***************************************************************************** * 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: St000415 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The size of the automorphism group of the rooted tree underlying the ordered tree. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(T): return factorial(len(T))*prod(statistic(S) for S in T) ----------------------------------------------------------------------------- Statistic values: [[]] => 1 [[],[]] => 2 [[[]]] => 1 [[],[],[]] => 6 [[],[[]]] => 2 [[[]],[]] => 2 [[[],[]]] => 2 [[[[]]]] => 1 [[],[],[],[]] => 24 [[],[],[[]]] => 6 [[],[[]],[]] => 6 [[],[[],[]]] => 4 [[],[[[]]]] => 2 [[[]],[],[]] => 6 [[[]],[[]]] => 2 [[[],[]],[]] => 4 [[[[]]],[]] => 2 [[[],[],[]]] => 6 [[[],[[]]]] => 2 [[[[]],[]]] => 2 [[[[],[]]]] => 2 [[[[[]]]]] => 1 [[],[],[],[],[]] => 120 [[],[],[],[[]]] => 24 [[],[],[[]],[]] => 24 [[],[],[[],[]]] => 12 [[],[],[[[]]]] => 6 [[],[[]],[],[]] => 24 [[],[[]],[[]]] => 6 [[],[[],[]],[]] => 12 [[],[[[]]],[]] => 6 [[],[[],[],[]]] => 12 [[],[[],[[]]]] => 4 [[],[[[]],[]]] => 4 [[],[[[],[]]]] => 4 [[],[[[[]]]]] => 2 [[[]],[],[],[]] => 24 [[[]],[],[[]]] => 6 [[[]],[[]],[]] => 6 [[[]],[[],[]]] => 4 [[[]],[[[]]]] => 2 [[[],[]],[],[]] => 12 [[[[]]],[],[]] => 6 [[[],[]],[[]]] => 4 [[[[]]],[[]]] => 2 [[[],[],[]],[]] => 12 [[[],[[]]],[]] => 4 [[[[]],[]],[]] => 4 [[[[],[]]],[]] => 4 [[[[[]]]],[]] => 2 [[[],[],[],[]]] => 24 [[[],[],[[]]]] => 6 [[[],[[]],[]]] => 6 [[[],[[],[]]]] => 4 [[[],[[[]]]]] => 2 [[[[]],[],[]]] => 6 [[[[]],[[]]]] => 2 [[[[],[]],[]]] => 4 [[[[[]]],[]]] => 2 [[[[],[],[]]]] => 6 [[[[],[[]]]]] => 2 [[[[[]],[]]]] => 2 [[[[[],[]]]]] => 2 [[[[[[]]]]]] => 1 [[],[],[],[],[],[]] => 720 [[],[],[],[],[[]]] => 120 [[],[],[],[[]],[]] => 120 [[],[],[],[[],[]]] => 48 [[],[],[],[[[]]]] => 24 [[],[],[[]],[],[]] => 120 [[],[],[[]],[[]]] => 24 [[],[],[[],[]],[]] => 48 [[],[],[[[]]],[]] => 24 [[],[],[[],[],[]]] => 36 [[],[],[[],[[]]]] => 12 [[],[],[[[]],[]]] => 12 [[],[],[[[],[]]]] => 12 [[],[],[[[[]]]]] => 6 [[],[[]],[],[],[]] => 120 [[],[[]],[],[[]]] => 24 [[],[[]],[[]],[]] => 24 [[],[[]],[[],[]]] => 12 [[],[[]],[[[]]]] => 6 [[],[[],[]],[],[]] => 48 [[],[[[]]],[],[]] => 24 [[],[[],[]],[[]]] => 12 [[],[[[]]],[[]]] => 6 [[],[[],[],[]],[]] => 36 [[],[[],[[]]],[]] => 12 [[],[[[]],[]],[]] => 12 [[],[[[],[]]],[]] => 12 [[],[[[[]]]],[]] => 6 [[],[[],[],[],[]]] => 48 [[],[[],[],[[]]]] => 12 [[],[[],[[]],[]]] => 12 [[],[[],[[],[]]]] => 8 [[],[[],[[[]]]]] => 4 [[],[[[]],[],[]]] => 12 [[],[[[]],[[]]]] => 4 [[],[[[],[]],[]]] => 8 [[],[[[[]]],[]]] => 4 [[],[[[],[],[]]]] => 12 [[],[[[],[[]]]]] => 4 [[],[[[[]],[]]]] => 4 [[],[[[[],[]]]]] => 4 [[],[[[[[]]]]]] => 2 [[[]],[],[],[],[]] => 120 [[[]],[],[],[[]]] => 24 [[[]],[],[[]],[]] => 24 [[[]],[],[[],[]]] => 12 [[[]],[],[[[]]]] => 6 [[[]],[[]],[],[]] => 24 [[[]],[[]],[[]]] => 6 [[[]],[[],[]],[]] => 12 [[[]],[[[]]],[]] => 6 [[[]],[[],[],[]]] => 12 [[[]],[[],[[]]]] => 4 [[[]],[[[]],[]]] => 4 [[[]],[[[],[]]]] => 4 [[[]],[[[[]]]]] => 2 [[[],[]],[],[],[]] => 48 [[[[]]],[],[],[]] => 24 [[[],[]],[],[[]]] => 12 [[[[]]],[],[[]]] => 6 [[[],[]],[[]],[]] => 12 [[[[]]],[[]],[]] => 6 [[[],[]],[[],[]]] => 8 [[[],[]],[[[]]]] => 4 [[[[]]],[[],[]]] => 4 [[[[]]],[[[]]]] => 2 [[[],[],[]],[],[]] => 36 [[[],[[]]],[],[]] => 12 [[[[]],[]],[],[]] => 12 [[[[],[]]],[],[]] => 12 [[[[[]]]],[],[]] => 6 [[[],[],[]],[[]]] => 12 [[[],[[]]],[[]]] => 4 [[[[]],[]],[[]]] => 4 [[[[],[]]],[[]]] => 4 [[[[[]]]],[[]]] => 2 [[[],[],[],[]],[]] => 48 [[[],[],[[]]],[]] => 12 [[[],[[]],[]],[]] => 12 [[[],[[],[]]],[]] => 8 [[[],[[[]]]],[]] => 4 [[[[]],[],[]],[]] => 12 [[[[]],[[]]],[]] => 4 [[[[],[]],[]],[]] => 8 [[[[[]]],[]],[]] => 4 [[[[],[],[]]],[]] => 12 [[[[],[[]]]],[]] => 4 [[[[[]],[]]],[]] => 4 [[[[[],[]]]],[]] => 4 [[[[[[]]]]],[]] => 2 [[[],[],[],[],[]]] => 120 [[[],[],[],[[]]]] => 24 [[[],[],[[]],[]]] => 24 [[[],[],[[],[]]]] => 12 [[[],[],[[[]]]]] => 6 [[[],[[]],[],[]]] => 24 [[[],[[]],[[]]]] => 6 [[[],[[],[]],[]]] => 12 [[[],[[[]]],[]]] => 6 [[[],[[],[],[]]]] => 12 [[[],[[],[[]]]]] => 4 [[[],[[[]],[]]]] => 4 [[[],[[[],[]]]]] => 4 [[[],[[[[]]]]]] => 2 [[[[]],[],[],[]]] => 24 [[[[]],[],[[]]]] => 6 [[[[]],[[]],[]]] => 6 [[[[]],[[],[]]]] => 4 [[[[]],[[[]]]]] => 2 [[[[],[]],[],[]]] => 12 [[[[[]]],[],[]]] => 6 [[[[],[]],[[]]]] => 4 [[[[[]]],[[]]]] => 2 [[[[],[],[]],[]]] => 12 [[[[],[[]]],[]]] => 4 [[[[[]],[]],[]]] => 4 [[[[[],[]]],[]]] => 4 [[[[[[]]]],[]]] => 2 [[[[],[],[],[]]]] => 24 [[[[],[],[[]]]]] => 6 [[[[],[[]],[]]]] => 6 [[[[],[[],[]]]]] => 4 [[[[],[[[]]]]]] => 2 [[[[[]],[],[]]]] => 6 [[[[[]],[[]]]]] => 2 [[[[[],[]],[]]]] => 4 [[[[[[]]],[]]]] => 2 [[[[[],[],[]]]]] => 6 [[[[[],[[]]]]]] => 2 [[[[[[]],[]]]]] => 2 [[[[[[],[]]]]]] => 2 [[[[[[[]]]]]]] => 1 [[],[],[],[],[],[],[]] => 5040 [[],[],[],[],[],[[]]] => 720 [[],[],[],[],[[]],[]] => 720 [[],[],[],[],[[],[]]] => 240 [[],[],[],[],[[[]]]] => 120 [[],[],[],[[]],[],[]] => 720 [[],[],[],[[]],[[]]] => 120 [[],[],[],[[],[]],[]] => 240 [[],[],[],[[[]]],[]] => 120 [[],[],[],[[],[],[]]] => 144 [[],[],[],[[],[[]]]] => 48 [[],[],[],[[[]],[]]] => 48 [[],[],[],[[[],[]]]] => 48 [[],[],[],[[[[]]]]] => 24 [[],[],[[]],[],[],[]] => 720 [[],[],[[]],[],[[]]] => 120 [[],[],[[]],[[]],[]] => 120 [[],[],[[]],[[],[]]] => 48 [[],[],[[]],[[[]]]] => 24 [[],[],[[],[]],[],[]] => 240 [[],[],[[[]]],[],[]] => 120 [[],[],[[],[]],[[]]] => 48 [[],[],[[[]]],[[]]] => 24 [[],[],[[],[],[]],[]] => 144 [[],[],[[],[[]]],[]] => 48 [[],[],[[[]],[]],[]] => 48 [[],[],[[[],[]]],[]] => 48 [[],[],[[[[]]]],[]] => 24 [[],[],[[],[],[],[]]] => 144 [[],[],[[],[],[[]]]] => 36 [[],[],[[],[[]],[]]] => 36 [[],[],[[],[[],[]]]] => 24 [[],[],[[],[[[]]]]] => 12 [[],[],[[[]],[],[]]] => 36 [[],[],[[[]],[[]]]] => 12 [[],[],[[[],[]],[]]] => 24 [[],[],[[[[]]],[]]] => 12 [[],[],[[[],[],[]]]] => 36 [[],[],[[[],[[]]]]] => 12 [[],[],[[[[]],[]]]] => 12 [[],[],[[[[],[]]]]] => 12 [[],[],[[[[[]]]]]] => 6 [[],[[]],[],[],[],[]] => 720 [[],[[]],[],[],[[]]] => 120 [[],[[]],[],[[]],[]] => 120 [[],[[]],[],[[],[]]] => 48 [[],[[]],[],[[[]]]] => 24 [[],[[]],[[]],[],[]] => 120 [[],[[]],[[]],[[]]] => 24 [[],[[]],[[],[]],[]] => 48 [[],[[]],[[[]]],[]] => 24 [[],[[]],[[],[],[]]] => 36 [[],[[]],[[],[[]]]] => 12 [[],[[]],[[[]],[]]] => 12 [[],[[]],[[[],[]]]] => 12 [[],[[]],[[[[]]]]] => 6 [[],[[],[]],[],[],[]] => 240 [[],[[[]]],[],[],[]] => 120 [[],[[],[]],[],[[]]] => 48 [[],[[[]]],[],[[]]] => 24 [[],[[],[]],[[]],[]] => 48 [[],[[[]]],[[]],[]] => 24 [[],[[],[]],[[],[]]] => 24 [[],[[],[]],[[[]]]] => 12 [[],[[[]]],[[],[]]] => 12 [[],[[[]]],[[[]]]] => 6 [[],[[],[],[]],[],[]] => 144 [[],[[],[[]]],[],[]] => 48 [[],[[[]],[]],[],[]] => 48 [[],[[[],[]]],[],[]] => 48 [[],[[[[]]]],[],[]] => 24 [[],[[],[],[]],[[]]] => 36 [[],[[],[[]]],[[]]] => 12 [[],[[[]],[]],[[]]] => 12 [[],[[[],[]]],[[]]] => 12 [[],[[[[]]]],[[]]] => 6 [[],[[],[],[],[]],[]] => 144 [[],[[],[],[[]]],[]] => 36 [[],[[],[[]],[]],[]] => 36 [[],[[],[[],[]]],[]] => 24 [[],[[],[[[]]]],[]] => 12 [[],[[[]],[],[]],[]] => 36 [[],[[[]],[[]]],[]] => 12 [[],[[[],[]],[]],[]] => 24 [[],[[[[]]],[]],[]] => 12 [[],[[[],[],[]]],[]] => 36 [[],[[[],[[]]]],[]] => 12 [[],[[[[]],[]]],[]] => 12 [[],[[[[],[]]]],[]] => 12 [[],[[[[[]]]]],[]] => 6 [[],[[],[],[],[],[]]] => 240 [[],[[],[],[],[[]]]] => 48 [[],[[],[],[[]],[]]] => 48 [[],[[],[],[[],[]]]] => 24 [[],[[],[],[[[]]]]] => 12 [[],[[],[[]],[],[]]] => 48 [[],[[],[[]],[[]]]] => 12 [[],[[],[[],[]],[]]] => 24 [[],[[],[[[]]],[]]] => 12 [[],[[],[[],[],[]]]] => 24 [[],[[],[[],[[]]]]] => 8 [[],[[],[[[]],[]]]] => 8 [[],[[],[[[],[]]]]] => 8 [[],[[],[[[[]]]]]] => 4 [[],[[[]],[],[],[]]] => 48 [[],[[[]],[],[[]]]] => 12 [[],[[[]],[[]],[]]] => 12 [[],[[[]],[[],[]]]] => 8 [[],[[[]],[[[]]]]] => 4 [[],[[[],[]],[],[]]] => 24 [[],[[[[]]],[],[]]] => 12 [[],[[[],[]],[[]]]] => 8 [[],[[[[]]],[[]]]] => 4 [[],[[[],[],[]],[]]] => 24 [[],[[[],[[]]],[]]] => 8 [[],[[[[]],[]],[]]] => 8 [[],[[[[],[]]],[]]] => 8 [[],[[[[[]]]],[]]] => 4 [[],[[[],[],[],[]]]] => 48 [[],[[[],[],[[]]]]] => 12 [[],[[[],[[]],[]]]] => 12 [[],[[[],[[],[]]]]] => 8 [[],[[[],[[[]]]]]] => 4 [[],[[[[]],[],[]]]] => 12 [[],[[[[]],[[]]]]] => 4 [[],[[[[],[]],[]]]] => 8 [[],[[[[[]]],[]]]] => 4 [[],[[[[],[],[]]]]] => 12 [[],[[[[],[[]]]]]] => 4 [[],[[[[[]],[]]]]] => 4 [[],[[[[[],[]]]]]] => 4 [[],[[[[[[]]]]]]] => 2 [[[]],[],[],[],[],[]] => 720 [[[]],[],[],[],[[]]] => 120 [[[]],[],[],[[]],[]] => 120 [[[]],[],[],[[],[]]] => 48 [[[]],[],[],[[[]]]] => 24 [[[]],[],[[]],[],[]] => 120 [[[]],[],[[]],[[]]] => 24 [[[]],[],[[],[]],[]] => 48 [[[]],[],[[[]]],[]] => 24 [[[]],[],[[],[],[]]] => 36 [[[]],[],[[],[[]]]] => 12 [[[]],[],[[[]],[]]] => 12 [[[]],[],[[[],[]]]] => 12 [[[]],[],[[[[]]]]] => 6 [[[]],[[]],[],[],[]] => 120 [[[]],[[]],[],[[]]] => 24 [[[]],[[]],[[]],[]] => 24 [[[]],[[]],[[],[]]] => 12 [[[]],[[]],[[[]]]] => 6 [[[]],[[],[]],[],[]] => 48 [[[]],[[[]]],[],[]] => 24 [[[]],[[],[]],[[]]] => 12 [[[]],[[[]]],[[]]] => 6 [[[]],[[],[],[]],[]] => 36 [[[]],[[],[[]]],[]] => 12 [[[]],[[[]],[]],[]] => 12 [[[]],[[[],[]]],[]] => 12 [[[]],[[[[]]]],[]] => 6 [[[]],[[],[],[],[]]] => 48 [[[]],[[],[],[[]]]] => 12 [[[]],[[],[[]],[]]] => 12 [[[]],[[],[[],[]]]] => 8 [[[]],[[],[[[]]]]] => 4 [[[]],[[[]],[],[]]] => 12 [[[]],[[[]],[[]]]] => 4 [[[]],[[[],[]],[]]] => 8 [[[]],[[[[]]],[]]] => 4 [[[]],[[[],[],[]]]] => 12 [[[]],[[[],[[]]]]] => 4 [[[]],[[[[]],[]]]] => 4 [[[]],[[[[],[]]]]] => 4 [[[]],[[[[[]]]]]] => 2 [[[],[]],[],[],[],[]] => 240 [[[[]]],[],[],[],[]] => 120 [[[],[]],[],[],[[]]] => 48 [[[[]]],[],[],[[]]] => 24 [[[],[]],[],[[]],[]] => 48 [[[[]]],[],[[]],[]] => 24 [[[],[]],[],[[],[]]] => 24 [[[],[]],[],[[[]]]] => 12 [[[[]]],[],[[],[]]] => 12 [[[[]]],[],[[[]]]] => 6 [[[],[]],[[]],[],[]] => 48 [[[[]]],[[]],[],[]] => 24 [[[],[]],[[]],[[]]] => 12 [[[[]]],[[]],[[]]] => 6 [[[],[]],[[],[]],[]] => 24 [[[],[]],[[[]]],[]] => 12 [[[[]]],[[],[]],[]] => 12 [[[[]]],[[[]]],[]] => 6 [[[],[]],[[],[],[]]] => 24 [[[],[]],[[],[[]]]] => 8 [[[],[]],[[[]],[]]] => 8 [[[],[]],[[[],[]]]] => 8 [[[],[]],[[[[]]]]] => 4 [[[[]]],[[],[],[]]] => 12 [[[[]]],[[],[[]]]] => 4 [[[[]]],[[[]],[]]] => 4 [[[[]]],[[[],[]]]] => 4 [[[[]]],[[[[]]]]] => 2 [[[],[],[]],[],[],[]] => 144 [[[],[[]]],[],[],[]] => 48 [[[[]],[]],[],[],[]] => 48 [[[[],[]]],[],[],[]] => 48 [[[[[]]]],[],[],[]] => 24 [[[],[],[]],[],[[]]] => 36 [[[],[[]]],[],[[]]] => 12 [[[[]],[]],[],[[]]] => 12 [[[[],[]]],[],[[]]] => 12 [[[[[]]]],[],[[]]] => 6 [[[],[],[]],[[]],[]] => 36 [[[],[[]]],[[]],[]] => 12 [[[[]],[]],[[]],[]] => 12 [[[[],[]]],[[]],[]] => 12 [[[[[]]]],[[]],[]] => 6 [[[],[],[]],[[],[]]] => 24 [[[],[],[]],[[[]]]] => 12 [[[],[[]]],[[],[]]] => 8 [[[],[[]]],[[[]]]] => 4 [[[[]],[]],[[],[]]] => 8 [[[[]],[]],[[[]]]] => 4 [[[[],[]]],[[],[]]] => 8 [[[[],[]]],[[[]]]] => 4 [[[[[]]]],[[],[]]] => 4 [[[[[]]]],[[[]]]] => 2 [[[],[],[],[]],[],[]] => 144 [[[],[],[[]]],[],[]] => 36 [[[],[[]],[]],[],[]] => 36 [[[],[[],[]]],[],[]] => 24 [[[],[[[]]]],[],[]] => 12 [[[[]],[],[]],[],[]] => 36 [[[[]],[[]]],[],[]] => 12 [[[[],[]],[]],[],[]] => 24 [[[[[]]],[]],[],[]] => 12 [[[[],[],[]]],[],[]] => 36 [[[[],[[]]]],[],[]] => 12 [[[[[]],[]]],[],[]] => 12 [[[[[],[]]]],[],[]] => 12 [[[[[[]]]]],[],[]] => 6 [[[],[],[],[]],[[]]] => 48 [[[],[],[[]]],[[]]] => 12 [[[],[[]],[]],[[]]] => 12 [[[],[[],[]]],[[]]] => 8 [[[],[[[]]]],[[]]] => 4 [[[[]],[],[]],[[]]] => 12 [[[[]],[[]]],[[]]] => 4 [[[[],[]],[]],[[]]] => 8 [[[[[]]],[]],[[]]] => 4 [[[[],[],[]]],[[]]] => 12 [[[[],[[]]]],[[]]] => 4 [[[[[]],[]]],[[]]] => 4 [[[[[],[]]]],[[]]] => 4 [[[[[[]]]]],[[]]] => 2 [[[],[],[],[],[]],[]] => 240 [[[],[],[],[[]]],[]] => 48 [[[],[],[[]],[]],[]] => 48 [[[],[],[[],[]]],[]] => 24 [[[],[],[[[]]]],[]] => 12 [[[],[[]],[],[]],[]] => 48 [[[],[[]],[[]]],[]] => 12 [[[],[[],[]],[]],[]] => 24 [[[],[[[]]],[]],[]] => 12 [[[],[[],[],[]]],[]] => 24 [[[],[[],[[]]]],[]] => 8 [[[],[[[]],[]]],[]] => 8 [[[],[[[],[]]]],[]] => 8 [[[],[[[[]]]]],[]] => 4 [[[[]],[],[],[]],[]] => 48 [[[[]],[],[[]]],[]] => 12 [[[[]],[[]],[]],[]] => 12 [[[[]],[[],[]]],[]] => 8 [[[[]],[[[]]]],[]] => 4 [[[[],[]],[],[]],[]] => 24 [[[[[]]],[],[]],[]] => 12 [[[[],[]],[[]]],[]] => 8 [[[[[]]],[[]]],[]] => 4 [[[[],[],[]],[]],[]] => 24 [[[[],[[]]],[]],[]] => 8 [[[[[]],[]],[]],[]] => 8 [[[[[],[]]],[]],[]] => 8 [[[[[[]]]],[]],[]] => 4 [[[[],[],[],[]]],[]] => 48 [[[[],[],[[]]]],[]] => 12 [[[[],[[]],[]]],[]] => 12 [[[[],[[],[]]]],[]] => 8 [[[[],[[[]]]]],[]] => 4 [[[[[]],[],[]]],[]] => 12 [[[[[]],[[]]]],[]] => 4 [[[[[],[]],[]]],[]] => 8 [[[[[[]]],[]]],[]] => 4 [[[[[],[],[]]]],[]] => 12 [[[[[],[[]]]]],[]] => 4 [[[[[[]],[]]]],[]] => 4 [[[[[[],[]]]]],[]] => 4 [[[[[[[]]]]]],[]] => 2 [[[],[],[],[],[],[]]] => 720 [[[],[],[],[],[[]]]] => 120 [[[],[],[],[[]],[]]] => 120 [[[],[],[],[[],[]]]] => 48 [[[],[],[],[[[]]]]] => 24 [[[],[],[[]],[],[]]] => 120 [[[],[],[[]],[[]]]] => 24 [[[],[],[[],[]],[]]] => 48 [[[],[],[[[]]],[]]] => 24 [[[],[],[[],[],[]]]] => 36 [[[],[],[[],[[]]]]] => 12 [[[],[],[[[]],[]]]] => 12 [[[],[],[[[],[]]]]] => 12 [[[],[],[[[[]]]]]] => 6 [[[],[[]],[],[],[]]] => 120 [[[],[[]],[],[[]]]] => 24 [[[],[[]],[[]],[]]] => 24 [[[],[[]],[[],[]]]] => 12 [[[],[[]],[[[]]]]] => 6 [[[],[[],[]],[],[]]] => 48 [[[],[[[]]],[],[]]] => 24 [[[],[[],[]],[[]]]] => 12 [[[],[[[]]],[[]]]] => 6 [[[],[[],[],[]],[]]] => 36 [[[],[[],[[]]],[]]] => 12 [[[],[[[]],[]],[]]] => 12 [[[],[[[],[]]],[]]] => 12 [[[],[[[[]]]],[]]] => 6 [[[],[[],[],[],[]]]] => 48 [[[],[[],[],[[]]]]] => 12 [[[],[[],[[]],[]]]] => 12 [[[],[[],[[],[]]]]] => 8 [[[],[[],[[[]]]]]] => 4 [[[],[[[]],[],[]]]] => 12 [[[],[[[]],[[]]]]] => 4 [[[],[[[],[]],[]]]] => 8 [[[],[[[[]]],[]]]] => 4 [[[],[[[],[],[]]]]] => 12 [[[],[[[],[[]]]]]] => 4 [[[],[[[[]],[]]]]] => 4 [[[],[[[[],[]]]]]] => 4 [[[],[[[[[]]]]]]] => 2 [[[[]],[],[],[],[]]] => 120 [[[[]],[],[],[[]]]] => 24 [[[[]],[],[[]],[]]] => 24 [[[[]],[],[[],[]]]] => 12 [[[[]],[],[[[]]]]] => 6 [[[[]],[[]],[],[]]] => 24 [[[[]],[[]],[[]]]] => 6 [[[[]],[[],[]],[]]] => 12 [[[[]],[[[]]],[]]] => 6 [[[[]],[[],[],[]]]] => 12 [[[[]],[[],[[]]]]] => 4 [[[[]],[[[]],[]]]] => 4 [[[[]],[[[],[]]]]] => 4 [[[[]],[[[[]]]]]] => 2 [[[[],[]],[],[],[]]] => 48 [[[[[]]],[],[],[]]] => 24 [[[[],[]],[],[[]]]] => 12 [[[[[]]],[],[[]]]] => 6 [[[[],[]],[[]],[]]] => 12 [[[[[]]],[[]],[]]] => 6 [[[[],[]],[[],[]]]] => 8 [[[[],[]],[[[]]]]] => 4 [[[[[]]],[[],[]]]] => 4 [[[[[]]],[[[]]]]] => 2 [[[[],[],[]],[],[]]] => 36 [[[[],[[]]],[],[]]] => 12 [[[[[]],[]],[],[]]] => 12 [[[[[],[]]],[],[]]] => 12 [[[[[[]]]],[],[]]] => 6 [[[[],[],[]],[[]]]] => 12 [[[[],[[]]],[[]]]] => 4 [[[[[]],[]],[[]]]] => 4 [[[[[],[]]],[[]]]] => 4 [[[[[[]]]],[[]]]] => 2 [[[[],[],[],[]],[]]] => 48 [[[[],[],[[]]],[]]] => 12 [[[[],[[]],[]],[]]] => 12 [[[[],[[],[]]],[]]] => 8 [[[[],[[[]]]],[]]] => 4 [[[[[]],[],[]],[]]] => 12 [[[[[]],[[]]],[]]] => 4 [[[[[],[]],[]],[]]] => 8 [[[[[[]]],[]],[]]] => 4 [[[[[],[],[]]],[]]] => 12 [[[[[],[[]]]],[]]] => 4 [[[[[[]],[]]],[]]] => 4 [[[[[[],[]]]],[]]] => 4 [[[[[[[]]]]],[]]] => 2 [[[[],[],[],[],[]]]] => 120 [[[[],[],[],[[]]]]] => 24 [[[[],[],[[]],[]]]] => 24 [[[[],[],[[],[]]]]] => 12 [[[[],[],[[[]]]]]] => 6 [[[[],[[]],[],[]]]] => 24 [[[[],[[]],[[]]]]] => 6 [[[[],[[],[]],[]]]] => 12 [[[[],[[[]]],[]]]] => 6 [[[[],[[],[],[]]]]] => 12 [[[[],[[],[[]]]]]] => 4 [[[[],[[[]],[]]]]] => 4 [[[[],[[[],[]]]]]] => 4 [[[[],[[[[]]]]]]] => 2 [[[[[]],[],[],[]]]] => 24 [[[[[]],[],[[]]]]] => 6 [[[[[]],[[]],[]]]] => 6 [[[[[]],[[],[]]]]] => 4 [[[[[]],[[[]]]]]] => 2 [[[[[],[]],[],[]]]] => 12 [[[[[[]]],[],[]]]] => 6 [[[[[],[]],[[]]]]] => 4 [[[[[[]]],[[]]]]] => 2 [[[[[],[],[]],[]]]] => 12 [[[[[],[[]]],[]]]] => 4 [[[[[[]],[]],[]]]] => 4 [[[[[[],[]]],[]]]] => 4 [[[[[[[]]]],[]]]] => 2 [[[[[],[],[],[]]]]] => 24 [[[[[],[],[[]]]]]] => 6 [[[[[],[[]],[]]]]] => 6 [[[[[],[[],[]]]]]] => 4 [[[[[],[[[]]]]]]] => 2 [[[[[[]],[],[]]]]] => 6 [[[[[[]],[[]]]]]] => 2 [[[[[[],[]],[]]]]] => 4 [[[[[[[]]],[]]]]] => 2 [[[[[[],[],[]]]]]] => 6 [[[[[[],[[]]]]]]] => 2 [[[[[[[]],[]]]]]] => 2 [[[[[[[],[]]]]]]] => 2 [[[[[[[[]]]]]]]] => 1 [[],[],[],[],[],[],[],[]] => 40320 [[],[],[],[],[],[],[[]]] => 5040 [[],[],[],[],[],[[]],[]] => 5040 [[],[],[],[],[],[[],[]]] => 1440 [[],[],[],[],[],[[[]]]] => 720 [[],[],[],[],[[]],[],[]] => 5040 [[],[],[],[],[[]],[[]]] => 720 [[],[],[],[],[[],[]],[]] => 1440 [[],[],[],[],[[[]]],[]] => 720 [[],[],[],[],[[],[],[]]] => 720 [[],[],[],[],[[],[[]]]] => 240 [[],[],[],[],[[[]],[]]] => 240 [[],[],[],[],[[[],[]]]] => 240 [[],[],[],[],[[[[]]]]] => 120 [[],[],[],[[]],[],[],[]] => 5040 [[],[],[],[[]],[],[[]]] => 720 [[],[],[],[[]],[[]],[]] => 720 [[],[],[],[[]],[[],[]]] => 240 [[],[],[],[[]],[[[]]]] => 120 [[],[],[],[[],[]],[],[]] => 1440 [[],[],[],[[[]]],[],[]] => 720 [[],[],[],[[],[]],[[]]] => 240 [[],[],[],[[[]]],[[]]] => 120 [[],[],[],[[],[],[]],[]] => 720 [[],[],[],[[],[[]]],[]] => 240 [[],[],[],[[[]],[]],[]] => 240 [[],[],[],[[[],[]]],[]] => 240 [[],[],[],[[[[]]]],[]] => 120 [[],[],[],[[],[],[],[]]] => 576 [[],[],[],[[],[],[[]]]] => 144 [[],[],[],[[],[[]],[]]] => 144 [[],[],[],[[],[[],[]]]] => 96 [[],[],[],[[],[[[]]]]] => 48 [[],[],[],[[[]],[],[]]] => 144 [[],[],[],[[[]],[[]]]] => 48 [[],[],[],[[[],[]],[]]] => 96 [[],[],[],[[[[]]],[]]] => 48 [[],[],[],[[[],[],[]]]] => 144 [[],[],[],[[[],[[]]]]] => 48 [[],[],[],[[[[]],[]]]] => 48 [[],[],[],[[[[],[]]]]] => 48 [[],[],[],[[[[[]]]]]] => 24 [[],[],[[]],[],[],[],[]] => 5040 [[],[],[[]],[],[],[[]]] => 720 [[],[],[[]],[],[[]],[]] => 720 [[],[],[[]],[],[[],[]]] => 240 [[],[],[[]],[],[[[]]]] => 120 [[],[],[[]],[[]],[],[]] => 720 [[],[],[[]],[[]],[[]]] => 120 [[],[],[[]],[[],[]],[]] => 240 [[],[],[[]],[[[]]],[]] => 120 [[],[],[[]],[[],[],[]]] => 144 [[],[],[[]],[[],[[]]]] => 48 [[],[],[[]],[[[]],[]]] => 48 [[],[],[[]],[[[],[]]]] => 48 [[],[],[[]],[[[[]]]]] => 24 [[],[],[[],[]],[],[],[]] => 1440 [[],[],[[[]]],[],[],[]] => 720 [[],[],[[],[]],[],[[]]] => 240 [[],[],[[[]]],[],[[]]] => 120 [[],[],[[],[]],[[]],[]] => 240 [[],[],[[[]]],[[]],[]] => 120 [[],[],[[],[]],[[],[]]] => 96 [[],[],[[],[]],[[[]]]] => 48 [[],[],[[[]]],[[],[]]] => 48 [[],[],[[[]]],[[[]]]] => 24 [[],[],[[],[],[]],[],[]] => 720 [[],[],[[],[[]]],[],[]] => 240 [[],[],[[[]],[]],[],[]] => 240 [[],[],[[[],[]]],[],[]] => 240 [[],[],[[[[]]]],[],[]] => 120 [[],[],[[],[],[]],[[]]] => 144 [[],[],[[],[[]]],[[]]] => 48 [[],[],[[[]],[]],[[]]] => 48 [[],[],[[[],[]]],[[]]] => 48 [[],[],[[[[]]]],[[]]] => 24 [[],[],[[],[],[],[]],[]] => 576 [[],[],[[],[],[[]]],[]] => 144 [[],[],[[],[[]],[]],[]] => 144 [[],[],[[],[[],[]]],[]] => 96 [[],[],[[],[[[]]]],[]] => 48 [[],[],[[[]],[],[]],[]] => 144 [[],[],[[[]],[[]]],[]] => 48 [[],[],[[[],[]],[]],[]] => 96 [[],[],[[[[]]],[]],[]] => 48 [[],[],[[[],[],[]]],[]] => 144 [[],[],[[[],[[]]]],[]] => 48 [[],[],[[[[]],[]]],[]] => 48 [[],[],[[[[],[]]]],[]] => 48 [[],[],[[[[[]]]]],[]] => 24 [[],[],[[],[],[],[],[]]] => 720 [[],[],[[],[],[],[[]]]] => 144 [[],[],[[],[],[[]],[]]] => 144 [[],[],[[],[],[[],[]]]] => 72 [[],[],[[],[],[[[]]]]] => 36 [[],[],[[],[[]],[],[]]] => 144 [[],[],[[],[[]],[[]]]] => 36 [[],[],[[],[[],[]],[]]] => 72 [[],[],[[],[[[]]],[]]] => 36 [[],[],[[],[[],[],[]]]] => 72 [[],[],[[],[[],[[]]]]] => 24 [[],[],[[],[[[]],[]]]] => 24 [[],[],[[],[[[],[]]]]] => 24 [[],[],[[],[[[[]]]]]] => 12 [[],[],[[[]],[],[],[]]] => 144 [[],[],[[[]],[],[[]]]] => 36 [[],[],[[[]],[[]],[]]] => 36 [[],[],[[[]],[[],[]]]] => 24 [[],[],[[[]],[[[]]]]] => 12 [[],[],[[[],[]],[],[]]] => 72 [[],[],[[[[]]],[],[]]] => 36 [[],[],[[[],[]],[[]]]] => 24 [[],[],[[[[]]],[[]]]] => 12 [[],[],[[[],[],[]],[]]] => 72 [[],[],[[[],[[]]],[]]] => 24 [[],[],[[[[]],[]],[]]] => 24 [[],[],[[[[],[]]],[]]] => 24 [[],[],[[[[[]]]],[]]] => 12 [[],[],[[[],[],[],[]]]] => 144 [[],[],[[[],[],[[]]]]] => 36 [[],[],[[[],[[]],[]]]] => 36 [[],[],[[[],[[],[]]]]] => 24 [[],[],[[[],[[[]]]]]] => 12 [[],[],[[[[]],[],[]]]] => 36 [[],[],[[[[]],[[]]]]] => 12 [[],[],[[[[],[]],[]]]] => 24 [[],[],[[[[[]]],[]]]] => 12 [[],[],[[[[],[],[]]]]] => 36 [[],[],[[[[],[[]]]]]] => 12 [[],[],[[[[[]],[]]]]] => 12 [[],[],[[[[[],[]]]]]] => 12 [[],[],[[[[[[]]]]]]] => 6 [[],[[]],[],[],[],[],[]] => 5040 [[],[[]],[],[],[],[[]]] => 720 [[],[[]],[],[],[[]],[]] => 720 [[],[[]],[],[],[[],[]]] => 240 [[],[[]],[],[],[[[]]]] => 120 [[],[[]],[],[[]],[],[]] => 720 [[],[[]],[],[[]],[[]]] => 120 [[],[[]],[],[[],[]],[]] => 240 [[],[[]],[],[[[]]],[]] => 120 [[],[[]],[],[[],[],[]]] => 144 [[],[[]],[],[[],[[]]]] => 48 [[],[[]],[],[[[]],[]]] => 48 [[],[[]],[],[[[],[]]]] => 48 [[],[[]],[],[[[[]]]]] => 24 [[],[[]],[[]],[],[],[]] => 720 [[],[[]],[[]],[],[[]]] => 120 [[],[[]],[[]],[[]],[]] => 120 [[],[[]],[[]],[[],[]]] => 48 [[],[[]],[[]],[[[]]]] => 24 [[],[[]],[[],[]],[],[]] => 240 [[],[[]],[[[]]],[],[]] => 120 [[],[[]],[[],[]],[[]]] => 48 [[],[[]],[[[]]],[[]]] => 24 [[],[[]],[[],[],[]],[]] => 144 [[],[[]],[[],[[]]],[]] => 48 [[],[[]],[[[]],[]],[]] => 48 [[],[[]],[[[],[]]],[]] => 48 [[],[[]],[[[[]]]],[]] => 24 [[],[[]],[[],[],[],[]]] => 144 [[],[[]],[[],[],[[]]]] => 36 [[],[[]],[[],[[]],[]]] => 36 [[],[[]],[[],[[],[]]]] => 24 [[],[[]],[[],[[[]]]]] => 12 [[],[[]],[[[]],[],[]]] => 36 [[],[[]],[[[]],[[]]]] => 12 [[],[[]],[[[],[]],[]]] => 24 [[],[[]],[[[[]]],[]]] => 12 [[],[[]],[[[],[],[]]]] => 36 [[],[[]],[[[],[[]]]]] => 12 [[],[[]],[[[[]],[]]]] => 12 [[],[[]],[[[[],[]]]]] => 12 [[],[[]],[[[[[]]]]]] => 6 [[],[[],[]],[],[],[],[]] => 1440 [[],[[[]]],[],[],[],[]] => 720 [[],[[],[]],[],[],[[]]] => 240 [[],[[[]]],[],[],[[]]] => 120 [[],[[],[]],[],[[]],[]] => 240 [[],[[[]]],[],[[]],[]] => 120 [[],[[],[]],[],[[],[]]] => 96 [[],[[],[]],[],[[[]]]] => 48 [[],[[[]]],[],[[],[]]] => 48 [[],[[[]]],[],[[[]]]] => 24 [[],[[],[]],[[]],[],[]] => 240 [[],[[[]]],[[]],[],[]] => 120 [[],[[],[]],[[]],[[]]] => 48 [[],[[[]]],[[]],[[]]] => 24 [[],[[],[]],[[],[]],[]] => 96 [[],[[],[]],[[[]]],[]] => 48 [[],[[[]]],[[],[]],[]] => 48 [[],[[[]]],[[[]]],[]] => 24 [[],[[],[]],[[],[],[]]] => 72 [[],[[],[]],[[],[[]]]] => 24 [[],[[],[]],[[[]],[]]] => 24 [[],[[],[]],[[[],[]]]] => 24 [[],[[],[]],[[[[]]]]] => 12 [[],[[[]]],[[],[],[]]] => 36 [[],[[[]]],[[],[[]]]] => 12 [[],[[[]]],[[[]],[]]] => 12 [[],[[[]]],[[[],[]]]] => 12 [[],[[[]]],[[[[]]]]] => 6 [[],[[],[],[]],[],[],[]] => 720 [[],[[],[[]]],[],[],[]] => 240 [[],[[[]],[]],[],[],[]] => 240 [[],[[[],[]]],[],[],[]] => 240 [[],[[[[]]]],[],[],[]] => 120 [[],[[],[],[]],[],[[]]] => 144 [[],[[],[[]]],[],[[]]] => 48 [[],[[[]],[]],[],[[]]] => 48 [[],[[[],[]]],[],[[]]] => 48 [[],[[[[]]]],[],[[]]] => 24 [[],[[],[],[]],[[]],[]] => 144 [[],[[],[[]]],[[]],[]] => 48 [[],[[[]],[]],[[]],[]] => 48 [[],[[[],[]]],[[]],[]] => 48 [[],[[[[]]]],[[]],[]] => 24 [[],[[],[],[]],[[],[]]] => 72 [[],[[],[],[]],[[[]]]] => 36 [[],[[],[[]]],[[],[]]] => 24 [[],[[],[[]]],[[[]]]] => 12 [[],[[[]],[]],[[],[]]] => 24 [[],[[[]],[]],[[[]]]] => 12 [[],[[[],[]]],[[],[]]] => 24 [[],[[[],[]]],[[[]]]] => 12 [[],[[[[]]]],[[],[]]] => 12 [[],[[[[]]]],[[[]]]] => 6 [[],[[],[],[],[]],[],[]] => 576 [[],[[],[],[[]]],[],[]] => 144 [[],[[],[[]],[]],[],[]] => 144 [[],[[],[[],[]]],[],[]] => 96 [[],[[],[[[]]]],[],[]] => 48 [[],[[[]],[],[]],[],[]] => 144 [[],[[[]],[[]]],[],[]] => 48 [[],[[[],[]],[]],[],[]] => 96 [[],[[[[]]],[]],[],[]] => 48 [[],[[[],[],[]]],[],[]] => 144 [[],[[[],[[]]]],[],[]] => 48 [[],[[[[]],[]]],[],[]] => 48 [[],[[[[],[]]]],[],[]] => 48 [[],[[[[[]]]]],[],[]] => 24 [[],[[],[],[],[]],[[]]] => 144 [[],[[],[],[[]]],[[]]] => 36 [[],[[],[[]],[]],[[]]] => 36 [[],[[],[[],[]]],[[]]] => 24 [[],[[],[[[]]]],[[]]] => 12 [[],[[[]],[],[]],[[]]] => 36 [[],[[[]],[[]]],[[]]] => 12 [[],[[[],[]],[]],[[]]] => 24 [[],[[[[]]],[]],[[]]] => 12 [[],[[[],[],[]]],[[]]] => 36 [[],[[[],[[]]]],[[]]] => 12 [[],[[[[]],[]]],[[]]] => 12 [[],[[[[],[]]]],[[]]] => 12 [[],[[[[[]]]]],[[]]] => 6 [[],[[],[],[],[],[]],[]] => 720 [[],[[],[],[],[[]]],[]] => 144 [[],[[],[],[[]],[]],[]] => 144 [[],[[],[],[[],[]]],[]] => 72 [[],[[],[],[[[]]]],[]] => 36 [[],[[],[[]],[],[]],[]] => 144 [[],[[],[[]],[[]]],[]] => 36 [[],[[],[[],[]],[]],[]] => 72 [[],[[],[[[]]],[]],[]] => 36 [[],[[],[[],[],[]]],[]] => 72 [[],[[],[[],[[]]]],[]] => 24 [[],[[],[[[]],[]]],[]] => 24 [[],[[],[[[],[]]]],[]] => 24 [[],[[],[[[[]]]]],[]] => 12 [[],[[[]],[],[],[]],[]] => 144 [[],[[[]],[],[[]]],[]] => 36 [[],[[[]],[[]],[]],[]] => 36 [[],[[[]],[[],[]]],[]] => 24 [[],[[[]],[[[]]]],[]] => 12 [[],[[[],[]],[],[]],[]] => 72 [[],[[[[]]],[],[]],[]] => 36 [[],[[[],[]],[[]]],[]] => 24 [[],[[[[]]],[[]]],[]] => 12 [[],[[[],[],[]],[]],[]] => 72 [[],[[[],[[]]],[]],[]] => 24 [[],[[[[]],[]],[]],[]] => 24 [[],[[[[],[]]],[]],[]] => 24 [[],[[[[[]]]],[]],[]] => 12 [[],[[[],[],[],[]]],[]] => 144 [[],[[[],[],[[]]]],[]] => 36 [[],[[[],[[]],[]]],[]] => 36 [[],[[[],[[],[]]]],[]] => 24 [[],[[[],[[[]]]]],[]] => 12 [[],[[[[]],[],[]]],[]] => 36 [[],[[[[]],[[]]]],[]] => 12 [[],[[[[],[]],[]]],[]] => 24 [[],[[[[[]]],[]]],[]] => 12 [[],[[[[],[],[]]]],[]] => 36 [[],[[[[],[[]]]]],[]] => 12 [[],[[[[[]],[]]]],[]] => 12 [[],[[[[[],[]]]]],[]] => 12 [[],[[[[[[]]]]]],[]] => 6 [[],[[],[],[],[],[],[]]] => 1440 [[],[[],[],[],[],[[]]]] => 240 [[],[[],[],[],[[]],[]]] => 240 [[],[[],[],[],[[],[]]]] => 96 [[],[[],[],[],[[[]]]]] => 48 [[],[[],[],[[]],[],[]]] => 240 [[],[[],[],[[]],[[]]]] => 48 [[],[[],[],[[],[]],[]]] => 96 [[],[[],[],[[[]]],[]]] => 48 [[],[[],[],[[],[],[]]]] => 72 [[],[[],[],[[],[[]]]]] => 24 [[],[[],[],[[[]],[]]]] => 24 [[],[[],[],[[[],[]]]]] => 24 [[],[[],[],[[[[]]]]]] => 12 [[],[[],[[]],[],[],[]]] => 240 [[],[[],[[]],[],[[]]]] => 48 [[],[[],[[]],[[]],[]]] => 48 [[],[[],[[]],[[],[]]]] => 24 [[],[[],[[]],[[[]]]]] => 12 [[],[[],[[],[]],[],[]]] => 96 [[],[[],[[[]]],[],[]]] => 48 [[],[[],[[],[]],[[]]]] => 24 [[],[[],[[[]]],[[]]]] => 12 [[],[[],[[],[],[]],[]]] => 72 [[],[[],[[],[[]]],[]]] => 24 [[],[[],[[[]],[]],[]]] => 24 [[],[[],[[[],[]]],[]]] => 24 [[],[[],[[[[]]]],[]]] => 12 [[],[[],[[],[],[],[]]]] => 96 [[],[[],[[],[],[[]]]]] => 24 [[],[[],[[],[[]],[]]]] => 24 [[],[[],[[],[[],[]]]]] => 16 [[],[[],[[],[[[]]]]]] => 8 [[],[[],[[[]],[],[]]]] => 24 [[],[[],[[[]],[[]]]]] => 8 [[],[[],[[[],[]],[]]]] => 16 [[],[[],[[[[]]],[]]]] => 8 [[],[[],[[[],[],[]]]]] => 24 [[],[[],[[[],[[]]]]]] => 8 [[],[[],[[[[]],[]]]]] => 8 [[],[[],[[[[],[]]]]]] => 8 [[],[[],[[[[[]]]]]]] => 4 [[],[[[]],[],[],[],[]]] => 240 [[],[[[]],[],[],[[]]]] => 48 [[],[[[]],[],[[]],[]]] => 48 [[],[[[]],[],[[],[]]]] => 24 [[],[[[]],[],[[[]]]]] => 12 [[],[[[]],[[]],[],[]]] => 48 [[],[[[]],[[]],[[]]]] => 12 [[],[[[]],[[],[]],[]]] => 24 [[],[[[]],[[[]]],[]]] => 12 [[],[[[]],[[],[],[]]]] => 24 [[],[[[]],[[],[[]]]]] => 8 [[],[[[]],[[[]],[]]]] => 8 [[],[[[]],[[[],[]]]]] => 8 [[],[[[]],[[[[]]]]]] => 4 [[],[[[],[]],[],[],[]]] => 96 [[],[[[[]]],[],[],[]]] => 48 [[],[[[],[]],[],[[]]]] => 24 [[],[[[[]]],[],[[]]]] => 12 [[],[[[],[]],[[]],[]]] => 24 [[],[[[[]]],[[]],[]]] => 12 [[],[[[],[]],[[],[]]]] => 16 [[],[[[],[]],[[[]]]]] => 8 [[],[[[[]]],[[],[]]]] => 8 [[],[[[[]]],[[[]]]]] => 4 [[],[[[],[],[]],[],[]]] => 72 [[],[[[],[[]]],[],[]]] => 24 [[],[[[[]],[]],[],[]]] => 24 [[],[[[[],[]]],[],[]]] => 24 [[],[[[[[]]]],[],[]]] => 12 [[],[[[],[],[]],[[]]]] => 24 [[],[[[],[[]]],[[]]]] => 8 [[],[[[[]],[]],[[]]]] => 8 [[],[[[[],[]]],[[]]]] => 8 [[],[[[[[]]]],[[]]]] => 4 [[],[[[],[],[],[]],[]]] => 96 [[],[[[],[],[[]]],[]]] => 24 [[],[[[],[[]],[]],[]]] => 24 [[],[[[],[[],[]]],[]]] => 16 [[],[[[],[[[]]]],[]]] => 8 [[],[[[[]],[],[]],[]]] => 24 [[],[[[[]],[[]]],[]]] => 8 [[],[[[[],[]],[]],[]]] => 16 [[],[[[[[]]],[]],[]]] => 8 [[],[[[[],[],[]]],[]]] => 24 [[],[[[[],[[]]]],[]]] => 8 [[],[[[[[]],[]]],[]]] => 8 [[],[[[[[],[]]]],[]]] => 8 [[],[[[[[[]]]]],[]]] => 4 [[],[[[],[],[],[],[]]]] => 240 [[],[[[],[],[],[[]]]]] => 48 [[],[[[],[],[[]],[]]]] => 48 [[],[[[],[],[[],[]]]]] => 24 [[],[[[],[],[[[]]]]]] => 12 [[],[[[],[[]],[],[]]]] => 48 [[],[[[],[[]],[[]]]]] => 12 [[],[[[],[[],[]],[]]]] => 24 [[],[[[],[[[]]],[]]]] => 12 [[],[[[],[[],[],[]]]]] => 24 [[],[[[],[[],[[]]]]]] => 8 [[],[[[],[[[]],[]]]]] => 8 [[],[[[],[[[],[]]]]]] => 8 [[],[[[],[[[[]]]]]]] => 4 [[],[[[[]],[],[],[]]]] => 48 [[],[[[[]],[],[[]]]]] => 12 [[],[[[[]],[[]],[]]]] => 12 [[],[[[[]],[[],[]]]]] => 8 [[],[[[[]],[[[]]]]]] => 4 [[],[[[[],[]],[],[]]]] => 24 [[],[[[[[]]],[],[]]]] => 12 [[],[[[[],[]],[[]]]]] => 8 [[],[[[[[]]],[[]]]]] => 4 [[],[[[[],[],[]],[]]]] => 24 [[],[[[[],[[]]],[]]]] => 8 [[],[[[[[]],[]],[]]]] => 8 [[],[[[[[],[]]],[]]]] => 8 [[],[[[[[[]]]],[]]]] => 4 [[],[[[[],[],[],[]]]]] => 48 [[],[[[[],[],[[]]]]]] => 12 [[],[[[[],[[]],[]]]]] => 12 [[],[[[[],[[],[]]]]]] => 8 [[],[[[[],[[[]]]]]]] => 4 [[],[[[[[]],[],[]]]]] => 12 [[],[[[[[]],[[]]]]]] => 4 [[],[[[[[],[]],[]]]]] => 8 [[],[[[[[[]]],[]]]]] => 4 [[],[[[[[],[],[]]]]]] => 12 [[],[[[[[],[[]]]]]]] => 4 [[],[[[[[[]],[]]]]]] => 4 [[],[[[[[[],[]]]]]]] => 4 [[],[[[[[[[]]]]]]]] => 2 [[[]],[],[],[],[],[],[]] => 5040 [[[]],[],[],[],[],[[]]] => 720 [[[]],[],[],[],[[]],[]] => 720 [[[]],[],[],[],[[],[]]] => 240 [[[]],[],[],[],[[[]]]] => 120 [[[]],[],[],[[]],[],[]] => 720 [[[]],[],[],[[]],[[]]] => 120 [[[]],[],[],[[],[]],[]] => 240 [[[]],[],[],[[[]]],[]] => 120 [[[]],[],[],[[],[],[]]] => 144 [[[]],[],[],[[],[[]]]] => 48 [[[]],[],[],[[[]],[]]] => 48 [[[]],[],[],[[[],[]]]] => 48 [[[]],[],[],[[[[]]]]] => 24 [[[]],[],[[]],[],[],[]] => 720 [[[]],[],[[]],[],[[]]] => 120 [[[]],[],[[]],[[]],[]] => 120 [[[]],[],[[]],[[],[]]] => 48 [[[]],[],[[]],[[[]]]] => 24 [[[]],[],[[],[]],[],[]] => 240 [[[]],[],[[[]]],[],[]] => 120 [[[]],[],[[],[]],[[]]] => 48 [[[]],[],[[[]]],[[]]] => 24 [[[]],[],[[],[],[]],[]] => 144 [[[]],[],[[],[[]]],[]] => 48 [[[]],[],[[[]],[]],[]] => 48 [[[]],[],[[[],[]]],[]] => 48 [[[]],[],[[[[]]]],[]] => 24 [[[]],[],[[],[],[],[]]] => 144 [[[]],[],[[],[],[[]]]] => 36 [[[]],[],[[],[[]],[]]] => 36 [[[]],[],[[],[[],[]]]] => 24 [[[]],[],[[],[[[]]]]] => 12 [[[]],[],[[[]],[],[]]] => 36 [[[]],[],[[[]],[[]]]] => 12 [[[]],[],[[[],[]],[]]] => 24 [[[]],[],[[[[]]],[]]] => 12 [[[]],[],[[[],[],[]]]] => 36 [[[]],[],[[[],[[]]]]] => 12 [[[]],[],[[[[]],[]]]] => 12 [[[]],[],[[[[],[]]]]] => 12 [[[]],[],[[[[[]]]]]] => 6 [[[]],[[]],[],[],[],[]] => 720 [[[]],[[]],[],[],[[]]] => 120 [[[]],[[]],[],[[]],[]] => 120 [[[]],[[]],[],[[],[]]] => 48 [[[]],[[]],[],[[[]]]] => 24 [[[]],[[]],[[]],[],[]] => 120 [[[]],[[]],[[]],[[]]] => 24 [[[]],[[]],[[],[]],[]] => 48 [[[]],[[]],[[[]]],[]] => 24 [[[]],[[]],[[],[],[]]] => 36 [[[]],[[]],[[],[[]]]] => 12 [[[]],[[]],[[[]],[]]] => 12 [[[]],[[]],[[[],[]]]] => 12 [[[]],[[]],[[[[]]]]] => 6 [[[]],[[],[]],[],[],[]] => 240 [[[]],[[[]]],[],[],[]] => 120 [[[]],[[],[]],[],[[]]] => 48 [[[]],[[[]]],[],[[]]] => 24 [[[]],[[],[]],[[]],[]] => 48 [[[]],[[[]]],[[]],[]] => 24 [[[]],[[],[]],[[],[]]] => 24 [[[]],[[],[]],[[[]]]] => 12 [[[]],[[[]]],[[],[]]] => 12 [[[]],[[[]]],[[[]]]] => 6 [[[]],[[],[],[]],[],[]] => 144 [[[]],[[],[[]]],[],[]] => 48 [[[]],[[[]],[]],[],[]] => 48 [[[]],[[[],[]]],[],[]] => 48 [[[]],[[[[]]]],[],[]] => 24 [[[]],[[],[],[]],[[]]] => 36 [[[]],[[],[[]]],[[]]] => 12 [[[]],[[[]],[]],[[]]] => 12 [[[]],[[[],[]]],[[]]] => 12 [[[]],[[[[]]]],[[]]] => 6 [[[]],[[],[],[],[]],[]] => 144 [[[]],[[],[],[[]]],[]] => 36 [[[]],[[],[[]],[]],[]] => 36 [[[]],[[],[[],[]]],[]] => 24 [[[]],[[],[[[]]]],[]] => 12 [[[]],[[[]],[],[]],[]] => 36 [[[]],[[[]],[[]]],[]] => 12 [[[]],[[[],[]],[]],[]] => 24 [[[]],[[[[]]],[]],[]] => 12 [[[]],[[[],[],[]]],[]] => 36 [[[]],[[[],[[]]]],[]] => 12 [[[]],[[[[]],[]]],[]] => 12 [[[]],[[[[],[]]]],[]] => 12 [[[]],[[[[[]]]]],[]] => 6 [[[]],[[],[],[],[],[]]] => 240 [[[]],[[],[],[],[[]]]] => 48 [[[]],[[],[],[[]],[]]] => 48 [[[]],[[],[],[[],[]]]] => 24 [[[]],[[],[],[[[]]]]] => 12 [[[]],[[],[[]],[],[]]] => 48 [[[]],[[],[[]],[[]]]] => 12 [[[]],[[],[[],[]],[]]] => 24 [[[]],[[],[[[]]],[]]] => 12 [[[]],[[],[[],[],[]]]] => 24 [[[]],[[],[[],[[]]]]] => 8 [[[]],[[],[[[]],[]]]] => 8 [[[]],[[],[[[],[]]]]] => 8 [[[]],[[],[[[[]]]]]] => 4 [[[]],[[[]],[],[],[]]] => 48 [[[]],[[[]],[],[[]]]] => 12 [[[]],[[[]],[[]],[]]] => 12 [[[]],[[[]],[[],[]]]] => 8 [[[]],[[[]],[[[]]]]] => 4 [[[]],[[[],[]],[],[]]] => 24 [[[]],[[[[]]],[],[]]] => 12 [[[]],[[[],[]],[[]]]] => 8 [[[]],[[[[]]],[[]]]] => 4 [[[]],[[[],[],[]],[]]] => 24 [[[]],[[[],[[]]],[]]] => 8 [[[]],[[[[]],[]],[]]] => 8 [[[]],[[[[],[]]],[]]] => 8 [[[]],[[[[[]]]],[]]] => 4 [[[]],[[[],[],[],[]]]] => 48 [[[]],[[[],[],[[]]]]] => 12 [[[]],[[[],[[]],[]]]] => 12 [[[]],[[[],[[],[]]]]] => 8 [[[]],[[[],[[[]]]]]] => 4 [[[]],[[[[]],[],[]]]] => 12 [[[]],[[[[]],[[]]]]] => 4 [[[]],[[[[],[]],[]]]] => 8 [[[]],[[[[[]]],[]]]] => 4 [[[]],[[[[],[],[]]]]] => 12 [[[]],[[[[],[[]]]]]] => 4 [[[]],[[[[[]],[]]]]] => 4 [[[]],[[[[[],[]]]]]] => 4 [[[]],[[[[[[]]]]]]] => 2 [[[],[]],[],[],[],[],[]] => 1440 [[[[]]],[],[],[],[],[]] => 720 [[[],[]],[],[],[],[[]]] => 240 [[[[]]],[],[],[],[[]]] => 120 [[[],[]],[],[],[[]],[]] => 240 [[[[]]],[],[],[[]],[]] => 120 [[[],[]],[],[],[[],[]]] => 96 [[[],[]],[],[],[[[]]]] => 48 [[[[]]],[],[],[[],[]]] => 48 [[[[]]],[],[],[[[]]]] => 24 [[[],[]],[],[[]],[],[]] => 240 [[[[]]],[],[[]],[],[]] => 120 [[[],[]],[],[[]],[[]]] => 48 [[[[]]],[],[[]],[[]]] => 24 ----------------------------------------------------------------------------- Created: Feb 25, 2016 at 21:01 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 25, 2016 at 21:01 by Martin Rubey