***************************************************************************** * 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: St001375 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The pancake length of a permutation. This is the minimal number of pancake moves needed to generate a permutation where a pancake move is a reversal of a prefix in a permutation. ----------------------------------------------------------------------------- References: [1] Blanco, S. A., Buehrle, C. Some relations on prefix reversal generators of the symmetric and hyperoctahedral group [[arXiv:1803.01760]] ----------------------------------------------------------------------------- Code: @cached_function def generate_group_from_generators(parent, gens): gens = list(gens) inds = range(len(gens)) assert all( gen.parent() == parent for gen in gens ) one = parent.one() level_set_cur = set([one]) found_elements = set([one]) level_sets = [] while level_set_cur: level_sets.append(level_set_cur) level_set_new = set() for x in level_set_cur: for i in inds: y = x * gens[i] if y not in found_elements: found_elements.add(y) level_set_new.add(y) level_set_cur = level_set_new return level_sets @cached_function def pancake_gens(n): return tuple(Permutations(n)(list(range(k,0,-1))+list(range(k+1,n+1))) for k in [2 .. n]) def statistic(sigma): n = len(sigma) level_sets = generate_group_from_generators(Permutations(n), pancake_gens(n)) i = 0 for level in level_sets: if sigma not in level: i += 1 else: return i ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 3 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 0 [1,2,4,3] => 3 [1,3,2,4] => 3 [1,3,4,2] => 3 [1,4,2,3] => 3 [1,4,3,2] => 3 [2,1,3,4] => 1 [2,1,4,3] => 3 [2,3,1,4] => 2 [2,3,4,1] => 2 [2,4,1,3] => 4 [2,4,3,1] => 3 [3,1,2,4] => 2 [3,1,4,2] => 4 [3,2,1,4] => 1 [3,2,4,1] => 3 [3,4,1,2] => 3 [3,4,2,1] => 2 [4,1,2,3] => 2 [4,1,3,2] => 3 [4,2,1,3] => 3 [4,2,3,1] => 4 [4,3,1,2] => 2 [4,3,2,1] => 1 [1,2,3,4,5] => 0 [1,2,3,5,4] => 3 [1,2,4,3,5] => 3 [1,2,4,5,3] => 4 [1,2,5,3,4] => 4 [1,2,5,4,3] => 3 [1,3,2,4,5] => 3 [1,3,2,5,4] => 5 [1,3,4,2,5] => 3 [1,3,4,5,2] => 3 [1,3,5,2,4] => 5 [1,3,5,4,2] => 4 [1,4,2,3,5] => 3 [1,4,2,5,3] => 5 [1,4,3,2,5] => 3 [1,4,3,5,2] => 5 [1,4,5,2,3] => 3 [1,4,5,3,2] => 4 [1,5,2,3,4] => 3 [1,5,2,4,3] => 4 [1,5,3,2,4] => 5 [1,5,3,4,2] => 5 [1,5,4,2,3] => 4 [1,5,4,3,2] => 3 [2,1,3,4,5] => 1 [2,1,3,5,4] => 4 [2,1,4,3,5] => 3 [2,1,4,5,3] => 3 [2,1,5,3,4] => 3 [2,1,5,4,3] => 4 [2,3,1,4,5] => 2 [2,3,1,5,4] => 4 [2,3,4,1,5] => 2 [2,3,4,5,1] => 2 [2,3,5,1,4] => 4 [2,3,5,4,1] => 3 [2,4,1,3,5] => 4 [2,4,1,5,3] => 5 [2,4,3,1,5] => 3 [2,4,3,5,1] => 5 [2,4,5,1,3] => 4 [2,4,5,3,1] => 4 [2,5,1,3,4] => 4 [2,5,1,4,3] => 5 [2,5,3,1,4] => 5 [2,5,3,4,1] => 4 [2,5,4,1,3] => 4 [2,5,4,3,1] => 3 [3,1,2,4,5] => 2 [3,1,2,5,4] => 4 [3,1,4,2,5] => 4 [3,1,4,5,2] => 4 [3,1,5,2,4] => 5 [3,1,5,4,2] => 5 [3,2,1,4,5] => 1 [3,2,1,5,4] => 3 [3,2,4,1,5] => 3 [3,2,4,5,1] => 3 [3,2,5,1,4] => 4 [3,2,5,4,1] => 4 [3,4,1,2,5] => 3 [3,4,1,5,2] => 4 [3,4,2,1,5] => 2 [3,4,2,5,1] => 4 [3,4,5,1,2] => 3 [3,4,5,2,1] => 2 [3,5,1,2,4] => 4 [3,5,1,4,2] => 5 [3,5,2,1,4] => 4 [3,5,2,4,1] => 5 [3,5,4,1,2] => 4 [3,5,4,2,1] => 3 [4,1,2,3,5] => 2 [4,1,2,5,3] => 4 [4,1,3,2,5] => 3 [4,1,3,5,2] => 5 [4,1,5,2,3] => 4 [4,1,5,3,2] => 4 [4,2,1,3,5] => 3 [4,2,1,5,3] => 4 [4,2,3,1,5] => 4 [4,2,3,5,1] => 4 [4,2,5,1,3] => 5 [4,2,5,3,1] => 5 [4,3,1,2,5] => 2 [4,3,1,5,2] => 4 [4,3,2,1,5] => 1 [4,3,2,5,1] => 3 [4,3,5,1,2] => 4 [4,3,5,2,1] => 3 [4,5,1,2,3] => 3 [4,5,1,3,2] => 4 [4,5,2,1,3] => 4 [4,5,2,3,1] => 4 [4,5,3,1,2] => 3 [4,5,3,2,1] => 2 [5,1,2,3,4] => 2 [5,1,2,4,3] => 3 [5,1,3,2,4] => 5 [5,1,3,4,2] => 4 [5,1,4,2,3] => 4 [5,1,4,3,2] => 3 [5,2,1,3,4] => 3 [5,2,1,4,3] => 4 [5,2,3,1,4] => 4 [5,2,3,4,1] => 4 [5,2,4,1,3] => 5 [5,2,4,3,1] => 4 [5,3,1,2,4] => 4 [5,3,1,4,2] => 5 [5,3,2,1,4] => 3 [5,3,2,4,1] => 4 [5,3,4,1,2] => 4 [5,3,4,2,1] => 4 [5,4,1,2,3] => 2 [5,4,1,3,2] => 3 [5,4,2,1,3] => 3 [5,4,2,3,1] => 4 [5,4,3,1,2] => 2 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 3 [1,2,3,5,4,6] => 3 [1,2,3,5,6,4] => 4 [1,2,3,6,4,5] => 4 [1,2,3,6,5,4] => 3 [1,2,4,3,5,6] => 3 [1,2,4,3,6,5] => 5 [1,2,4,5,3,6] => 4 [1,2,4,5,6,3] => 4 [1,2,4,6,3,5] => 6 [1,2,4,6,5,3] => 5 [1,2,5,3,4,6] => 4 [1,2,5,3,6,4] => 6 [1,2,5,4,3,6] => 3 [1,2,5,4,6,3] => 5 [1,2,5,6,3,4] => 4 [1,2,5,6,4,3] => 4 [1,2,6,3,4,5] => 4 [1,2,6,3,5,4] => 5 [1,2,6,4,3,5] => 5 [1,2,6,4,5,3] => 6 [1,2,6,5,3,4] => 4 [1,2,6,5,4,3] => 3 [1,3,2,4,5,6] => 3 [1,3,2,4,6,5] => 6 [1,3,2,5,4,6] => 5 [1,3,2,5,6,4] => 5 [1,3,2,6,4,5] => 5 [1,3,2,6,5,4] => 5 [1,3,4,2,5,6] => 3 [1,3,4,2,6,5] => 5 [1,3,4,5,2,6] => 3 [1,3,4,5,6,2] => 3 [1,3,4,6,2,5] => 5 [1,3,4,6,5,2] => 4 [1,3,5,2,4,6] => 5 [1,3,5,2,6,4] => 6 [1,3,5,4,2,6] => 4 [1,3,5,4,6,2] => 6 [1,3,5,6,2,4] => 5 [1,3,5,6,4,2] => 5 [1,3,6,2,4,5] => 5 [1,3,6,2,5,4] => 6 [1,3,6,4,2,5] => 6 [1,3,6,4,5,2] => 5 [1,3,6,5,2,4] => 6 [1,3,6,5,4,2] => 4 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 5 [1,4,2,5,3,6] => 5 [1,4,2,5,6,3] => 5 [1,4,2,6,3,5] => 6 [1,4,2,6,5,3] => 6 [1,4,3,2,5,6] => 3 [1,4,3,2,6,5] => 5 [1,4,3,5,2,6] => 5 [1,4,3,5,6,2] => 5 [1,4,3,6,2,5] => 6 [1,4,3,6,5,2] => 6 [1,4,5,2,3,6] => 3 [1,4,5,2,6,3] => 5 [1,4,5,3,2,6] => 4 [1,4,5,3,6,2] => 5 [1,4,5,6,2,3] => 3 [1,4,5,6,3,2] => 4 [1,4,6,2,3,5] => 5 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 6 [1,4,6,3,5,2] => 6 [1,4,6,5,2,3] => 4 [1,4,6,5,3,2] => 5 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 5 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 6 [1,5,2,6,3,4] => 5 [1,5,2,6,4,3] => 6 [1,5,3,2,4,6] => 5 [1,5,3,2,6,4] => 6 [1,5,3,4,2,6] => 5 [1,5,3,4,6,2] => 5 [1,5,3,6,2,4] => 6 [1,5,3,6,4,2] => 6 [1,5,4,2,3,6] => 4 [1,5,4,2,6,3] => 6 [1,5,4,3,2,6] => 3 [1,5,4,3,6,2] => 5 [1,5,4,6,2,3] => 5 [1,5,4,6,3,2] => 5 [1,5,6,2,3,4] => 3 [1,5,6,2,4,3] => 4 [1,5,6,3,2,4] => 5 [1,5,6,3,4,2] => 5 [1,5,6,4,2,3] => 5 [1,5,6,4,3,2] => 4 [1,6,2,3,4,5] => 3 [1,6,2,3,5,4] => 4 [1,6,2,4,3,5] => 6 [1,6,2,4,5,3] => 5 [1,6,2,5,3,4] => 5 [1,6,2,5,4,3] => 4 [1,6,3,2,4,5] => 5 [1,6,3,2,5,4] => 6 [1,6,3,4,2,5] => 5 [1,6,3,4,5,2] => 5 [1,6,3,5,2,4] => 6 [1,6,3,5,4,2] => 6 [1,6,4,2,3,5] => 5 [1,6,4,2,5,3] => 6 [1,6,4,3,2,5] => 5 [1,6,4,3,5,2] => 6 [1,6,4,5,2,3] => 5 [1,6,4,5,3,2] => 5 [1,6,5,2,3,4] => 4 [1,6,5,2,4,3] => 5 [1,6,5,3,2,4] => 5 [1,6,5,3,4,2] => 5 [1,6,5,4,2,3] => 4 [1,6,5,4,3,2] => 3 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 4 [2,1,3,5,4,6] => 4 [2,1,3,5,6,4] => 5 [2,1,3,6,4,5] => 5 [2,1,3,6,5,4] => 4 [2,1,4,3,5,6] => 3 [2,1,4,3,6,5] => 5 [2,1,4,5,3,6] => 3 [2,1,4,5,6,3] => 3 [2,1,4,6,3,5] => 5 [2,1,4,6,5,3] => 4 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 5 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 5 [2,1,5,6,3,4] => 3 [2,1,5,6,4,3] => 4 [2,1,6,3,4,5] => 3 [2,1,6,3,5,4] => 4 [2,1,6,4,3,5] => 5 [2,1,6,4,5,3] => 5 [2,1,6,5,3,4] => 4 [2,1,6,5,4,3] => 4 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 5 [2,3,1,5,4,6] => 4 [2,3,1,5,6,4] => 4 [2,3,1,6,4,5] => 4 [2,3,1,6,5,4] => 5 [2,3,4,1,5,6] => 2 [2,3,4,1,6,5] => 4 [2,3,4,5,1,6] => 2 [2,3,4,5,6,1] => 2 [2,3,4,6,1,5] => 4 [2,3,4,6,5,1] => 3 [2,3,5,1,4,6] => 4 [2,3,5,1,6,4] => 5 [2,3,5,4,1,6] => 3 [2,3,5,4,6,1] => 5 [2,3,5,6,1,4] => 4 [2,3,5,6,4,1] => 4 [2,3,6,1,4,5] => 4 [2,3,6,1,5,4] => 5 [2,3,6,4,1,5] => 5 [2,3,6,4,5,1] => 4 [2,3,6,5,1,4] => 5 [2,3,6,5,4,1] => 3 [2,4,1,3,5,6] => 4 [2,4,1,3,6,5] => 6 [2,4,1,5,3,6] => 5 [2,4,1,5,6,3] => 5 [2,4,1,6,3,5] => 6 [2,4,1,6,5,3] => 6 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 5 [2,4,3,5,1,6] => 5 [2,4,3,5,6,1] => 5 [2,4,3,6,1,5] => 5 [2,4,3,6,5,1] => 5 [2,4,5,1,3,6] => 4 [2,4,5,1,6,3] => 5 [2,4,5,3,1,6] => 4 [2,4,5,3,6,1] => 5 [2,4,5,6,1,3] => 4 [2,4,5,6,3,1] => 4 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 6 [2,4,6,3,1,5] => 6 [2,4,6,3,5,1] => 6 [2,4,6,5,1,3] => 5 [2,4,6,5,3,1] => 5 [2,5,1,3,4,6] => 4 [2,5,1,3,6,4] => 6 [2,5,1,4,3,6] => 5 [2,5,1,4,6,3] => 6 [2,5,1,6,3,4] => 5 [2,5,1,6,4,3] => 5 [2,5,3,1,4,6] => 5 [2,5,3,1,6,4] => 6 [2,5,3,4,1,6] => 4 [2,5,3,4,6,1] => 5 [2,5,3,6,1,4] => 6 [2,5,3,6,4,1] => 6 [2,5,4,1,3,6] => 4 [2,5,4,1,6,3] => 5 [2,5,4,3,1,6] => 3 [2,5,4,3,6,1] => 5 [2,5,4,6,1,3] => 6 [2,5,4,6,3,1] => 5 [2,5,6,1,3,4] => 4 [2,5,6,1,4,3] => 5 [2,5,6,3,1,4] => 5 [2,5,6,3,4,1] => 5 [2,5,6,4,1,3] => 5 [2,5,6,4,3,1] => 4 [2,6,1,3,4,5] => 4 [2,6,1,3,5,4] => 5 [2,6,1,4,3,5] => 6 [2,6,1,4,5,3] => 5 [2,6,1,5,3,4] => 5 [2,6,1,5,4,3] => 5 [2,6,3,1,4,5] => 5 [2,6,3,1,5,4] => 6 [2,6,3,4,1,5] => 5 [2,6,3,4,5,1] => 4 [2,6,3,5,1,4] => 6 [2,6,3,5,4,1] => 5 [2,6,4,1,3,5] => 6 [2,6,4,1,5,3] => 6 [2,6,4,3,1,5] => 5 [2,6,4,3,5,1] => 5 [2,6,4,5,1,3] => 6 [2,6,4,5,3,1] => 6 [2,6,5,1,3,4] => 4 [2,6,5,1,4,3] => 5 [2,6,5,3,1,4] => 5 [2,6,5,3,4,1] => 4 [2,6,5,4,1,3] => 4 [2,6,5,4,3,1] => 3 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 5 [3,1,2,5,4,6] => 4 [3,1,2,5,6,4] => 4 [3,1,2,6,4,5] => 4 [3,1,2,6,5,4] => 5 [3,1,4,2,5,6] => 4 [3,1,4,2,6,5] => 6 [3,1,4,5,2,6] => 4 [3,1,4,5,6,2] => 4 [3,1,4,6,2,5] => 6 [3,1,4,6,5,2] => 5 [3,1,5,2,4,6] => 5 [3,1,5,2,6,4] => 6 [3,1,5,4,2,6] => 5 [3,1,5,4,6,2] => 6 [3,1,5,6,2,4] => 5 [3,1,5,6,4,2] => 5 [3,1,6,2,4,5] => 5 [3,1,6,2,5,4] => 6 [3,1,6,4,2,5] => 6 [3,1,6,4,5,2] => 5 [3,1,6,5,2,4] => 5 [3,1,6,5,4,2] => 5 [3,2,1,4,5,6] => 1 [3,2,1,4,6,5] => 4 [3,2,1,5,4,6] => 3 [3,2,1,5,6,4] => 3 [3,2,1,6,4,5] => 3 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 3 [3,2,4,1,6,5] => 5 [3,2,4,5,1,6] => 3 [3,2,4,5,6,1] => 3 [3,2,4,6,1,5] => 5 [3,2,4,6,5,1] => 4 [3,2,5,1,4,6] => 4 [3,2,5,1,6,4] => 5 [3,2,5,4,1,6] => 4 [3,2,5,4,6,1] => 5 [3,2,5,6,1,4] => 5 [3,2,5,6,4,1] => 5 [3,2,6,1,4,5] => 4 [3,2,6,1,5,4] => 5 [3,2,6,4,1,5] => 5 [3,2,6,4,5,1] => 5 [3,2,6,5,1,4] => 4 [3,2,6,5,4,1] => 4 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 5 [3,4,1,5,2,6] => 4 [3,4,1,5,6,2] => 4 [3,4,1,6,2,5] => 6 [3,4,1,6,5,2] => 5 [3,4,2,1,5,6] => 2 [3,4,2,1,6,5] => 4 [3,4,2,5,1,6] => 4 [3,4,2,5,6,1] => 4 [3,4,2,6,1,5] => 5 [3,4,2,6,5,1] => 5 [3,4,5,1,2,6] => 3 [3,4,5,1,6,2] => 4 [3,4,5,2,1,6] => 2 [3,4,5,2,6,1] => 4 [3,4,5,6,1,2] => 3 [3,4,5,6,2,1] => 2 [3,4,6,1,2,5] => 5 [3,4,6,1,5,2] => 5 [3,4,6,2,1,5] => 4 [3,4,6,2,5,1] => 5 [3,4,6,5,1,2] => 4 [3,4,6,5,2,1] => 3 [3,5,1,2,4,6] => 4 [3,5,1,2,6,4] => 6 [3,5,1,4,2,6] => 5 [3,5,1,4,6,2] => 6 [3,5,1,6,2,4] => 6 [3,5,1,6,4,2] => 6 [3,5,2,1,4,6] => 4 [3,5,2,1,6,4] => 5 [3,5,2,4,1,6] => 5 [3,5,2,4,6,1] => 6 [3,5,2,6,1,4] => 6 [3,5,2,6,4,1] => 6 [3,5,4,1,2,6] => 4 [3,5,4,1,6,2] => 5 [3,5,4,2,1,6] => 3 [3,5,4,2,6,1] => 5 [3,5,4,6,1,2] => 6 [3,5,4,6,2,1] => 5 [3,5,6,1,2,4] => 5 [3,5,6,1,4,2] => 6 [3,5,6,2,1,4] => 4 [3,5,6,2,4,1] => 5 [3,5,6,4,1,2] => 5 [3,5,6,4,2,1] => 4 [3,6,1,2,4,5] => 4 [3,6,1,2,5,4] => 5 [3,6,1,4,2,5] => 6 [3,6,1,4,5,2] => 6 [3,6,1,5,2,4] => 6 [3,6,1,5,4,2] => 5 [3,6,2,1,4,5] => 4 [3,6,2,1,5,4] => 5 [3,6,2,4,1,5] => 6 [3,6,2,4,5,1] => 5 [3,6,2,5,1,4] => 6 [3,6,2,5,4,1] => 5 [3,6,4,1,2,5] => 6 [3,6,4,1,5,2] => 6 [3,6,4,2,1,5] => 5 [3,6,4,2,5,1] => 6 [3,6,4,5,1,2] => 5 [3,6,4,5,2,1] => 4 [3,6,5,1,2,4] => 4 [3,6,5,1,4,2] => 5 [3,6,5,2,1,4] => 5 [3,6,5,2,4,1] => 5 [3,6,5,4,1,2] => 4 [3,6,5,4,2,1] => 3 [4,1,2,3,5,6] => 2 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 4 [4,1,2,5,6,3] => 4 [4,1,2,6,3,5] => 5 [4,1,2,6,5,3] => 5 [4,1,3,2,5,6] => 3 [4,1,3,2,6,5] => 5 [4,1,3,5,2,6] => 5 [4,1,3,5,6,2] => 5 [4,1,3,6,2,5] => 6 [4,1,3,6,5,2] => 6 [4,1,5,2,3,6] => 4 [4,1,5,2,6,3] => 6 [4,1,5,3,2,6] => 4 [4,1,5,3,6,2] => 6 [4,1,5,6,2,3] => 4 [4,1,5,6,3,2] => 4 [4,1,6,2,3,5] => 5 [4,1,6,2,5,3] => 6 [4,1,6,3,2,5] => 5 [4,1,6,3,5,2] => 6 [4,1,6,5,2,3] => 5 [4,1,6,5,3,2] => 5 [4,2,1,3,5,6] => 3 [4,2,1,3,6,5] => 5 [4,2,1,5,3,6] => 4 [4,2,1,5,6,3] => 4 [4,2,1,6,3,5] => 5 [4,2,1,6,5,3] => 5 [4,2,3,1,5,6] => 4 [4,2,3,1,6,5] => 6 [4,2,3,5,1,6] => 4 [4,2,3,5,6,1] => 4 [4,2,3,6,1,5] => 6 [4,2,3,6,5,1] => 5 [4,2,5,1,3,6] => 5 [4,2,5,1,6,3] => 6 [4,2,5,3,1,6] => 5 [4,2,5,3,6,1] => 6 [4,2,5,6,1,3] => 5 [4,2,5,6,3,1] => 5 [4,2,6,1,3,5] => 6 [4,2,6,1,5,3] => 6 [4,2,6,3,1,5] => 6 [4,2,6,3,5,1] => 6 [4,2,6,5,1,3] => 5 [4,2,6,5,3,1] => 5 [4,3,1,2,5,6] => 2 [4,3,1,2,6,5] => 4 [4,3,1,5,2,6] => 4 [4,3,1,5,6,2] => 4 [4,3,1,6,2,5] => 5 [4,3,1,6,5,2] => 5 [4,3,2,1,5,6] => 1 [4,3,2,1,6,5] => 3 [4,3,2,5,1,6] => 3 [4,3,2,5,6,1] => 3 [4,3,2,6,1,5] => 4 [4,3,2,6,5,1] => 4 [4,3,5,1,2,6] => 4 [4,3,5,1,6,2] => 5 [4,3,5,2,1,6] => 3 [4,3,5,2,6,1] => 5 [4,3,5,6,1,2] => 4 [4,3,5,6,2,1] => 3 [4,3,6,1,2,5] => 4 [4,3,6,1,5,2] => 6 [4,3,6,2,1,5] => 5 [4,3,6,2,5,1] => 5 [4,3,6,5,1,2] => 4 [4,3,6,5,2,1] => 4 [4,5,1,2,3,6] => 3 [4,5,1,2,6,3] => 5 [4,5,1,3,2,6] => 4 [4,5,1,3,6,2] => 6 [4,5,1,6,2,3] => 5 [4,5,1,6,3,2] => 4 [4,5,2,1,3,6] => 4 [4,5,2,1,6,3] => 4 [4,5,2,3,1,6] => 4 [4,5,2,3,6,1] => 5 [4,5,2,6,1,3] => 5 [4,5,2,6,3,1] => 5 [4,5,3,1,2,6] => 3 [4,5,3,1,6,2] => 5 [4,5,3,2,1,6] => 2 [4,5,3,2,6,1] => 4 [4,5,3,6,1,2] => 5 [4,5,3,6,2,1] => 4 [4,5,6,1,2,3] => 3 [4,5,6,1,3,2] => 4 [4,5,6,2,1,3] => 4 [4,5,6,2,3,1] => 4 [4,5,6,3,1,2] => 3 [4,5,6,3,2,1] => 2 [4,6,1,2,3,5] => 4 [4,6,1,2,5,3] => 5 [4,6,1,3,2,5] => 5 [4,6,1,3,5,2] => 6 [4,6,1,5,2,3] => 6 [4,6,1,5,3,2] => 5 [4,6,2,1,3,5] => 5 [4,6,2,1,5,3] => 6 [4,6,2,3,1,5] => 6 [4,6,2,3,5,1] => 6 [4,6,2,5,1,3] => 7 [4,6,2,5,3,1] => 6 [4,6,3,1,2,5] => 5 [4,6,3,1,5,2] => 6 [4,6,3,2,1,5] => 4 [4,6,3,2,5,1] => 5 [4,6,3,5,1,2] => 5 [4,6,3,5,2,1] => 5 [4,6,5,1,2,3] => 4 [4,6,5,1,3,2] => 5 [4,6,5,2,1,3] => 5 [4,6,5,2,3,1] => 5 [4,6,5,3,1,2] => 4 [4,6,5,3,2,1] => 3 [5,1,2,3,4,6] => 2 [5,1,2,3,6,4] => 4 [5,1,2,4,3,6] => 3 [5,1,2,4,6,3] => 5 [5,1,2,6,3,4] => 4 [5,1,2,6,4,3] => 5 [5,1,3,2,4,6] => 5 [5,1,3,2,6,4] => 5 [5,1,3,4,2,6] => 4 [5,1,3,4,6,2] => 5 [5,1,3,6,2,4] => 6 [5,1,3,6,4,2] => 6 [5,1,4,2,3,6] => 4 [5,1,4,2,6,3] => 6 [5,1,4,3,2,6] => 3 [5,1,4,3,6,2] => 5 [5,1,4,6,2,3] => 5 [5,1,4,6,3,2] => 5 [5,1,6,2,3,4] => 4 [5,1,6,2,4,3] => 5 [5,1,6,3,2,4] => 6 [5,1,6,3,4,2] => 6 [5,1,6,4,2,3] => 5 [5,1,6,4,3,2] => 4 [5,2,1,3,4,6] => 3 [5,2,1,3,6,4] => 5 [5,2,1,4,3,6] => 4 [5,2,1,4,6,3] => 5 [5,2,1,6,3,4] => 5 [5,2,1,6,4,3] => 4 [5,2,3,1,4,6] => 4 [5,2,3,1,6,4] => 6 [5,2,3,4,1,6] => 4 [5,2,3,4,6,1] => 4 [5,2,3,6,1,4] => 6 [5,2,3,6,4,1] => 5 [5,2,4,1,3,6] => 5 [5,2,4,1,6,3] => 6 [5,2,4,3,1,6] => 4 [5,2,4,3,6,1] => 5 [5,2,4,6,1,3] => 6 [5,2,4,6,3,1] => 6 [5,2,6,1,3,4] => 5 [5,2,6,1,4,3] => 5 [5,2,6,3,1,4] => 6 [5,2,6,3,4,1] => 6 [5,2,6,4,1,3] => 6 [5,2,6,4,3,1] => 5 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 5 [5,3,1,4,2,6] => 5 [5,3,1,4,6,2] => 6 [5,3,1,6,2,4] => 6 [5,3,1,6,4,2] => 6 [5,3,2,1,4,6] => 3 [5,3,2,1,6,4] => 4 [5,3,2,4,1,6] => 4 [5,3,2,4,6,1] => 5 [5,3,2,6,1,4] => 5 [5,3,2,6,4,1] => 5 [5,3,4,1,2,6] => 4 [5,3,4,1,6,2] => 6 [5,3,4,2,1,6] => 4 [5,3,4,2,6,1] => 6 [5,3,4,6,1,2] => 5 [5,3,4,6,2,1] => 4 [5,3,6,1,2,4] => 5 [5,3,6,1,4,2] => 7 [5,3,6,2,1,4] => 5 [5,3,6,2,4,1] => 6 [5,3,6,4,1,2] => 5 [5,3,6,4,2,1] => 5 [5,4,1,2,3,6] => 2 [5,4,1,2,6,3] => 4 [5,4,1,3,2,6] => 3 [5,4,1,3,6,2] => 5 [5,4,1,6,2,3] => 4 [5,4,1,6,3,2] => 5 [5,4,2,1,3,6] => 3 [5,4,2,1,6,3] => 5 [5,4,2,3,1,6] => 4 [5,4,2,3,6,1] => 4 [5,4,2,6,1,3] => 5 [5,4,2,6,3,1] => 5 [5,4,3,1,2,6] => 2 [5,4,3,1,6,2] => 4 [5,4,3,2,1,6] => 1 [5,4,3,2,6,1] => 3 [5,4,3,6,1,2] => 4 [5,4,3,6,2,1] => 3 [5,4,6,1,2,3] => 4 [5,4,6,1,3,2] => 5 [5,4,6,2,1,3] => 5 [5,4,6,2,3,1] => 5 [5,4,6,3,1,2] => 4 [5,4,6,3,2,1] => 3 [5,6,1,2,3,4] => 3 [5,6,1,2,4,3] => 4 [5,6,1,3,2,4] => 6 [5,6,1,3,4,2] => 5 [5,6,1,4,2,3] => 5 [5,6,1,4,3,2] => 4 [5,6,2,1,3,4] => 4 [5,6,2,1,4,3] => 4 [5,6,2,3,1,4] => 5 [5,6,2,3,4,1] => 5 [5,6,2,4,1,3] => 5 [5,6,2,4,3,1] => 4 [5,6,3,1,2,4] => 5 [5,6,3,1,4,2] => 5 [5,6,3,2,1,4] => 4 [5,6,3,2,4,1] => 4 [5,6,3,4,1,2] => 5 [5,6,3,4,2,1] => 4 [5,6,4,1,2,3] => 3 [5,6,4,1,3,2] => 4 [5,6,4,2,1,3] => 4 [5,6,4,2,3,1] => 5 [5,6,4,3,1,2] => 3 [5,6,4,3,2,1] => 2 [6,1,2,3,4,5] => 2 [6,1,2,3,5,4] => 3 [6,1,2,4,3,5] => 5 [6,1,2,4,5,3] => 4 [6,1,2,5,3,4] => 4 [6,1,2,5,4,3] => 3 [6,1,3,2,4,5] => 5 [6,1,3,2,5,4] => 5 [6,1,3,4,2,5] => 5 [6,1,3,4,5,2] => 4 [6,1,3,5,2,4] => 6 [6,1,3,5,4,2] => 5 [6,1,4,2,3,5] => 5 [6,1,4,2,5,3] => 6 [6,1,4,3,2,5] => 5 [6,1,4,3,5,2] => 5 [6,1,4,5,2,3] => 5 [6,1,4,5,3,2] => 4 [6,1,5,2,3,4] => 4 [6,1,5,2,4,3] => 5 [6,1,5,3,2,4] => 5 [6,1,5,3,4,2] => 6 [6,1,5,4,2,3] => 4 [6,1,5,4,3,2] => 3 [6,2,1,3,4,5] => 3 [6,2,1,3,5,4] => 4 [6,2,1,4,3,5] => 5 [6,2,1,4,5,3] => 5 [6,2,1,5,3,4] => 5 [6,2,1,5,4,3] => 4 [6,2,3,1,4,5] => 4 [6,2,3,1,5,4] => 5 [6,2,3,4,1,5] => 4 [6,2,3,4,5,1] => 4 [6,2,3,5,1,4] => 5 [6,2,3,5,4,1] => 5 [6,2,4,1,3,5] => 6 [6,2,4,1,5,3] => 6 [6,2,4,3,1,5] => 5 [6,2,4,3,5,1] => 6 [6,2,4,5,1,3] => 6 [6,2,4,5,3,1] => 5 [6,2,5,1,3,4] => 5 [6,2,5,1,4,3] => 5 [6,2,5,3,1,4] => 6 [6,2,5,3,4,1] => 5 [6,2,5,4,1,3] => 5 [6,2,5,4,3,1] => 4 [6,3,1,2,4,5] => 4 [6,3,1,2,5,4] => 5 [6,3,1,4,2,5] => 6 [6,3,1,4,5,2] => 5 [6,3,1,5,2,4] => 6 [6,3,1,5,4,2] => 5 [6,3,2,1,4,5] => 3 [6,3,2,1,5,4] => 4 [6,3,2,4,1,5] => 5 [6,3,2,4,5,1] => 5 [6,3,2,5,1,4] => 5 [6,3,2,5,4,1] => 4 [6,3,4,1,2,5] => 5 [6,3,4,1,5,2] => 6 [6,3,4,2,1,5] => 4 [6,3,4,2,5,1] => 5 [6,3,4,5,1,2] => 5 [6,3,4,5,2,1] => 4 [6,3,5,1,2,4] => 5 [6,3,5,1,4,2] => 6 [6,3,5,2,1,4] => 5 [6,3,5,2,4,1] => 6 [6,3,5,4,1,2] => 4 [6,3,5,4,2,1] => 4 [6,4,1,2,3,5] => 4 [6,4,1,2,5,3] => 5 [6,4,1,3,2,5] => 5 [6,4,1,3,5,2] => 6 [6,4,1,5,2,3] => 5 [6,4,1,5,3,2] => 5 [6,4,2,1,3,5] => 5 [6,4,2,1,5,3] => 5 [6,4,2,3,1,5] => 6 [6,4,2,3,5,1] => 5 [6,4,2,5,1,3] => 6 [6,4,2,5,3,1] => 6 [6,4,3,1,2,5] => 4 [6,4,3,1,5,2] => 5 [6,4,3,2,1,5] => 3 [6,4,3,2,5,1] => 4 [6,4,3,5,1,2] => 4 [6,4,3,5,2,1] => 4 [6,4,5,1,2,3] => 4 [6,4,5,1,3,2] => 5 [6,4,5,2,1,3] => 5 [6,4,5,2,3,1] => 6 [6,4,5,3,1,2] => 5 [6,4,5,3,2,1] => 4 [6,5,1,2,3,4] => 2 [6,5,1,2,4,3] => 3 [6,5,1,3,2,4] => 5 [6,5,1,3,4,2] => 4 [6,5,1,4,2,3] => 4 [6,5,1,4,3,2] => 3 [6,5,2,1,3,4] => 3 [6,5,2,1,4,3] => 4 [6,5,2,3,1,4] => 4 [6,5,2,3,4,1] => 4 [6,5,2,4,1,3] => 5 [6,5,2,4,3,1] => 4 [6,5,3,1,2,4] => 4 [6,5,3,1,4,2] => 5 [6,5,3,2,1,4] => 3 [6,5,3,2,4,1] => 4 [6,5,3,4,1,2] => 4 [6,5,3,4,2,1] => 4 [6,5,4,1,2,3] => 2 [6,5,4,1,3,2] => 3 [6,5,4,2,1,3] => 3 [6,5,4,2,3,1] => 4 [6,5,4,3,1,2] => 2 [6,5,4,3,2,1] => 1 [1,2,3,4,5,6,7] => 0 [1,2,3,4,5,7,6] => 3 [1,2,3,4,6,5,7] => 3 [1,2,3,4,6,7,5] => 4 [1,2,3,4,7,5,6] => 4 [1,2,3,4,7,6,5] => 3 [1,2,3,5,4,6,7] => 3 [1,2,3,5,4,7,6] => 5 [1,2,3,5,6,4,7] => 4 [1,2,3,5,6,7,4] => 4 [1,2,3,5,7,4,6] => 6 [1,2,3,5,7,6,4] => 5 [1,2,3,6,4,5,7] => 4 [1,2,3,6,4,7,5] => 6 [1,2,3,6,5,4,7] => 3 [1,2,3,6,5,7,4] => 5 [1,2,3,6,7,4,5] => 4 [1,2,3,6,7,5,4] => 4 [1,2,3,7,4,5,6] => 4 [1,2,3,7,4,6,5] => 5 [1,2,3,7,5,4,6] => 5 [1,2,3,7,5,6,4] => 6 [1,2,3,7,6,4,5] => 4 [1,2,3,7,6,5,4] => 3 [1,2,4,3,5,6,7] => 3 [1,2,4,3,5,7,6] => 6 [1,2,4,3,6,5,7] => 5 [1,2,4,3,6,7,5] => 5 [1,2,4,3,7,5,6] => 5 [1,2,4,3,7,6,5] => 5 [1,2,4,5,3,6,7] => 4 [1,2,4,5,3,7,6] => 5 [1,2,4,5,6,3,7] => 4 [1,2,4,5,6,7,3] => 4 [1,2,4,5,7,3,6] => 6 [1,2,4,5,7,6,3] => 5 [1,2,4,6,3,5,7] => 6 [1,2,4,6,3,7,5] => 7 [1,2,4,6,5,3,7] => 5 [1,2,4,6,5,7,3] => 7 [1,2,4,6,7,3,5] => 6 [1,2,4,6,7,5,3] => 6 [1,2,4,7,3,5,6] => 6 [1,2,4,7,3,6,5] => 6 [1,2,4,7,5,3,6] => 7 [1,2,4,7,5,6,3] => 6 [1,2,4,7,6,3,5] => 6 [1,2,4,7,6,5,3] => 5 [1,2,5,3,4,6,7] => 4 [1,2,5,3,4,7,6] => 5 [1,2,5,3,6,4,7] => 6 [1,2,5,3,6,7,4] => 6 [1,2,5,3,7,4,6] => 7 [1,2,5,3,7,6,4] => 6 [1,2,5,4,3,6,7] => 3 [1,2,5,4,3,7,6] => 5 [1,2,5,4,6,3,7] => 5 [1,2,5,4,6,7,3] => 5 [1,2,5,4,7,3,6] => 6 [1,2,5,4,7,6,3] => 6 [1,2,5,6,3,4,7] => 4 [1,2,5,6,3,7,4] => 6 [1,2,5,6,4,3,7] => 4 [1,2,5,6,4,7,3] => 6 [1,2,5,6,7,3,4] => 4 [1,2,5,6,7,4,3] => 4 [1,2,5,7,3,4,6] => 6 [1,2,5,7,3,6,4] => 7 [1,2,5,7,4,3,6] => 6 [1,2,5,7,4,6,3] => 7 [1,2,5,7,6,3,4] => 5 [1,2,5,7,6,4,3] => 5 [1,2,6,3,4,5,7] => 4 [1,2,6,3,4,7,5] => 6 [1,2,6,3,5,4,7] => 5 [1,2,6,3,5,7,4] => 7 [1,2,6,3,7,4,5] => 6 [1,2,6,3,7,5,4] => 6 [1,2,6,4,3,5,7] => 5 [1,2,6,4,3,7,5] => 6 [1,2,6,4,5,3,7] => 6 [1,2,6,4,5,7,3] => 6 [1,2,6,4,7,3,5] => 7 [1,2,6,4,7,5,3] => 7 [1,2,6,5,3,4,7] => 4 [1,2,6,5,3,7,4] => 6 [1,2,6,5,4,3,7] => 3 [1,2,6,5,4,7,3] => 5 [1,2,6,5,7,3,4] => 6 [1,2,6,5,7,4,3] => 5 [1,2,6,7,3,4,5] => 4 [1,2,6,7,3,5,4] => 5 [1,2,6,7,4,3,5] => 6 [1,2,6,7,4,5,3] => 6 [1,2,6,7,5,3,4] => 5 [1,2,6,7,5,4,3] => 4 [1,2,7,3,4,5,6] => 4 [1,2,7,3,4,6,5] => 5 [1,2,7,3,5,4,6] => 7 [1,2,7,3,5,6,4] => 6 [1,2,7,3,6,4,5] => 6 [1,2,7,3,6,5,4] => 5 [1,2,7,4,3,5,6] => 5 [1,2,7,4,3,6,5] => 6 [1,2,7,4,5,3,6] => 6 [1,2,7,4,5,6,3] => 6 [1,2,7,4,6,3,5] => 7 [1,2,7,4,6,5,3] => 6 [1,2,7,5,3,4,6] => 6 [1,2,7,5,3,6,4] => 7 [1,2,7,5,4,3,6] => 5 [1,2,7,5,4,6,3] => 6 [1,2,7,5,6,3,4] => 6 [1,2,7,5,6,4,3] => 6 [1,2,7,6,3,4,5] => 4 [1,2,7,6,3,5,4] => 5 [1,2,7,6,4,3,5] => 5 [1,2,7,6,4,5,3] => 6 [1,2,7,6,5,3,4] => 4 [1,2,7,6,5,4,3] => 3 [1,3,2,4,5,6,7] => 3 [1,3,2,4,5,7,6] => 6 [1,3,2,4,6,5,7] => 6 [1,3,2,4,6,7,5] => 7 [1,3,2,4,7,5,6] => 7 [1,3,2,4,7,6,5] => 6 [1,3,2,5,4,6,7] => 5 [1,3,2,5,4,7,6] => 7 [1,3,2,5,6,4,7] => 5 [1,3,2,5,6,7,4] => 5 [1,3,2,5,7,4,6] => 7 [1,3,2,5,7,6,4] => 6 [1,3,2,6,4,5,7] => 5 [1,3,2,6,4,7,5] => 7 [1,3,2,6,5,4,7] => 5 [1,3,2,6,5,7,4] => 7 [1,3,2,6,7,4,5] => 5 [1,3,2,6,7,5,4] => 6 [1,3,2,7,4,5,6] => 5 [1,3,2,7,4,6,5] => 6 [1,3,2,7,5,4,6] => 7 [1,3,2,7,5,6,4] => 7 [1,3,2,7,6,4,5] => 6 [1,3,2,7,6,5,4] => 5 [1,3,4,2,5,6,7] => 3 [1,3,4,2,5,7,6] => 6 [1,3,4,2,6,5,7] => 5 [1,3,4,2,6,7,5] => 5 [1,3,4,2,7,5,6] => 5 [1,3,4,2,7,6,5] => 5 [1,3,4,5,2,6,7] => 3 [1,3,4,5,2,7,6] => 5 [1,3,4,5,6,2,7] => 3 [1,3,4,5,6,7,2] => 3 [1,3,4,5,7,2,6] => 5 [1,3,4,5,7,6,2] => 4 [1,3,4,6,2,5,7] => 5 [1,3,4,6,2,7,5] => 6 [1,3,4,6,5,2,7] => 4 [1,3,4,6,5,7,2] => 6 [1,3,4,6,7,2,5] => 5 [1,3,4,6,7,5,2] => 5 [1,3,4,7,2,5,6] => 5 [1,3,4,7,2,6,5] => 6 [1,3,4,7,5,2,6] => 6 [1,3,4,7,5,6,2] => 5 [1,3,4,7,6,2,5] => 6 [1,3,4,7,6,5,2] => 4 [1,3,5,2,4,6,7] => 5 [1,3,5,2,4,7,6] => 7 [1,3,5,2,6,4,7] => 6 [1,3,5,2,6,7,4] => 6 [1,3,5,2,7,4,6] => 7 [1,3,5,2,7,6,4] => 7 [1,3,5,4,2,6,7] => 4 [1,3,5,4,2,7,6] => 6 [1,3,5,4,6,2,7] => 6 [1,3,5,4,6,7,2] => 6 [1,3,5,4,7,2,6] => 6 [1,3,5,4,7,6,2] => 6 [1,3,5,6,2,4,7] => 5 [1,3,5,6,2,7,4] => 7 [1,3,5,6,4,2,7] => 5 [1,3,5,6,4,7,2] => 6 [1,3,5,6,7,2,4] => 5 [1,3,5,6,7,4,2] => 5 [1,3,5,7,2,4,6] => 7 [1,3,5,7,2,6,4] => 7 [1,3,5,7,4,2,6] => 7 [1,3,5,7,4,6,2] => 7 [1,3,5,7,6,2,4] => 6 [1,3,5,7,6,4,2] => 6 [1,3,6,2,4,5,7] => 5 [1,3,6,2,4,7,5] => 7 [1,3,6,2,5,4,7] => 6 [1,3,6,2,5,7,4] => 7 [1,3,6,2,7,4,5] => 7 [1,3,6,2,7,5,4] => 6 [1,3,6,4,2,5,7] => 6 [1,3,6,4,2,7,5] => 7 [1,3,6,4,5,2,7] => 5 [1,3,6,4,5,7,2] => 6 [1,3,6,4,7,2,5] => 7 [1,3,6,4,7,5,2] => 7 [1,3,6,5,2,4,7] => 6 [1,3,6,5,2,7,4] => 6 [1,3,6,5,4,2,7] => 4 [1,3,6,5,4,7,2] => 6 [1,3,6,5,7,2,4] => 7 [1,3,6,5,7,4,2] => 6 [1,3,6,7,2,4,5] => 5 [1,3,6,7,2,5,4] => 6 [1,3,6,7,4,2,5] => 7 [1,3,6,7,4,5,2] => 6 [1,3,6,7,5,2,4] => 7 [1,3,6,7,5,4,2] => 5 [1,3,7,2,4,5,6] => 5 [1,3,7,2,4,6,5] => 6 [1,3,7,2,5,4,6] => 7 [1,3,7,2,5,6,4] => 7 [1,3,7,2,6,4,5] => 7 [1,3,7,2,6,5,4] => 6 [1,3,7,4,2,5,6] => 6 [1,3,7,4,2,6,5] => 7 [1,3,7,4,5,2,6] => 7 [1,3,7,4,5,6,2] => 5 [1,3,7,4,6,2,5] => 7 [1,3,7,4,6,5,2] => 6 [1,3,7,5,2,4,6] => 7 [1,3,7,5,2,6,4] => 8 [1,3,7,5,4,2,6] => 6 [1,3,7,5,4,6,2] => 6 [1,3,7,5,6,2,4] => 7 [1,3,7,5,6,4,2] => 7 [1,3,7,6,2,4,5] => 6 [1,3,7,6,2,5,4] => 6 [1,3,7,6,4,2,5] => 6 [1,3,7,6,4,5,2] => 5 [1,3,7,6,5,2,4] => 6 [1,3,7,6,5,4,2] => 4 [1,4,2,3,5,6,7] => 3 [1,4,2,3,5,7,6] => 6 [1,4,2,3,6,5,7] => 5 [1,4,2,3,6,7,5] => 5 [1,4,2,3,7,5,6] => 5 [1,4,2,3,7,6,5] => 5 [1,4,2,5,3,6,7] => 5 [1,4,2,5,3,7,6] => 7 [1,4,2,5,6,3,7] => 5 [1,4,2,5,6,7,3] => 5 [1,4,2,5,7,3,6] => 7 [1,4,2,5,7,6,3] => 6 [1,4,2,6,3,5,7] => 6 [1,4,2,6,3,7,5] => 7 [1,4,2,6,5,3,7] => 6 [1,4,2,6,5,7,3] => 7 [1,4,2,6,7,3,5] => 7 [1,4,2,6,7,5,3] => 7 [1,4,2,7,3,5,6] => 6 [1,4,2,7,3,6,5] => 7 [1,4,2,7,5,3,6] => 7 [1,4,2,7,5,6,3] => 7 [1,4,2,7,6,3,5] => 6 [1,4,2,7,6,5,3] => 6 [1,4,3,2,5,6,7] => 3 [1,4,3,2,5,7,6] => 6 [1,4,3,2,6,5,7] => 5 [1,4,3,2,6,7,5] => 5 [1,4,3,2,7,5,6] => 5 [1,4,3,2,7,6,5] => 6 [1,4,3,5,2,6,7] => 5 [1,4,3,5,2,7,6] => 6 [1,4,3,5,6,2,7] => 5 [1,4,3,5,6,7,2] => 5 [1,4,3,5,7,2,6] => 7 [1,4,3,5,7,6,2] => 6 [1,4,3,6,2,5,7] => 6 [1,4,3,6,2,7,5] => 7 [1,4,3,6,5,2,7] => 6 [1,4,3,6,5,7,2] => 7 [1,4,3,6,7,2,5] => 6 [1,4,3,6,7,5,2] => 7 [1,4,3,7,2,5,6] => 6 [1,4,3,7,2,6,5] => 6 [1,4,3,7,5,2,6] => 7 [1,4,3,7,5,6,2] => 7 [1,4,3,7,6,2,5] => 6 [1,4,3,7,6,5,2] => 6 [1,4,5,2,3,6,7] => 3 [1,4,5,2,3,7,6] => 5 [1,4,5,2,6,3,7] => 5 [1,4,5,2,6,7,3] => 5 [1,4,5,2,7,3,6] => 6 [1,4,5,2,7,6,3] => 6 [1,4,5,3,2,6,7] => 4 [1,4,5,3,2,7,6] => 6 [1,4,5,3,6,2,7] => 5 [1,4,5,3,6,7,2] => 5 [1,4,5,3,7,2,6] => 7 [1,4,5,3,7,6,2] => 6 [1,4,5,6,2,3,7] => 3 [1,4,5,6,2,7,3] => 5 [1,4,5,6,3,2,7] => 4 [1,4,5,6,3,7,2] => 5 [1,4,5,6,7,2,3] => 3 [1,4,5,6,7,3,2] => 4 [1,4,5,7,2,3,6] => 5 [1,4,5,7,2,6,3] => 6 [1,4,5,7,3,2,6] => 6 [1,4,5,7,3,6,2] => 6 [1,4,5,7,6,2,3] => 4 [1,4,5,7,6,3,2] => 5 [1,4,6,2,3,5,7] => 5 [1,4,6,2,3,7,5] => 6 [1,4,6,2,5,3,7] => 6 [1,4,6,2,5,7,3] => 7 [1,4,6,2,7,3,5] => 7 [1,4,6,2,7,5,3] => 7 [1,4,6,3,2,5,7] => 6 [1,4,6,3,2,7,5] => 7 [1,4,6,3,5,2,7] => 6 [1,4,6,3,5,7,2] => 7 [1,4,6,3,7,2,5] => 7 [1,4,6,3,7,5,2] => 7 [1,4,6,5,2,3,7] => 4 [1,4,6,5,2,7,3] => 6 [1,4,6,5,3,2,7] => 5 ----------------------------------------------------------------------------- Created: Mar 25, 2019 at 14:37 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Mar 09, 2023 at 13:53 by Tilman Möller