***************************************************************************** * 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: St000973 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The length of the boundary of an ordered tree. This is the sum of the number of edges to the left most and the right most leaf. ----------------------------------------------------------------------------- References: [1] Davenport, D. E., Shapiro, L. W., Pudwell, L. K., Woodson, L. C. The boundary of ordered trees [[MathSciNet:3355976]] ----------------------------------------------------------------------------- Code: def statistic(T): b = 0 C = T while len(C) > 0: C = C[0] b += 1 C = T while len(C) > 0: C = C[-1] b += 1 return b ----------------------------------------------------------------------------- Statistic values: [[]] => 2 [[],[]] => 2 [[[]]] => 4 [[],[],[]] => 2 [[],[[]]] => 3 [[[]],[]] => 3 [[[],[]]] => 4 [[[[]]]] => 6 [[],[],[],[]] => 2 [[],[],[[]]] => 3 [[],[[]],[]] => 2 [[],[[],[]]] => 3 [[],[[[]]]] => 4 [[[]],[],[]] => 3 [[[]],[[]]] => 4 [[[],[]],[]] => 3 [[[[]]],[]] => 4 [[[],[],[]]] => 4 [[[],[[]]]] => 5 [[[[]],[]]] => 5 [[[[],[]]]] => 6 [[[[[]]]]] => 8 [[],[],[],[],[]] => 2 [[],[],[],[[]]] => 3 [[],[],[[]],[]] => 2 [[],[],[[],[]]] => 3 [[],[],[[[]]]] => 4 [[],[[]],[],[]] => 2 [[],[[]],[[]]] => 3 [[],[[],[]],[]] => 2 [[],[[[]]],[]] => 2 [[],[[],[],[]]] => 3 [[],[[],[[]]]] => 4 [[],[[[]],[]]] => 3 [[],[[[],[]]]] => 4 [[],[[[[]]]]] => 5 [[[]],[],[],[]] => 3 [[[]],[],[[]]] => 4 [[[]],[[]],[]] => 3 [[[]],[[],[]]] => 4 [[[]],[[[]]]] => 5 [[[],[]],[],[]] => 3 [[[[]]],[],[]] => 4 [[[],[]],[[]]] => 4 [[[[]]],[[]]] => 5 [[[],[],[]],[]] => 3 [[[],[[]]],[]] => 3 [[[[]],[]],[]] => 4 [[[[],[]]],[]] => 4 [[[[[]]]],[]] => 5 [[[],[],[],[]]] => 4 [[[],[],[[]]]] => 5 [[[],[[]],[]]] => 4 [[[],[[],[]]]] => 5 [[[],[[[]]]]] => 6 [[[[]],[],[]]] => 5 [[[[]],[[]]]] => 6 [[[[],[]],[]]] => 5 [[[[[]]],[]]] => 6 [[[[],[],[]]]] => 6 [[[[],[[]]]]] => 7 [[[[[]],[]]]] => 7 [[[[[],[]]]]] => 8 [[[[[[]]]]]] => 10 [[],[],[],[],[],[]] => 2 [[],[],[],[],[[]]] => 3 [[],[],[],[[]],[]] => 2 [[],[],[],[[],[]]] => 3 [[],[],[],[[[]]]] => 4 [[],[],[[]],[],[]] => 2 [[],[],[[]],[[]]] => 3 [[],[],[[],[]],[]] => 2 [[],[],[[[]]],[]] => 2 [[],[],[[],[],[]]] => 3 [[],[],[[],[[]]]] => 4 [[],[],[[[]],[]]] => 3 [[],[],[[[],[]]]] => 4 [[],[],[[[[]]]]] => 5 [[],[[]],[],[],[]] => 2 [[],[[]],[],[[]]] => 3 [[],[[]],[[]],[]] => 2 [[],[[]],[[],[]]] => 3 [[],[[]],[[[]]]] => 4 [[],[[],[]],[],[]] => 2 [[],[[[]]],[],[]] => 2 [[],[[],[]],[[]]] => 3 [[],[[[]]],[[]]] => 3 [[],[[],[],[]],[]] => 2 [[],[[],[[]]],[]] => 2 [[],[[[]],[]],[]] => 2 [[],[[[],[]]],[]] => 2 [[],[[[[]]]],[]] => 2 [[],[[],[],[],[]]] => 3 [[],[[],[],[[]]]] => 4 [[],[[],[[]],[]]] => 3 [[],[[],[[],[]]]] => 4 [[],[[],[[[]]]]] => 5 [[],[[[]],[],[]]] => 3 [[],[[[]],[[]]]] => 4 [[],[[[],[]],[]]] => 3 [[],[[[[]]],[]]] => 3 [[],[[[],[],[]]]] => 4 [[],[[[],[[]]]]] => 5 [[],[[[[]],[]]]] => 4 [[],[[[[],[]]]]] => 5 [[],[[[[[]]]]]] => 6 [[[]],[],[],[],[]] => 3 [[[]],[],[],[[]]] => 4 [[[]],[],[[]],[]] => 3 [[[]],[],[[],[]]] => 4 [[[]],[],[[[]]]] => 5 [[[]],[[]],[],[]] => 3 [[[]],[[]],[[]]] => 4 [[[]],[[],[]],[]] => 3 [[[]],[[[]]],[]] => 3 [[[]],[[],[],[]]] => 4 [[[]],[[],[[]]]] => 5 [[[]],[[[]],[]]] => 4 [[[]],[[[],[]]]] => 5 [[[]],[[[[]]]]] => 6 [[[],[]],[],[],[]] => 3 [[[[]]],[],[],[]] => 4 [[[],[]],[],[[]]] => 4 [[[[]]],[],[[]]] => 5 [[[],[]],[[]],[]] => 3 [[[[]]],[[]],[]] => 4 [[[],[]],[[],[]]] => 4 [[[],[]],[[[]]]] => 5 [[[[]]],[[],[]]] => 5 [[[[]]],[[[]]]] => 6 [[[],[],[]],[],[]] => 3 [[[],[[]]],[],[]] => 3 [[[[]],[]],[],[]] => 4 [[[[],[]]],[],[]] => 4 [[[[[]]]],[],[]] => 5 [[[],[],[]],[[]]] => 4 [[[],[[]]],[[]]] => 4 [[[[]],[]],[[]]] => 5 [[[[],[]]],[[]]] => 5 [[[[[]]]],[[]]] => 6 [[[],[],[],[]],[]] => 3 [[[],[],[[]]],[]] => 3 [[[],[[]],[]],[]] => 3 [[[],[[],[]]],[]] => 3 [[[],[[[]]]],[]] => 3 [[[[]],[],[]],[]] => 4 [[[[]],[[]]],[]] => 4 [[[[],[]],[]],[]] => 4 [[[[[]]],[]],[]] => 5 [[[[],[],[]]],[]] => 4 [[[[],[[]]]],[]] => 4 [[[[[]],[]]],[]] => 5 [[[[[],[]]]],[]] => 5 [[[[[[]]]]],[]] => 6 [[[],[],[],[],[]]] => 4 [[[],[],[],[[]]]] => 5 [[[],[],[[]],[]]] => 4 [[[],[],[[],[]]]] => 5 [[[],[],[[[]]]]] => 6 [[[],[[]],[],[]]] => 4 [[[],[[]],[[]]]] => 5 [[[],[[],[]],[]]] => 4 [[[],[[[]]],[]]] => 4 [[[],[[],[],[]]]] => 5 [[[],[[],[[]]]]] => 6 [[[],[[[]],[]]]] => 5 [[[],[[[],[]]]]] => 6 [[[],[[[[]]]]]] => 7 [[[[]],[],[],[]]] => 5 [[[[]],[],[[]]]] => 6 [[[[]],[[]],[]]] => 5 [[[[]],[[],[]]]] => 6 [[[[]],[[[]]]]] => 7 [[[[],[]],[],[]]] => 5 [[[[[]]],[],[]]] => 6 [[[[],[]],[[]]]] => 6 [[[[[]]],[[]]]] => 7 [[[[],[],[]],[]]] => 5 [[[[],[[]]],[]]] => 5 [[[[[]],[]],[]]] => 6 [[[[[],[]]],[]]] => 6 [[[[[[]]]],[]]] => 7 [[[[],[],[],[]]]] => 6 [[[[],[],[[]]]]] => 7 [[[[],[[]],[]]]] => 6 [[[[],[[],[]]]]] => 7 [[[[],[[[]]]]]] => 8 [[[[[]],[],[]]]] => 7 [[[[[]],[[]]]]] => 8 [[[[[],[]],[]]]] => 7 [[[[[[]]],[]]]] => 8 [[[[[],[],[]]]]] => 8 [[[[[],[[]]]]]] => 9 [[[[[[]],[]]]]] => 9 [[[[[[],[]]]]]] => 10 [[[[[[[]]]]]]] => 12 [[],[],[],[],[],[],[]] => 2 [[],[],[],[],[],[[]]] => 3 [[],[],[],[],[[]],[]] => 2 [[],[],[],[],[[],[]]] => 3 [[],[],[],[],[[[]]]] => 4 [[],[],[],[[]],[],[]] => 2 [[],[],[],[[]],[[]]] => 3 [[],[],[],[[],[]],[]] => 2 [[],[],[],[[[]]],[]] => 2 [[],[],[],[[],[],[]]] => 3 [[],[],[],[[],[[]]]] => 4 [[],[],[],[[[]],[]]] => 3 [[],[],[],[[[],[]]]] => 4 [[],[],[],[[[[]]]]] => 5 [[],[],[[]],[],[],[]] => 2 [[],[],[[]],[],[[]]] => 3 [[],[],[[]],[[]],[]] => 2 [[],[],[[]],[[],[]]] => 3 [[],[],[[]],[[[]]]] => 4 [[],[],[[],[]],[],[]] => 2 [[],[],[[[]]],[],[]] => 2 [[],[],[[],[]],[[]]] => 3 [[],[],[[[]]],[[]]] => 3 [[],[],[[],[],[]],[]] => 2 [[],[],[[],[[]]],[]] => 2 [[],[],[[[]],[]],[]] => 2 [[],[],[[[],[]]],[]] => 2 [[],[],[[[[]]]],[]] => 2 [[],[],[[],[],[],[]]] => 3 [[],[],[[],[],[[]]]] => 4 [[],[],[[],[[]],[]]] => 3 [[],[],[[],[[],[]]]] => 4 [[],[],[[],[[[]]]]] => 5 [[],[],[[[]],[],[]]] => 3 [[],[],[[[]],[[]]]] => 4 [[],[],[[[],[]],[]]] => 3 [[],[],[[[[]]],[]]] => 3 [[],[],[[[],[],[]]]] => 4 [[],[],[[[],[[]]]]] => 5 [[],[],[[[[]],[]]]] => 4 [[],[],[[[[],[]]]]] => 5 [[],[],[[[[[]]]]]] => 6 [[],[[]],[],[],[],[]] => 2 [[],[[]],[],[],[[]]] => 3 [[],[[]],[],[[]],[]] => 2 [[],[[]],[],[[],[]]] => 3 [[],[[]],[],[[[]]]] => 4 [[],[[]],[[]],[],[]] => 2 [[],[[]],[[]],[[]]] => 3 [[],[[]],[[],[]],[]] => 2 [[],[[]],[[[]]],[]] => 2 [[],[[]],[[],[],[]]] => 3 [[],[[]],[[],[[]]]] => 4 [[],[[]],[[[]],[]]] => 3 [[],[[]],[[[],[]]]] => 4 [[],[[]],[[[[]]]]] => 5 [[],[[],[]],[],[],[]] => 2 [[],[[[]]],[],[],[]] => 2 [[],[[],[]],[],[[]]] => 3 [[],[[[]]],[],[[]]] => 3 [[],[[],[]],[[]],[]] => 2 [[],[[[]]],[[]],[]] => 2 [[],[[],[]],[[],[]]] => 3 [[],[[],[]],[[[]]]] => 4 [[],[[[]]],[[],[]]] => 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 [[],[[],[],[],[[]]]] => 4 [[],[[],[],[[]],[]]] => 3 [[],[[],[],[[],[]]]] => 4 [[],[[],[],[[[]]]]] => 5 [[],[[],[[]],[],[]]] => 3 [[],[[],[[]],[[]]]] => 4 [[],[[],[[],[]],[]]] => 3 [[],[[],[[[]]],[]]] => 3 [[],[[],[[],[],[]]]] => 4 [[],[[],[[],[[]]]]] => 5 [[],[[],[[[]],[]]]] => 4 [[],[[],[[[],[]]]]] => 5 [[],[[],[[[[]]]]]] => 6 [[],[[[]],[],[],[]]] => 3 [[],[[[]],[],[[]]]] => 4 [[],[[[]],[[]],[]]] => 3 [[],[[[]],[[],[]]]] => 4 [[],[[[]],[[[]]]]] => 5 [[],[[[],[]],[],[]]] => 3 [[],[[[[]]],[],[]]] => 3 [[],[[[],[]],[[]]]] => 4 [[],[[[[]]],[[]]]] => 4 [[],[[[],[],[]],[]]] => 3 [[],[[[],[[]]],[]]] => 3 [[],[[[[]],[]],[]]] => 3 [[],[[[[],[]]],[]]] => 3 [[],[[[[[]]]],[]]] => 3 [[],[[[],[],[],[]]]] => 4 [[],[[[],[],[[]]]]] => 5 [[],[[[],[[]],[]]]] => 4 [[],[[[],[[],[]]]]] => 5 [[],[[[],[[[]]]]]] => 6 [[],[[[[]],[],[]]]] => 4 [[],[[[[]],[[]]]]] => 5 [[],[[[[],[]],[]]]] => 4 [[],[[[[[]]],[]]]] => 4 [[],[[[[],[],[]]]]] => 5 [[],[[[[],[[]]]]]] => 6 [[],[[[[[]],[]]]]] => 5 [[],[[[[[],[]]]]]] => 6 [[],[[[[[[]]]]]]] => 7 [[[]],[],[],[],[],[]] => 3 [[[]],[],[],[],[[]]] => 4 [[[]],[],[],[[]],[]] => 3 [[[]],[],[],[[],[]]] => 4 [[[]],[],[],[[[]]]] => 5 [[[]],[],[[]],[],[]] => 3 [[[]],[],[[]],[[]]] => 4 [[[]],[],[[],[]],[]] => 3 [[[]],[],[[[]]],[]] => 3 [[[]],[],[[],[],[]]] => 4 [[[]],[],[[],[[]]]] => 5 [[[]],[],[[[]],[]]] => 4 [[[]],[],[[[],[]]]] => 5 [[[]],[],[[[[]]]]] => 6 [[[]],[[]],[],[],[]] => 3 [[[]],[[]],[],[[]]] => 4 [[[]],[[]],[[]],[]] => 3 [[[]],[[]],[[],[]]] => 4 [[[]],[[]],[[[]]]] => 5 [[[]],[[],[]],[],[]] => 3 [[[]],[[[]]],[],[]] => 3 [[[]],[[],[]],[[]]] => 4 [[[]],[[[]]],[[]]] => 4 [[[]],[[],[],[]],[]] => 3 [[[]],[[],[[]]],[]] => 3 [[[]],[[[]],[]],[]] => 3 [[[]],[[[],[]]],[]] => 3 [[[]],[[[[]]]],[]] => 3 [[[]],[[],[],[],[]]] => 4 [[[]],[[],[],[[]]]] => 5 [[[]],[[],[[]],[]]] => 4 [[[]],[[],[[],[]]]] => 5 [[[]],[[],[[[]]]]] => 6 [[[]],[[[]],[],[]]] => 4 [[[]],[[[]],[[]]]] => 5 [[[]],[[[],[]],[]]] => 4 [[[]],[[[[]]],[]]] => 4 [[[]],[[[],[],[]]]] => 5 [[[]],[[[],[[]]]]] => 6 [[[]],[[[[]],[]]]] => 5 [[[]],[[[[],[]]]]] => 6 [[[]],[[[[[]]]]]] => 7 [[[],[]],[],[],[],[]] => 3 [[[[]]],[],[],[],[]] => 4 [[[],[]],[],[],[[]]] => 4 [[[[]]],[],[],[[]]] => 5 [[[],[]],[],[[]],[]] => 3 [[[[]]],[],[[]],[]] => 4 [[[],[]],[],[[],[]]] => 4 [[[],[]],[],[[[]]]] => 5 [[[[]]],[],[[],[]]] => 5 [[[[]]],[],[[[]]]] => 6 [[[],[]],[[]],[],[]] => 3 [[[[]]],[[]],[],[]] => 4 [[[],[]],[[]],[[]]] => 4 [[[[]]],[[]],[[]]] => 5 [[[],[]],[[],[]],[]] => 3 [[[],[]],[[[]]],[]] => 3 [[[[]]],[[],[]],[]] => 4 [[[[]]],[[[]]],[]] => 4 [[[],[]],[[],[],[]]] => 4 [[[],[]],[[],[[]]]] => 5 [[[],[]],[[[]],[]]] => 4 [[[],[]],[[[],[]]]] => 5 [[[],[]],[[[[]]]]] => 6 [[[[]]],[[],[],[]]] => 5 [[[[]]],[[],[[]]]] => 6 [[[[]]],[[[]],[]]] => 5 [[[[]]],[[[],[]]]] => 6 [[[[]]],[[[[]]]]] => 7 [[[],[],[]],[],[],[]] => 3 [[[],[[]]],[],[],[]] => 3 [[[[]],[]],[],[],[]] => 4 [[[[],[]]],[],[],[]] => 4 [[[[[]]]],[],[],[]] => 5 [[[],[],[]],[],[[]]] => 4 [[[],[[]]],[],[[]]] => 4 [[[[]],[]],[],[[]]] => 5 [[[[],[]]],[],[[]]] => 5 [[[[[]]]],[],[[]]] => 6 [[[],[],[]],[[]],[]] => 3 [[[],[[]]],[[]],[]] => 3 [[[[]],[]],[[]],[]] => 4 [[[[],[]]],[[]],[]] => 4 [[[[[]]]],[[]],[]] => 5 [[[],[],[]],[[],[]]] => 4 [[[],[],[]],[[[]]]] => 5 [[[],[[]]],[[],[]]] => 4 [[[],[[]]],[[[]]]] => 5 [[[[]],[]],[[],[]]] => 5 [[[[]],[]],[[[]]]] => 6 [[[[],[]]],[[],[]]] => 5 [[[[],[]]],[[[]]]] => 6 [[[[[]]]],[[],[]]] => 6 [[[[[]]]],[[[]]]] => 7 [[[],[],[],[]],[],[]] => 3 [[[],[],[[]]],[],[]] => 3 [[[],[[]],[]],[],[]] => 3 [[[],[[],[]]],[],[]] => 3 [[[],[[[]]]],[],[]] => 3 [[[[]],[],[]],[],[]] => 4 [[[[]],[[]]],[],[]] => 4 [[[[],[]],[]],[],[]] => 4 [[[[[]]],[]],[],[]] => 5 [[[[],[],[]]],[],[]] => 4 [[[[],[[]]]],[],[]] => 4 [[[[[]],[]]],[],[]] => 5 [[[[[],[]]]],[],[]] => 5 [[[[[[]]]]],[],[]] => 6 [[[],[],[],[]],[[]]] => 4 [[[],[],[[]]],[[]]] => 4 [[[],[[]],[]],[[]]] => 4 [[[],[[],[]]],[[]]] => 4 [[[],[[[]]]],[[]]] => 4 [[[[]],[],[]],[[]]] => 5 [[[[]],[[]]],[[]]] => 5 [[[[],[]],[]],[[]]] => 5 [[[[[]]],[]],[[]]] => 6 [[[[],[],[]]],[[]]] => 5 [[[[],[[]]]],[[]]] => 5 [[[[[]],[]]],[[]]] => 6 [[[[[],[]]]],[[]]] => 6 [[[[[[]]]]],[[]]] => 7 [[[],[],[],[],[]],[]] => 3 [[[],[],[],[[]]],[]] => 3 [[[],[],[[]],[]],[]] => 3 [[[],[],[[],[]]],[]] => 3 [[[],[],[[[]]]],[]] => 3 [[[],[[]],[],[]],[]] => 3 [[[],[[]],[[]]],[]] => 3 [[[],[[],[]],[]],[]] => 3 [[[],[[[]]],[]],[]] => 3 [[[],[[],[],[]]],[]] => 3 [[[],[[],[[]]]],[]] => 3 [[[],[[[]],[]]],[]] => 3 [[[],[[[],[]]]],[]] => 3 [[[],[[[[]]]]],[]] => 3 [[[[]],[],[],[]],[]] => 4 [[[[]],[],[[]]],[]] => 4 [[[[]],[[]],[]],[]] => 4 [[[[]],[[],[]]],[]] => 4 [[[[]],[[[]]]],[]] => 4 [[[[],[]],[],[]],[]] => 4 [[[[[]]],[],[]],[]] => 5 [[[[],[]],[[]]],[]] => 4 [[[[[]]],[[]]],[]] => 5 [[[[],[],[]],[]],[]] => 4 [[[[],[[]]],[]],[]] => 4 [[[[[]],[]],[]],[]] => 5 [[[[[],[]]],[]],[]] => 5 [[[[[[]]]],[]],[]] => 6 [[[[],[],[],[]]],[]] => 4 [[[[],[],[[]]]],[]] => 4 [[[[],[[]],[]]],[]] => 4 [[[[],[[],[]]]],[]] => 4 [[[[],[[[]]]]],[]] => 4 [[[[[]],[],[]]],[]] => 5 [[[[[]],[[]]]],[]] => 5 [[[[[],[]],[]]],[]] => 5 [[[[[[]]],[]]],[]] => 6 [[[[[],[],[]]]],[]] => 5 [[[[[],[[]]]]],[]] => 5 [[[[[[]],[]]]],[]] => 6 [[[[[[],[]]]]],[]] => 6 [[[[[[[]]]]]],[]] => 7 [[[],[],[],[],[],[]]] => 4 [[[],[],[],[],[[]]]] => 5 [[[],[],[],[[]],[]]] => 4 [[[],[],[],[[],[]]]] => 5 [[[],[],[],[[[]]]]] => 6 [[[],[],[[]],[],[]]] => 4 [[[],[],[[]],[[]]]] => 5 [[[],[],[[],[]],[]]] => 4 [[[],[],[[[]]],[]]] => 4 [[[],[],[[],[],[]]]] => 5 [[[],[],[[],[[]]]]] => 6 [[[],[],[[[]],[]]]] => 5 [[[],[],[[[],[]]]]] => 6 [[[],[],[[[[]]]]]] => 7 [[[],[[]],[],[],[]]] => 4 [[[],[[]],[],[[]]]] => 5 [[[],[[]],[[]],[]]] => 4 [[[],[[]],[[],[]]]] => 5 [[[],[[]],[[[]]]]] => 6 [[[],[[],[]],[],[]]] => 4 [[[],[[[]]],[],[]]] => 4 [[[],[[],[]],[[]]]] => 5 [[[],[[[]]],[[]]]] => 5 [[[],[[],[],[]],[]]] => 4 [[[],[[],[[]]],[]]] => 4 [[[],[[[]],[]],[]]] => 4 [[[],[[[],[]]],[]]] => 4 [[[],[[[[]]]],[]]] => 4 [[[],[[],[],[],[]]]] => 5 [[[],[[],[],[[]]]]] => 6 [[[],[[],[[]],[]]]] => 5 [[[],[[],[[],[]]]]] => 6 [[[],[[],[[[]]]]]] => 7 [[[],[[[]],[],[]]]] => 5 [[[],[[[]],[[]]]]] => 6 [[[],[[[],[]],[]]]] => 5 [[[],[[[[]]],[]]]] => 5 [[[],[[[],[],[]]]]] => 6 [[[],[[[],[[]]]]]] => 7 [[[],[[[[]],[]]]]] => 6 [[[],[[[[],[]]]]]] => 7 [[[],[[[[[]]]]]]] => 8 [[[[]],[],[],[],[]]] => 5 [[[[]],[],[],[[]]]] => 6 [[[[]],[],[[]],[]]] => 5 [[[[]],[],[[],[]]]] => 6 [[[[]],[],[[[]]]]] => 7 [[[[]],[[]],[],[]]] => 5 [[[[]],[[]],[[]]]] => 6 [[[[]],[[],[]],[]]] => 5 [[[[]],[[[]]],[]]] => 5 [[[[]],[[],[],[]]]] => 6 [[[[]],[[],[[]]]]] => 7 [[[[]],[[[]],[]]]] => 6 [[[[]],[[[],[]]]]] => 7 [[[[]],[[[[]]]]]] => 8 [[[[],[]],[],[],[]]] => 5 [[[[[]]],[],[],[]]] => 6 [[[[],[]],[],[[]]]] => 6 [[[[[]]],[],[[]]]] => 7 [[[[],[]],[[]],[]]] => 5 [[[[[]]],[[]],[]]] => 6 [[[[],[]],[[],[]]]] => 6 [[[[],[]],[[[]]]]] => 7 [[[[[]]],[[],[]]]] => 7 [[[[[]]],[[[]]]]] => 8 [[[[],[],[]],[],[]]] => 5 [[[[],[[]]],[],[]]] => 5 [[[[[]],[]],[],[]]] => 6 [[[[[],[]]],[],[]]] => 6 [[[[[[]]]],[],[]]] => 7 [[[[],[],[]],[[]]]] => 6 [[[[],[[]]],[[]]]] => 6 [[[[[]],[]],[[]]]] => 7 [[[[[],[]]],[[]]]] => 7 [[[[[[]]]],[[]]]] => 8 [[[[],[],[],[]],[]]] => 5 [[[[],[],[[]]],[]]] => 5 [[[[],[[]],[]],[]]] => 5 [[[[],[[],[]]],[]]] => 5 [[[[],[[[]]]],[]]] => 5 [[[[[]],[],[]],[]]] => 6 [[[[[]],[[]]],[]]] => 6 [[[[[],[]],[]],[]]] => 6 [[[[[[]]],[]],[]]] => 7 [[[[[],[],[]]],[]]] => 6 [[[[[],[[]]]],[]]] => 6 [[[[[[]],[]]],[]]] => 7 [[[[[[],[]]]],[]]] => 7 [[[[[[[]]]]],[]]] => 8 [[[[],[],[],[],[]]]] => 6 [[[[],[],[],[[]]]]] => 7 [[[[],[],[[]],[]]]] => 6 [[[[],[],[[],[]]]]] => 7 [[[[],[],[[[]]]]]] => 8 [[[[],[[]],[],[]]]] => 6 [[[[],[[]],[[]]]]] => 7 [[[[],[[],[]],[]]]] => 6 [[[[],[[[]]],[]]]] => 6 [[[[],[[],[],[]]]]] => 7 [[[[],[[],[[]]]]]] => 8 [[[[],[[[]],[]]]]] => 7 [[[[],[[[],[]]]]]] => 8 [[[[],[[[[]]]]]]] => 9 [[[[[]],[],[],[]]]] => 7 [[[[[]],[],[[]]]]] => 8 [[[[[]],[[]],[]]]] => 7 [[[[[]],[[],[]]]]] => 8 [[[[[]],[[[]]]]]] => 9 [[[[[],[]],[],[]]]] => 7 [[[[[[]]],[],[]]]] => 8 [[[[[],[]],[[]]]]] => 8 [[[[[[]]],[[]]]]] => 9 [[[[[],[],[]],[]]]] => 7 [[[[[],[[]]],[]]]] => 7 [[[[[[]],[]],[]]]] => 8 [[[[[[],[]]],[]]]] => 8 [[[[[[[]]]],[]]]] => 9 [[[[[],[],[],[]]]]] => 8 [[[[[],[],[[]]]]]] => 9 [[[[[],[[]],[]]]]] => 8 [[[[[],[[],[]]]]]] => 9 [[[[[],[[[]]]]]]] => 10 [[[[[[]],[],[]]]]] => 9 [[[[[[]],[[]]]]]] => 10 [[[[[[],[]],[]]]]] => 9 [[[[[[[]]],[]]]]] => 10 [[[[[[],[],[]]]]]] => 10 [[[[[[],[[]]]]]]] => 11 [[[[[[[]],[]]]]]] => 11 [[[[[[[],[]]]]]]] => 12 [[[[[[[[]]]]]]]] => 14 [[],[],[],[],[],[],[],[]] => 2 [[],[],[],[],[],[],[[]]] => 3 [[],[],[],[],[],[[]],[]] => 2 [[],[],[],[],[],[[],[]]] => 3 [[],[],[],[],[],[[[]]]] => 4 [[],[],[],[],[[]],[],[]] => 2 [[],[],[],[],[[]],[[]]] => 3 [[],[],[],[],[[],[]],[]] => 2 [[],[],[],[],[[[]]],[]] => 2 [[],[],[],[],[[],[],[]]] => 3 [[],[],[],[],[[],[[]]]] => 4 [[],[],[],[],[[[]],[]]] => 3 [[],[],[],[],[[[],[]]]] => 4 [[],[],[],[],[[[[]]]]] => 5 [[],[],[],[[]],[],[],[]] => 2 [[],[],[],[[]],[],[[]]] => 3 [[],[],[],[[]],[[]],[]] => 2 [[],[],[],[[]],[[],[]]] => 3 [[],[],[],[[]],[[[]]]] => 4 [[],[],[],[[],[]],[],[]] => 2 [[],[],[],[[[]]],[],[]] => 2 [[],[],[],[[],[]],[[]]] => 3 [[],[],[],[[[]]],[[]]] => 3 [[],[],[],[[],[],[]],[]] => 2 [[],[],[],[[],[[]]],[]] => 2 [[],[],[],[[[]],[]],[]] => 2 [[],[],[],[[[],[]]],[]] => 2 [[],[],[],[[[[]]]],[]] => 2 [[],[],[],[[],[],[],[]]] => 3 [[],[],[],[[],[],[[]]]] => 4 [[],[],[],[[],[[]],[]]] => 3 [[],[],[],[[],[[],[]]]] => 4 [[],[],[],[[],[[[]]]]] => 5 [[],[],[],[[[]],[],[]]] => 3 [[],[],[],[[[]],[[]]]] => 4 [[],[],[],[[[],[]],[]]] => 3 [[],[],[],[[[[]]],[]]] => 3 [[],[],[],[[[],[],[]]]] => 4 [[],[],[],[[[],[[]]]]] => 5 [[],[],[],[[[[]],[]]]] => 4 [[],[],[],[[[[],[]]]]] => 5 [[],[],[],[[[[[]]]]]] => 6 [[],[],[[]],[],[],[],[]] => 2 [[],[],[[]],[],[],[[]]] => 3 [[],[],[[]],[],[[]],[]] => 2 [[],[],[[]],[],[[],[]]] => 3 [[],[],[[]],[],[[[]]]] => 4 [[],[],[[]],[[]],[],[]] => 2 [[],[],[[]],[[]],[[]]] => 3 [[],[],[[]],[[],[]],[]] => 2 [[],[],[[]],[[[]]],[]] => 2 [[],[],[[]],[[],[],[]]] => 3 [[],[],[[]],[[],[[]]]] => 4 [[],[],[[]],[[[]],[]]] => 3 [[],[],[[]],[[[],[]]]] => 4 [[],[],[[]],[[[[]]]]] => 5 [[],[],[[],[]],[],[],[]] => 2 [[],[],[[[]]],[],[],[]] => 2 [[],[],[[],[]],[],[[]]] => 3 [[],[],[[[]]],[],[[]]] => 3 [[],[],[[],[]],[[]],[]] => 2 [[],[],[[[]]],[[]],[]] => 2 [[],[],[[],[]],[[],[]]] => 3 [[],[],[[],[]],[[[]]]] => 4 [[],[],[[[]]],[[],[]]] => 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 [[],[],[[],[],[],[[]]]] => 4 [[],[],[[],[],[[]],[]]] => 3 [[],[],[[],[],[[],[]]]] => 4 [[],[],[[],[],[[[]]]]] => 5 [[],[],[[],[[]],[],[]]] => 3 [[],[],[[],[[]],[[]]]] => 4 [[],[],[[],[[],[]],[]]] => 3 [[],[],[[],[[[]]],[]]] => 3 [[],[],[[],[[],[],[]]]] => 4 [[],[],[[],[[],[[]]]]] => 5 [[],[],[[],[[[]],[]]]] => 4 [[],[],[[],[[[],[]]]]] => 5 [[],[],[[],[[[[]]]]]] => 6 [[],[],[[[]],[],[],[]]] => 3 [[],[],[[[]],[],[[]]]] => 4 [[],[],[[[]],[[]],[]]] => 3 [[],[],[[[]],[[],[]]]] => 4 [[],[],[[[]],[[[]]]]] => 5 [[],[],[[[],[]],[],[]]] => 3 [[],[],[[[[]]],[],[]]] => 3 [[],[],[[[],[]],[[]]]] => 4 [[],[],[[[[]]],[[]]]] => 4 [[],[],[[[],[],[]],[]]] => 3 [[],[],[[[],[[]]],[]]] => 3 [[],[],[[[[]],[]],[]]] => 3 [[],[],[[[[],[]]],[]]] => 3 [[],[],[[[[[]]]],[]]] => 3 [[],[],[[[],[],[],[]]]] => 4 [[],[],[[[],[],[[]]]]] => 5 [[],[],[[[],[[]],[]]]] => 4 [[],[],[[[],[[],[]]]]] => 5 [[],[],[[[],[[[]]]]]] => 6 [[],[],[[[[]],[],[]]]] => 4 [[],[],[[[[]],[[]]]]] => 5 [[],[],[[[[],[]],[]]]] => 4 [[],[],[[[[[]]],[]]]] => 4 [[],[],[[[[],[],[]]]]] => 5 [[],[],[[[[],[[]]]]]] => 6 [[],[],[[[[[]],[]]]]] => 5 [[],[],[[[[[],[]]]]]] => 6 [[],[],[[[[[[]]]]]]] => 7 [[],[[]],[],[],[],[],[]] => 2 [[],[[]],[],[],[],[[]]] => 3 [[],[[]],[],[],[[]],[]] => 2 [[],[[]],[],[],[[],[]]] => 3 [[],[[]],[],[],[[[]]]] => 4 [[],[[]],[],[[]],[],[]] => 2 [[],[[]],[],[[]],[[]]] => 3 [[],[[]],[],[[],[]],[]] => 2 [[],[[]],[],[[[]]],[]] => 2 [[],[[]],[],[[],[],[]]] => 3 [[],[[]],[],[[],[[]]]] => 4 [[],[[]],[],[[[]],[]]] => 3 [[],[[]],[],[[[],[]]]] => 4 [[],[[]],[],[[[[]]]]] => 5 [[],[[]],[[]],[],[],[]] => 2 [[],[[]],[[]],[],[[]]] => 3 [[],[[]],[[]],[[]],[]] => 2 [[],[[]],[[]],[[],[]]] => 3 [[],[[]],[[]],[[[]]]] => 4 [[],[[]],[[],[]],[],[]] => 2 [[],[[]],[[[]]],[],[]] => 2 [[],[[]],[[],[]],[[]]] => 3 [[],[[]],[[[]]],[[]]] => 3 [[],[[]],[[],[],[]],[]] => 2 [[],[[]],[[],[[]]],[]] => 2 [[],[[]],[[[]],[]],[]] => 2 [[],[[]],[[[],[]]],[]] => 2 [[],[[]],[[[[]]]],[]] => 2 [[],[[]],[[],[],[],[]]] => 3 [[],[[]],[[],[],[[]]]] => 4 [[],[[]],[[],[[]],[]]] => 3 [[],[[]],[[],[[],[]]]] => 4 [[],[[]],[[],[[[]]]]] => 5 [[],[[]],[[[]],[],[]]] => 3 [[],[[]],[[[]],[[]]]] => 4 [[],[[]],[[[],[]],[]]] => 3 [[],[[]],[[[[]]],[]]] => 3 [[],[[]],[[[],[],[]]]] => 4 [[],[[]],[[[],[[]]]]] => 5 [[],[[]],[[[[]],[]]]] => 4 [[],[[]],[[[[],[]]]]] => 5 [[],[[]],[[[[[]]]]]] => 6 [[],[[],[]],[],[],[],[]] => 2 [[],[[[]]],[],[],[],[]] => 2 [[],[[],[]],[],[],[[]]] => 3 [[],[[[]]],[],[],[[]]] => 3 [[],[[],[]],[],[[]],[]] => 2 [[],[[[]]],[],[[]],[]] => 2 [[],[[],[]],[],[[],[]]] => 3 [[],[[],[]],[],[[[]]]] => 4 [[],[[[]]],[],[[],[]]] => 3 [[],[[[]]],[],[[[]]]] => 4 [[],[[],[]],[[]],[],[]] => 2 [[],[[[]]],[[]],[],[]] => 2 [[],[[],[]],[[]],[[]]] => 3 [[],[[[]]],[[]],[[]]] => 3 [[],[[],[]],[[],[]],[]] => 2 [[],[[],[]],[[[]]],[]] => 2 [[],[[[]]],[[],[]],[]] => 2 [[],[[[]]],[[[]]],[]] => 2 [[],[[],[]],[[],[],[]]] => 3 [[],[[],[]],[[],[[]]]] => 4 [[],[[],[]],[[[]],[]]] => 3 [[],[[],[]],[[[],[]]]] => 4 [[],[[],[]],[[[[]]]]] => 5 [[],[[[]]],[[],[],[]]] => 3 [[],[[[]]],[[],[[]]]] => 4 [[],[[[]]],[[[]],[]]] => 3 [[],[[[]]],[[[],[]]]] => 4 [[],[[[]]],[[[[]]]]] => 5 [[],[[],[],[]],[],[],[]] => 2 [[],[[],[[]]],[],[],[]] => 2 [[],[[[]],[]],[],[],[]] => 2 [[],[[[],[]]],[],[],[]] => 2 [[],[[[[]]]],[],[],[]] => 2 [[],[[],[],[]],[],[[]]] => 3 [[],[[],[[]]],[],[[]]] => 3 [[],[[[]],[]],[],[[]]] => 3 [[],[[[],[]]],[],[[]]] => 3 [[],[[[[]]]],[],[[]]] => 3 [[],[[],[],[]],[[]],[]] => 2 [[],[[],[[]]],[[]],[]] => 2 [[],[[[]],[]],[[]],[]] => 2 [[],[[[],[]]],[[]],[]] => 2 [[],[[[[]]]],[[]],[]] => 2 [[],[[],[],[]],[[],[]]] => 3 [[],[[],[],[]],[[[]]]] => 4 [[],[[],[[]]],[[],[]]] => 3 [[],[[],[[]]],[[[]]]] => 4 [[],[[[]],[]],[[],[]]] => 3 [[],[[[]],[]],[[[]]]] => 4 [[],[[[],[]]],[[],[]]] => 3 [[],[[[],[]]],[[[]]]] => 4 [[],[[[[]]]],[[],[]]] => 3 [[],[[[[]]]],[[[]]]] => 4 [[],[[],[],[],[]],[],[]] => 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 [[],[[],[],[],[],[]],[]] => 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 [[],[[],[],[],[],[[]]]] => 4 [[],[[],[],[],[[]],[]]] => 3 [[],[[],[],[],[[],[]]]] => 4 [[],[[],[],[],[[[]]]]] => 5 [[],[[],[],[[]],[],[]]] => 3 [[],[[],[],[[]],[[]]]] => 4 [[],[[],[],[[],[]],[]]] => 3 [[],[[],[],[[[]]],[]]] => 3 [[],[[],[],[[],[],[]]]] => 4 [[],[[],[],[[],[[]]]]] => 5 [[],[[],[],[[[]],[]]]] => 4 [[],[[],[],[[[],[]]]]] => 5 [[],[[],[],[[[[]]]]]] => 6 [[],[[],[[]],[],[],[]]] => 3 [[],[[],[[]],[],[[]]]] => 4 [[],[[],[[]],[[]],[]]] => 3 [[],[[],[[]],[[],[]]]] => 4 [[],[[],[[]],[[[]]]]] => 5 [[],[[],[[],[]],[],[]]] => 3 [[],[[],[[[]]],[],[]]] => 3 [[],[[],[[],[]],[[]]]] => 4 [[],[[],[[[]]],[[]]]] => 4 [[],[[],[[],[],[]],[]]] => 3 [[],[[],[[],[[]]],[]]] => 3 [[],[[],[[[]],[]],[]]] => 3 [[],[[],[[[],[]]],[]]] => 3 [[],[[],[[[[]]]],[]]] => 3 [[],[[],[[],[],[],[]]]] => 4 [[],[[],[[],[],[[]]]]] => 5 [[],[[],[[],[[]],[]]]] => 4 [[],[[],[[],[[],[]]]]] => 5 [[],[[],[[],[[[]]]]]] => 6 [[],[[],[[[]],[],[]]]] => 4 [[],[[],[[[]],[[]]]]] => 5 [[],[[],[[[],[]],[]]]] => 4 [[],[[],[[[[]]],[]]]] => 4 [[],[[],[[[],[],[]]]]] => 5 [[],[[],[[[],[[]]]]]] => 6 [[],[[],[[[[]],[]]]]] => 5 [[],[[],[[[[],[]]]]]] => 6 [[],[[],[[[[[]]]]]]] => 7 [[],[[[]],[],[],[],[]]] => 3 [[],[[[]],[],[],[[]]]] => 4 [[],[[[]],[],[[]],[]]] => 3 [[],[[[]],[],[[],[]]]] => 4 [[],[[[]],[],[[[]]]]] => 5 [[],[[[]],[[]],[],[]]] => 3 [[],[[[]],[[]],[[]]]] => 4 [[],[[[]],[[],[]],[]]] => 3 [[],[[[]],[[[]]],[]]] => 3 [[],[[[]],[[],[],[]]]] => 4 [[],[[[]],[[],[[]]]]] => 5 [[],[[[]],[[[]],[]]]] => 4 [[],[[[]],[[[],[]]]]] => 5 [[],[[[]],[[[[]]]]]] => 6 [[],[[[],[]],[],[],[]]] => 3 [[],[[[[]]],[],[],[]]] => 3 [[],[[[],[]],[],[[]]]] => 4 [[],[[[[]]],[],[[]]]] => 4 [[],[[[],[]],[[]],[]]] => 3 [[],[[[[]]],[[]],[]]] => 3 [[],[[[],[]],[[],[]]]] => 4 [[],[[[],[]],[[[]]]]] => 5 [[],[[[[]]],[[],[]]]] => 4 [[],[[[[]]],[[[]]]]] => 5 [[],[[[],[],[]],[],[]]] => 3 [[],[[[],[[]]],[],[]]] => 3 [[],[[[[]],[]],[],[]]] => 3 [[],[[[[],[]]],[],[]]] => 3 [[],[[[[[]]]],[],[]]] => 3 [[],[[[],[],[]],[[]]]] => 4 [[],[[[],[[]]],[[]]]] => 4 [[],[[[[]],[]],[[]]]] => 4 [[],[[[[],[]]],[[]]]] => 4 [[],[[[[[]]]],[[]]]] => 4 [[],[[[],[],[],[]],[]]] => 3 [[],[[[],[],[[]]],[]]] => 3 [[],[[[],[[]],[]],[]]] => 3 [[],[[[],[[],[]]],[]]] => 3 [[],[[[],[[[]]]],[]]] => 3 [[],[[[[]],[],[]],[]]] => 3 [[],[[[[]],[[]]],[]]] => 3 [[],[[[[],[]],[]],[]]] => 3 [[],[[[[[]]],[]],[]]] => 3 [[],[[[[],[],[]]],[]]] => 3 [[],[[[[],[[]]]],[]]] => 3 [[],[[[[[]],[]]],[]]] => 3 [[],[[[[[],[]]]],[]]] => 3 [[],[[[[[[]]]]],[]]] => 3 [[],[[[],[],[],[],[]]]] => 4 [[],[[[],[],[],[[]]]]] => 5 [[],[[[],[],[[]],[]]]] => 4 [[],[[[],[],[[],[]]]]] => 5 [[],[[[],[],[[[]]]]]] => 6 [[],[[[],[[]],[],[]]]] => 4 [[],[[[],[[]],[[]]]]] => 5 [[],[[[],[[],[]],[]]]] => 4 [[],[[[],[[[]]],[]]]] => 4 [[],[[[],[[],[],[]]]]] => 5 [[],[[[],[[],[[]]]]]] => 6 [[],[[[],[[[]],[]]]]] => 5 [[],[[[],[[[],[]]]]]] => 6 [[],[[[],[[[[]]]]]]] => 7 [[],[[[[]],[],[],[]]]] => 4 [[],[[[[]],[],[[]]]]] => 5 [[],[[[[]],[[]],[]]]] => 4 [[],[[[[]],[[],[]]]]] => 5 [[],[[[[]],[[[]]]]]] => 6 [[],[[[[],[]],[],[]]]] => 4 [[],[[[[[]]],[],[]]]] => 4 [[],[[[[],[]],[[]]]]] => 5 [[],[[[[[]]],[[]]]]] => 5 [[],[[[[],[],[]],[]]]] => 4 [[],[[[[],[[]]],[]]]] => 4 [[],[[[[[]],[]],[]]]] => 4 [[],[[[[[],[]]],[]]]] => 4 [[],[[[[[[]]]],[]]]] => 4 [[],[[[[],[],[],[]]]]] => 5 [[],[[[[],[],[[]]]]]] => 6 [[],[[[[],[[]],[]]]]] => 5 [[],[[[[],[[],[]]]]]] => 6 [[],[[[[],[[[]]]]]]] => 7 [[],[[[[[]],[],[]]]]] => 5 [[],[[[[[]],[[]]]]]] => 6 [[],[[[[[],[]],[]]]]] => 5 [[],[[[[[[]]],[]]]]] => 5 [[],[[[[[],[],[]]]]]] => 6 [[],[[[[[],[[]]]]]]] => 7 [[],[[[[[[]],[]]]]]] => 6 [[],[[[[[[],[]]]]]]] => 7 [[],[[[[[[[]]]]]]]] => 8 [[[]],[],[],[],[],[],[]] => 3 [[[]],[],[],[],[],[[]]] => 4 [[[]],[],[],[],[[]],[]] => 3 [[[]],[],[],[],[[],[]]] => 4 [[[]],[],[],[],[[[]]]] => 5 [[[]],[],[],[[]],[],[]] => 3 [[[]],[],[],[[]],[[]]] => 4 [[[]],[],[],[[],[]],[]] => 3 [[[]],[],[],[[[]]],[]] => 3 [[[]],[],[],[[],[],[]]] => 4 [[[]],[],[],[[],[[]]]] => 5 [[[]],[],[],[[[]],[]]] => 4 [[[]],[],[],[[[],[]]]] => 5 [[[]],[],[],[[[[]]]]] => 6 [[[]],[],[[]],[],[],[]] => 3 [[[]],[],[[]],[],[[]]] => 4 [[[]],[],[[]],[[]],[]] => 3 [[[]],[],[[]],[[],[]]] => 4 [[[]],[],[[]],[[[]]]] => 5 [[[]],[],[[],[]],[],[]] => 3 [[[]],[],[[[]]],[],[]] => 3 [[[]],[],[[],[]],[[]]] => 4 [[[]],[],[[[]]],[[]]] => 4 [[[]],[],[[],[],[]],[]] => 3 [[[]],[],[[],[[]]],[]] => 3 [[[]],[],[[[]],[]],[]] => 3 [[[]],[],[[[],[]]],[]] => 3 [[[]],[],[[[[]]]],[]] => 3 [[[]],[],[[],[],[],[]]] => 4 [[[]],[],[[],[],[[]]]] => 5 [[[]],[],[[],[[]],[]]] => 4 [[[]],[],[[],[[],[]]]] => 5 [[[]],[],[[],[[[]]]]] => 6 [[[]],[],[[[]],[],[]]] => 4 [[[]],[],[[[]],[[]]]] => 5 [[[]],[],[[[],[]],[]]] => 4 [[[]],[],[[[[]]],[]]] => 4 [[[]],[],[[[],[],[]]]] => 5 [[[]],[],[[[],[[]]]]] => 6 [[[]],[],[[[[]],[]]]] => 5 [[[]],[],[[[[],[]]]]] => 6 [[[]],[],[[[[[]]]]]] => 7 [[[]],[[]],[],[],[],[]] => 3 [[[]],[[]],[],[],[[]]] => 4 [[[]],[[]],[],[[]],[]] => 3 [[[]],[[]],[],[[],[]]] => 4 [[[]],[[]],[],[[[]]]] => 5 [[[]],[[]],[[]],[],[]] => 3 [[[]],[[]],[[]],[[]]] => 4 [[[]],[[]],[[],[]],[]] => 3 [[[]],[[]],[[[]]],[]] => 3 [[[]],[[]],[[],[],[]]] => 4 [[[]],[[]],[[],[[]]]] => 5 [[[]],[[]],[[[]],[]]] => 4 [[[]],[[]],[[[],[]]]] => 5 [[[]],[[]],[[[[]]]]] => 6 [[[]],[[],[]],[],[],[]] => 3 [[[]],[[[]]],[],[],[]] => 3 [[[]],[[],[]],[],[[]]] => 4 [[[]],[[[]]],[],[[]]] => 4 [[[]],[[],[]],[[]],[]] => 3 [[[]],[[[]]],[[]],[]] => 3 [[[]],[[],[]],[[],[]]] => 4 [[[]],[[],[]],[[[]]]] => 5 [[[]],[[[]]],[[],[]]] => 4 [[[]],[[[]]],[[[]]]] => 5 [[[]],[[],[],[]],[],[]] => 3 [[[]],[[],[[]]],[],[]] => 3 [[[]],[[[]],[]],[],[]] => 3 [[[]],[[[],[]]],[],[]] => 3 [[[]],[[[[]]]],[],[]] => 3 [[[]],[[],[],[]],[[]]] => 4 [[[]],[[],[[]]],[[]]] => 4 [[[]],[[[]],[]],[[]]] => 4 [[[]],[[[],[]]],[[]]] => 4 [[[]],[[[[]]]],[[]]] => 4 [[[]],[[],[],[],[]],[]] => 3 [[[]],[[],[],[[]]],[]] => 3 [[[]],[[],[[]],[]],[]] => 3 [[[]],[[],[[],[]]],[]] => 3 [[[]],[[],[[[]]]],[]] => 3 [[[]],[[[]],[],[]],[]] => 3 [[[]],[[[]],[[]]],[]] => 3 [[[]],[[[],[]],[]],[]] => 3 [[[]],[[[[]]],[]],[]] => 3 [[[]],[[[],[],[]]],[]] => 3 [[[]],[[[],[[]]]],[]] => 3 [[[]],[[[[]],[]]],[]] => 3 [[[]],[[[[],[]]]],[]] => 3 [[[]],[[[[[]]]]],[]] => 3 [[[]],[[],[],[],[],[]]] => 4 [[[]],[[],[],[],[[]]]] => 5 [[[]],[[],[],[[]],[]]] => 4 [[[]],[[],[],[[],[]]]] => 5 [[[]],[[],[],[[[]]]]] => 6 [[[]],[[],[[]],[],[]]] => 4 [[[]],[[],[[]],[[]]]] => 5 [[[]],[[],[[],[]],[]]] => 4 [[[]],[[],[[[]]],[]]] => 4 [[[]],[[],[[],[],[]]]] => 5 [[[]],[[],[[],[[]]]]] => 6 [[[]],[[],[[[]],[]]]] => 5 [[[]],[[],[[[],[]]]]] => 6 [[[]],[[],[[[[]]]]]] => 7 [[[]],[[[]],[],[],[]]] => 4 [[[]],[[[]],[],[[]]]] => 5 [[[]],[[[]],[[]],[]]] => 4 [[[]],[[[]],[[],[]]]] => 5 [[[]],[[[]],[[[]]]]] => 6 [[[]],[[[],[]],[],[]]] => 4 [[[]],[[[[]]],[],[]]] => 4 [[[]],[[[],[]],[[]]]] => 5 [[[]],[[[[]]],[[]]]] => 5 [[[]],[[[],[],[]],[]]] => 4 [[[]],[[[],[[]]],[]]] => 4 [[[]],[[[[]],[]],[]]] => 4 [[[]],[[[[],[]]],[]]] => 4 [[[]],[[[[[]]]],[]]] => 4 [[[]],[[[],[],[],[]]]] => 5 [[[]],[[[],[],[[]]]]] => 6 [[[]],[[[],[[]],[]]]] => 5 [[[]],[[[],[[],[]]]]] => 6 [[[]],[[[],[[[]]]]]] => 7 [[[]],[[[[]],[],[]]]] => 5 [[[]],[[[[]],[[]]]]] => 6 [[[]],[[[[],[]],[]]]] => 5 [[[]],[[[[[]]],[]]]] => 5 [[[]],[[[[],[],[]]]]] => 6 [[[]],[[[[],[[]]]]]] => 7 [[[]],[[[[[]],[]]]]] => 6 [[[]],[[[[[],[]]]]]] => 7 [[[]],[[[[[[]]]]]]] => 8 [[[],[]],[],[],[],[],[]] => 3 [[[[]]],[],[],[],[],[]] => 4 [[[],[]],[],[],[],[[]]] => 4 [[[[]]],[],[],[],[[]]] => 5 [[[],[]],[],[],[[]],[]] => 3 [[[[]]],[],[],[[]],[]] => 4 [[[],[]],[],[],[[],[]]] => 4 [[[],[]],[],[],[[[]]]] => 5 [[[[]]],[],[],[[],[]]] => 5 [[[[]]],[],[],[[[]]]] => 6 [[[],[]],[],[[]],[],[]] => 3 [[[[]]],[],[[]],[],[]] => 4 [[[],[]],[],[[]],[[]]] => 4 [[[[]]],[],[[]],[[]]] => 5 ----------------------------------------------------------------------------- Created: Sep 06, 2017 at 23:23 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 06, 2017 at 23:23 by Martin Rubey