[]]] => 16 [[],[[],[[]],[[],[]]]] => 17 [[],[[],[[]],[[[]]]]] => 18 [[],[[],[[],[]],[],[]]] => 16 [[],[[],[[[]]],[],[]]] => 17 [[],[[],[[],[]],[[]]]] => 17 [[],[[],[[[]]],[[]]]] => 18 [[],[[],[[],[],[]],[]]] => 17 [[],[[],[[],[[]]],[]]] => 18 [[],[[],[[[]],[]],[]]] => 18 [[],[[],[[[],[]]],[]]] => 19 [[],[[],[[[[]]]],[]]] => 20 [[],[[],[[],[],[],[]]]] => 18 [[],[[],[[],[],[[]]]]] => 19 [[],[[],[[],[[]],[]]]] => 19 [[],[[],[[],[[],[]]]]] => 20 [[],[[],[[],[[[]]]]]] => 21 [[],[[],[[[]],[],[]]]] => 19 [[],[[],[[[]],[[]]]]] => 20 [[],[[],[[[],[]],[]]]] => 20 [[],[[],[[[[]]],[]]]] => 21 [[],[[],[[[],[],[]]]]] => 21 [[],[[],[[[],[[]]]]]] => 22 [[],[[],[[[[]],[]]]]] => 22 [[],[[],[[[[],[]]]]]] => 23 [[],[[],[[[[[]]]]]]] => 24 [[],[[[]],[],[],[],[]]] => 15 [[],[[[]],[],[],[[]]]] => 16 [[],[[[]],[],[[]],[]]] => 16 [[],[[[]],[],[[],[]]]] => 17 [[],[[[]],[],[[[]]]]] => 18 [[],[[[]],[[]],[],[]]] => 16 [[],[[[]],[[]],[[]]]] => 17 [[],[[[]],[[],[]],[]]] => 17 [[],[[[]],[[[]]],[]]] => 18 [[],[[[]],[[],[],[]]]] => 18 [[],[[[]],[[],[[]]]]] => 19 [[],[[[]],[[[]],[]]]] => 19 [[],[[[]],[[[],[]]]]] => 20 [[],[[[]],[[[[]]]]]] => 21 [[],[[[],[]],[],[],[]]] => 16 [[],[[[[]]],[],[],[]]] => 17 [[],[[[],[]],[],[[]]]] => 17 [[],[[[[]]],[],[[]]]] => 18 [[],[[[],[]],[[]],[]]] => 17 [[],[[[[]]],[[]],[]]] => 18 [[],[[[],[]],[[],[]]]] => 18 [[],[[[],[]],[[[]]]]] => 19 [[],[[[[]]],[[],[]]]] => 19 [[],[[[[]]],[[[]]]]] => 20 [[],[[[],[],[]],[],[]]] => 17 [[],[[[],[[]]],[],[]]] => 18 [[],[[[[]],[]],[],[]]] => 18 [[],[[[[],[]]],[],[]]] => 19 [[],[[[[[]]]],[],[]]] => 20 [[],[[[],[],[]],[[]]]] => 18 [[],[[[],[[]]],[[]]]] => 19 [[],[[[[]],[]],[[]]]] => 19 [[],[[[[],[]]],[[]]]] => 20 [[],[[[[[]]]],[[]]]] => 21 [[],[[[],[],[],[]],[]]] => 18 [[],[[[],[],[[]]],[]]] => 19 [[],[[[],[[]],[]],[]]] => 19 [[],[[[],[[],[]]],[]]] => 20 [[],[[[],[[[]]]],[]]] => 21 [[],[[[[]],[],[]],[]]] => 19 [[],[[[[]],[[]]],[]]] => 20 [[],[[[[],[]],[]],[]]] => 20 [[],[[[[[]]],[]],[]]] => 21 [[],[[[[],[],[]]],[]]] => 21 [[],[[[[],[[]]]],[]]] => 22 [[],[[[[[]],[]]],[]]] => 22 [[],[[[[[],[]]]],[]]] => 23 [[],[[[[[[]]]]],[]]] => 24 [[],[[[],[],[],[],[]]]] => 19 [[],[[[],[],[],[[]]]]] => 20 [[],[[[],[],[[]],[]]]] => 20 [[],[[[],[],[[],[]]]]] => 21 [[],[[[],[],[[[]]]]]] => 22 [[],[[[],[[]],[],[]]]] => 20 [[],[[[],[[]],[[]]]]] => 21 [[],[[[],[[],[]],[]]]] => 21 [[],[[[],[[[]]],[]]]] => 22 [[],[[[],[[],[],[]]]]] => 22 [[],[[[],[[],[[]]]]]] => 23 [[],[[[],[[[]],[]]]]] => 23 [[],[[[],[[[],[]]]]]] => 24 [[],[[[],[[[[]]]]]]] => 25 [[],[[[[]],[],[],[]]]] => 20 [[],[[[[]],[],[[]]]]] => 21 [[],[[[[]],[[]],[]]]] => 21 [[],[[[[]],[[],[]]]]] => 22 [[],[[[[]],[[[]]]]]] => 23 [[],[[[[],[]],[],[]]]] => 21 [[],[[[[[]]],[],[]]]] => 22 [[],[[[[],[]],[[]]]]] => 22 [[],[[[[[]]],[[]]]]] => 23 [[],[[[[],[],[]],[]]]] => 22 [[],[[[[],[[]]],[]]]] => 23 [[],[[[[[]],[]],[]]]] => 23 [[],[[[[[],[]]],[]]]] => 24 [[],[[[[[[]]]],[]]]] => 25 [[],[[[[],[],[],[]]]]] => 23 [[],[[[[],[],[[]]]]]] => 24 [[],[[[[],[[]],[]]]]] => 24 [[],[[[[],[[],[]]]]]] => 25 [[],[[[[],[[[]]]]]]] => 26 [[],[[[[[]],[],[]]]]] => 24 [[],[[[[[]],[[]]]]]] => 25 [[],[[[[[],[]],[]]]]] => 25 [[],[[[[[[]]],[]]]]] => 26 [[],[[[[[],[],[]]]]]] => 26 [[],[[[[[],[[]]]]]]] => 27 [[],[[[[[[]],[]]]]]] => 27 [[],[[[[[[],[]]]]]]] => 28 [[],[[[[[[[]]]]]]]] => 29 [[[]],[],[],[],[],[],[]] => 9 [[[]],[],[],[],[],[[]]] => 10 [[[]],[],[],[],[[]],[]] => 10 [[[]],[],[],[],[[],[]]] => 11 [[[]],[],[],[],[[[]]]] => 12 [[[]],[],[],[[]],[],[]] => 10 [[[]],[],[],[[]],[[]]] => 11 [[[]],[],[],[[],[]],[]] => 11 [[[]],[],[],[[[]]],[]] => 12 [[[]],[],[],[[],[],[]]] => 12 [[[]],[],[],[[],[[]]]] => 13 [[[]],[],[],[[[]],[]]] => 13 [[[]],[],[],[[[],[]]]] => 14 [[[]],[],[],[[[[]]]]] => 15 [[[]],[],[[]],[],[],[]] => 10 [[[]],[],[[]],[],[[]]] => 11 [[[]],[],[[]],[[]],[]] => 11 [[[]],[],[[]],[[],[]]] => 12 [[[]],[],[[]],[[[]]]] => 13 [[[]],[],[[],[]],[],[]] => 11 [[[]],[],[[[]]],[],[]] => 12 [[[]],[],[[],[]],[[]]] => 12 [[[]],[],[[[]]],[[]]] => 13 [[[]],[],[[],[],[]],[]] => 12 [[[]],[],[[],[[]]],[]] => 13 [[[]],[],[[[]],[]],[]] => 13 [[[]],[],[[[],[]]],[]] => 14 [[[]],[],[[[[]]]],[]] => 15 [[[]],[],[[],[],[],[]]] => 13 [[[]],[],[[],[],[[]]]] => 14 [[[]],[],[[],[[]],[]]] => 14 [[[]],[],[[],[[],[]]]] => 15 [[[]],[],[[],[[[]]]]] => 16 [[[]],[],[[[]],[],[]]] => 14 [[[]],[],[[[]],[[]]]] => 15 [[[]],[],[[[],[]],[]]] => 15 [[[]],[],[[[[]]],[]]] => 16 [[[]],[],[[[],[],[]]]] => 16 [[[]],[],[[[],[[]]]]] => 17 [[[]],[],[[[[]],[]]]] => 17 [[[]],[],[[[[],[]]]]] => 18 [[[]],[],[[[[[]]]]]] => 19 [[[]],[[]],[],[],[],[]] => 10 [[[]],[[]],[],[],[[]]] => 11 [[[]],[[]],[],[[]],[]] => 11 [[[]],[[]],[],[[],[]]] => 12 [[[]],[[]],[],[[[]]]] => 13 [[[]],[[]],[[]],[],[]] => 11 [[[]],[[]],[[]],[[]]] => 12 [[[]],[[]],[[],[]],[]] => 12 [[[]],[[]],[[[]]],[]] => 13 [[[]],[[]],[[],[],[]]] => 13 [[[]],[[]],[[],[[]]]] => 14 [[[]],[[]],[[[]],[]]] => 14 [[[]],[[]],[[[],[]]]] => 15 [[[]],[[]],[[[[]]]]] => 16 [[[]],[[],[]],[],[],[]] => 11 [[[]],[[[]]],[],[],[]] => 12 [[[]],[[],[]],[],[[]]] => 12 [[[]],[[[]]],[],[[]]] => 13 [[[]],[[],[]],[[]],[]] => 12 [[[]],[[[]]],[[]],[]] => 13 [[[]],[[],[]],[[],[]]] => 13 [[[]],[[],[]],[[[]]]] => 14 [[[]],[[[]]],[[],[]]] => 14 [[[]],[[[]]],[[[]]]] => 15 [[[]],[[],[],[]],[],[]] => 12 [[[]],[[],[[]]],[],[]] => 13 [[[]],[[[]],[]],[],[]] => 13 [[[]],[[[],[]]],[],[]] => 14 [[[]],[[[[]]]],[],[]] => 15 [[[]],[[],[],[]],[[]]] => 13 [[[]],[[],[[]]],[[]]] => 14 [[[]],[[[]],[]],[[]]] => 14 [[[]],[[[],[]]],[[]]] => 15 [[[]],[[[[]]]],[[]]] => 16 [[[]],[[],[],[],[]],[]] => 13 [[[]],[[],[],[[]]],[]] => 14 [[[]],[[],[[]],[]],[]] => 14 [[[]],[[],[[],[]]],[]] => 15 [[[]],[[],[[[]]]],[]] => 16 [[[]],[[[]],[],[]],[]] => 14 [[[]],[[[]],[[]]],[]] => 15 [[[]],[[[],[]],[]],[]] => 15 [[[]],[[[[]]],[]],[]] => 16 [[[]],[[[],[],[]]],[]] => 16 [[[]],[[[],[[]]]],[]] => 17 [[[]],[[[[]],[]]],[]] => 17 [[[]],[[[[],[]]]],[]] => 18 [[[]],[[[[[]]]]],[]] => 19 [[[]],[[],[],[],[],[]]] => 14 [[[]],[[],[],[],[[]]]] => 15 [[[]],[[],[],[[]],[]]] => 15 [[[]],[[],[],[[],[]]]] => 16 [[[]],[[],[],[[[]]]]] => 17 [[[]],[[],[[]],[],[]]] => 15 [[[]],[[],[[]],[[]]]] => 16 [[[]],[[],[[],[]],[]]] => 16 [[[]],[[],[[[]]],[]]] => 17 [[[]],[[],[[],[],[]]]] => 17 [[[]],[[],[[],[[]]]]] => 18 [[[]],[[],[[[]],[]]]] => 18 [[[]],[[],[[[],[]]]]] => 19 [[[]],[[],[[[[]]]]]] => 20 [[[]],[[[]],[],[],[]]] => 15 [[[]],[[[]],[],[[]]]] => 16 [[[]],[[[]],[[]],[]]] => 16 [[[]],[[[]],[[],[]]]] => 17 [[[]],[[[]],[[[]]]]] => 18 [[[]],[[[],[]],[],[]]] => 16 [[[]],[[[[]]],[],[]]] => 17 [[[]],[[[],[]],[[]]]] => 17 [[[]],[[[[]]],[[]]]] => 18 [[[]],[[[],[],[]],[]]] => 17 [[[]],[[[],[[]]],[]]] => 18 [[[]],[[[[]],[]],[]]] => 18 [[[]],[[[[],[]]],[]]] => 19 [[[]],[[[[[]]]],[]]] => 20 [[[]],[[[],[],[],[]]]] => 18 [[[]],[[[],[],[[]]]]] => 19 [[[]],[[[],[[]],[]]]] => 19 [[[]],[[[],[[],[]]]]] => 20 [[[]],[[[],[[[]]]]]] => 21 [[[]],[[[[]],[],[]]]] => 19 [[[]],[[[[]],[[]]]]] => 20 [[[]],[[[[],[]],[]]]] => 20 [[[]],[[[[[]]],[]]]] => 21 [[[]],[[[[],[],[]]]]] => 21 [[[]],[[[[],[[]]]]]] => 22 [[[]],[[[[[]],[]]]]] => 22 [[[]],[[[[[],[]]]]]] => 23 [[[]],[[[[[[]]]]]]] => 24 [[[],[]],[],[],[],[],[]] => 10 [[[[]]],[],[],[],[],[]] => 11 [[[],[]],[],[],[],[[]]] => 11 [[[[]]],[],[],[],[[]]] => 12 [[[],[]],[],[],[[]],[]] => 11 [[[[]]],[],[],[[]],[]] => 12 [[[],[]],[],[],[[],[]]] => 12 [[[],[]],[],[],[[[]]]] => 13 [[[[]]],[],[],[[],[]]] => 13 [[[[]]],[],[],[[[]]]] => 14 [[[],[]],[],[[]],[],[]] => 11 [[[[]]],[],[[]],[],[]] => 12 [[[],[]],[],[[]],[[]]] => 12 [[[[]]],[],[[]],[[]]] => 13 ----------------------------------------------------------------------------- Created: Feb 22, 2016 at 16:19 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 22, 2016 at 16:19 by Martin Rubey