***************************************************************************** * 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: St000417 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The size of the automorphism group of the ordered tree. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(T): children = [S for S in T] multiplicities = [(S, children.count(S)) for S in set(children)] return prod(statistic(S)^m*factorial(m) for (S, m) in multiplicities) ----------------------------------------------------------------------------- Statistic values: [[]] => 1 [[],[]] => 2 [[[]]] => 1 [[],[],[]] => 6 [[],[[]]] => 1 [[[]],[]] => 1 [[[],[]]] => 2 [[[[]]]] => 1 [[],[],[],[]] => 24 [[],[],[[]]] => 2 [[],[[]],[]] => 2 [[],[[],[]]] => 2 [[],[[[]]]] => 1 [[[]],[],[]] => 2 [[[]],[[]]] => 2 [[[],[]],[]] => 2 [[[[]]],[]] => 1 [[[],[],[]]] => 6 [[[],[[]]]] => 1 [[[[]],[]]] => 1 [[[[],[]]]] => 2 [[[[[]]]]] => 1 [[],[],[],[],[]] => 120 [[],[],[],[[]]] => 6 [[],[],[[]],[]] => 6 [[],[],[[],[]]] => 4 [[],[],[[[]]]] => 2 [[],[[]],[],[]] => 6 [[],[[]],[[]]] => 2 [[],[[],[]],[]] => 4 [[],[[[]]],[]] => 2 [[],[[],[],[]]] => 6 [[],[[],[[]]]] => 1 [[],[[[]],[]]] => 1 [[],[[[],[]]]] => 2 [[],[[[[]]]]] => 1 [[[]],[],[],[]] => 6 [[[]],[],[[]]] => 2 [[[]],[[]],[]] => 2 [[[]],[[],[]]] => 2 [[[]],[[[]]]] => 1 [[[],[]],[],[]] => 4 [[[[]]],[],[]] => 2 [[[],[]],[[]]] => 2 [[[[]]],[[]]] => 1 [[[],[],[]],[]] => 6 [[[],[[]]],[]] => 1 [[[[]],[]],[]] => 1 [[[[],[]]],[]] => 2 [[[[[]]]],[]] => 1 [[[],[],[],[]]] => 24 [[[],[],[[]]]] => 2 [[[],[[]],[]]] => 2 [[[],[[],[]]]] => 2 [[[],[[[]]]]] => 1 [[[[]],[],[]]] => 2 [[[[]],[[]]]] => 2 [[[[],[]],[]]] => 2 [[[[[]]],[]]] => 1 [[[[],[],[]]]] => 6 [[[[],[[]]]]] => 1 [[[[[]],[]]]] => 1 [[[[[],[]]]]] => 2 [[[[[[]]]]]] => 1 [[],[],[],[],[],[]] => 720 [[],[],[],[],[[]]] => 24 [[],[],[],[[]],[]] => 24 [[],[],[],[[],[]]] => 12 [[],[],[],[[[]]]] => 6 [[],[],[[]],[],[]] => 24 [[],[],[[]],[[]]] => 4 [[],[],[[],[]],[]] => 12 [[],[],[[[]]],[]] => 6 [[],[],[[],[],[]]] => 12 [[],[],[[],[[]]]] => 2 [[],[],[[[]],[]]] => 2 [[],[],[[[],[]]]] => 4 [[],[],[[[[]]]]] => 2 [[],[[]],[],[],[]] => 24 [[],[[]],[],[[]]] => 4 [[],[[]],[[]],[]] => 4 [[],[[]],[[],[]]] => 2 [[],[[]],[[[]]]] => 1 [[],[[],[]],[],[]] => 12 [[],[[[]]],[],[]] => 6 [[],[[],[]],[[]]] => 2 [[],[[[]]],[[]]] => 1 [[],[[],[],[]],[]] => 12 [[],[[],[[]]],[]] => 2 [[],[[[]],[]],[]] => 2 [[],[[[],[]]],[]] => 4 [[],[[[[]]]],[]] => 2 [[],[[],[],[],[]]] => 24 [[],[[],[],[[]]]] => 2 [[],[[],[[]],[]]] => 2 [[],[[],[[],[]]]] => 2 [[],[[],[[[]]]]] => 1 [[],[[[]],[],[]]] => 2 [[],[[[]],[[]]]] => 2 [[],[[[],[]],[]]] => 2 [[],[[[[]]],[]]] => 1 [[],[[[],[],[]]]] => 6 [[],[[[],[[]]]]] => 1 [[],[[[[]],[]]]] => 1 [[],[[[[],[]]]]] => 2 [[],[[[[[]]]]]] => 1 [[[]],[],[],[],[]] => 24 [[[]],[],[],[[]]] => 4 [[[]],[],[[]],[]] => 4 [[[]],[],[[],[]]] => 2 [[[]],[],[[[]]]] => 1 [[[]],[[]],[],[]] => 4 [[[]],[[]],[[]]] => 6 [[[]],[[],[]],[]] => 2 [[[]],[[[]]],[]] => 1 [[[]],[[],[],[]]] => 6 [[[]],[[],[[]]]] => 1 [[[]],[[[]],[]]] => 1 [[[]],[[[],[]]]] => 2 [[[]],[[[[]]]]] => 1 [[[],[]],[],[],[]] => 12 [[[[]]],[],[],[]] => 6 [[[],[]],[],[[]]] => 2 [[[[]]],[],[[]]] => 1 [[[],[]],[[]],[]] => 2 [[[[]]],[[]],[]] => 1 [[[],[]],[[],[]]] => 8 [[[],[]],[[[]]]] => 2 [[[[]]],[[],[]]] => 2 [[[[]]],[[[]]]] => 2 [[[],[],[]],[],[]] => 12 [[[],[[]]],[],[]] => 2 [[[[]],[]],[],[]] => 2 [[[[],[]]],[],[]] => 4 [[[[[]]]],[],[]] => 2 [[[],[],[]],[[]]] => 6 [[[],[[]]],[[]]] => 1 [[[[]],[]],[[]]] => 1 [[[[],[]]],[[]]] => 2 [[[[[]]]],[[]]] => 1 [[[],[],[],[]],[]] => 24 [[[],[],[[]]],[]] => 2 [[[],[[]],[]],[]] => 2 [[[],[[],[]]],[]] => 2 [[[],[[[]]]],[]] => 1 [[[[]],[],[]],[]] => 2 [[[[]],[[]]],[]] => 2 [[[[],[]],[]],[]] => 2 [[[[[]]],[]],[]] => 1 [[[[],[],[]]],[]] => 6 [[[[],[[]]]],[]] => 1 [[[[[]],[]]],[]] => 1 [[[[[],[]]]],[]] => 2 [[[[[[]]]]],[]] => 1 [[[],[],[],[],[]]] => 120 [[[],[],[],[[]]]] => 6 [[[],[],[[]],[]]] => 6 [[[],[],[[],[]]]] => 4 [[[],[],[[[]]]]] => 2 [[[],[[]],[],[]]] => 6 [[[],[[]],[[]]]] => 2 [[[],[[],[]],[]]] => 4 [[[],[[[]]],[]]] => 2 [[[],[[],[],[]]]] => 6 [[[],[[],[[]]]]] => 1 [[[],[[[]],[]]]] => 1 [[[],[[[],[]]]]] => 2 [[[],[[[[]]]]]] => 1 [[[[]],[],[],[]]] => 6 [[[[]],[],[[]]]] => 2 [[[[]],[[]],[]]] => 2 [[[[]],[[],[]]]] => 2 [[[[]],[[[]]]]] => 1 [[[[],[]],[],[]]] => 4 [[[[[]]],[],[]]] => 2 [[[[],[]],[[]]]] => 2 [[[[[]]],[[]]]] => 1 [[[[],[],[]],[]]] => 6 [[[[],[[]]],[]]] => 1 [[[[[]],[]],[]]] => 1 [[[[[],[]]],[]]] => 2 [[[[[[]]]],[]]] => 1 [[[[],[],[],[]]]] => 24 [[[[],[],[[]]]]] => 2 [[[[],[[]],[]]]] => 2 [[[[],[[],[]]]]] => 2 [[[[],[[[]]]]]] => 1 [[[[[]],[],[]]]] => 2 [[[[[]],[[]]]]] => 2 [[[[[],[]],[]]]] => 2 [[[[[[]]],[]]]] => 1 [[[[[],[],[]]]]] => 6 [[[[[],[[]]]]]] => 1 [[[[[[]],[]]]]] => 1 [[[[[[],[]]]]]] => 2 [[[[[[[]]]]]]] => 1 [[],[],[],[],[],[],[]] => 5040 [[],[],[],[],[],[[]]] => 120 [[],[],[],[],[[]],[]] => 120 [[],[],[],[],[[],[]]] => 48 [[],[],[],[],[[[]]]] => 24 [[],[],[],[[]],[],[]] => 120 [[],[],[],[[]],[[]]] => 12 [[],[],[],[[],[]],[]] => 48 [[],[],[],[[[]]],[]] => 24 [[],[],[],[[],[],[]]] => 36 [[],[],[],[[],[[]]]] => 6 [[],[],[],[[[]],[]]] => 6 [[],[],[],[[[],[]]]] => 12 [[],[],[],[[[[]]]]] => 6 [[],[],[[]],[],[],[]] => 120 [[],[],[[]],[],[[]]] => 12 [[],[],[[]],[[]],[]] => 12 [[],[],[[]],[[],[]]] => 4 [[],[],[[]],[[[]]]] => 2 [[],[],[[],[]],[],[]] => 48 [[],[],[[[]]],[],[]] => 24 [[],[],[[],[]],[[]]] => 4 [[],[],[[[]]],[[]]] => 2 [[],[],[[],[],[]],[]] => 36 [[],[],[[],[[]]],[]] => 6 [[],[],[[[]],[]],[]] => 6 [[],[],[[[],[]]],[]] => 12 [[],[],[[[[]]]],[]] => 6 [[],[],[[],[],[],[]]] => 48 [[],[],[[],[],[[]]]] => 4 [[],[],[[],[[]],[]]] => 4 [[],[],[[],[[],[]]]] => 4 [[],[],[[],[[[]]]]] => 2 [[],[],[[[]],[],[]]] => 4 [[],[],[[[]],[[]]]] => 4 [[],[],[[[],[]],[]]] => 4 [[],[],[[[[]]],[]]] => 2 [[],[],[[[],[],[]]]] => 12 [[],[],[[[],[[]]]]] => 2 [[],[],[[[[]],[]]]] => 2 [[],[],[[[[],[]]]]] => 4 [[],[],[[[[[]]]]]] => 2 [[],[[]],[],[],[],[]] => 120 [[],[[]],[],[],[[]]] => 12 [[],[[]],[],[[]],[]] => 12 [[],[[]],[],[[],[]]] => 4 [[],[[]],[],[[[]]]] => 2 [[],[[]],[[]],[],[]] => 12 [[],[[]],[[]],[[]]] => 6 [[],[[]],[[],[]],[]] => 4 [[],[[]],[[[]]],[]] => 2 [[],[[]],[[],[],[]]] => 6 [[],[[]],[[],[[]]]] => 1 [[],[[]],[[[]],[]]] => 1 [[],[[]],[[[],[]]]] => 2 [[],[[]],[[[[]]]]] => 1 [[],[[],[]],[],[],[]] => 48 [[],[[[]]],[],[],[]] => 24 [[],[[],[]],[],[[]]] => 4 [[],[[[]]],[],[[]]] => 2 [[],[[],[]],[[]],[]] => 4 [[],[[[]]],[[]],[]] => 2 [[],[[],[]],[[],[]]] => 8 [[],[[],[]],[[[]]]] => 2 [[],[[[]]],[[],[]]] => 2 [[],[[[]]],[[[]]]] => 2 [[],[[],[],[]],[],[]] => 36 [[],[[],[[]]],[],[]] => 6 [[],[[[]],[]],[],[]] => 6 [[],[[[],[]]],[],[]] => 12 [[],[[[[]]]],[],[]] => 6 [[],[[],[],[]],[[]]] => 6 [[],[[],[[]]],[[]]] => 1 [[],[[[]],[]],[[]]] => 1 [[],[[[],[]]],[[]]] => 2 [[],[[[[]]]],[[]]] => 1 [[],[[],[],[],[]],[]] => 48 [[],[[],[],[[]]],[]] => 4 [[],[[],[[]],[]],[]] => 4 [[],[[],[[],[]]],[]] => 4 [[],[[],[[[]]]],[]] => 2 [[],[[[]],[],[]],[]] => 4 [[],[[[]],[[]]],[]] => 4 [[],[[[],[]],[]],[]] => 4 [[],[[[[]]],[]],[]] => 2 [[],[[[],[],[]]],[]] => 12 [[],[[[],[[]]]],[]] => 2 [[],[[[[]],[]]],[]] => 2 [[],[[[[],[]]]],[]] => 4 [[],[[[[[]]]]],[]] => 2 [[],[[],[],[],[],[]]] => 120 [[],[[],[],[],[[]]]] => 6 [[],[[],[],[[]],[]]] => 6 [[],[[],[],[[],[]]]] => 4 [[],[[],[],[[[]]]]] => 2 [[],[[],[[]],[],[]]] => 6 [[],[[],[[]],[[]]]] => 2 [[],[[],[[],[]],[]]] => 4 [[],[[],[[[]]],[]]] => 2 [[],[[],[[],[],[]]]] => 6 [[],[[],[[],[[]]]]] => 1 [[],[[],[[[]],[]]]] => 1 [[],[[],[[[],[]]]]] => 2 [[],[[],[[[[]]]]]] => 1 [[],[[[]],[],[],[]]] => 6 [[],[[[]],[],[[]]]] => 2 [[],[[[]],[[]],[]]] => 2 [[],[[[]],[[],[]]]] => 2 [[],[[[]],[[[]]]]] => 1 [[],[[[],[]],[],[]]] => 4 [[],[[[[]]],[],[]]] => 2 [[],[[[],[]],[[]]]] => 2 [[],[[[[]]],[[]]]] => 1 [[],[[[],[],[]],[]]] => 6 [[],[[[],[[]]],[]]] => 1 [[],[[[[]],[]],[]]] => 1 [[],[[[[],[]]],[]]] => 2 [[],[[[[[]]]],[]]] => 1 [[],[[[],[],[],[]]]] => 24 [[],[[[],[],[[]]]]] => 2 [[],[[[],[[]],[]]]] => 2 [[],[[[],[[],[]]]]] => 2 [[],[[[],[[[]]]]]] => 1 [[],[[[[]],[],[]]]] => 2 [[],[[[[]],[[]]]]] => 2 [[],[[[[],[]],[]]]] => 2 [[],[[[[[]]],[]]]] => 1 [[],[[[[],[],[]]]]] => 6 [[],[[[[],[[]]]]]] => 1 [[],[[[[[]],[]]]]] => 1 [[],[[[[[],[]]]]]] => 2 [[],[[[[[[]]]]]]] => 1 [[[]],[],[],[],[],[]] => 120 [[[]],[],[],[],[[]]] => 12 [[[]],[],[],[[]],[]] => 12 [[[]],[],[],[[],[]]] => 4 [[[]],[],[],[[[]]]] => 2 [[[]],[],[[]],[],[]] => 12 [[[]],[],[[]],[[]]] => 6 [[[]],[],[[],[]],[]] => 4 [[[]],[],[[[]]],[]] => 2 [[[]],[],[[],[],[]]] => 6 [[[]],[],[[],[[]]]] => 1 [[[]],[],[[[]],[]]] => 1 [[[]],[],[[[],[]]]] => 2 [[[]],[],[[[[]]]]] => 1 [[[]],[[]],[],[],[]] => 12 [[[]],[[]],[],[[]]] => 6 [[[]],[[]],[[]],[]] => 6 [[[]],[[]],[[],[]]] => 4 [[[]],[[]],[[[]]]] => 2 [[[]],[[],[]],[],[]] => 4 [[[]],[[[]]],[],[]] => 2 [[[]],[[],[]],[[]]] => 4 [[[]],[[[]]],[[]]] => 2 [[[]],[[],[],[]],[]] => 6 [[[]],[[],[[]]],[]] => 1 [[[]],[[[]],[]],[]] => 1 [[[]],[[[],[]]],[]] => 2 [[[]],[[[[]]]],[]] => 1 [[[]],[[],[],[],[]]] => 24 [[[]],[[],[],[[]]]] => 2 [[[]],[[],[[]],[]]] => 2 [[[]],[[],[[],[]]]] => 2 [[[]],[[],[[[]]]]] => 1 [[[]],[[[]],[],[]]] => 2 [[[]],[[[]],[[]]]] => 2 [[[]],[[[],[]],[]]] => 2 [[[]],[[[[]]],[]]] => 1 [[[]],[[[],[],[]]]] => 6 [[[]],[[[],[[]]]]] => 1 [[[]],[[[[]],[]]]] => 1 [[[]],[[[[],[]]]]] => 2 [[[]],[[[[[]]]]]] => 1 [[[],[]],[],[],[],[]] => 48 [[[[]]],[],[],[],[]] => 24 [[[],[]],[],[],[[]]] => 4 [[[[]]],[],[],[[]]] => 2 [[[],[]],[],[[]],[]] => 4 [[[[]]],[],[[]],[]] => 2 [[[],[]],[],[[],[]]] => 8 [[[],[]],[],[[[]]]] => 2 [[[[]]],[],[[],[]]] => 2 [[[[]]],[],[[[]]]] => 2 [[[],[]],[[]],[],[]] => 4 [[[[]]],[[]],[],[]] => 2 [[[],[]],[[]],[[]]] => 4 [[[[]]],[[]],[[]]] => 2 [[[],[]],[[],[]],[]] => 8 [[[],[]],[[[]]],[]] => 2 [[[[]]],[[],[]],[]] => 2 [[[[]]],[[[]]],[]] => 2 [[[],[]],[[],[],[]]] => 12 [[[],[]],[[],[[]]]] => 2 [[[],[]],[[[]],[]]] => 2 [[[],[]],[[[],[]]]] => 4 [[[],[]],[[[[]]]]] => 2 [[[[]]],[[],[],[]]] => 6 [[[[]]],[[],[[]]]] => 1 [[[[]]],[[[]],[]]] => 1 [[[[]]],[[[],[]]]] => 2 [[[[]]],[[[[]]]]] => 1 [[[],[],[]],[],[],[]] => 36 [[[],[[]]],[],[],[]] => 6 [[[[]],[]],[],[],[]] => 6 [[[[],[]]],[],[],[]] => 12 [[[[[]]]],[],[],[]] => 6 [[[],[],[]],[],[[]]] => 6 [[[],[[]]],[],[[]]] => 1 [[[[]],[]],[],[[]]] => 1 [[[[],[]]],[],[[]]] => 2 [[[[[]]]],[],[[]]] => 1 [[[],[],[]],[[]],[]] => 6 [[[],[[]]],[[]],[]] => 1 [[[[]],[]],[[]],[]] => 1 [[[[],[]]],[[]],[]] => 2 [[[[[]]]],[[]],[]] => 1 [[[],[],[]],[[],[]]] => 12 [[[],[],[]],[[[]]]] => 6 [[[],[[]]],[[],[]]] => 2 [[[],[[]]],[[[]]]] => 1 [[[[]],[]],[[],[]]] => 2 [[[[]],[]],[[[]]]] => 1 [[[[],[]]],[[],[]]] => 4 [[[[],[]]],[[[]]]] => 2 [[[[[]]]],[[],[]]] => 2 [[[[[]]]],[[[]]]] => 1 [[[],[],[],[]],[],[]] => 48 [[[],[],[[]]],[],[]] => 4 [[[],[[]],[]],[],[]] => 4 [[[],[[],[]]],[],[]] => 4 [[[],[[[]]]],[],[]] => 2 [[[[]],[],[]],[],[]] => 4 [[[[]],[[]]],[],[]] => 4 [[[[],[]],[]],[],[]] => 4 [[[[[]]],[]],[],[]] => 2 [[[[],[],[]]],[],[]] => 12 [[[[],[[]]]],[],[]] => 2 [[[[[]],[]]],[],[]] => 2 [[[[[],[]]]],[],[]] => 4 [[[[[[]]]]],[],[]] => 2 [[[],[],[],[]],[[]]] => 24 [[[],[],[[]]],[[]]] => 2 [[[],[[]],[]],[[]]] => 2 [[[],[[],[]]],[[]]] => 2 [[[],[[[]]]],[[]]] => 1 [[[[]],[],[]],[[]]] => 2 [[[[]],[[]]],[[]]] => 2 [[[[],[]],[]],[[]]] => 2 [[[[[]]],[]],[[]]] => 1 [[[[],[],[]]],[[]]] => 6 [[[[],[[]]]],[[]]] => 1 [[[[[]],[]]],[[]]] => 1 [[[[[],[]]]],[[]]] => 2 [[[[[[]]]]],[[]]] => 1 [[[],[],[],[],[]],[]] => 120 [[[],[],[],[[]]],[]] => 6 [[[],[],[[]],[]],[]] => 6 [[[],[],[[],[]]],[]] => 4 [[[],[],[[[]]]],[]] => 2 [[[],[[]],[],[]],[]] => 6 [[[],[[]],[[]]],[]] => 2 [[[],[[],[]],[]],[]] => 4 [[[],[[[]]],[]],[]] => 2 [[[],[[],[],[]]],[]] => 6 [[[],[[],[[]]]],[]] => 1 [[[],[[[]],[]]],[]] => 1 [[[],[[[],[]]]],[]] => 2 [[[],[[[[]]]]],[]] => 1 [[[[]],[],[],[]],[]] => 6 [[[[]],[],[[]]],[]] => 2 [[[[]],[[]],[]],[]] => 2 [[[[]],[[],[]]],[]] => 2 [[[[]],[[[]]]],[]] => 1 [[[[],[]],[],[]],[]] => 4 [[[[[]]],[],[]],[]] => 2 [[[[],[]],[[]]],[]] => 2 [[[[[]]],[[]]],[]] => 1 [[[[],[],[]],[]],[]] => 6 [[[[],[[]]],[]],[]] => 1 [[[[[]],[]],[]],[]] => 1 [[[[[],[]]],[]],[]] => 2 [[[[[[]]]],[]],[]] => 1 [[[[],[],[],[]]],[]] => 24 [[[[],[],[[]]]],[]] => 2 [[[[],[[]],[]]],[]] => 2 [[[[],[[],[]]]],[]] => 2 [[[[],[[[]]]]],[]] => 1 [[[[[]],[],[]]],[]] => 2 [[[[[]],[[]]]],[]] => 2 [[[[[],[]],[]]],[]] => 2 [[[[[[]]],[]]],[]] => 1 [[[[[],[],[]]]],[]] => 6 [[[[[],[[]]]]],[]] => 1 [[[[[[]],[]]]],[]] => 1 [[[[[[],[]]]]],[]] => 2 [[[[[[[]]]]]],[]] => 1 [[[],[],[],[],[],[]]] => 720 [[[],[],[],[],[[]]]] => 24 [[[],[],[],[[]],[]]] => 24 [[[],[],[],[[],[]]]] => 12 [[[],[],[],[[[]]]]] => 6 [[[],[],[[]],[],[]]] => 24 [[[],[],[[]],[[]]]] => 4 [[[],[],[[],[]],[]]] => 12 [[[],[],[[[]]],[]]] => 6 [[[],[],[[],[],[]]]] => 12 [[[],[],[[],[[]]]]] => 2 [[[],[],[[[]],[]]]] => 2 [[[],[],[[[],[]]]]] => 4 [[[],[],[[[[]]]]]] => 2 [[[],[[]],[],[],[]]] => 24 [[[],[[]],[],[[]]]] => 4 [[[],[[]],[[]],[]]] => 4 [[[],[[]],[[],[]]]] => 2 [[[],[[]],[[[]]]]] => 1 [[[],[[],[]],[],[]]] => 12 [[[],[[[]]],[],[]]] => 6 [[[],[[],[]],[[]]]] => 2 [[[],[[[]]],[[]]]] => 1 [[[],[[],[],[]],[]]] => 12 [[[],[[],[[]]],[]]] => 2 [[[],[[[]],[]],[]]] => 2 [[[],[[[],[]]],[]]] => 4 [[[],[[[[]]]],[]]] => 2 [[[],[[],[],[],[]]]] => 24 [[[],[[],[],[[]]]]] => 2 [[[],[[],[[]],[]]]] => 2 [[[],[[],[[],[]]]]] => 2 [[[],[[],[[[]]]]]] => 1 [[[],[[[]],[],[]]]] => 2 [[[],[[[]],[[]]]]] => 2 [[[],[[[],[]],[]]]] => 2 [[[],[[[[]]],[]]]] => 1 [[[],[[[],[],[]]]]] => 6 [[[],[[[],[[]]]]]] => 1 [[[],[[[[]],[]]]]] => 1 [[[],[[[[],[]]]]]] => 2 [[[],[[[[[]]]]]]] => 1 [[[[]],[],[],[],[]]] => 24 [[[[]],[],[],[[]]]] => 4 [[[[]],[],[[]],[]]] => 4 [[[[]],[],[[],[]]]] => 2 [[[[]],[],[[[]]]]] => 1 [[[[]],[[]],[],[]]] => 4 [[[[]],[[]],[[]]]] => 6 [[[[]],[[],[]],[]]] => 2 [[[[]],[[[]]],[]]] => 1 [[[[]],[[],[],[]]]] => 6 [[[[]],[[],[[]]]]] => 1 [[[[]],[[[]],[]]]] => 1 [[[[]],[[[],[]]]]] => 2 [[[[]],[[[[]]]]]] => 1 [[[[],[]],[],[],[]]] => 12 [[[[[]]],[],[],[]]] => 6 [[[[],[]],[],[[]]]] => 2 [[[[[]]],[],[[]]]] => 1 [[[[],[]],[[]],[]]] => 2 [[[[[]]],[[]],[]]] => 1 [[[[],[]],[[],[]]]] => 8 [[[[],[]],[[[]]]]] => 2 [[[[[]]],[[],[]]]] => 2 [[[[[]]],[[[]]]]] => 2 [[[[],[],[]],[],[]]] => 12 [[[[],[[]]],[],[]]] => 2 [[[[[]],[]],[],[]]] => 2 [[[[[],[]]],[],[]]] => 4 [[[[[[]]]],[],[]]] => 2 [[[[],[],[]],[[]]]] => 6 [[[[],[[]]],[[]]]] => 1 [[[[[]],[]],[[]]]] => 1 [[[[[],[]]],[[]]]] => 2 [[[[[[]]]],[[]]]] => 1 [[[[],[],[],[]],[]]] => 24 [[[[],[],[[]]],[]]] => 2 [[[[],[[]],[]],[]]] => 2 [[[[],[[],[]]],[]]] => 2 [[[[],[[[]]]],[]]] => 1 [[[[[]],[],[]],[]]] => 2 [[[[[]],[[]]],[]]] => 2 [[[[[],[]],[]],[]]] => 2 [[[[[[]]],[]],[]]] => 1 [[[[[],[],[]]],[]]] => 6 [[[[[],[[]]]],[]]] => 1 [[[[[[]],[]]],[]]] => 1 [[[[[[],[]]]],[]]] => 2 [[[[[[[]]]]],[]]] => 1 [[[[],[],[],[],[]]]] => 120 [[[[],[],[],[[]]]]] => 6 [[[[],[],[[]],[]]]] => 6 [[[[],[],[[],[]]]]] => 4 [[[[],[],[[[]]]]]] => 2 [[[[],[[]],[],[]]]] => 6 [[[[],[[]],[[]]]]] => 2 [[[[],[[],[]],[]]]] => 4 [[[[],[[[]]],[]]]] => 2 [[[[],[[],[],[]]]]] => 6 [[[[],[[],[[]]]]]] => 1 [[[[],[[[]],[]]]]] => 1 [[[[],[[[],[]]]]]] => 2 [[[[],[[[[]]]]]]] => 1 [[[[[]],[],[],[]]]] => 6 [[[[[]],[],[[]]]]] => 2 [[[[[]],[[]],[]]]] => 2 [[[[[]],[[],[]]]]] => 2 [[[[[]],[[[]]]]]] => 1 [[[[[],[]],[],[]]]] => 4 [[[[[[]]],[],[]]]] => 2 [[[[[],[]],[[]]]]] => 2 [[[[[[]]],[[]]]]] => 1 [[[[[],[],[]],[]]]] => 6 [[[[[],[[]]],[]]]] => 1 [[[[[[]],[]],[]]]] => 1 [[[[[[],[]]],[]]]] => 2 [[[[[[[]]]],[]]]] => 1 [[[[[],[],[],[]]]]] => 24 [[[[[],[],[[]]]]]] => 2 [[[[[],[[]],[]]]]] => 2 [[[[[],[[],[]]]]]] => 2 [[[[[],[[[]]]]]]] => 1 [[[[[[]],[],[]]]]] => 2 [[[[[[]],[[]]]]]] => 2 [[[[[[],[]],[]]]]] => 2 [[[[[[[]]],[]]]]] => 1 [[[[[[],[],[]]]]]] => 6 [[[[[[],[[]]]]]]] => 1 [[[[[[[]],[]]]]]] => 1 [[[[[[[],[]]]]]]] => 2 [[[[[[[[]]]]]]]] => 1 [[],[],[],[],[],[],[],[]] => 40320 [[],[],[],[],[],[],[[]]] => 720 [[],[],[],[],[],[[]],[]] => 720 [[],[],[],[],[],[[],[]]] => 240 [[],[],[],[],[],[[[]]]] => 120 [[],[],[],[],[[]],[],[]] => 720 [[],[],[],[],[[]],[[]]] => 48 [[],[],[],[],[[],[]],[]] => 240 [[],[],[],[],[[[]]],[]] => 120 [[],[],[],[],[[],[],[]]] => 144 [[],[],[],[],[[],[[]]]] => 24 [[],[],[],[],[[[]],[]]] => 24 [[],[],[],[],[[[],[]]]] => 48 [[],[],[],[],[[[[]]]]] => 24 [[],[],[],[[]],[],[],[]] => 720 [[],[],[],[[]],[],[[]]] => 48 [[],[],[],[[]],[[]],[]] => 48 [[],[],[],[[]],[[],[]]] => 12 [[],[],[],[[]],[[[]]]] => 6 [[],[],[],[[],[]],[],[]] => 240 [[],[],[],[[[]]],[],[]] => 120 [[],[],[],[[],[]],[[]]] => 12 [[],[],[],[[[]]],[[]]] => 6 [[],[],[],[[],[],[]],[]] => 144 [[],[],[],[[],[[]]],[]] => 24 [[],[],[],[[[]],[]],[]] => 24 [[],[],[],[[[],[]]],[]] => 48 [[],[],[],[[[[]]]],[]] => 24 [[],[],[],[[],[],[],[]]] => 144 [[],[],[],[[],[],[[]]]] => 12 [[],[],[],[[],[[]],[]]] => 12 [[],[],[],[[],[[],[]]]] => 12 [[],[],[],[[],[[[]]]]] => 6 [[],[],[],[[[]],[],[]]] => 12 [[],[],[],[[[]],[[]]]] => 12 [[],[],[],[[[],[]],[]]] => 12 [[],[],[],[[[[]]],[]]] => 6 [[],[],[],[[[],[],[]]]] => 36 [[],[],[],[[[],[[]]]]] => 6 [[],[],[],[[[[]],[]]]] => 6 [[],[],[],[[[[],[]]]]] => 12 [[],[],[],[[[[[]]]]]] => 6 [[],[],[[]],[],[],[],[]] => 720 [[],[],[[]],[],[],[[]]] => 48 [[],[],[[]],[],[[]],[]] => 48 [[],[],[[]],[],[[],[]]] => 12 [[],[],[[]],[],[[[]]]] => 6 [[],[],[[]],[[]],[],[]] => 48 [[],[],[[]],[[]],[[]]] => 12 [[],[],[[]],[[],[]],[]] => 12 [[],[],[[]],[[[]]],[]] => 6 [[],[],[[]],[[],[],[]]] => 12 [[],[],[[]],[[],[[]]]] => 2 [[],[],[[]],[[[]],[]]] => 2 [[],[],[[]],[[[],[]]]] => 4 [[],[],[[]],[[[[]]]]] => 2 [[],[],[[],[]],[],[],[]] => 240 [[],[],[[[]]],[],[],[]] => 120 [[],[],[[],[]],[],[[]]] => 12 [[],[],[[[]]],[],[[]]] => 6 [[],[],[[],[]],[[]],[]] => 12 [[],[],[[[]]],[[]],[]] => 6 [[],[],[[],[]],[[],[]]] => 16 [[],[],[[],[]],[[[]]]] => 4 [[],[],[[[]]],[[],[]]] => 4 [[],[],[[[]]],[[[]]]] => 4 [[],[],[[],[],[]],[],[]] => 144 [[],[],[[],[[]]],[],[]] => 24 [[],[],[[[]],[]],[],[]] => 24 [[],[],[[[],[]]],[],[]] => 48 [[],[],[[[[]]]],[],[]] => 24 [[],[],[[],[],[]],[[]]] => 12 [[],[],[[],[[]]],[[]]] => 2 [[],[],[[[]],[]],[[]]] => 2 [[],[],[[[],[]]],[[]]] => 4 [[],[],[[[[]]]],[[]]] => 2 [[],[],[[],[],[],[]],[]] => 144 [[],[],[[],[],[[]]],[]] => 12 [[],[],[[],[[]],[]],[]] => 12 [[],[],[[],[[],[]]],[]] => 12 [[],[],[[],[[[]]]],[]] => 6 [[],[],[[[]],[],[]],[]] => 12 [[],[],[[[]],[[]]],[]] => 12 [[],[],[[[],[]],[]],[]] => 12 [[],[],[[[[]]],[]],[]] => 6 [[],[],[[[],[],[]]],[]] => 36 [[],[],[[[],[[]]]],[]] => 6 [[],[],[[[[]],[]]],[]] => 6 [[],[],[[[[],[]]]],[]] => 12 [[],[],[[[[[]]]]],[]] => 6 [[],[],[[],[],[],[],[]]] => 240 [[],[],[[],[],[],[[]]]] => 12 [[],[],[[],[],[[]],[]]] => 12 [[],[],[[],[],[[],[]]]] => 8 [[],[],[[],[],[[[]]]]] => 4 [[],[],[[],[[]],[],[]]] => 12 [[],[],[[],[[]],[[]]]] => 4 [[],[],[[],[[],[]],[]]] => 8 [[],[],[[],[[[]]],[]]] => 4 [[],[],[[],[[],[],[]]]] => 12 [[],[],[[],[[],[[]]]]] => 2 [[],[],[[],[[[]],[]]]] => 2 [[],[],[[],[[[],[]]]]] => 4 [[],[],[[],[[[[]]]]]] => 2 [[],[],[[[]],[],[],[]]] => 12 [[],[],[[[]],[],[[]]]] => 4 [[],[],[[[]],[[]],[]]] => 4 [[],[],[[[]],[[],[]]]] => 4 [[],[],[[[]],[[[]]]]] => 2 [[],[],[[[],[]],[],[]]] => 8 [[],[],[[[[]]],[],[]]] => 4 [[],[],[[[],[]],[[]]]] => 4 [[],[],[[[[]]],[[]]]] => 2 [[],[],[[[],[],[]],[]]] => 12 [[],[],[[[],[[]]],[]]] => 2 [[],[],[[[[]],[]],[]]] => 2 [[],[],[[[[],[]]],[]]] => 4 [[],[],[[[[[]]]],[]]] => 2 [[],[],[[[],[],[],[]]]] => 48 [[],[],[[[],[],[[]]]]] => 4 [[],[],[[[],[[]],[]]]] => 4 [[],[],[[[],[[],[]]]]] => 4 [[],[],[[[],[[[]]]]]] => 2 [[],[],[[[[]],[],[]]]] => 4 [[],[],[[[[]],[[]]]]] => 4 [[],[],[[[[],[]],[]]]] => 4 [[],[],[[[[[]]],[]]]] => 2 [[],[],[[[[],[],[]]]]] => 12 [[],[],[[[[],[[]]]]]] => 2 [[],[],[[[[[]],[]]]]] => 2 [[],[],[[[[[],[]]]]]] => 4 [[],[],[[[[[[]]]]]]] => 2 [[],[[]],[],[],[],[],[]] => 720 [[],[[]],[],[],[],[[]]] => 48 [[],[[]],[],[],[[]],[]] => 48 [[],[[]],[],[],[[],[]]] => 12 [[],[[]],[],[],[[[]]]] => 6 [[],[[]],[],[[]],[],[]] => 48 [[],[[]],[],[[]],[[]]] => 12 [[],[[]],[],[[],[]],[]] => 12 [[],[[]],[],[[[]]],[]] => 6 [[],[[]],[],[[],[],[]]] => 12 [[],[[]],[],[[],[[]]]] => 2 [[],[[]],[],[[[]],[]]] => 2 [[],[[]],[],[[[],[]]]] => 4 [[],[[]],[],[[[[]]]]] => 2 [[],[[]],[[]],[],[],[]] => 48 [[],[[]],[[]],[],[[]]] => 12 [[],[[]],[[]],[[]],[]] => 12 [[],[[]],[[]],[[],[]]] => 4 [[],[[]],[[]],[[[]]]] => 2 [[],[[]],[[],[]],[],[]] => 12 [[],[[]],[[[]]],[],[]] => 6 [[],[[]],[[],[]],[[]]] => 4 [[],[[]],[[[]]],[[]]] => 2 [[],[[]],[[],[],[]],[]] => 12 [[],[[]],[[],[[]]],[]] => 2 [[],[[]],[[[]],[]],[]] => 2 [[],[[]],[[[],[]]],[]] => 4 [[],[[]],[[[[]]]],[]] => 2 [[],[[]],[[],[],[],[]]] => 24 [[],[[]],[[],[],[[]]]] => 2 [[],[[]],[[],[[]],[]]] => 2 [[],[[]],[[],[[],[]]]] => 2 [[],[[]],[[],[[[]]]]] => 1 [[],[[]],[[[]],[],[]]] => 2 [[],[[]],[[[]],[[]]]] => 2 [[],[[]],[[[],[]],[]]] => 2 [[],[[]],[[[[]]],[]]] => 1 [[],[[]],[[[],[],[]]]] => 6 [[],[[]],[[[],[[]]]]] => 1 [[],[[]],[[[[]],[]]]] => 1 [[],[[]],[[[[],[]]]]] => 2 [[],[[]],[[[[[]]]]]] => 1 [[],[[],[]],[],[],[],[]] => 240 [[],[[[]]],[],[],[],[]] => 120 [[],[[],[]],[],[],[[]]] => 12 [[],[[[]]],[],[],[[]]] => 6 [[],[[],[]],[],[[]],[]] => 12 [[],[[[]]],[],[[]],[]] => 6 [[],[[],[]],[],[[],[]]] => 16 [[],[[],[]],[],[[[]]]] => 4 [[],[[[]]],[],[[],[]]] => 4 [[],[[[]]],[],[[[]]]] => 4 [[],[[],[]],[[]],[],[]] => 12 [[],[[[]]],[[]],[],[]] => 6 [[],[[],[]],[[]],[[]]] => 4 [[],[[[]]],[[]],[[]]] => 2 [[],[[],[]],[[],[]],[]] => 16 [[],[[],[]],[[[]]],[]] => 4 [[],[[[]]],[[],[]],[]] => 4 [[],[[[]]],[[[]]],[]] => 4 [[],[[],[]],[[],[],[]]] => 12 [[],[[],[]],[[],[[]]]] => 2 [[],[[],[]],[[[]],[]]] => 2 [[],[[],[]],[[[],[]]]] => 4 [[],[[],[]],[[[[]]]]] => 2 [[],[[[]]],[[],[],[]]] => 6 [[],[[[]]],[[],[[]]]] => 1 [[],[[[]]],[[[]],[]]] => 1 [[],[[[]]],[[[],[]]]] => 2 [[],[[[]]],[[[[]]]]] => 1 [[],[[],[],[]],[],[],[]] => 144 [[],[[],[[]]],[],[],[]] => 24 [[],[[[]],[]],[],[],[]] => 24 [[],[[[],[]]],[],[],[]] => 48 [[],[[[[]]]],[],[],[]] => 24 [[],[[],[],[]],[],[[]]] => 12 [[],[[],[[]]],[],[[]]] => 2 [[],[[[]],[]],[],[[]]] => 2 [[],[[[],[]]],[],[[]]] => 4 [[],[[[[]]]],[],[[]]] => 2 [[],[[],[],[]],[[]],[]] => 12 [[],[[],[[]]],[[]],[]] => 2 [[],[[[]],[]],[[]],[]] => 2 [[],[[[],[]]],[[]],[]] => 4 [[],[[[[]]]],[[]],[]] => 2 [[],[[],[],[]],[[],[]]] => 12 [[],[[],[],[]],[[[]]]] => 6 [[],[[],[[]]],[[],[]]] => 2 [[],[[],[[]]],[[[]]]] => 1 [[],[[[]],[]],[[],[]]] => 2 [[],[[[]],[]],[[[]]]] => 1 [[],[[[],[]]],[[],[]]] => 4 [[],[[[],[]]],[[[]]]] => 2 [[],[[[[]]]],[[],[]]] => 2 [[],[[[[]]]],[[[]]]] => 1 [[],[[],[],[],[]],[],[]] => 144 [[],[[],[],[[]]],[],[]] => 12 [[],[[],[[]],[]],[],[]] => 12 [[],[[],[[],[]]],[],[]] => 12 [[],[[],[[[]]]],[],[]] => 6 [[],[[[]],[],[]],[],[]] => 12 [[],[[[]],[[]]],[],[]] => 12 [[],[[[],[]],[]],[],[]] => 12 [[],[[[[]]],[]],[],[]] => 6 [[],[[[],[],[]]],[],[]] => 36 [[],[[[],[[]]]],[],[]] => 6 [[],[[[[]],[]]],[],[]] => 6 [[],[[[[],[]]]],[],[]] => 12 [[],[[[[[]]]]],[],[]] => 6 [[],[[],[],[],[]],[[]]] => 24 [[],[[],[],[[]]],[[]]] => 2 [[],[[],[[]],[]],[[]]] => 2 [[],[[],[[],[]]],[[]]] => 2 [[],[[],[[[]]]],[[]]] => 1 [[],[[[]],[],[]],[[]]] => 2 [[],[[[]],[[]]],[[]]] => 2 [[],[[[],[]],[]],[[]]] => 2 [[],[[[[]]],[]],[[]]] => 1 [[],[[[],[],[]]],[[]]] => 6 [[],[[[],[[]]]],[[]]] => 1 [[],[[[[]],[]]],[[]]] => 1 [[],[[[[],[]]]],[[]]] => 2 [[],[[[[[]]]]],[[]]] => 1 [[],[[],[],[],[],[]],[]] => 240 [[],[[],[],[],[[]]],[]] => 12 [[],[[],[],[[]],[]],[]] => 12 [[],[[],[],[[],[]]],[]] => 8 [[],[[],[],[[[]]]],[]] => 4 [[],[[],[[]],[],[]],[]] => 12 [[],[[],[[]],[[]]],[]] => 4 [[],[[],[[],[]],[]],[]] => 8 [[],[[],[[[]]],[]],[]] => 4 [[],[[],[[],[],[]]],[]] => 12 [[],[[],[[],[[]]]],[]] => 2 [[],[[],[[[]],[]]],[]] => 2 [[],[[],[[[],[]]]],[]] => 4 [[],[[],[[[[]]]]],[]] => 2 [[],[[[]],[],[],[]],[]] => 12 [[],[[[]],[],[[]]],[]] => 4 [[],[[[]],[[]],[]],[]] => 4 [[],[[[]],[[],[]]],[]] => 4 [[],[[[]],[[[]]]],[]] => 2 [[],[[[],[]],[],[]],[]] => 8 [[],[[[[]]],[],[]],[]] => 4 [[],[[[],[]],[[]]],[]] => 4 [[],[[[[]]],[[]]],[]] => 2 [[],[[[],[],[]],[]],[]] => 12 [[],[[[],[[]]],[]],[]] => 2 [[],[[[[]],[]],[]],[]] => 2 [[],[[[[],[]]],[]],[]] => 4 [[],[[[[[]]]],[]],[]] => 2 [[],[[[],[],[],[]]],[]] => 48 [[],[[[],[],[[]]]],[]] => 4 [[],[[[],[[]],[]]],[]] => 4 [[],[[[],[[],[]]]],[]] => 4 [[],[[[],[[[]]]]],[]] => 2 [[],[[[[]],[],[]]],[]] => 4 [[],[[[[]],[[]]]],[]] => 4 [[],[[[[],[]],[]]],[]] => 4 [[],[[[[[]]],[]]],[]] => 2 [[],[[[[],[],[]]]],[]] => 12 [[],[[[[],[[]]]]],[]] => 2 [[],[[[[[]],[]]]],[]] => 2 [[],[[[[[],[]]]]],[]] => 4 [[],[[[[[[]]]]]],[]] => 2 [[],[[],[],[],[],[],[]]] => 720 [[],[[],[],[],[],[[]]]] => 24 [[],[[],[],[],[[]],[]]] => 24 [[],[[],[],[],[[],[]]]] => 12 [[],[[],[],[],[[[]]]]] => 6 [[],[[],[],[[]],[],[]]] => 24 [[],[[],[],[[]],[[]]]] => 4 [[],[[],[],[[],[]],[]]] => 12 [[],[[],[],[[[]]],[]]] => 6 [[],[[],[],[[],[],[]]]] => 12 [[],[[],[],[[],[[]]]]] => 2 [[],[[],[],[[[]],[]]]] => 2 [[],[[],[],[[[],[]]]]] => 4 [[],[[],[],[[[[]]]]]] => 2 [[],[[],[[]],[],[],[]]] => 24 [[],[[],[[]],[],[[]]]] => 4 [[],[[],[[]],[[]],[]]] => 4 [[],[[],[[]],[[],[]]]] => 2 [[],[[],[[]],[[[]]]]] => 1 [[],[[],[[],[]],[],[]]] => 12 [[],[[],[[[]]],[],[]]] => 6 [[],[[],[[],[]],[[]]]] => 2 [[],[[],[[[]]],[[]]]] => 1 [[],[[],[[],[],[]],[]]] => 12 [[],[[],[[],[[]]],[]]] => 2 [[],[[],[[[]],[]],[]]] => 2 [[],[[],[[[],[]]],[]]] => 4 [[],[[],[[[[]]]],[]]] => 2 [[],[[],[[],[],[],[]]]] => 24 [[],[[],[[],[],[[]]]]] => 2 [[],[[],[[],[[]],[]]]] => 2 [[],[[],[[],[[],[]]]]] => 2 [[],[[],[[],[[[]]]]]] => 1 [[],[[],[[[]],[],[]]]] => 2 [[],[[],[[[]],[[]]]]] => 2 [[],[[],[[[],[]],[]]]] => 2 [[],[[],[[[[]]],[]]]] => 1 [[],[[],[[[],[],[]]]]] => 6 [[],[[],[[[],[[]]]]]] => 1 [[],[[],[[[[]],[]]]]] => 1 [[],[[],[[[[],[]]]]]] => 2 [[],[[],[[[[[]]]]]]] => 1 [[],[[[]],[],[],[],[]]] => 24 [[],[[[]],[],[],[[]]]] => 4 [[],[[[]],[],[[]],[]]] => 4 [[],[[[]],[],[[],[]]]] => 2 [[],[[[]],[],[[[]]]]] => 1 [[],[[[]],[[]],[],[]]] => 4 [[],[[[]],[[]],[[]]]] => 6 [[],[[[]],[[],[]],[]]] => 2 [[],[[[]],[[[]]],[]]] => 1 [[],[[[]],[[],[],[]]]] => 6 [[],[[[]],[[],[[]]]]] => 1 [[],[[[]],[[[]],[]]]] => 1 [[],[[[]],[[[],[]]]]] => 2 [[],[[[]],[[[[]]]]]] => 1 [[],[[[],[]],[],[],[]]] => 12 [[],[[[[]]],[],[],[]]] => 6 [[],[[[],[]],[],[[]]]] => 2 [[],[[[[]]],[],[[]]]] => 1 [[],[[[],[]],[[]],[]]] => 2 [[],[[[[]]],[[]],[]]] => 1 [[],[[[],[]],[[],[]]]] => 8 [[],[[[],[]],[[[]]]]] => 2 [[],[[[[]]],[[],[]]]] => 2 [[],[[[[]]],[[[]]]]] => 2 [[],[[[],[],[]],[],[]]] => 12 [[],[[[],[[]]],[],[]]] => 2 [[],[[[[]],[]],[],[]]] => 2 [[],[[[[],[]]],[],[]]] => 4 [[],[[[[[]]]],[],[]]] => 2 [[],[[[],[],[]],[[]]]] => 6 [[],[[[],[[]]],[[]]]] => 1 [[],[[[[]],[]],[[]]]] => 1 [[],[[[[],[]]],[[]]]] => 2 [[],[[[[[]]]],[[]]]] => 1 [[],[[[],[],[],[]],[]]] => 24 [[],[[[],[],[[]]],[]]] => 2 [[],[[[],[[]],[]],[]]] => 2 [[],[[[],[[],[]]],[]]] => 2 [[],[[[],[[[]]]],[]]] => 1 [[],[[[[]],[],[]],[]]] => 2 [[],[[[[]],[[]]],[]]] => 2 [[],[[[[],[]],[]],[]]] => 2 [[],[[[[[]]],[]],[]]] => 1 [[],[[[[],[],[]]],[]]] => 6 [[],[[[[],[[]]]],[]]] => 1 [[],[[[[[]],[]]],[]]] => 1 [[],[[[[[],[]]]],[]]] => 2 [[],[[[[[[]]]]],[]]] => 1 [[],[[[],[],[],[],[]]]] => 120 [[],[[[],[],[],[[]]]]] => 6 [[],[[[],[],[[]],[]]]] => 6 [[],[[[],[],[[],[]]]]] => 4 [[],[[[],[],[[[]]]]]] => 2 [[],[[[],[[]],[],[]]]] => 6 [[],[[[],[[]],[[]]]]] => 2 [[],[[[],[[],[]],[]]]] => 4 [[],[[[],[[[]]],[]]]] => 2 [[],[[[],[[],[],[]]]]] => 6 [[],[[[],[[],[[]]]]]] => 1 [[],[[[],[[[]],[]]]]] => 1 [[],[[[],[[[],[]]]]]] => 2 [[],[[[],[[[[]]]]]]] => 1 [[],[[[[]],[],[],[]]]] => 6 [[],[[[[]],[],[[]]]]] => 2 [[],[[[[]],[[]],[]]]] => 2 [[],[[[[]],[[],[]]]]] => 2 [[],[[[[]],[[[]]]]]] => 1 [[],[[[[],[]],[],[]]]] => 4 [[],[[[[[]]],[],[]]]] => 2 [[],[[[[],[]],[[]]]]] => 2 [[],[[[[[]]],[[]]]]] => 1 [[],[[[[],[],[]],[]]]] => 6 [[],[[[[],[[]]],[]]]] => 1 [[],[[[[[]],[]],[]]]] => 1 [[],[[[[[],[]]],[]]]] => 2 [[],[[[[[[]]]],[]]]] => 1 [[],[[[[],[],[],[]]]]] => 24 [[],[[[[],[],[[]]]]]] => 2 [[],[[[[],[[]],[]]]]] => 2 [[],[[[[],[[],[]]]]]] => 2 [[],[[[[],[[[]]]]]]] => 1 [[],[[[[[]],[],[]]]]] => 2 [[],[[[[[]],[[]]]]]] => 2 [[],[[[[[],[]],[]]]]] => 2 [[],[[[[[[]]],[]]]]] => 1 [[],[[[[[],[],[]]]]]] => 6 [[],[[[[[],[[]]]]]]] => 1 [[],[[[[[[]],[]]]]]] => 1 [[],[[[[[[],[]]]]]]] => 2 [[],[[[[[[[]]]]]]]] => 1 [[[]],[],[],[],[],[],[]] => 720 [[[]],[],[],[],[],[[]]] => 48 [[[]],[],[],[],[[]],[]] => 48 [[[]],[],[],[],[[],[]]] => 12 [[[]],[],[],[],[[[]]]] => 6 [[[]],[],[],[[]],[],[]] => 48 [[[]],[],[],[[]],[[]]] => 12 [[[]],[],[],[[],[]],[]] => 12 [[[]],[],[],[[[]]],[]] => 6 [[[]],[],[],[[],[],[]]] => 12 [[[]],[],[],[[],[[]]]] => 2 [[[]],[],[],[[[]],[]]] => 2 [[[]],[],[],[[[],[]]]] => 4 [[[]],[],[],[[[[]]]]] => 2 [[[]],[],[[]],[],[],[]] => 48 [[[]],[],[[]],[],[[]]] => 12 [[[]],[],[[]],[[]],[]] => 12 [[[]],[],[[]],[[],[]]] => 4 [[[]],[],[[]],[[[]]]] => 2 [[[]],[],[[],[]],[],[]] => 12 [[[]],[],[[[]]],[],[]] => 6 [[[]],[],[[],[]],[[]]] => 4 [[[]],[],[[[]]],[[]]] => 2 [[[]],[],[[],[],[]],[]] => 12 [[[]],[],[[],[[]]],[]] => 2 [[[]],[],[[[]],[]],[]] => 2 [[[]],[],[[[],[]]],[]] => 4 [[[]],[],[[[[]]]],[]] => 2 [[[]],[],[[],[],[],[]]] => 24 [[[]],[],[[],[],[[]]]] => 2 [[[]],[],[[],[[]],[]]] => 2 [[[]],[],[[],[[],[]]]] => 2 [[[]],[],[[],[[[]]]]] => 1 [[[]],[],[[[]],[],[]]] => 2 [[[]],[],[[[]],[[]]]] => 2 [[[]],[],[[[],[]],[]]] => 2 [[[]],[],[[[[]]],[]]] => 1 [[[]],[],[[[],[],[]]]] => 6 [[[]],[],[[[],[[]]]]] => 1 [[[]],[],[[[[]],[]]]] => 1 [[[]],[],[[[[],[]]]]] => 2 [[[]],[],[[[[[]]]]]] => 1 [[[]],[[]],[],[],[],[]] => 48 [[[]],[[]],[],[],[[]]] => 12 [[[]],[[]],[],[[]],[]] => 12 [[[]],[[]],[],[[],[]]] => 4 [[[]],[[]],[],[[[]]]] => 2 [[[]],[[]],[[]],[],[]] => 12 [[[]],[[]],[[]],[[]]] => 24 [[[]],[[]],[[],[]],[]] => 4 [[[]],[[]],[[[]]],[]] => 2 [[[]],[[]],[[],[],[]]] => 12 [[[]],[[]],[[],[[]]]] => 2 [[[]],[[]],[[[]],[]]] => 2 [[[]],[[]],[[[],[]]]] => 4 [[[]],[[]],[[[[]]]]] => 2 [[[]],[[],[]],[],[],[]] => 12 [[[]],[[[]]],[],[],[]] => 6 [[[]],[[],[]],[],[[]]] => 4 [[[]],[[[]]],[],[[]]] => 2 [[[]],[[],[]],[[]],[]] => 4 [[[]],[[[]]],[[]],[]] => 2 [[[]],[[],[]],[[],[]]] => 8 [[[]],[[],[]],[[[]]]] => 2 [[[]],[[[]]],[[],[]]] => 2 [[[]],[[[]]],[[[]]]] => 2 [[[]],[[],[],[]],[],[]] => 12 [[[]],[[],[[]]],[],[]] => 2 [[[]],[[[]],[]],[],[]] => 2 [[[]],[[[],[]]],[],[]] => 4 [[[]],[[[[]]]],[],[]] => 2 [[[]],[[],[],[]],[[]]] => 12 [[[]],[[],[[]]],[[]]] => 2 [[[]],[[[]],[]],[[]]] => 2 [[[]],[[[],[]]],[[]]] => 4 [[[]],[[[[]]]],[[]]] => 2 [[[]],[[],[],[],[]],[]] => 24 [[[]],[[],[],[[]]],[]] => 2 [[[]],[[],[[]],[]],[]] => 2 [[[]],[[],[[],[]]],[]] => 2 [[[]],[[],[[[]]]],[]] => 1 [[[]],[[[]],[],[]],[]] => 2 [[[]],[[[]],[[]]],[]] => 2 [[[]],[[[],[]],[]],[]] => 2 [[[]],[[[[]]],[]],[]] => 1 [[[]],[[[],[],[]]],[]] => 6 [[[]],[[[],[[]]]],[]] => 1 [[[]],[[[[]],[]]],[]] => 1 [[[]],[[[[],[]]]],[]] => 2 [[[]],[[[[[]]]]],[]] => 1 [[[]],[[],[],[],[],[]]] => 120 [[[]],[[],[],[],[[]]]] => 6 [[[]],[[],[],[[]],[]]] => 6 [[[]],[[],[],[[],[]]]] => 4 [[[]],[[],[],[[[]]]]] => 2 [[[]],[[],[[]],[],[]]] => 6 [[[]],[[],[[]],[[]]]] => 2 [[[]],[[],[[],[]],[]]] => 4 [[[]],[[],[[[]]],[]]] => 2 [[[]],[[],[[],[],[]]]] => 6 [[[]],[[],[[],[[]]]]] => 1 [[[]],[[],[[[]],[]]]] => 1 [[[]],[[],[[[],[]]]]] => 2 [[[]],[[],[[[[]]]]]] => 1 [[[]],[[[]],[],[],[]]] => 6 [[[]],[[[]],[],[[]]]] => 2 [[[]],[[[]],[[]],[]]] => 2 [[[]],[[[]],[[],[]]]] => 2 [[[]],[[[]],[[[]]]]] => 1 [[[]],[[[],[]],[],[]]] => 4 [[[]],[[[[]]],[],[]]] => 2 [[[]],[[[],[]],[[]]]] => 2 [[[]],[[[[]]],[[]]]] => 1 [[[]],[[[],[],[]],[]]] => 6 [[[]],[[[],[[]]],[]]] => 1 [[[]],[[[[]],[]],[]]] => 1 [[[]],[[[[],[]]],[]]] => 2 [[[]],[[[[[]]]],[]]] => 1 [[[]],[[[],[],[],[]]]] => 24 [[[]],[[[],[],[[]]]]] => 2 [[[]],[[[],[[]],[]]]] => 2 [[[]],[[[],[[],[]]]]] => 2 [[[]],[[[],[[[]]]]]] => 1 [[[]],[[[[]],[],[]]]] => 2 [[[]],[[[[]],[[]]]]] => 2 [[[]],[[[[],[]],[]]]] => 2 [[[]],[[[[[]]],[]]]] => 1 [[[]],[[[[],[],[]]]]] => 6 [[[]],[[[[],[[]]]]]] => 1 [[[]],[[[[[]],[]]]]] => 1 [[[]],[[[[[],[]]]]]] => 2 [[[]],[[[[[[]]]]]]] => 1 [[[],[]],[],[],[],[],[]] => 240 [[[[]]],[],[],[],[],[]] => 120 [[[],[]],[],[],[],[[]]] => 12 [[[[]]],[],[],[],[[]]] => 6 [[[],[]],[],[],[[]],[]] => 12 [[[[]]],[],[],[[]],[]] => 6 [[[],[]],[],[],[[],[]]] => 16 [[[],[]],[],[],[[[]]]] => 4 [[[[]]],[],[],[[],[]]] => 4 [[[[]]],[],[],[[[]]]] => 4 [[[],[]],[],[[]],[],[]] => 12 [[[[]]],[],[[]],[],[]] => 6 [[[],[]],[],[[]],[[]]] => 4 [[[[]]],[],[[]],[[]]] => 2 ----------------------------------------------------------------------------- Created: Feb 26, 2016 at 08:25 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 26, 2016 at 08:25 by Martin Rubey