***************************************************************************** * 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: St001683 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. ----------------------------------------------------------------------------- References: [1] Thamrongpairoj, S., Remmel, J. B. Positional Marked Patterns in Permutations [[arXiv:2102.03867]] ----------------------------------------------------------------------------- Code: def statistic(pi, tau=[1,3,2], mark=1): """ The number of positions i such that tau occurs in pi and the mark is at position i. EXAMPLES:: sage: pi = Permutation([2,6,4,8,1,5,7,3]) sage: tau = Permutation([1,4,3,2]) sage: statistic(pi, tau, 1) 2 Table before section 3.2:: sage: q = QQ["q"].gen() sage: [sum(q^statistic(pi, [1,2,3], 0) for pi in Permutations(n)) for n in range(1,7)] [1, 2, q + 5, 2*q^2 + 8*q + 14, 6*q^3 + 25*q^2 + 47*q + 42, 24*q^4 + 104*q^3 + 216*q^2 + 244*q + 132] """ return len(set([pos[mark] for pos in pi.pattern_positions(tau)])) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 0 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 0 [2,3,1] => 0 [3,1,2] => 0 [3,2,1] => 0 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 1 [1,4,3,2] => 2 [2,1,3,4] => 0 [2,1,4,3] => 1 [2,3,1,4] => 0 [2,3,4,1] => 0 [2,4,1,3] => 1 [2,4,3,1] => 1 [3,1,2,4] => 0 [3,1,4,2] => 1 [3,2,1,4] => 0 [3,2,4,1] => 0 [3,4,1,2] => 0 [3,4,2,1] => 0 [4,1,2,3] => 0 [4,1,3,2] => 1 [4,2,1,3] => 0 [4,2,3,1] => 0 [4,3,1,2] => 0 [4,3,2,1] => 0 [1,2,3,4,5] => 0 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 2 [1,2,5,3,4] => 1 [1,2,5,4,3] => 2 [1,3,2,4,5] => 1 [1,3,2,5,4] => 2 [1,3,4,2,5] => 2 [1,3,4,5,2] => 3 [1,3,5,2,4] => 2 [1,3,5,4,2] => 3 [1,4,2,3,5] => 1 [1,4,2,5,3] => 2 [1,4,3,2,5] => 2 [1,4,3,5,2] => 3 [1,4,5,2,3] => 2 [1,4,5,3,2] => 3 [1,5,2,3,4] => 1 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 3 [1,5,4,2,3] => 2 [1,5,4,3,2] => 3 [2,1,3,4,5] => 0 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => 2 [2,1,5,3,4] => 1 [2,1,5,4,3] => 2 [2,3,1,4,5] => 0 [2,3,1,5,4] => 1 [2,3,4,1,5] => 0 [2,3,4,5,1] => 0 [2,3,5,1,4] => 1 [2,3,5,4,1] => 1 [2,4,1,3,5] => 1 [2,4,1,5,3] => 2 [2,4,3,1,5] => 1 [2,4,3,5,1] => 1 [2,4,5,1,3] => 2 [2,4,5,3,1] => 2 [2,5,1,3,4] => 1 [2,5,1,4,3] => 2 [2,5,3,1,4] => 1 [2,5,3,4,1] => 1 [2,5,4,1,3] => 2 [2,5,4,3,1] => 2 [3,1,2,4,5] => 0 [3,1,2,5,4] => 1 [3,1,4,2,5] => 1 [3,1,4,5,2] => 2 [3,1,5,2,4] => 1 [3,1,5,4,2] => 2 [3,2,1,4,5] => 0 [3,2,1,5,4] => 1 [3,2,4,1,5] => 0 [3,2,4,5,1] => 0 [3,2,5,1,4] => 1 [3,2,5,4,1] => 1 [3,4,1,2,5] => 0 [3,4,1,5,2] => 1 [3,4,2,1,5] => 0 [3,4,2,5,1] => 0 [3,4,5,1,2] => 0 [3,4,5,2,1] => 0 [3,5,1,2,4] => 1 [3,5,1,4,2] => 2 [3,5,2,1,4] => 1 [3,5,2,4,1] => 1 [3,5,4,1,2] => 1 [3,5,4,2,1] => 1 [4,1,2,3,5] => 0 [4,1,2,5,3] => 1 [4,1,3,2,5] => 1 [4,1,3,5,2] => 2 [4,1,5,2,3] => 1 [4,1,5,3,2] => 2 [4,2,1,3,5] => 0 [4,2,1,5,3] => 1 [4,2,3,1,5] => 0 [4,2,3,5,1] => 0 [4,2,5,1,3] => 1 [4,2,5,3,1] => 1 [4,3,1,2,5] => 0 [4,3,1,5,2] => 1 [4,3,2,1,5] => 0 [4,3,2,5,1] => 0 [4,3,5,1,2] => 0 [4,3,5,2,1] => 0 [4,5,1,2,3] => 0 [4,5,1,3,2] => 1 [4,5,2,1,3] => 0 [4,5,2,3,1] => 0 [4,5,3,1,2] => 0 [4,5,3,2,1] => 0 [5,1,2,3,4] => 0 [5,1,2,4,3] => 1 [5,1,3,2,4] => 1 [5,1,3,4,2] => 2 [5,1,4,2,3] => 1 [5,1,4,3,2] => 2 [5,2,1,3,4] => 0 [5,2,1,4,3] => 1 [5,2,3,1,4] => 0 [5,2,3,4,1] => 0 [5,2,4,1,3] => 1 [5,2,4,3,1] => 1 [5,3,1,2,4] => 0 [5,3,1,4,2] => 1 [5,3,2,1,4] => 0 [5,3,2,4,1] => 0 [5,3,4,1,2] => 0 [5,3,4,2,1] => 0 [5,4,1,2,3] => 0 [5,4,1,3,2] => 1 [5,4,2,1,3] => 0 [5,4,2,3,1] => 0 [5,4,3,1,2] => 0 [5,4,3,2,1] => 0 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 1 [1,2,3,5,4,6] => 1 [1,2,3,5,6,4] => 2 [1,2,3,6,4,5] => 1 [1,2,3,6,5,4] => 2 [1,2,4,3,5,6] => 1 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 2 [1,2,4,5,6,3] => 3 [1,2,4,6,3,5] => 2 [1,2,4,6,5,3] => 3 [1,2,5,3,4,6] => 1 [1,2,5,3,6,4] => 2 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 3 [1,2,5,6,3,4] => 2 [1,2,5,6,4,3] => 3 [1,2,6,3,4,5] => 1 [1,2,6,3,5,4] => 2 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 3 [1,2,6,5,3,4] => 2 [1,2,6,5,4,3] => 3 [1,3,2,4,5,6] => 1 [1,3,2,4,6,5] => 2 [1,3,2,5,4,6] => 2 [1,3,2,5,6,4] => 3 [1,3,2,6,4,5] => 2 [1,3,2,6,5,4] => 3 [1,3,4,2,5,6] => 2 [1,3,4,2,6,5] => 3 [1,3,4,5,2,6] => 3 [1,3,4,5,6,2] => 4 [1,3,4,6,2,5] => 3 [1,3,4,6,5,2] => 4 [1,3,5,2,4,6] => 2 [1,3,5,2,6,4] => 3 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 4 [1,3,5,6,2,4] => 3 [1,3,5,6,4,2] => 4 [1,3,6,2,4,5] => 2 [1,3,6,2,5,4] => 3 [1,3,6,4,2,5] => 3 [1,3,6,4,5,2] => 4 [1,3,6,5,2,4] => 3 [1,3,6,5,4,2] => 4 [1,4,2,3,5,6] => 1 [1,4,2,3,6,5] => 2 [1,4,2,5,3,6] => 2 [1,4,2,5,6,3] => 3 [1,4,2,6,3,5] => 2 [1,4,2,6,5,3] => 3 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 3 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 4 [1,4,3,6,2,5] => 3 [1,4,3,6,5,2] => 4 [1,4,5,2,3,6] => 2 [1,4,5,2,6,3] => 3 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 4 [1,4,5,6,2,3] => 3 [1,4,5,6,3,2] => 4 [1,4,6,2,3,5] => 2 [1,4,6,2,5,3] => 3 [1,4,6,3,2,5] => 3 [1,4,6,3,5,2] => 4 [1,4,6,5,2,3] => 3 [1,4,6,5,3,2] => 4 [1,5,2,3,4,6] => 1 [1,5,2,3,6,4] => 2 [1,5,2,4,3,6] => 2 [1,5,2,4,6,3] => 3 [1,5,2,6,3,4] => 2 [1,5,2,6,4,3] => 3 [1,5,3,2,4,6] => 2 [1,5,3,2,6,4] => 3 [1,5,3,4,2,6] => 3 [1,5,3,4,6,2] => 4 [1,5,3,6,2,4] => 3 [1,5,3,6,4,2] => 4 [1,5,4,2,3,6] => 2 [1,5,4,2,6,3] => 3 [1,5,4,3,2,6] => 3 [1,5,4,3,6,2] => 4 [1,5,4,6,2,3] => 3 [1,5,4,6,3,2] => 4 [1,5,6,2,3,4] => 2 [1,5,6,2,4,3] => 3 [1,5,6,3,2,4] => 3 [1,5,6,3,4,2] => 4 [1,5,6,4,2,3] => 3 [1,5,6,4,3,2] => 4 [1,6,2,3,4,5] => 1 [1,6,2,3,5,4] => 2 [1,6,2,4,3,5] => 2 [1,6,2,4,5,3] => 3 [1,6,2,5,3,4] => 2 [1,6,2,5,4,3] => 3 [1,6,3,2,4,5] => 2 [1,6,3,2,5,4] => 3 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 4 [1,6,3,5,2,4] => 3 [1,6,3,5,4,2] => 4 [1,6,4,2,3,5] => 2 [1,6,4,2,5,3] => 3 [1,6,4,3,2,5] => 3 [1,6,4,3,5,2] => 4 [1,6,4,5,2,3] => 3 [1,6,4,5,3,2] => 4 [1,6,5,2,3,4] => 2 [1,6,5,2,4,3] => 3 [1,6,5,3,2,4] => 3 [1,6,5,3,4,2] => 4 [1,6,5,4,2,3] => 3 [1,6,5,4,3,2] => 4 [2,1,3,4,5,6] => 0 [2,1,3,4,6,5] => 1 [2,1,3,5,4,6] => 1 [2,1,3,5,6,4] => 2 [2,1,3,6,4,5] => 1 [2,1,3,6,5,4] => 2 [2,1,4,3,5,6] => 1 [2,1,4,3,6,5] => 2 [2,1,4,5,3,6] => 2 [2,1,4,5,6,3] => 3 [2,1,4,6,3,5] => 2 [2,1,4,6,5,3] => 3 [2,1,5,3,4,6] => 1 [2,1,5,3,6,4] => 2 [2,1,5,4,3,6] => 2 [2,1,5,4,6,3] => 3 [2,1,5,6,3,4] => 2 [2,1,5,6,4,3] => 3 [2,1,6,3,4,5] => 1 [2,1,6,3,5,4] => 2 [2,1,6,4,3,5] => 2 [2,1,6,4,5,3] => 3 [2,1,6,5,3,4] => 2 [2,1,6,5,4,3] => 3 [2,3,1,4,5,6] => 0 [2,3,1,4,6,5] => 1 [2,3,1,5,4,6] => 1 [2,3,1,5,6,4] => 2 [2,3,1,6,4,5] => 1 [2,3,1,6,5,4] => 2 [2,3,4,1,5,6] => 0 [2,3,4,1,6,5] => 1 [2,3,4,5,1,6] => 0 [2,3,4,5,6,1] => 0 [2,3,4,6,1,5] => 1 [2,3,4,6,5,1] => 1 [2,3,5,1,4,6] => 1 [2,3,5,1,6,4] => 2 [2,3,5,4,1,6] => 1 [2,3,5,4,6,1] => 1 [2,3,5,6,1,4] => 2 [2,3,5,6,4,1] => 2 [2,3,6,1,4,5] => 1 [2,3,6,1,5,4] => 2 [2,3,6,4,1,5] => 1 [2,3,6,4,5,1] => 1 [2,3,6,5,1,4] => 2 [2,3,6,5,4,1] => 2 [2,4,1,3,5,6] => 1 [2,4,1,3,6,5] => 2 [2,4,1,5,3,6] => 2 [2,4,1,5,6,3] => 3 [2,4,1,6,3,5] => 2 [2,4,1,6,5,3] => 3 [2,4,3,1,5,6] => 1 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 1 [2,4,3,5,6,1] => 1 [2,4,3,6,1,5] => 2 [2,4,3,6,5,1] => 2 [2,4,5,1,3,6] => 2 [2,4,5,1,6,3] => 3 [2,4,5,3,1,6] => 2 [2,4,5,3,6,1] => 2 [2,4,5,6,1,3] => 3 [2,4,5,6,3,1] => 3 [2,4,6,1,3,5] => 2 [2,4,6,1,5,3] => 3 [2,4,6,3,1,5] => 2 [2,4,6,3,5,1] => 2 [2,4,6,5,1,3] => 3 [2,4,6,5,3,1] => 3 [2,5,1,3,4,6] => 1 [2,5,1,3,6,4] => 2 [2,5,1,4,3,6] => 2 [2,5,1,4,6,3] => 3 [2,5,1,6,3,4] => 2 [2,5,1,6,4,3] => 3 [2,5,3,1,4,6] => 1 [2,5,3,1,6,4] => 2 [2,5,3,4,1,6] => 1 [2,5,3,4,6,1] => 1 [2,5,3,6,1,4] => 2 [2,5,3,6,4,1] => 2 [2,5,4,1,3,6] => 2 [2,5,4,1,6,3] => 3 [2,5,4,3,1,6] => 2 [2,5,4,3,6,1] => 2 [2,5,4,6,1,3] => 3 [2,5,4,6,3,1] => 3 [2,5,6,1,3,4] => 2 [2,5,6,1,4,3] => 3 [2,5,6,3,1,4] => 2 [2,5,6,3,4,1] => 2 [2,5,6,4,1,3] => 3 [2,5,6,4,3,1] => 3 [2,6,1,3,4,5] => 1 [2,6,1,3,5,4] => 2 [2,6,1,4,3,5] => 2 [2,6,1,4,5,3] => 3 [2,6,1,5,3,4] => 2 [2,6,1,5,4,3] => 3 [2,6,3,1,4,5] => 1 [2,6,3,1,5,4] => 2 [2,6,3,4,1,5] => 1 [2,6,3,4,5,1] => 1 [2,6,3,5,1,4] => 2 [2,6,3,5,4,1] => 2 [2,6,4,1,3,5] => 2 [2,6,4,1,5,3] => 3 [2,6,4,3,1,5] => 2 [2,6,4,3,5,1] => 2 [2,6,4,5,1,3] => 3 [2,6,4,5,3,1] => 3 [2,6,5,1,3,4] => 2 [2,6,5,1,4,3] => 3 [2,6,5,3,1,4] => 2 [2,6,5,3,4,1] => 2 [2,6,5,4,1,3] => 3 [2,6,5,4,3,1] => 3 [3,1,2,4,5,6] => 0 [3,1,2,4,6,5] => 1 [3,1,2,5,4,6] => 1 [3,1,2,5,6,4] => 2 [3,1,2,6,4,5] => 1 [3,1,2,6,5,4] => 2 [3,1,4,2,5,6] => 1 [3,1,4,2,6,5] => 2 [3,1,4,5,2,6] => 2 [3,1,4,5,6,2] => 3 [3,1,4,6,2,5] => 2 [3,1,4,6,5,2] => 3 [3,1,5,2,4,6] => 1 [3,1,5,2,6,4] => 2 [3,1,5,4,2,6] => 2 [3,1,5,4,6,2] => 3 [3,1,5,6,2,4] => 2 [3,1,5,6,4,2] => 3 [3,1,6,2,4,5] => 1 [3,1,6,2,5,4] => 2 [3,1,6,4,2,5] => 2 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 2 [3,1,6,5,4,2] => 3 [3,2,1,4,5,6] => 0 [3,2,1,4,6,5] => 1 [3,2,1,5,4,6] => 1 [3,2,1,5,6,4] => 2 [3,2,1,6,4,5] => 1 [3,2,1,6,5,4] => 2 [3,2,4,1,5,6] => 0 [3,2,4,1,6,5] => 1 [3,2,4,5,1,6] => 0 [3,2,4,5,6,1] => 0 [3,2,4,6,1,5] => 1 [3,2,4,6,5,1] => 1 [3,2,5,1,4,6] => 1 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 1 [3,2,5,4,6,1] => 1 [3,2,5,6,1,4] => 2 [3,2,5,6,4,1] => 2 [3,2,6,1,4,5] => 1 [3,2,6,1,5,4] => 2 [3,2,6,4,1,5] => 1 [3,2,6,4,5,1] => 1 [3,2,6,5,1,4] => 2 [3,2,6,5,4,1] => 2 [3,4,1,2,5,6] => 0 [3,4,1,2,6,5] => 1 [3,4,1,5,2,6] => 1 [3,4,1,5,6,2] => 2 [3,4,1,6,2,5] => 1 [3,4,1,6,5,2] => 2 [3,4,2,1,5,6] => 0 [3,4,2,1,6,5] => 1 [3,4,2,5,1,6] => 0 [3,4,2,5,6,1] => 0 [3,4,2,6,1,5] => 1 [3,4,2,6,5,1] => 1 [3,4,5,1,2,6] => 0 [3,4,5,1,6,2] => 1 [3,4,5,2,1,6] => 0 [3,4,5,2,6,1] => 0 [3,4,5,6,1,2] => 0 [3,4,5,6,2,1] => 0 [3,4,6,1,2,5] => 1 [3,4,6,1,5,2] => 2 [3,4,6,2,1,5] => 1 [3,4,6,2,5,1] => 1 [3,4,6,5,1,2] => 1 [3,4,6,5,2,1] => 1 [3,5,1,2,4,6] => 1 [3,5,1,2,6,4] => 2 [3,5,1,4,2,6] => 2 [3,5,1,4,6,2] => 3 [3,5,1,6,2,4] => 2 [3,5,1,6,4,2] => 3 [3,5,2,1,4,6] => 1 [3,5,2,1,6,4] => 2 [3,5,2,4,1,6] => 1 [3,5,2,4,6,1] => 1 [3,5,2,6,1,4] => 2 [3,5,2,6,4,1] => 2 [3,5,4,1,2,6] => 1 [3,5,4,1,6,2] => 2 [3,5,4,2,1,6] => 1 [3,5,4,2,6,1] => 1 [3,5,4,6,1,2] => 1 [3,5,4,6,2,1] => 1 [3,5,6,1,2,4] => 2 [3,5,6,1,4,2] => 3 [3,5,6,2,1,4] => 2 [3,5,6,2,4,1] => 2 [3,5,6,4,1,2] => 2 [3,5,6,4,2,1] => 2 [3,6,1,2,4,5] => 1 [3,6,1,2,5,4] => 2 [3,6,1,4,2,5] => 2 [3,6,1,4,5,2] => 3 [3,6,1,5,2,4] => 2 [3,6,1,5,4,2] => 3 [3,6,2,1,4,5] => 1 [3,6,2,1,5,4] => 2 [3,6,2,4,1,5] => 1 [3,6,2,4,5,1] => 1 [3,6,2,5,1,4] => 2 [3,6,2,5,4,1] => 2 [3,6,4,1,2,5] => 1 [3,6,4,1,5,2] => 2 [3,6,4,2,1,5] => 1 [3,6,4,2,5,1] => 1 [3,6,4,5,1,2] => 1 [3,6,4,5,2,1] => 1 [3,6,5,1,2,4] => 2 [3,6,5,1,4,2] => 3 [3,6,5,2,1,4] => 2 [3,6,5,2,4,1] => 2 [3,6,5,4,1,2] => 2 [3,6,5,4,2,1] => 2 [4,1,2,3,5,6] => 0 [4,1,2,3,6,5] => 1 [4,1,2,5,3,6] => 1 [4,1,2,5,6,3] => 2 [4,1,2,6,3,5] => 1 [4,1,2,6,5,3] => 2 [4,1,3,2,5,6] => 1 [4,1,3,2,6,5] => 2 [4,1,3,5,2,6] => 2 [4,1,3,5,6,2] => 3 [4,1,3,6,2,5] => 2 [4,1,3,6,5,2] => 3 [4,1,5,2,3,6] => 1 [4,1,5,2,6,3] => 2 [4,1,5,3,2,6] => 2 [4,1,5,3,6,2] => 3 [4,1,5,6,2,3] => 2 [4,1,5,6,3,2] => 3 [4,1,6,2,3,5] => 1 [4,1,6,2,5,3] => 2 [4,1,6,3,2,5] => 2 [4,1,6,3,5,2] => 3 [4,1,6,5,2,3] => 2 [4,1,6,5,3,2] => 3 [4,2,1,3,5,6] => 0 [4,2,1,3,6,5] => 1 [4,2,1,5,3,6] => 1 [4,2,1,5,6,3] => 2 [4,2,1,6,3,5] => 1 [4,2,1,6,5,3] => 2 [4,2,3,1,5,6] => 0 [4,2,3,1,6,5] => 1 [4,2,3,5,1,6] => 0 [4,2,3,5,6,1] => 0 [4,2,3,6,1,5] => 1 [4,2,3,6,5,1] => 1 [4,2,5,1,3,6] => 1 [4,2,5,1,6,3] => 2 [4,2,5,3,1,6] => 1 [4,2,5,3,6,1] => 1 [4,2,5,6,1,3] => 2 [4,2,5,6,3,1] => 2 [4,2,6,1,3,5] => 1 [4,2,6,1,5,3] => 2 [4,2,6,3,1,5] => 1 [4,2,6,3,5,1] => 1 [4,2,6,5,1,3] => 2 [4,2,6,5,3,1] => 2 [4,3,1,2,5,6] => 0 [4,3,1,2,6,5] => 1 [4,3,1,5,2,6] => 1 [4,3,1,5,6,2] => 2 [4,3,1,6,2,5] => 1 [4,3,1,6,5,2] => 2 [4,3,2,1,5,6] => 0 [4,3,2,1,6,5] => 1 [4,3,2,5,1,6] => 0 [4,3,2,5,6,1] => 0 [4,3,2,6,1,5] => 1 [4,3,2,6,5,1] => 1 [4,3,5,1,2,6] => 0 [4,3,5,1,6,2] => 1 [4,3,5,2,1,6] => 0 [4,3,5,2,6,1] => 0 [4,3,5,6,1,2] => 0 [4,3,5,6,2,1] => 0 [4,3,6,1,2,5] => 1 [4,3,6,1,5,2] => 2 [4,3,6,2,1,5] => 1 [4,3,6,2,5,1] => 1 [4,3,6,5,1,2] => 1 [4,3,6,5,2,1] => 1 [4,5,1,2,3,6] => 0 [4,5,1,2,6,3] => 1 [4,5,1,3,2,6] => 1 [4,5,1,3,6,2] => 2 [4,5,1,6,2,3] => 1 [4,5,1,6,3,2] => 2 [4,5,2,1,3,6] => 0 [4,5,2,1,6,3] => 1 [4,5,2,3,1,6] => 0 [4,5,2,3,6,1] => 0 [4,5,2,6,1,3] => 1 [4,5,2,6,3,1] => 1 [4,5,3,1,2,6] => 0 [4,5,3,1,6,2] => 1 [4,5,3,2,1,6] => 0 [4,5,3,2,6,1] => 0 [4,5,3,6,1,2] => 0 [4,5,3,6,2,1] => 0 [4,5,6,1,2,3] => 0 [4,5,6,1,3,2] => 1 [4,5,6,2,1,3] => 0 [4,5,6,2,3,1] => 0 [4,5,6,3,1,2] => 0 [4,5,6,3,2,1] => 0 [4,6,1,2,3,5] => 1 [4,6,1,2,5,3] => 2 [4,6,1,3,2,5] => 2 [4,6,1,3,5,2] => 3 [4,6,1,5,2,3] => 2 [4,6,1,5,3,2] => 3 [4,6,2,1,3,5] => 1 [4,6,2,1,5,3] => 2 [4,6,2,3,1,5] => 1 [4,6,2,3,5,1] => 1 [4,6,2,5,1,3] => 2 [4,6,2,5,3,1] => 2 [4,6,3,1,2,5] => 1 [4,6,3,1,5,2] => 2 [4,6,3,2,1,5] => 1 [4,6,3,2,5,1] => 1 [4,6,3,5,1,2] => 1 [4,6,3,5,2,1] => 1 [4,6,5,1,2,3] => 1 [4,6,5,1,3,2] => 2 [4,6,5,2,1,3] => 1 [4,6,5,2,3,1] => 1 [4,6,5,3,1,2] => 1 [4,6,5,3,2,1] => 1 [5,1,2,3,4,6] => 0 [5,1,2,3,6,4] => 1 [5,1,2,4,3,6] => 1 [5,1,2,4,6,3] => 2 [5,1,2,6,3,4] => 1 [5,1,2,6,4,3] => 2 [5,1,3,2,4,6] => 1 [5,1,3,2,6,4] => 2 [5,1,3,4,2,6] => 2 [5,1,3,4,6,2] => 3 [5,1,3,6,2,4] => 2 [5,1,3,6,4,2] => 3 [5,1,4,2,3,6] => 1 [5,1,4,2,6,3] => 2 [5,1,4,3,2,6] => 2 [5,1,4,3,6,2] => 3 [5,1,4,6,2,3] => 2 [5,1,4,6,3,2] => 3 [5,1,6,2,3,4] => 1 [5,1,6,2,4,3] => 2 [5,1,6,3,2,4] => 2 [5,1,6,3,4,2] => 3 [5,1,6,4,2,3] => 2 [5,1,6,4,3,2] => 3 [5,2,1,3,4,6] => 0 [5,2,1,3,6,4] => 1 [5,2,1,4,3,6] => 1 [5,2,1,4,6,3] => 2 [5,2,1,6,3,4] => 1 [5,2,1,6,4,3] => 2 [5,2,3,1,4,6] => 0 [5,2,3,1,6,4] => 1 [5,2,3,4,1,6] => 0 [5,2,3,4,6,1] => 0 [5,2,3,6,1,4] => 1 [5,2,3,6,4,1] => 1 [5,2,4,1,3,6] => 1 [5,2,4,1,6,3] => 2 [5,2,4,3,1,6] => 1 [5,2,4,3,6,1] => 1 [5,2,4,6,1,3] => 2 [5,2,4,6,3,1] => 2 [5,2,6,1,3,4] => 1 [5,2,6,1,4,3] => 2 [5,2,6,3,1,4] => 1 [5,2,6,3,4,1] => 1 [5,2,6,4,1,3] => 2 [5,2,6,4,3,1] => 2 [5,3,1,2,4,6] => 0 [5,3,1,2,6,4] => 1 [5,3,1,4,2,6] => 1 [5,3,1,4,6,2] => 2 [5,3,1,6,2,4] => 1 [5,3,1,6,4,2] => 2 [5,3,2,1,4,6] => 0 [5,3,2,1,6,4] => 1 [5,3,2,4,1,6] => 0 [5,3,2,4,6,1] => 0 [5,3,2,6,1,4] => 1 [5,3,2,6,4,1] => 1 [5,3,4,1,2,6] => 0 [5,3,4,1,6,2] => 1 [5,3,4,2,1,6] => 0 [5,3,4,2,6,1] => 0 [5,3,4,6,1,2] => 0 [5,3,4,6,2,1] => 0 [5,3,6,1,2,4] => 1 [5,3,6,1,4,2] => 2 [5,3,6,2,1,4] => 1 [5,3,6,2,4,1] => 1 [5,3,6,4,1,2] => 1 [5,3,6,4,2,1] => 1 [5,4,1,2,3,6] => 0 [5,4,1,2,6,3] => 1 [5,4,1,3,2,6] => 1 [5,4,1,3,6,2] => 2 [5,4,1,6,2,3] => 1 [5,4,1,6,3,2] => 2 [5,4,2,1,3,6] => 0 [5,4,2,1,6,3] => 1 [5,4,2,3,1,6] => 0 [5,4,2,3,6,1] => 0 [5,4,2,6,1,3] => 1 [5,4,2,6,3,1] => 1 [5,4,3,1,2,6] => 0 [5,4,3,1,6,2] => 1 [5,4,3,2,1,6] => 0 [5,4,3,2,6,1] => 0 [5,4,3,6,1,2] => 0 [5,4,3,6,2,1] => 0 [5,4,6,1,2,3] => 0 [5,4,6,1,3,2] => 1 [5,4,6,2,1,3] => 0 [5,4,6,2,3,1] => 0 [5,4,6,3,1,2] => 0 [5,4,6,3,2,1] => 0 [5,6,1,2,3,4] => 0 [5,6,1,2,4,3] => 1 [5,6,1,3,2,4] => 1 [5,6,1,3,4,2] => 2 [5,6,1,4,2,3] => 1 [5,6,1,4,3,2] => 2 [5,6,2,1,3,4] => 0 [5,6,2,1,4,3] => 1 [5,6,2,3,1,4] => 0 [5,6,2,3,4,1] => 0 [5,6,2,4,1,3] => 1 [5,6,2,4,3,1] => 1 [5,6,3,1,2,4] => 0 [5,6,3,1,4,2] => 1 [5,6,3,2,1,4] => 0 [5,6,3,2,4,1] => 0 [5,6,3,4,1,2] => 0 [5,6,3,4,2,1] => 0 [5,6,4,1,2,3] => 0 [5,6,4,1,3,2] => 1 [5,6,4,2,1,3] => 0 [5,6,4,2,3,1] => 0 [5,6,4,3,1,2] => 0 [5,6,4,3,2,1] => 0 [6,1,2,3,4,5] => 0 [6,1,2,3,5,4] => 1 [6,1,2,4,3,5] => 1 [6,1,2,4,5,3] => 2 [6,1,2,5,3,4] => 1 [6,1,2,5,4,3] => 2 [6,1,3,2,4,5] => 1 [6,1,3,2,5,4] => 2 [6,1,3,4,2,5] => 2 [6,1,3,4,5,2] => 3 [6,1,3,5,2,4] => 2 [6,1,3,5,4,2] => 3 [6,1,4,2,3,5] => 1 [6,1,4,2,5,3] => 2 [6,1,4,3,2,5] => 2 [6,1,4,3,5,2] => 3 [6,1,4,5,2,3] => 2 [6,1,4,5,3,2] => 3 [6,1,5,2,3,4] => 1 [6,1,5,2,4,3] => 2 [6,1,5,3,2,4] => 2 [6,1,5,3,4,2] => 3 [6,1,5,4,2,3] => 2 [6,1,5,4,3,2] => 3 [6,2,1,3,4,5] => 0 [6,2,1,3,5,4] => 1 [6,2,1,4,3,5] => 1 [6,2,1,4,5,3] => 2 [6,2,1,5,3,4] => 1 [6,2,1,5,4,3] => 2 [6,2,3,1,4,5] => 0 [6,2,3,1,5,4] => 1 [6,2,3,4,1,5] => 0 [6,2,3,4,5,1] => 0 [6,2,3,5,1,4] => 1 [6,2,3,5,4,1] => 1 [6,2,4,1,3,5] => 1 [6,2,4,1,5,3] => 2 [6,2,4,3,1,5] => 1 [6,2,4,3,5,1] => 1 [6,2,4,5,1,3] => 2 [6,2,4,5,3,1] => 2 [6,2,5,1,3,4] => 1 [6,2,5,1,4,3] => 2 [6,2,5,3,1,4] => 1 [6,2,5,3,4,1] => 1 [6,2,5,4,1,3] => 2 [6,2,5,4,3,1] => 2 [6,3,1,2,4,5] => 0 [6,3,1,2,5,4] => 1 [6,3,1,4,2,5] => 1 [6,3,1,4,5,2] => 2 [6,3,1,5,2,4] => 1 [6,3,1,5,4,2] => 2 [6,3,2,1,4,5] => 0 [6,3,2,1,5,4] => 1 [6,3,2,4,1,5] => 0 [6,3,2,4,5,1] => 0 [6,3,2,5,1,4] => 1 [6,3,2,5,4,1] => 1 [6,3,4,1,2,5] => 0 [6,3,4,1,5,2] => 1 [6,3,4,2,1,5] => 0 [6,3,4,2,5,1] => 0 [6,3,4,5,1,2] => 0 [6,3,4,5,2,1] => 0 [6,3,5,1,2,4] => 1 [6,3,5,1,4,2] => 2 [6,3,5,2,1,4] => 1 [6,3,5,2,4,1] => 1 [6,3,5,4,1,2] => 1 [6,3,5,4,2,1] => 1 [6,4,1,2,3,5] => 0 [6,4,1,2,5,3] => 1 [6,4,1,3,2,5] => 1 [6,4,1,3,5,2] => 2 [6,4,1,5,2,3] => 1 [6,4,1,5,3,2] => 2 [6,4,2,1,3,5] => 0 [6,4,2,1,5,3] => 1 [6,4,2,3,1,5] => 0 [6,4,2,3,5,1] => 0 [6,4,2,5,1,3] => 1 [6,4,2,5,3,1] => 1 [6,4,3,1,2,5] => 0 [6,4,3,1,5,2] => 1 [6,4,3,2,1,5] => 0 [6,4,3,2,5,1] => 0 [6,4,3,5,1,2] => 0 [6,4,3,5,2,1] => 0 [6,4,5,1,2,3] => 0 [6,4,5,1,3,2] => 1 [6,4,5,2,1,3] => 0 [6,4,5,2,3,1] => 0 [6,4,5,3,1,2] => 0 [6,4,5,3,2,1] => 0 [6,5,1,2,3,4] => 0 [6,5,1,2,4,3] => 1 [6,5,1,3,2,4] => 1 [6,5,1,3,4,2] => 2 [6,5,1,4,2,3] => 1 [6,5,1,4,3,2] => 2 [6,5,2,1,3,4] => 0 [6,5,2,1,4,3] => 1 [6,5,2,3,1,4] => 0 [6,5,2,3,4,1] => 0 [6,5,2,4,1,3] => 1 [6,5,2,4,3,1] => 1 [6,5,3,1,2,4] => 0 [6,5,3,1,4,2] => 1 [6,5,3,2,1,4] => 0 [6,5,3,2,4,1] => 0 [6,5,3,4,1,2] => 0 [6,5,3,4,2,1] => 0 [6,5,4,1,2,3] => 0 [6,5,4,1,3,2] => 1 [6,5,4,2,1,3] => 0 [6,5,4,2,3,1] => 0 [6,5,4,3,1,2] => 0 [6,5,4,3,2,1] => 0 [1,2,3,4,5,6,7] => 0 [1,2,3,4,5,7,6] => 1 [1,2,3,4,6,5,7] => 1 [1,2,3,4,6,7,5] => 2 [1,2,3,4,7,5,6] => 1 [1,2,3,4,7,6,5] => 2 [1,2,3,5,4,6,7] => 1 [1,2,3,5,4,7,6] => 2 [1,2,3,5,6,4,7] => 2 [1,2,3,5,6,7,4] => 3 [1,2,3,5,7,4,6] => 2 [1,2,3,5,7,6,4] => 3 [1,2,3,6,4,5,7] => 1 [1,2,3,6,4,7,5] => 2 [1,2,3,6,5,4,7] => 2 [1,2,3,6,5,7,4] => 3 [1,2,3,6,7,4,5] => 2 [1,2,3,6,7,5,4] => 3 [1,2,3,7,4,5,6] => 1 [1,2,3,7,4,6,5] => 2 [1,2,3,7,5,4,6] => 2 [1,2,3,7,5,6,4] => 3 [1,2,3,7,6,4,5] => 2 [1,2,3,7,6,5,4] => 3 [1,2,4,3,5,6,7] => 1 [1,2,4,3,5,7,6] => 2 [1,2,4,3,6,5,7] => 2 [1,2,4,3,6,7,5] => 3 [1,2,4,3,7,5,6] => 2 [1,2,4,3,7,6,5] => 3 [1,2,4,5,3,6,7] => 2 [1,2,4,5,3,7,6] => 3 [1,2,4,5,6,3,7] => 3 [1,2,4,5,6,7,3] => 4 [1,2,4,5,7,3,6] => 3 [1,2,4,5,7,6,3] => 4 [1,2,4,6,3,5,7] => 2 [1,2,4,6,3,7,5] => 3 [1,2,4,6,5,3,7] => 3 [1,2,4,6,5,7,3] => 4 [1,2,4,6,7,3,5] => 3 [1,2,4,6,7,5,3] => 4 [1,2,4,7,3,5,6] => 2 [1,2,4,7,3,6,5] => 3 [1,2,4,7,5,3,6] => 3 [1,2,4,7,5,6,3] => 4 [1,2,4,7,6,3,5] => 3 [1,2,4,7,6,5,3] => 4 [1,2,5,3,4,6,7] => 1 [1,2,5,3,4,7,6] => 2 [1,2,5,3,6,4,7] => 2 [1,2,5,3,6,7,4] => 3 [1,2,5,3,7,4,6] => 2 [1,2,5,3,7,6,4] => 3 [1,2,5,4,3,6,7] => 2 [1,2,5,4,3,7,6] => 3 [1,2,5,4,6,3,7] => 3 [1,2,5,4,6,7,3] => 4 [1,2,5,4,7,3,6] => 3 [1,2,5,4,7,6,3] => 4 [1,2,5,6,3,4,7] => 2 [1,2,5,6,3,7,4] => 3 [1,2,5,6,4,3,7] => 3 [1,2,5,6,4,7,3] => 4 [1,2,5,6,7,3,4] => 3 [1,2,5,6,7,4,3] => 4 [1,2,5,7,3,4,6] => 2 [1,2,5,7,3,6,4] => 3 [1,2,5,7,4,3,6] => 3 [1,2,5,7,4,6,3] => 4 [1,2,5,7,6,3,4] => 3 [1,2,5,7,6,4,3] => 4 [1,2,6,3,4,5,7] => 1 [1,2,6,3,4,7,5] => 2 [1,2,6,3,5,4,7] => 2 [1,2,6,3,5,7,4] => 3 [1,2,6,3,7,4,5] => 2 [1,2,6,3,7,5,4] => 3 [1,2,6,4,3,5,7] => 2 [1,2,6,4,3,7,5] => 3 [1,2,6,4,5,3,7] => 3 [1,2,6,4,5,7,3] => 4 [1,2,6,4,7,3,5] => 3 [1,2,6,4,7,5,3] => 4 [1,2,6,5,3,4,7] => 2 [1,2,6,5,3,7,4] => 3 [1,2,6,5,4,3,7] => 3 [1,2,6,5,4,7,3] => 4 [1,2,6,5,7,3,4] => 3 [1,2,6,5,7,4,3] => 4 [1,2,6,7,3,4,5] => 2 [1,2,6,7,3,5,4] => 3 [1,2,6,7,4,3,5] => 3 [1,2,6,7,4,5,3] => 4 [1,2,6,7,5,3,4] => 3 [1,2,6,7,5,4,3] => 4 [1,2,7,3,4,5,6] => 1 [1,2,7,3,4,6,5] => 2 [1,2,7,3,5,4,6] => 2 [1,2,7,3,5,6,4] => 3 [1,2,7,3,6,4,5] => 2 [1,2,7,3,6,5,4] => 3 [1,2,7,4,3,5,6] => 2 [1,2,7,4,3,6,5] => 3 [1,2,7,4,5,3,6] => 3 [1,2,7,4,5,6,3] => 4 [1,2,7,4,6,3,5] => 3 [1,2,7,4,6,5,3] => 4 [1,2,7,5,3,4,6] => 2 [1,2,7,5,3,6,4] => 3 [1,2,7,5,4,3,6] => 3 [1,2,7,5,4,6,3] => 4 [1,2,7,5,6,3,4] => 3 [1,2,7,5,6,4,3] => 4 [1,2,7,6,3,4,5] => 2 [1,2,7,6,3,5,4] => 3 [1,2,7,6,4,3,5] => 3 [1,2,7,6,4,5,3] => 4 [1,2,7,6,5,3,4] => 3 [1,2,7,6,5,4,3] => 4 [1,3,2,4,5,6,7] => 1 [1,3,2,4,5,7,6] => 2 [1,3,2,4,6,5,7] => 2 [1,3,2,4,6,7,5] => 3 [1,3,2,4,7,5,6] => 2 [1,3,2,4,7,6,5] => 3 [1,3,2,5,4,6,7] => 2 [1,3,2,5,4,7,6] => 3 [1,3,2,5,6,4,7] => 3 [1,3,2,5,6,7,4] => 4 [1,3,2,5,7,4,6] => 3 [1,3,2,5,7,6,4] => 4 [1,3,2,6,4,5,7] => 2 [1,3,2,6,4,7,5] => 3 [1,3,2,6,5,4,7] => 3 [1,3,2,6,5,7,4] => 4 [1,3,2,6,7,4,5] => 3 [1,3,2,6,7,5,4] => 4 [1,3,2,7,4,5,6] => 2 [1,3,2,7,4,6,5] => 3 [1,3,2,7,5,4,6] => 3 [1,3,2,7,5,6,4] => 4 [1,3,2,7,6,4,5] => 3 [1,3,2,7,6,5,4] => 4 [1,3,4,2,5,6,7] => 2 [1,3,4,2,5,7,6] => 3 [1,3,4,2,6,5,7] => 3 [1,3,4,2,6,7,5] => 4 [1,3,4,2,7,5,6] => 3 [1,3,4,2,7,6,5] => 4 [1,3,4,5,2,6,7] => 3 [1,3,4,5,2,7,6] => 4 [1,3,4,5,6,2,7] => 4 [1,3,4,5,6,7,2] => 5 [1,3,4,5,7,2,6] => 4 [1,3,4,5,7,6,2] => 5 [1,3,4,6,2,5,7] => 3 [1,3,4,6,2,7,5] => 4 [1,3,4,6,5,2,7] => 4 [1,3,4,6,5,7,2] => 5 [1,3,4,6,7,2,5] => 4 [1,3,4,6,7,5,2] => 5 [1,3,4,7,2,5,6] => 3 [1,3,4,7,2,6,5] => 4 [1,3,4,7,5,2,6] => 4 [1,3,4,7,5,6,2] => 5 [1,3,4,7,6,2,5] => 4 [1,3,4,7,6,5,2] => 5 [1,3,5,2,4,6,7] => 2 [1,3,5,2,4,7,6] => 3 [1,3,5,2,6,4,7] => 3 [1,3,5,2,6,7,4] => 4 [1,3,5,2,7,4,6] => 3 [1,3,5,2,7,6,4] => 4 [1,3,5,4,2,6,7] => 3 [1,3,5,4,2,7,6] => 4 [1,3,5,4,6,2,7] => 4 [1,3,5,4,6,7,2] => 5 [1,3,5,4,7,2,6] => 4 [1,3,5,4,7,6,2] => 5 [1,3,5,6,2,4,7] => 3 [1,3,5,6,2,7,4] => 4 [1,3,5,6,4,2,7] => 4 [1,3,5,6,4,7,2] => 5 [1,3,5,6,7,2,4] => 4 [1,3,5,6,7,4,2] => 5 [1,3,5,7,2,4,6] => 3 [1,3,5,7,2,6,4] => 4 [1,3,5,7,4,2,6] => 4 [1,3,5,7,4,6,2] => 5 [1,3,5,7,6,2,4] => 4 [1,3,5,7,6,4,2] => 5 [1,3,6,2,4,5,7] => 2 [1,3,6,2,4,7,5] => 3 [1,3,6,2,5,4,7] => 3 [1,3,6,2,5,7,4] => 4 [1,3,6,2,7,4,5] => 3 [1,3,6,2,7,5,4] => 4 [1,3,6,4,2,5,7] => 3 [1,3,6,4,2,7,5] => 4 [1,3,6,4,5,2,7] => 4 [1,3,6,4,5,7,2] => 5 [1,3,6,4,7,2,5] => 4 [1,3,6,4,7,5,2] => 5 [1,3,6,5,2,4,7] => 3 [1,3,6,5,2,7,4] => 4 [1,3,6,5,4,2,7] => 4 [1,3,6,5,4,7,2] => 5 [1,3,6,5,7,2,4] => 4 [1,3,6,5,7,4,2] => 5 [1,3,6,7,2,4,5] => 3 [1,3,6,7,2,5,4] => 4 [1,3,6,7,4,2,5] => 4 [1,3,6,7,4,5,2] => 5 [1,3,6,7,5,2,4] => 4 [1,3,6,7,5,4,2] => 5 [1,3,7,2,4,5,6] => 2 [1,3,7,2,4,6,5] => 3 [1,3,7,2,5,4,6] => 3 [1,3,7,2,5,6,4] => 4 [1,3,7,2,6,4,5] => 3 [1,3,7,2,6,5,4] => 4 [1,3,7,4,2,5,6] => 3 [1,3,7,4,2,6,5] => 4 [1,3,7,4,5,2,6] => 4 [1,3,7,4,5,6,2] => 5 [1,3,7,4,6,2,5] => 4 [1,3,7,4,6,5,2] => 5 [1,3,7,5,2,4,6] => 3 [1,3,7,5,2,6,4] => 4 [1,3,7,5,4,2,6] => 4 [1,3,7,5,4,6,2] => 5 [1,3,7,5,6,2,4] => 4 [1,3,7,5,6,4,2] => 5 [1,3,7,6,2,4,5] => 3 [1,3,7,6,2,5,4] => 4 [1,3,7,6,4,2,5] => 4 [1,3,7,6,4,5,2] => 5 [1,3,7,6,5,2,4] => 4 [1,3,7,6,5,4,2] => 5 [1,4,2,3,5,6,7] => 1 [1,4,2,3,5,7,6] => 2 [1,4,2,3,6,5,7] => 2 [1,4,2,3,6,7,5] => 3 [1,4,2,3,7,5,6] => 2 [1,4,2,3,7,6,5] => 3 [1,4,2,5,3,6,7] => 2 [1,4,2,5,3,7,6] => 3 [1,4,2,5,6,3,7] => 3 [1,4,2,5,6,7,3] => 4 [1,4,2,5,7,3,6] => 3 [1,4,2,5,7,6,3] => 4 [1,4,2,6,3,5,7] => 2 [1,4,2,6,3,7,5] => 3 [1,4,2,6,5,3,7] => 3 [1,4,2,6,5,7,3] => 4 [1,4,2,6,7,3,5] => 3 [1,4,2,6,7,5,3] => 4 [1,4,2,7,3,5,6] => 2 [1,4,2,7,3,6,5] => 3 [1,4,2,7,5,3,6] => 3 [1,4,2,7,5,6,3] => 4 [1,4,2,7,6,3,5] => 3 [1,4,2,7,6,5,3] => 4 [1,4,3,2,5,6,7] => 2 [1,4,3,2,5,7,6] => 3 [1,4,3,2,6,5,7] => 3 [1,4,3,2,6,7,5] => 4 [1,4,3,2,7,5,6] => 3 [1,4,3,2,7,6,5] => 4 [1,4,3,5,2,6,7] => 3 [1,4,3,5,2,7,6] => 4 [1,4,3,5,6,2,7] => 4 [1,4,3,5,6,7,2] => 5 [1,4,3,5,7,2,6] => 4 [1,4,3,5,7,6,2] => 5 [1,4,3,6,2,5,7] => 3 [1,4,3,6,2,7,5] => 4 [1,4,3,6,5,2,7] => 4 [1,4,3,6,5,7,2] => 5 [1,4,3,6,7,2,5] => 4 [1,4,3,6,7,5,2] => 5 [1,4,3,7,2,5,6] => 3 [1,4,3,7,2,6,5] => 4 [1,4,3,7,5,2,6] => 4 [1,4,3,7,5,6,2] => 5 [1,4,3,7,6,2,5] => 4 [1,4,3,7,6,5,2] => 5 [1,4,5,2,3,6,7] => 2 [1,4,5,2,3,7,6] => 3 [1,4,5,2,6,3,7] => 3 [1,4,5,2,6,7,3] => 4 [1,4,5,2,7,3,6] => 3 [1,4,5,2,7,6,3] => 4 [1,4,5,3,2,6,7] => 3 [1,4,5,3,2,7,6] => 4 [1,4,5,3,6,2,7] => 4 [1,4,5,3,6,7,2] => 5 [1,4,5,3,7,2,6] => 4 [1,4,5,3,7,6,2] => 5 [1,4,5,6,2,3,7] => 3 [1,4,5,6,2,7,3] => 4 [1,4,5,6,3,2,7] => 4 [1,4,5,6,3,7,2] => 5 [1,4,5,6,7,2,3] => 4 [1,4,5,6,7,3,2] => 5 [1,4,5,7,2,3,6] => 3 [1,4,5,7,2,6,3] => 4 [1,4,5,7,3,2,6] => 4 [1,4,5,7,3,6,2] => 5 [1,4,5,7,6,2,3] => 4 [1,4,5,7,6,3,2] => 5 [1,4,6,2,3,5,7] => 2 [1,4,6,2,3,7,5] => 3 [1,4,6,2,5,3,7] => 3 [1,4,6,2,5,7,3] => 4 [1,4,6,2,7,3,5] => 3 [1,4,6,2,7,5,3] => 4 [1,4,6,3,2,5,7] => 3 [1,4,6,3,2,7,5] => 4 [1,4,6,3,5,2,7] => 4 [1,4,6,3,5,7,2] => 5 [1,4,6,3,7,2,5] => 4 [1,4,6,3,7,5,2] => 5 [1,4,6,5,2,3,7] => 3 [1,4,6,5,2,7,3] => 4 [1,4,6,5,3,2,7] => 4 ----------------------------------------------------------------------------- Created: Feb 16, 2021 at 10:57 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 10, 2023 at 12:13 by Tilman MÃ¶ller