***************************************************************************** * 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: St000416 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The number of inequivalent increasing trees of an ordered tree. The total number of increasing trees is [[St000085]]. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Butcher group]] ----------------------------------------------------------------------------- Code: def automorphism_group_ordered(T): children = [S for S in T] multiplicities = [(S, children.count(S)) for S in set(children)] return prod(automorphism_group_ordered(S)^m*factorial(m) for (S, m) in multiplicities) def statistic(B): return factorial(B.node_number())/automorphism_group_ordered(B)/B.tree_factorial() ----------------------------------------------------------------------------- Statistic values: [[]] => 1 [[],[]] => 1 [[[]]] => 1 [[],[],[]] => 1 [[],[[]]] => 3 [[[]],[]] => 3 [[[],[]]] => 1 [[[[]]]] => 1 [[],[],[],[]] => 1 [[],[],[[]]] => 6 [[],[[]],[]] => 6 [[],[[],[]]] => 4 [[],[[[]]]] => 4 [[[]],[],[]] => 6 [[[]],[[]]] => 3 [[[],[]],[]] => 4 [[[[]]],[]] => 4 [[[],[],[]]] => 1 [[[],[[]]]] => 3 [[[[]],[]]] => 3 [[[[],[]]]] => 1 [[[[[]]]]] => 1 [[],[],[],[],[]] => 1 [[],[],[],[[]]] => 10 [[],[],[[]],[]] => 10 [[],[],[[],[]]] => 10 [[],[],[[[]]]] => 10 [[],[[]],[],[]] => 10 [[],[[]],[[]]] => 15 [[],[[],[]],[]] => 10 [[],[[[]]],[]] => 10 [[],[[],[],[]]] => 5 [[],[[],[[]]]] => 15 [[],[[[]],[]]] => 15 [[],[[[],[]]]] => 5 [[],[[[[]]]]] => 5 [[[]],[],[],[]] => 10 [[[]],[],[[]]] => 15 [[[]],[[]],[]] => 15 [[[]],[[],[]]] => 10 [[[]],[[[]]]] => 10 [[[],[]],[],[]] => 10 [[[[]]],[],[]] => 10 [[[],[]],[[]]] => 10 [[[[]]],[[]]] => 10 [[[],[],[]],[]] => 5 [[[],[[]]],[]] => 15 [[[[]],[]],[]] => 15 [[[[],[]]],[]] => 5 [[[[[]]]],[]] => 5 [[[],[],[],[]]] => 1 [[[],[],[[]]]] => 6 [[[],[[]],[]]] => 6 [[[],[[],[]]]] => 4 [[[],[[[]]]]] => 4 [[[[]],[],[]]] => 6 [[[[]],[[]]]] => 3 [[[[],[]],[]]] => 4 [[[[[]]],[]]] => 4 [[[[],[],[]]]] => 1 [[[[],[[]]]]] => 3 [[[[[]],[]]]] => 3 [[[[[],[]]]]] => 1 [[[[[[]]]]]] => 1 [[],[],[],[],[],[]] => 1 [[],[],[],[],[[]]] => 15 [[],[],[],[[]],[]] => 15 [[],[],[],[[],[]]] => 20 [[],[],[],[[[]]]] => 20 [[],[],[[]],[],[]] => 15 [[],[],[[]],[[]]] => 45 [[],[],[[],[]],[]] => 20 [[],[],[[[]]],[]] => 20 [[],[],[[],[],[]]] => 15 [[],[],[[],[[]]]] => 45 [[],[],[[[]],[]]] => 45 [[],[],[[[],[]]]] => 15 [[],[],[[[[]]]]] => 15 [[],[[]],[],[],[]] => 15 [[],[[]],[],[[]]] => 45 [[],[[]],[[]],[]] => 45 [[],[[]],[[],[]]] => 60 [[],[[]],[[[]]]] => 60 [[],[[],[]],[],[]] => 20 [[],[[[]]],[],[]] => 20 [[],[[],[]],[[]]] => 60 [[],[[[]]],[[]]] => 60 [[],[[],[],[]],[]] => 15 [[],[[],[[]]],[]] => 45 [[],[[[]],[]],[]] => 45 [[],[[[],[]]],[]] => 15 [[],[[[[]]]],[]] => 15 [[],[[],[],[],[]]] => 6 [[],[[],[],[[]]]] => 36 [[],[[],[[]],[]]] => 36 [[],[[],[[],[]]]] => 24 [[],[[],[[[]]]]] => 24 [[],[[[]],[],[]]] => 36 [[],[[[]],[[]]]] => 18 [[],[[[],[]],[]]] => 24 [[],[[[[]]],[]]] => 24 [[],[[[],[],[]]]] => 6 [[],[[[],[[]]]]] => 18 [[],[[[[]],[]]]] => 18 [[],[[[[],[]]]]] => 6 [[],[[[[[]]]]]] => 6 [[[]],[],[],[],[]] => 15 [[[]],[],[],[[]]] => 45 [[[]],[],[[]],[]] => 45 [[[]],[],[[],[]]] => 60 [[[]],[],[[[]]]] => 60 [[[]],[[]],[],[]] => 45 [[[]],[[]],[[]]] => 15 [[[]],[[],[]],[]] => 60 [[[]],[[[]]],[]] => 60 [[[]],[[],[],[]]] => 15 [[[]],[[],[[]]]] => 45 [[[]],[[[]],[]]] => 45 [[[]],[[[],[]]]] => 15 [[[]],[[[[]]]]] => 15 [[[],[]],[],[],[]] => 20 [[[[]]],[],[],[]] => 20 [[[],[]],[],[[]]] => 60 [[[[]]],[],[[]]] => 60 [[[],[]],[[]],[]] => 60 [[[[]]],[[]],[]] => 60 [[[],[]],[[],[]]] => 10 [[[],[]],[[[]]]] => 20 [[[[]]],[[],[]]] => 20 [[[[]]],[[[]]]] => 10 [[[],[],[]],[],[]] => 15 [[[],[[]]],[],[]] => 45 [[[[]],[]],[],[]] => 45 [[[[],[]]],[],[]] => 15 [[[[[]]]],[],[]] => 15 [[[],[],[]],[[]]] => 15 [[[],[[]]],[[]]] => 45 [[[[]],[]],[[]]] => 45 [[[[],[]]],[[]]] => 15 [[[[[]]]],[[]]] => 15 [[[],[],[],[]],[]] => 6 [[[],[],[[]]],[]] => 36 [[[],[[]],[]],[]] => 36 [[[],[[],[]]],[]] => 24 [[[],[[[]]]],[]] => 24 [[[[]],[],[]],[]] => 36 [[[[]],[[]]],[]] => 18 [[[[],[]],[]],[]] => 24 [[[[[]]],[]],[]] => 24 [[[[],[],[]]],[]] => 6 [[[[],[[]]]],[]] => 18 [[[[[]],[]]],[]] => 18 [[[[[],[]]]],[]] => 6 [[[[[[]]]]],[]] => 6 [[[],[],[],[],[]]] => 1 [[[],[],[],[[]]]] => 10 [[[],[],[[]],[]]] => 10 [[[],[],[[],[]]]] => 10 [[[],[],[[[]]]]] => 10 [[[],[[]],[],[]]] => 10 [[[],[[]],[[]]]] => 15 [[[],[[],[]],[]]] => 10 [[[],[[[]]],[]]] => 10 [[[],[[],[],[]]]] => 5 [[[],[[],[[]]]]] => 15 [[[],[[[]],[]]]] => 15 [[[],[[[],[]]]]] => 5 [[[],[[[[]]]]]] => 5 [[[[]],[],[],[]]] => 10 [[[[]],[],[[]]]] => 15 [[[[]],[[]],[]]] => 15 [[[[]],[[],[]]]] => 10 [[[[]],[[[]]]]] => 10 [[[[],[]],[],[]]] => 10 [[[[[]]],[],[]]] => 10 [[[[],[]],[[]]]] => 10 [[[[[]]],[[]]]] => 10 [[[[],[],[]],[]]] => 5 [[[[],[[]]],[]]] => 15 [[[[[]],[]],[]]] => 15 [[[[[],[]]],[]]] => 5 [[[[[[]]]],[]]] => 5 [[[[],[],[],[]]]] => 1 [[[[],[],[[]]]]] => 6 [[[[],[[]],[]]]] => 6 [[[[],[[],[]]]]] => 4 [[[[],[[[]]]]]] => 4 [[[[[]],[],[]]]] => 6 [[[[[]],[[]]]]] => 3 [[[[[],[]],[]]]] => 4 [[[[[[]]],[]]]] => 4 [[[[[],[],[]]]]] => 1 [[[[[],[[]]]]]] => 3 [[[[[[]],[]]]]] => 3 [[[[[[],[]]]]]] => 1 [[[[[[[]]]]]]] => 1 [[],[],[],[],[],[],[]] => 1 [[],[],[],[],[],[[]]] => 21 [[],[],[],[],[[]],[]] => 21 [[],[],[],[],[[],[]]] => 35 [[],[],[],[],[[[]]]] => 35 [[],[],[],[[]],[],[]] => 21 [[],[],[],[[]],[[]]] => 105 [[],[],[],[[],[]],[]] => 35 [[],[],[],[[[]]],[]] => 35 [[],[],[],[[],[],[]]] => 35 [[],[],[],[[],[[]]]] => 105 [[],[],[],[[[]],[]]] => 105 [[],[],[],[[[],[]]]] => 35 [[],[],[],[[[[]]]]] => 35 [[],[],[[]],[],[],[]] => 21 [[],[],[[]],[],[[]]] => 105 [[],[],[[]],[[]],[]] => 105 [[],[],[[]],[[],[]]] => 210 [[],[],[[]],[[[]]]] => 210 [[],[],[[],[]],[],[]] => 35 [[],[],[[[]]],[],[]] => 35 [[],[],[[],[]],[[]]] => 210 [[],[],[[[]]],[[]]] => 210 [[],[],[[],[],[]],[]] => 35 [[],[],[[],[[]]],[]] => 105 [[],[],[[[]],[]],[]] => 105 [[],[],[[[],[]]],[]] => 35 [[],[],[[[[]]]],[]] => 35 [[],[],[[],[],[],[]]] => 21 [[],[],[[],[],[[]]]] => 126 [[],[],[[],[[]],[]]] => 126 [[],[],[[],[[],[]]]] => 84 [[],[],[[],[[[]]]]] => 84 [[],[],[[[]],[],[]]] => 126 [[],[],[[[]],[[]]]] => 63 [[],[],[[[],[]],[]]] => 84 [[],[],[[[[]]],[]]] => 84 [[],[],[[[],[],[]]]] => 21 [[],[],[[[],[[]]]]] => 63 [[],[],[[[[]],[]]]] => 63 [[],[],[[[[],[]]]]] => 21 [[],[],[[[[[]]]]]] => 21 [[],[[]],[],[],[],[]] => 21 [[],[[]],[],[],[[]]] => 105 [[],[[]],[],[[]],[]] => 105 [[],[[]],[],[[],[]]] => 210 [[],[[]],[],[[[]]]] => 210 [[],[[]],[[]],[],[]] => 105 [[],[[]],[[]],[[]]] => 105 [[],[[]],[[],[]],[]] => 210 [[],[[]],[[[]]],[]] => 210 [[],[[]],[[],[],[]]] => 105 [[],[[]],[[],[[]]]] => 315 [[],[[]],[[[]],[]]] => 315 [[],[[]],[[[],[]]]] => 105 [[],[[]],[[[[]]]]] => 105 [[],[[],[]],[],[],[]] => 35 [[],[[[]]],[],[],[]] => 35 [[],[[],[]],[],[[]]] => 210 [[],[[[]]],[],[[]]] => 210 [[],[[],[]],[[]],[]] => 210 [[],[[[]]],[[]],[]] => 210 [[],[[],[]],[[],[]]] => 70 [[],[[],[]],[[[]]]] => 140 [[],[[[]]],[[],[]]] => 140 [[],[[[]]],[[[]]]] => 70 [[],[[],[],[]],[],[]] => 35 [[],[[],[[]]],[],[]] => 105 [[],[[[]],[]],[],[]] => 105 [[],[[[],[]]],[],[]] => 35 [[],[[[[]]]],[],[]] => 35 [[],[[],[],[]],[[]]] => 105 [[],[[],[[]]],[[]]] => 315 [[],[[[]],[]],[[]]] => 315 [[],[[[],[]]],[[]]] => 105 [[],[[[[]]]],[[]]] => 105 [[],[[],[],[],[]],[]] => 21 [[],[[],[],[[]]],[]] => 126 [[],[[],[[]],[]],[]] => 126 [[],[[],[[],[]]],[]] => 84 [[],[[],[[[]]]],[]] => 84 [[],[[[]],[],[]],[]] => 126 [[],[[[]],[[]]],[]] => 63 [[],[[[],[]],[]],[]] => 84 [[],[[[[]]],[]],[]] => 84 [[],[[[],[],[]]],[]] => 21 [[],[[[],[[]]]],[]] => 63 [[],[[[[]],[]]],[]] => 63 [[],[[[[],[]]]],[]] => 21 [[],[[[[[]]]]],[]] => 21 [[],[[],[],[],[],[]]] => 7 [[],[[],[],[],[[]]]] => 70 [[],[[],[],[[]],[]]] => 70 [[],[[],[],[[],[]]]] => 70 [[],[[],[],[[[]]]]] => 70 [[],[[],[[]],[],[]]] => 70 [[],[[],[[]],[[]]]] => 105 [[],[[],[[],[]],[]]] => 70 [[],[[],[[[]]],[]]] => 70 [[],[[],[[],[],[]]]] => 35 [[],[[],[[],[[]]]]] => 105 [[],[[],[[[]],[]]]] => 105 [[],[[],[[[],[]]]]] => 35 [[],[[],[[[[]]]]]] => 35 [[],[[[]],[],[],[]]] => 70 [[],[[[]],[],[[]]]] => 105 [[],[[[]],[[]],[]]] => 105 [[],[[[]],[[],[]]]] => 70 [[],[[[]],[[[]]]]] => 70 [[],[[[],[]],[],[]]] => 70 [[],[[[[]]],[],[]]] => 70 [[],[[[],[]],[[]]]] => 70 [[],[[[[]]],[[]]]] => 70 [[],[[[],[],[]],[]]] => 35 [[],[[[],[[]]],[]]] => 105 [[],[[[[]],[]],[]]] => 105 [[],[[[[],[]]],[]]] => 35 [[],[[[[[]]]],[]]] => 35 [[],[[[],[],[],[]]]] => 7 [[],[[[],[],[[]]]]] => 42 [[],[[[],[[]],[]]]] => 42 [[],[[[],[[],[]]]]] => 28 [[],[[[],[[[]]]]]] => 28 [[],[[[[]],[],[]]]] => 42 [[],[[[[]],[[]]]]] => 21 [[],[[[[],[]],[]]]] => 28 [[],[[[[[]]],[]]]] => 28 [[],[[[[],[],[]]]]] => 7 [[],[[[[],[[]]]]]] => 21 [[],[[[[[]],[]]]]] => 21 [[],[[[[[],[]]]]]] => 7 [[],[[[[[[]]]]]]] => 7 [[[]],[],[],[],[],[]] => 21 [[[]],[],[],[],[[]]] => 105 [[[]],[],[],[[]],[]] => 105 [[[]],[],[],[[],[]]] => 210 [[[]],[],[],[[[]]]] => 210 [[[]],[],[[]],[],[]] => 105 [[[]],[],[[]],[[]]] => 105 [[[]],[],[[],[]],[]] => 210 [[[]],[],[[[]]],[]] => 210 [[[]],[],[[],[],[]]] => 105 [[[]],[],[[],[[]]]] => 315 [[[]],[],[[[]],[]]] => 315 [[[]],[],[[[],[]]]] => 105 [[[]],[],[[[[]]]]] => 105 [[[]],[[]],[],[],[]] => 105 [[[]],[[]],[],[[]]] => 105 [[[]],[[]],[[]],[]] => 105 [[[]],[[]],[[],[]]] => 105 [[[]],[[]],[[[]]]] => 105 [[[]],[[],[]],[],[]] => 210 [[[]],[[[]]],[],[]] => 210 [[[]],[[],[]],[[]]] => 105 [[[]],[[[]]],[[]]] => 105 [[[]],[[],[],[]],[]] => 105 [[[]],[[],[[]]],[]] => 315 [[[]],[[[]],[]],[]] => 315 [[[]],[[[],[]]],[]] => 105 [[[]],[[[[]]]],[]] => 105 [[[]],[[],[],[],[]]] => 21 [[[]],[[],[],[[]]]] => 126 [[[]],[[],[[]],[]]] => 126 [[[]],[[],[[],[]]]] => 84 [[[]],[[],[[[]]]]] => 84 [[[]],[[[]],[],[]]] => 126 [[[]],[[[]],[[]]]] => 63 [[[]],[[[],[]],[]]] => 84 [[[]],[[[[]]],[]]] => 84 [[[]],[[[],[],[]]]] => 21 [[[]],[[[],[[]]]]] => 63 [[[]],[[[[]],[]]]] => 63 [[[]],[[[[],[]]]]] => 21 [[[]],[[[[[]]]]]] => 21 [[[],[]],[],[],[],[]] => 35 [[[[]]],[],[],[],[]] => 35 [[[],[]],[],[],[[]]] => 210 [[[[]]],[],[],[[]]] => 210 [[[],[]],[],[[]],[]] => 210 [[[[]]],[],[[]],[]] => 210 [[[],[]],[],[[],[]]] => 70 [[[],[]],[],[[[]]]] => 140 [[[[]]],[],[[],[]]] => 140 [[[[]]],[],[[[]]]] => 70 [[[],[]],[[]],[],[]] => 210 [[[[]]],[[]],[],[]] => 210 [[[],[]],[[]],[[]]] => 105 [[[[]]],[[]],[[]]] => 105 [[[],[]],[[],[]],[]] => 70 [[[],[]],[[[]]],[]] => 140 [[[[]]],[[],[]],[]] => 140 [[[[]]],[[[]]],[]] => 70 [[[],[]],[[],[],[]]] => 35 [[[],[]],[[],[[]]]] => 105 [[[],[]],[[[]],[]]] => 105 [[[],[]],[[[],[]]]] => 35 [[[],[]],[[[[]]]]] => 35 [[[[]]],[[],[],[]]] => 35 [[[[]]],[[],[[]]]] => 105 [[[[]]],[[[]],[]]] => 105 [[[[]]],[[[],[]]]] => 35 [[[[]]],[[[[]]]]] => 35 [[[],[],[]],[],[],[]] => 35 [[[],[[]]],[],[],[]] => 105 [[[[]],[]],[],[],[]] => 105 [[[[],[]]],[],[],[]] => 35 [[[[[]]]],[],[],[]] => 35 [[[],[],[]],[],[[]]] => 105 [[[],[[]]],[],[[]]] => 315 [[[[]],[]],[],[[]]] => 315 [[[[],[]]],[],[[]]] => 105 [[[[[]]]],[],[[]]] => 105 [[[],[],[]],[[]],[]] => 105 [[[],[[]]],[[]],[]] => 315 [[[[]],[]],[[]],[]] => 315 [[[[],[]]],[[]],[]] => 105 [[[[[]]]],[[]],[]] => 105 [[[],[],[]],[[],[]]] => 35 [[[],[],[]],[[[]]]] => 35 [[[],[[]]],[[],[]]] => 105 [[[],[[]]],[[[]]]] => 105 [[[[]],[]],[[],[]]] => 105 [[[[]],[]],[[[]]]] => 105 [[[[],[]]],[[],[]]] => 35 [[[[],[]]],[[[]]]] => 35 [[[[[]]]],[[],[]]] => 35 [[[[[]]]],[[[]]]] => 35 [[[],[],[],[]],[],[]] => 21 [[[],[],[[]]],[],[]] => 126 [[[],[[]],[]],[],[]] => 126 [[[],[[],[]]],[],[]] => 84 [[[],[[[]]]],[],[]] => 84 [[[[]],[],[]],[],[]] => 126 [[[[]],[[]]],[],[]] => 63 [[[[],[]],[]],[],[]] => 84 [[[[[]]],[]],[],[]] => 84 [[[[],[],[]]],[],[]] => 21 [[[[],[[]]]],[],[]] => 63 [[[[[]],[]]],[],[]] => 63 [[[[[],[]]]],[],[]] => 21 [[[[[[]]]]],[],[]] => 21 [[[],[],[],[]],[[]]] => 21 [[[],[],[[]]],[[]]] => 126 [[[],[[]],[]],[[]]] => 126 [[[],[[],[]]],[[]]] => 84 [[[],[[[]]]],[[]]] => 84 [[[[]],[],[]],[[]]] => 126 [[[[]],[[]]],[[]]] => 63 [[[[],[]],[]],[[]]] => 84 [[[[[]]],[]],[[]]] => 84 [[[[],[],[]]],[[]]] => 21 [[[[],[[]]]],[[]]] => 63 [[[[[]],[]]],[[]]] => 63 [[[[[],[]]]],[[]]] => 21 [[[[[[]]]]],[[]]] => 21 [[[],[],[],[],[]],[]] => 7 [[[],[],[],[[]]],[]] => 70 [[[],[],[[]],[]],[]] => 70 [[[],[],[[],[]]],[]] => 70 [[[],[],[[[]]]],[]] => 70 [[[],[[]],[],[]],[]] => 70 [[[],[[]],[[]]],[]] => 105 [[[],[[],[]],[]],[]] => 70 [[[],[[[]]],[]],[]] => 70 [[[],[[],[],[]]],[]] => 35 [[[],[[],[[]]]],[]] => 105 [[[],[[[]],[]]],[]] => 105 [[[],[[[],[]]]],[]] => 35 [[[],[[[[]]]]],[]] => 35 [[[[]],[],[],[]],[]] => 70 [[[[]],[],[[]]],[]] => 105 [[[[]],[[]],[]],[]] => 105 [[[[]],[[],[]]],[]] => 70 [[[[]],[[[]]]],[]] => 70 [[[[],[]],[],[]],[]] => 70 [[[[[]]],[],[]],[]] => 70 [[[[],[]],[[]]],[]] => 70 [[[[[]]],[[]]],[]] => 70 [[[[],[],[]],[]],[]] => 35 [[[[],[[]]],[]],[]] => 105 [[[[[]],[]],[]],[]] => 105 [[[[[],[]]],[]],[]] => 35 [[[[[[]]]],[]],[]] => 35 [[[[],[],[],[]]],[]] => 7 [[[[],[],[[]]]],[]] => 42 [[[[],[[]],[]]],[]] => 42 [[[[],[[],[]]]],[]] => 28 [[[[],[[[]]]]],[]] => 28 [[[[[]],[],[]]],[]] => 42 [[[[[]],[[]]]],[]] => 21 [[[[[],[]],[]]],[]] => 28 [[[[[[]]],[]]],[]] => 28 [[[[[],[],[]]]],[]] => 7 [[[[[],[[]]]]],[]] => 21 [[[[[[]],[]]]],[]] => 21 [[[[[[],[]]]]],[]] => 7 [[[[[[[]]]]]],[]] => 7 [[[],[],[],[],[],[]]] => 1 [[[],[],[],[],[[]]]] => 15 [[[],[],[],[[]],[]]] => 15 [[[],[],[],[[],[]]]] => 20 [[[],[],[],[[[]]]]] => 20 [[[],[],[[]],[],[]]] => 15 [[[],[],[[]],[[]]]] => 45 [[[],[],[[],[]],[]]] => 20 [[[],[],[[[]]],[]]] => 20 [[[],[],[[],[],[]]]] => 15 [[[],[],[[],[[]]]]] => 45 [[[],[],[[[]],[]]]] => 45 [[[],[],[[[],[]]]]] => 15 [[[],[],[[[[]]]]]] => 15 [[[],[[]],[],[],[]]] => 15 [[[],[[]],[],[[]]]] => 45 [[[],[[]],[[]],[]]] => 45 [[[],[[]],[[],[]]]] => 60 [[[],[[]],[[[]]]]] => 60 [[[],[[],[]],[],[]]] => 20 [[[],[[[]]],[],[]]] => 20 [[[],[[],[]],[[]]]] => 60 [[[],[[[]]],[[]]]] => 60 [[[],[[],[],[]],[]]] => 15 [[[],[[],[[]]],[]]] => 45 [[[],[[[]],[]],[]]] => 45 [[[],[[[],[]]],[]]] => 15 [[[],[[[[]]]],[]]] => 15 [[[],[[],[],[],[]]]] => 6 [[[],[[],[],[[]]]]] => 36 [[[],[[],[[]],[]]]] => 36 [[[],[[],[[],[]]]]] => 24 [[[],[[],[[[]]]]]] => 24 [[[],[[[]],[],[]]]] => 36 [[[],[[[]],[[]]]]] => 18 [[[],[[[],[]],[]]]] => 24 [[[],[[[[]]],[]]]] => 24 [[[],[[[],[],[]]]]] => 6 [[[],[[[],[[]]]]]] => 18 [[[],[[[[]],[]]]]] => 18 [[[],[[[[],[]]]]]] => 6 [[[],[[[[[]]]]]]] => 6 [[[[]],[],[],[],[]]] => 15 [[[[]],[],[],[[]]]] => 45 [[[[]],[],[[]],[]]] => 45 [[[[]],[],[[],[]]]] => 60 [[[[]],[],[[[]]]]] => 60 [[[[]],[[]],[],[]]] => 45 [[[[]],[[]],[[]]]] => 15 [[[[]],[[],[]],[]]] => 60 [[[[]],[[[]]],[]]] => 60 [[[[]],[[],[],[]]]] => 15 [[[[]],[[],[[]]]]] => 45 [[[[]],[[[]],[]]]] => 45 [[[[]],[[[],[]]]]] => 15 [[[[]],[[[[]]]]]] => 15 [[[[],[]],[],[],[]]] => 20 [[[[[]]],[],[],[]]] => 20 [[[[],[]],[],[[]]]] => 60 [[[[[]]],[],[[]]]] => 60 [[[[],[]],[[]],[]]] => 60 [[[[[]]],[[]],[]]] => 60 [[[[],[]],[[],[]]]] => 10 [[[[],[]],[[[]]]]] => 20 [[[[[]]],[[],[]]]] => 20 [[[[[]]],[[[]]]]] => 10 [[[[],[],[]],[],[]]] => 15 [[[[],[[]]],[],[]]] => 45 [[[[[]],[]],[],[]]] => 45 [[[[[],[]]],[],[]]] => 15 [[[[[[]]]],[],[]]] => 15 [[[[],[],[]],[[]]]] => 15 [[[[],[[]]],[[]]]] => 45 [[[[[]],[]],[[]]]] => 45 [[[[[],[]]],[[]]]] => 15 [[[[[[]]]],[[]]]] => 15 [[[[],[],[],[]],[]]] => 6 [[[[],[],[[]]],[]]] => 36 [[[[],[[]],[]],[]]] => 36 [[[[],[[],[]]],[]]] => 24 [[[[],[[[]]]],[]]] => 24 [[[[[]],[],[]],[]]] => 36 [[[[[]],[[]]],[]]] => 18 [[[[[],[]],[]],[]]] => 24 [[[[[[]]],[]],[]]] => 24 [[[[[],[],[]]],[]]] => 6 [[[[[],[[]]]],[]]] => 18 [[[[[[]],[]]],[]]] => 18 [[[[[[],[]]]],[]]] => 6 [[[[[[[]]]]],[]]] => 6 [[[[],[],[],[],[]]]] => 1 [[[[],[],[],[[]]]]] => 10 [[[[],[],[[]],[]]]] => 10 [[[[],[],[[],[]]]]] => 10 [[[[],[],[[[]]]]]] => 10 [[[[],[[]],[],[]]]] => 10 [[[[],[[]],[[]]]]] => 15 [[[[],[[],[]],[]]]] => 10 [[[[],[[[]]],[]]]] => 10 [[[[],[[],[],[]]]]] => 5 [[[[],[[],[[]]]]]] => 15 [[[[],[[[]],[]]]]] => 15 [[[[],[[[],[]]]]]] => 5 [[[[],[[[[]]]]]]] => 5 [[[[[]],[],[],[]]]] => 10 [[[[[]],[],[[]]]]] => 15 [[[[[]],[[]],[]]]] => 15 [[[[[]],[[],[]]]]] => 10 [[[[[]],[[[]]]]]] => 10 [[[[[],[]],[],[]]]] => 10 [[[[[[]]],[],[]]]] => 10 [[[[[],[]],[[]]]]] => 10 [[[[[[]]],[[]]]]] => 10 [[[[[],[],[]],[]]]] => 5 [[[[[],[[]]],[]]]] => 15 [[[[[[]],[]],[]]]] => 15 [[[[[[],[]]],[]]]] => 5 [[[[[[[]]]],[]]]] => 5 [[[[[],[],[],[]]]]] => 1 [[[[[],[],[[]]]]]] => 6 [[[[[],[[]],[]]]]] => 6 [[[[[],[[],[]]]]]] => 4 [[[[[],[[[]]]]]]] => 4 [[[[[[]],[],[]]]]] => 6 [[[[[[]],[[]]]]]] => 3 [[[[[[],[]],[]]]]] => 4 [[[[[[[]]],[]]]]] => 4 [[[[[[],[],[]]]]]] => 1 [[[[[[],[[]]]]]]] => 3 [[[[[[[]],[]]]]]] => 3 [[[[[[[],[]]]]]]] => 1 [[[[[[[[]]]]]]]] => 1 [[],[],[],[],[],[],[],[]] => 1 [[],[],[],[],[],[],[[]]] => 28 [[],[],[],[],[],[[]],[]] => 28 [[],[],[],[],[],[[],[]]] => 56 [[],[],[],[],[],[[[]]]] => 56 [[],[],[],[],[[]],[],[]] => 28 [[],[],[],[],[[]],[[]]] => 210 [[],[],[],[],[[],[]],[]] => 56 [[],[],[],[],[[[]]],[]] => 56 [[],[],[],[],[[],[],[]]] => 70 [[],[],[],[],[[],[[]]]] => 210 [[],[],[],[],[[[]],[]]] => 210 [[],[],[],[],[[[],[]]]] => 70 [[],[],[],[],[[[[]]]]] => 70 [[],[],[],[[]],[],[],[]] => 28 [[],[],[],[[]],[],[[]]] => 210 [[],[],[],[[]],[[]],[]] => 210 [[],[],[],[[]],[[],[]]] => 560 [[],[],[],[[]],[[[]]]] => 560 [[],[],[],[[],[]],[],[]] => 56 [[],[],[],[[[]]],[],[]] => 56 [[],[],[],[[],[]],[[]]] => 560 [[],[],[],[[[]]],[[]]] => 560 [[],[],[],[[],[],[]],[]] => 70 [[],[],[],[[],[[]]],[]] => 210 [[],[],[],[[[]],[]],[]] => 210 [[],[],[],[[[],[]]],[]] => 70 [[],[],[],[[[[]]]],[]] => 70 [[],[],[],[[],[],[],[]]] => 56 [[],[],[],[[],[],[[]]]] => 336 [[],[],[],[[],[[]],[]]] => 336 [[],[],[],[[],[[],[]]]] => 224 [[],[],[],[[],[[[]]]]] => 224 [[],[],[],[[[]],[],[]]] => 336 [[],[],[],[[[]],[[]]]] => 168 [[],[],[],[[[],[]],[]]] => 224 [[],[],[],[[[[]]],[]]] => 224 [[],[],[],[[[],[],[]]]] => 56 [[],[],[],[[[],[[]]]]] => 168 [[],[],[],[[[[]],[]]]] => 168 [[],[],[],[[[[],[]]]]] => 56 [[],[],[],[[[[[]]]]]] => 56 [[],[],[[]],[],[],[],[]] => 28 [[],[],[[]],[],[],[[]]] => 210 [[],[],[[]],[],[[]],[]] => 210 [[],[],[[]],[],[[],[]]] => 560 [[],[],[[]],[],[[[]]]] => 560 [[],[],[[]],[[]],[],[]] => 210 [[],[],[[]],[[]],[[]]] => 420 [[],[],[[]],[[],[]],[]] => 560 [[],[],[[]],[[[]]],[]] => 560 [[],[],[[]],[[],[],[]]] => 420 [[],[],[[]],[[],[[]]]] => 1260 [[],[],[[]],[[[]],[]]] => 1260 [[],[],[[]],[[[],[]]]] => 420 [[],[],[[]],[[[[]]]]] => 420 [[],[],[[],[]],[],[],[]] => 56 [[],[],[[[]]],[],[],[]] => 56 [[],[],[[],[]],[],[[]]] => 560 [[],[],[[[]]],[],[[]]] => 560 [[],[],[[],[]],[[]],[]] => 560 [[],[],[[[]]],[[]],[]] => 560 [[],[],[[],[]],[[],[]]] => 280 [[],[],[[],[]],[[[]]]] => 560 [[],[],[[[]]],[[],[]]] => 560 [[],[],[[[]]],[[[]]]] => 280 [[],[],[[],[],[]],[],[]] => 70 [[],[],[[],[[]]],[],[]] => 210 [[],[],[[[]],[]],[],[]] => 210 [[],[],[[[],[]]],[],[]] => 70 [[],[],[[[[]]]],[],[]] => 70 [[],[],[[],[],[]],[[]]] => 420 [[],[],[[],[[]]],[[]]] => 1260 [[],[],[[[]],[]],[[]]] => 1260 [[],[],[[[],[]]],[[]]] => 420 [[],[],[[[[]]]],[[]]] => 420 [[],[],[[],[],[],[]],[]] => 56 [[],[],[[],[],[[]]],[]] => 336 [[],[],[[],[[]],[]],[]] => 336 [[],[],[[],[[],[]]],[]] => 224 [[],[],[[],[[[]]]],[]] => 224 [[],[],[[[]],[],[]],[]] => 336 [[],[],[[[]],[[]]],[]] => 168 [[],[],[[[],[]],[]],[]] => 224 [[],[],[[[[]]],[]],[]] => 224 [[],[],[[[],[],[]]],[]] => 56 [[],[],[[[],[[]]]],[]] => 168 [[],[],[[[[]],[]]],[]] => 168 [[],[],[[[[],[]]]],[]] => 56 [[],[],[[[[[]]]]],[]] => 56 [[],[],[[],[],[],[],[]]] => 28 [[],[],[[],[],[],[[]]]] => 280 [[],[],[[],[],[[]],[]]] => 280 [[],[],[[],[],[[],[]]]] => 280 [[],[],[[],[],[[[]]]]] => 280 [[],[],[[],[[]],[],[]]] => 280 [[],[],[[],[[]],[[]]]] => 420 [[],[],[[],[[],[]],[]]] => 280 [[],[],[[],[[[]]],[]]] => 280 [[],[],[[],[[],[],[]]]] => 140 [[],[],[[],[[],[[]]]]] => 420 [[],[],[[],[[[]],[]]]] => 420 [[],[],[[],[[[],[]]]]] => 140 [[],[],[[],[[[[]]]]]] => 140 [[],[],[[[]],[],[],[]]] => 280 [[],[],[[[]],[],[[]]]] => 420 [[],[],[[[]],[[]],[]]] => 420 [[],[],[[[]],[[],[]]]] => 280 [[],[],[[[]],[[[]]]]] => 280 [[],[],[[[],[]],[],[]]] => 280 [[],[],[[[[]]],[],[]]] => 280 [[],[],[[[],[]],[[]]]] => 280 [[],[],[[[[]]],[[]]]] => 280 [[],[],[[[],[],[]],[]]] => 140 [[],[],[[[],[[]]],[]]] => 420 [[],[],[[[[]],[]],[]]] => 420 [[],[],[[[[],[]]],[]]] => 140 [[],[],[[[[[]]]],[]]] => 140 [[],[],[[[],[],[],[]]]] => 28 [[],[],[[[],[],[[]]]]] => 168 [[],[],[[[],[[]],[]]]] => 168 [[],[],[[[],[[],[]]]]] => 112 [[],[],[[[],[[[]]]]]] => 112 [[],[],[[[[]],[],[]]]] => 168 [[],[],[[[[]],[[]]]]] => 84 [[],[],[[[[],[]],[]]]] => 112 [[],[],[[[[[]]],[]]]] => 112 [[],[],[[[[],[],[]]]]] => 28 [[],[],[[[[],[[]]]]]] => 84 [[],[],[[[[[]],[]]]]] => 84 [[],[],[[[[[],[]]]]]] => 28 [[],[],[[[[[[]]]]]]] => 28 [[],[[]],[],[],[],[],[]] => 28 [[],[[]],[],[],[],[[]]] => 210 [[],[[]],[],[],[[]],[]] => 210 [[],[[]],[],[],[[],[]]] => 560 [[],[[]],[],[],[[[]]]] => 560 [[],[[]],[],[[]],[],[]] => 210 [[],[[]],[],[[]],[[]]] => 420 [[],[[]],[],[[],[]],[]] => 560 [[],[[]],[],[[[]]],[]] => 560 [[],[[]],[],[[],[],[]]] => 420 [[],[[]],[],[[],[[]]]] => 1260 [[],[[]],[],[[[]],[]]] => 1260 [[],[[]],[],[[[],[]]]] => 420 [[],[[]],[],[[[[]]]]] => 420 [[],[[]],[[]],[],[],[]] => 210 [[],[[]],[[]],[],[[]]] => 420 [[],[[]],[[]],[[]],[]] => 420 [[],[[]],[[]],[[],[]]] => 840 [[],[[]],[[]],[[[]]]] => 840 [[],[[]],[[],[]],[],[]] => 560 [[],[[]],[[[]]],[],[]] => 560 [[],[[]],[[],[]],[[]]] => 840 [[],[[]],[[[]]],[[]]] => 840 [[],[[]],[[],[],[]],[]] => 420 [[],[[]],[[],[[]]],[]] => 1260 [[],[[]],[[[]],[]],[]] => 1260 [[],[[]],[[[],[]]],[]] => 420 [[],[[]],[[[[]]]],[]] => 420 [[],[[]],[[],[],[],[]]] => 168 [[],[[]],[[],[],[[]]]] => 1008 [[],[[]],[[],[[]],[]]] => 1008 [[],[[]],[[],[[],[]]]] => 672 [[],[[]],[[],[[[]]]]] => 672 [[],[[]],[[[]],[],[]]] => 1008 [[],[[]],[[[]],[[]]]] => 504 [[],[[]],[[[],[]],[]]] => 672 [[],[[]],[[[[]]],[]]] => 672 [[],[[]],[[[],[],[]]]] => 168 [[],[[]],[[[],[[]]]]] => 504 [[],[[]],[[[[]],[]]]] => 504 [[],[[]],[[[[],[]]]]] => 168 [[],[[]],[[[[[]]]]]] => 168 [[],[[],[]],[],[],[],[]] => 56 [[],[[[]]],[],[],[],[]] => 56 [[],[[],[]],[],[],[[]]] => 560 [[],[[[]]],[],[],[[]]] => 560 [[],[[],[]],[],[[]],[]] => 560 [[],[[[]]],[],[[]],[]] => 560 [[],[[],[]],[],[[],[]]] => 280 [[],[[],[]],[],[[[]]]] => 560 [[],[[[]]],[],[[],[]]] => 560 [[],[[[]]],[],[[[]]]] => 280 [[],[[],[]],[[]],[],[]] => 560 [[],[[[]]],[[]],[],[]] => 560 [[],[[],[]],[[]],[[]]] => 840 [[],[[[]]],[[]],[[]]] => 840 [[],[[],[]],[[],[]],[]] => 280 [[],[[],[]],[[[]]],[]] => 560 [[],[[[]]],[[],[]],[]] => 560 [[],[[[]]],[[[]]],[]] => 280 [[],[[],[]],[[],[],[]]] => 280 [[],[[],[]],[[],[[]]]] => 840 [[],[[],[]],[[[]],[]]] => 840 [[],[[],[]],[[[],[]]]] => 280 [[],[[],[]],[[[[]]]]] => 280 [[],[[[]]],[[],[],[]]] => 280 [[],[[[]]],[[],[[]]]] => 840 [[],[[[]]],[[[]],[]]] => 840 [[],[[[]]],[[[],[]]]] => 280 [[],[[[]]],[[[[]]]]] => 280 [[],[[],[],[]],[],[],[]] => 70 [[],[[],[[]]],[],[],[]] => 210 [[],[[[]],[]],[],[],[]] => 210 [[],[[[],[]]],[],[],[]] => 70 [[],[[[[]]]],[],[],[]] => 70 [[],[[],[],[]],[],[[]]] => 420 [[],[[],[[]]],[],[[]]] => 1260 [[],[[[]],[]],[],[[]]] => 1260 [[],[[[],[]]],[],[[]]] => 420 [[],[[[[]]]],[],[[]]] => 420 [[],[[],[],[]],[[]],[]] => 420 [[],[[],[[]]],[[]],[]] => 1260 [[],[[[]],[]],[[]],[]] => 1260 [[],[[[],[]]],[[]],[]] => 420 [[],[[[[]]]],[[]],[]] => 420 [[],[[],[],[]],[[],[]]] => 280 [[],[[],[],[]],[[[]]]] => 280 [[],[[],[[]]],[[],[]]] => 840 [[],[[],[[]]],[[[]]]] => 840 [[],[[[]],[]],[[],[]]] => 840 [[],[[[]],[]],[[[]]]] => 840 [[],[[[],[]]],[[],[]]] => 280 [[],[[[],[]]],[[[]]]] => 280 [[],[[[[]]]],[[],[]]] => 280 [[],[[[[]]]],[[[]]]] => 280 [[],[[],[],[],[]],[],[]] => 56 [[],[[],[],[[]]],[],[]] => 336 [[],[[],[[]],[]],[],[]] => 336 [[],[[],[[],[]]],[],[]] => 224 [[],[[],[[[]]]],[],[]] => 224 [[],[[[]],[],[]],[],[]] => 336 [[],[[[]],[[]]],[],[]] => 168 [[],[[[],[]],[]],[],[]] => 224 [[],[[[[]]],[]],[],[]] => 224 [[],[[[],[],[]]],[],[]] => 56 [[],[[[],[[]]]],[],[]] => 168 [[],[[[[]],[]]],[],[]] => 168 [[],[[[[],[]]]],[],[]] => 56 [[],[[[[[]]]]],[],[]] => 56 [[],[[],[],[],[]],[[]]] => 168 [[],[[],[],[[]]],[[]]] => 1008 [[],[[],[[]],[]],[[]]] => 1008 [[],[[],[[],[]]],[[]]] => 672 [[],[[],[[[]]]],[[]]] => 672 [[],[[[]],[],[]],[[]]] => 1008 [[],[[[]],[[]]],[[]]] => 504 [[],[[[],[]],[]],[[]]] => 672 [[],[[[[]]],[]],[[]]] => 672 [[],[[[],[],[]]],[[]]] => 168 [[],[[[],[[]]]],[[]]] => 504 [[],[[[[]],[]]],[[]]] => 504 [[],[[[[],[]]]],[[]]] => 168 [[],[[[[[]]]]],[[]]] => 168 [[],[[],[],[],[],[]],[]] => 28 [[],[[],[],[],[[]]],[]] => 280 [[],[[],[],[[]],[]],[]] => 280 [[],[[],[],[[],[]]],[]] => 280 [[],[[],[],[[[]]]],[]] => 280 [[],[[],[[]],[],[]],[]] => 280 [[],[[],[[]],[[]]],[]] => 420 [[],[[],[[],[]],[]],[]] => 280 [[],[[],[[[]]],[]],[]] => 280 [[],[[],[[],[],[]]],[]] => 140 [[],[[],[[],[[]]]],[]] => 420 [[],[[],[[[]],[]]],[]] => 420 [[],[[],[[[],[]]]],[]] => 140 [[],[[],[[[[]]]]],[]] => 140 [[],[[[]],[],[],[]],[]] => 280 [[],[[[]],[],[[]]],[]] => 420 [[],[[[]],[[]],[]],[]] => 420 [[],[[[]],[[],[]]],[]] => 280 [[],[[[]],[[[]]]],[]] => 280 [[],[[[],[]],[],[]],[]] => 280 [[],[[[[]]],[],[]],[]] => 280 [[],[[[],[]],[[]]],[]] => 280 [[],[[[[]]],[[]]],[]] => 280 [[],[[[],[],[]],[]],[]] => 140 [[],[[[],[[]]],[]],[]] => 420 [[],[[[[]],[]],[]],[]] => 420 [[],[[[[],[]]],[]],[]] => 140 [[],[[[[[]]]],[]],[]] => 140 [[],[[[],[],[],[]]],[]] => 28 [[],[[[],[],[[]]]],[]] => 168 [[],[[[],[[]],[]]],[]] => 168 [[],[[[],[[],[]]]],[]] => 112 [[],[[[],[[[]]]]],[]] => 112 [[],[[[[]],[],[]]],[]] => 168 [[],[[[[]],[[]]]],[]] => 84 [[],[[[[],[]],[]]],[]] => 112 [[],[[[[[]]],[]]],[]] => 112 [[],[[[[],[],[]]]],[]] => 28 [[],[[[[],[[]]]]],[]] => 84 [[],[[[[[]],[]]]],[]] => 84 [[],[[[[[],[]]]]],[]] => 28 [[],[[[[[[]]]]]],[]] => 28 [[],[[],[],[],[],[],[]]] => 8 [[],[[],[],[],[],[[]]]] => 120 [[],[[],[],[],[[]],[]]] => 120 [[],[[],[],[],[[],[]]]] => 160 [[],[[],[],[],[[[]]]]] => 160 [[],[[],[],[[]],[],[]]] => 120 [[],[[],[],[[]],[[]]]] => 360 [[],[[],[],[[],[]],[]]] => 160 [[],[[],[],[[[]]],[]]] => 160 [[],[[],[],[[],[],[]]]] => 120 [[],[[],[],[[],[[]]]]] => 360 [[],[[],[],[[[]],[]]]] => 360 [[],[[],[],[[[],[]]]]] => 120 [[],[[],[],[[[[]]]]]] => 120 [[],[[],[[]],[],[],[]]] => 120 [[],[[],[[]],[],[[]]]] => 360 [[],[[],[[]],[[]],[]]] => 360 [[],[[],[[]],[[],[]]]] => 480 [[],[[],[[]],[[[]]]]] => 480 [[],[[],[[],[]],[],[]]] => 160 [[],[[],[[[]]],[],[]]] => 160 [[],[[],[[],[]],[[]]]] => 480 [[],[[],[[[]]],[[]]]] => 480 [[],[[],[[],[],[]],[]]] => 120 [[],[[],[[],[[]]],[]]] => 360 [[],[[],[[[]],[]],[]]] => 360 [[],[[],[[[],[]]],[]]] => 120 [[],[[],[[[[]]]],[]]] => 120 [[],[[],[[],[],[],[]]]] => 48 [[],[[],[[],[],[[]]]]] => 288 [[],[[],[[],[[]],[]]]] => 288 [[],[[],[[],[[],[]]]]] => 192 [[],[[],[[],[[[]]]]]] => 192 [[],[[],[[[]],[],[]]]] => 288 [[],[[],[[[]],[[]]]]] => 144 [[],[[],[[[],[]],[]]]] => 192 [[],[[],[[[[]]],[]]]] => 192 [[],[[],[[[],[],[]]]]] => 48 [[],[[],[[[],[[]]]]]] => 144 [[],[[],[[[[]],[]]]]] => 144 [[],[[],[[[[],[]]]]]] => 48 [[],[[],[[[[[]]]]]]] => 48 [[],[[[]],[],[],[],[]]] => 120 [[],[[[]],[],[],[[]]]] => 360 [[],[[[]],[],[[]],[]]] => 360 [[],[[[]],[],[[],[]]]] => 480 [[],[[[]],[],[[[]]]]] => 480 [[],[[[]],[[]],[],[]]] => 360 [[],[[[]],[[]],[[]]]] => 120 [[],[[[]],[[],[]],[]]] => 480 [[],[[[]],[[[]]],[]]] => 480 [[],[[[]],[[],[],[]]]] => 120 [[],[[[]],[[],[[]]]]] => 360 [[],[[[]],[[[]],[]]]] => 360 [[],[[[]],[[[],[]]]]] => 120 [[],[[[]],[[[[]]]]]] => 120 [[],[[[],[]],[],[],[]]] => 160 [[],[[[[]]],[],[],[]]] => 160 [[],[[[],[]],[],[[]]]] => 480 [[],[[[[]]],[],[[]]]] => 480 [[],[[[],[]],[[]],[]]] => 480 [[],[[[[]]],[[]],[]]] => 480 [[],[[[],[]],[[],[]]]] => 80 [[],[[[],[]],[[[]]]]] => 160 [[],[[[[]]],[[],[]]]] => 160 [[],[[[[]]],[[[]]]]] => 80 [[],[[[],[],[]],[],[]]] => 120 [[],[[[],[[]]],[],[]]] => 360 [[],[[[[]],[]],[],[]]] => 360 [[],[[[[],[]]],[],[]]] => 120 [[],[[[[[]]]],[],[]]] => 120 [[],[[[],[],[]],[[]]]] => 120 [[],[[[],[[]]],[[]]]] => 360 [[],[[[[]],[]],[[]]]] => 360 [[],[[[[],[]]],[[]]]] => 120 [[],[[[[[]]]],[[]]]] => 120 [[],[[[],[],[],[]],[]]] => 48 [[],[[[],[],[[]]],[]]] => 288 [[],[[[],[[]],[]],[]]] => 288 [[],[[[],[[],[]]],[]]] => 192 [[],[[[],[[[]]]],[]]] => 192 [[],[[[[]],[],[]],[]]] => 288 [[],[[[[]],[[]]],[]]] => 144 [[],[[[[],[]],[]],[]]] => 192 [[],[[[[[]]],[]],[]]] => 192 [[],[[[[],[],[]]],[]]] => 48 [[],[[[[],[[]]]],[]]] => 144 [[],[[[[[]],[]]],[]]] => 144 [[],[[[[[],[]]]],[]]] => 48 [[],[[[[[[]]]]],[]]] => 48 [[],[[[],[],[],[],[]]]] => 8 [[],[[[],[],[],[[]]]]] => 80 [[],[[[],[],[[]],[]]]] => 80 [[],[[[],[],[[],[]]]]] => 80 [[],[[[],[],[[[]]]]]] => 80 [[],[[[],[[]],[],[]]]] => 80 [[],[[[],[[]],[[]]]]] => 120 [[],[[[],[[],[]],[]]]] => 80 [[],[[[],[[[]]],[]]]] => 80 [[],[[[],[[],[],[]]]]] => 40 [[],[[[],[[],[[]]]]]] => 120 [[],[[[],[[[]],[]]]]] => 120 [[],[[[],[[[],[]]]]]] => 40 [[],[[[],[[[[]]]]]]] => 40 [[],[[[[]],[],[],[]]]] => 80 [[],[[[[]],[],[[]]]]] => 120 [[],[[[[]],[[]],[]]]] => 120 [[],[[[[]],[[],[]]]]] => 80 [[],[[[[]],[[[]]]]]] => 80 [[],[[[[],[]],[],[]]]] => 80 [[],[[[[[]]],[],[]]]] => 80 [[],[[[[],[]],[[]]]]] => 80 [[],[[[[[]]],[[]]]]] => 80 [[],[[[[],[],[]],[]]]] => 40 [[],[[[[],[[]]],[]]]] => 120 [[],[[[[[]],[]],[]]]] => 120 [[],[[[[[],[]]],[]]]] => 40 [[],[[[[[[]]]],[]]]] => 40 [[],[[[[],[],[],[]]]]] => 8 [[],[[[[],[],[[]]]]]] => 48 [[],[[[[],[[]],[]]]]] => 48 [[],[[[[],[[],[]]]]]] => 32 [[],[[[[],[[[]]]]]]] => 32 [[],[[[[[]],[],[]]]]] => 48 [[],[[[[[]],[[]]]]]] => 24 [[],[[[[[],[]],[]]]]] => 32 [[],[[[[[[]]],[]]]]] => 32 [[],[[[[[],[],[]]]]]] => 8 [[],[[[[[],[[]]]]]]] => 24 [[],[[[[[[]],[]]]]]] => 24 [[],[[[[[[],[]]]]]]] => 8 [[],[[[[[[[]]]]]]]] => 8 [[[]],[],[],[],[],[],[]] => 28 [[[]],[],[],[],[],[[]]] => 210 [[[]],[],[],[],[[]],[]] => 210 [[[]],[],[],[],[[],[]]] => 560 [[[]],[],[],[],[[[]]]] => 560 [[[]],[],[],[[]],[],[]] => 210 [[[]],[],[],[[]],[[]]] => 420 [[[]],[],[],[[],[]],[]] => 560 [[[]],[],[],[[[]]],[]] => 560 [[[]],[],[],[[],[],[]]] => 420 [[[]],[],[],[[],[[]]]] => 1260 [[[]],[],[],[[[]],[]]] => 1260 [[[]],[],[],[[[],[]]]] => 420 [[[]],[],[],[[[[]]]]] => 420 [[[]],[],[[]],[],[],[]] => 210 [[[]],[],[[]],[],[[]]] => 420 [[[]],[],[[]],[[]],[]] => 420 [[[]],[],[[]],[[],[]]] => 840 [[[]],[],[[]],[[[]]]] => 840 [[[]],[],[[],[]],[],[]] => 560 [[[]],[],[[[]]],[],[]] => 560 [[[]],[],[[],[]],[[]]] => 840 [[[]],[],[[[]]],[[]]] => 840 [[[]],[],[[],[],[]],[]] => 420 [[[]],[],[[],[[]]],[]] => 1260 [[[]],[],[[[]],[]],[]] => 1260 [[[]],[],[[[],[]]],[]] => 420 [[[]],[],[[[[]]]],[]] => 420 [[[]],[],[[],[],[],[]]] => 168 [[[]],[],[[],[],[[]]]] => 1008 [[[]],[],[[],[[]],[]]] => 1008 [[[]],[],[[],[[],[]]]] => 672 [[[]],[],[[],[[[]]]]] => 672 [[[]],[],[[[]],[],[]]] => 1008 [[[]],[],[[[]],[[]]]] => 504 [[[]],[],[[[],[]],[]]] => 672 [[[]],[],[[[[]]],[]]] => 672 [[[]],[],[[[],[],[]]]] => 168 [[[]],[],[[[],[[]]]]] => 504 [[[]],[],[[[[]],[]]]] => 504 [[[]],[],[[[[],[]]]]] => 168 [[[]],[],[[[[[]]]]]] => 168 [[[]],[[]],[],[],[],[]] => 210 [[[]],[[]],[],[],[[]]] => 420 [[[]],[[]],[],[[]],[]] => 420 [[[]],[[]],[],[[],[]]] => 840 [[[]],[[]],[],[[[]]]] => 840 [[[]],[[]],[[]],[],[]] => 420 [[[]],[[]],[[]],[[]]] => 105 [[[]],[[]],[[],[]],[]] => 840 [[[]],[[]],[[[]]],[]] => 840 [[[]],[[]],[[],[],[]]] => 210 [[[]],[[]],[[],[[]]]] => 630 [[[]],[[]],[[[]],[]]] => 630 [[[]],[[]],[[[],[]]]] => 210 [[[]],[[]],[[[[]]]]] => 210 [[[]],[[],[]],[],[],[]] => 560 [[[]],[[[]]],[],[],[]] => 560 [[[]],[[],[]],[],[[]]] => 840 [[[]],[[[]]],[],[[]]] => 840 [[[]],[[],[]],[[]],[]] => 840 [[[]],[[[]]],[[]],[]] => 840 [[[]],[[],[]],[[],[]]] => 280 [[[]],[[],[]],[[[]]]] => 560 [[[]],[[[]]],[[],[]]] => 560 [[[]],[[[]]],[[[]]]] => 280 [[[]],[[],[],[]],[],[]] => 420 [[[]],[[],[[]]],[],[]] => 1260 [[[]],[[[]],[]],[],[]] => 1260 [[[]],[[[],[]]],[],[]] => 420 [[[]],[[[[]]]],[],[]] => 420 [[[]],[[],[],[]],[[]]] => 210 [[[]],[[],[[]]],[[]]] => 630 [[[]],[[[]],[]],[[]]] => 630 [[[]],[[[],[]]],[[]]] => 210 [[[]],[[[[]]]],[[]]] => 210 [[[]],[[],[],[],[]],[]] => 168 [[[]],[[],[],[[]]],[]] => 1008 [[[]],[[],[[]],[]],[]] => 1008 [[[]],[[],[[],[]]],[]] => 672 [[[]],[[],[[[]]]],[]] => 672 [[[]],[[[]],[],[]],[]] => 1008 [[[]],[[[]],[[]]],[]] => 504 [[[]],[[[],[]],[]],[]] => 672 [[[]],[[[[]]],[]],[]] => 672 [[[]],[[[],[],[]]],[]] => 168 [[[]],[[[],[[]]]],[]] => 504 [[[]],[[[[]],[]]],[]] => 504 [[[]],[[[[],[]]]],[]] => 168 [[[]],[[[[[]]]]],[]] => 168 [[[]],[[],[],[],[],[]]] => 28 [[[]],[[],[],[],[[]]]] => 280 [[[]],[[],[],[[]],[]]] => 280 [[[]],[[],[],[[],[]]]] => 280 [[[]],[[],[],[[[]]]]] => 280 [[[]],[[],[[]],[],[]]] => 280 [[[]],[[],[[]],[[]]]] => 420 [[[]],[[],[[],[]],[]]] => 280 [[[]],[[],[[[]]],[]]] => 280 [[[]],[[],[[],[],[]]]] => 140 [[[]],[[],[[],[[]]]]] => 420 [[[]],[[],[[[]],[]]]] => 420 [[[]],[[],[[[],[]]]]] => 140 [[[]],[[],[[[[]]]]]] => 140 [[[]],[[[]],[],[],[]]] => 280 [[[]],[[[]],[],[[]]]] => 420 [[[]],[[[]],[[]],[]]] => 420 [[[]],[[[]],[[],[]]]] => 280 [[[]],[[[]],[[[]]]]] => 280 [[[]],[[[],[]],[],[]]] => 280 [[[]],[[[[]]],[],[]]] => 280 [[[]],[[[],[]],[[]]]] => 280 [[[]],[[[[]]],[[]]]] => 280 [[[]],[[[],[],[]],[]]] => 140 [[[]],[[[],[[]]],[]]] => 420 [[[]],[[[[]],[]],[]]] => 420 [[[]],[[[[],[]]],[]]] => 140 [[[]],[[[[[]]]],[]]] => 140 [[[]],[[[],[],[],[]]]] => 28 [[[]],[[[],[],[[]]]]] => 168 [[[]],[[[],[[]],[]]]] => 168 [[[]],[[[],[[],[]]]]] => 112 [[[]],[[[],[[[]]]]]] => 112 [[[]],[[[[]],[],[]]]] => 168 [[[]],[[[[]],[[]]]]] => 84 [[[]],[[[[],[]],[]]]] => 112 [[[]],[[[[[]]],[]]]] => 112 [[[]],[[[[],[],[]]]]] => 28 [[[]],[[[[],[[]]]]]] => 84 [[[]],[[[[[]],[]]]]] => 84 [[[]],[[[[[],[]]]]]] => 28 [[[]],[[[[[[]]]]]]] => 28 [[[],[]],[],[],[],[],[]] => 56 [[[[]]],[],[],[],[],[]] => 56 [[[],[]],[],[],[],[[]]] => 560 [[[[]]],[],[],[],[[]]] => 560 [[[],[]],[],[],[[]],[]] => 560 [[[[]]],[],[],[[]],[]] => 560 [[[],[]],[],[],[[],[]]] => 280 [[[],[]],[],[],[[[]]]] => 560 [[[[]]],[],[],[[],[]]] => 560 [[[[]]],[],[],[[[]]]] => 280 [[[],[]],[],[[]],[],[]] => 560 [[[[]]],[],[[]],[],[]] => 560 [[[],[]],[],[[]],[[]]] => 840 [[[[]]],[],[[]],[[]]] => 840 ----------------------------------------------------------------------------- Created: Feb 26, 2016 at 08:30 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 26, 2016 at 08:58 by Martin Rubey