***************************************************************************** * 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: St001671 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: Haglund's hag of a permutation. Let $edif$ be the sum of the differences of exceedence tops and bottoms, let $\pi_E$ the subsequence of exceedence tops and let $\pi_N$ be the subsequence of non-exceedence tops. Finally, let $L$ be the number of pairs of indices $k < i$ such that $\pi_k \leq i < \pi_i$. Then $hag(\pi) = edif + inv(\pi_E) - inv(\pi_N) + L$, where $inv$ denotes the number of inversions of a word. ----------------------------------------------------------------------------- References: [1] Wilson, M. C. An interesting new Mahonian permutation statistic [[MathSciNet:2745700]] ----------------------------------------------------------------------------- Code: def statistic(pi): standard = sage.combinat.permutation.to_standard pi_E = standard([pi_i for i, pi_i in enumerate(pi, 1) if i < pi_i]) pi_N = standard([pi_i for i, pi_i in enumerate(pi, 1) if i >= pi_i]) edif = sum(pi_i - i for i, pi_i in enumerate(pi, 1) if i < pi_i) L = sum(sum(1 for k in range(1, i) if pi(k) <= i) for i, pi_i in enumerate(pi, 1) if i < pi_i) return edif + pi_E.number_of_inversions() - pi_N.number_of_inversions() + L ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 2 [2,1,3] => 1 [2,3,1] => 3 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 0 [1,2,4,3] => 3 [1,3,2,4] => 2 [1,3,4,2] => 5 [1,4,2,3] => 3 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 4 [2,3,1,4] => 3 [2,3,4,1] => 6 [2,4,1,3] => 4 [2,4,3,1] => 3 [3,1,2,4] => 2 [3,1,4,2] => 5 [3,2,1,4] => 1 [3,2,4,1] => 4 [3,4,1,2] => 4 [3,4,2,1] => 3 [4,1,2,3] => 3 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 1 [4,3,1,2] => 5 [4,3,2,1] => 4 [1,2,3,4,5] => 0 [1,2,3,5,4] => 4 [1,2,4,3,5] => 3 [1,2,4,5,3] => 7 [1,2,5,3,4] => 4 [1,2,5,4,3] => 3 [1,3,2,4,5] => 2 [1,3,2,5,4] => 6 [1,3,4,2,5] => 5 [1,3,4,5,2] => 9 [1,3,5,2,4] => 6 [1,3,5,4,2] => 5 [1,4,2,3,5] => 3 [1,4,2,5,3] => 7 [1,4,3,2,5] => 2 [1,4,3,5,2] => 6 [1,4,5,2,3] => 6 [1,4,5,3,2] => 5 [1,5,2,3,4] => 4 [1,5,2,4,3] => 3 [1,5,3,2,4] => 3 [1,5,3,4,2] => 2 [1,5,4,2,3] => 7 [1,5,4,3,2] => 6 [2,1,3,4,5] => 1 [2,1,3,5,4] => 5 [2,1,4,3,5] => 4 [2,1,4,5,3] => 8 [2,1,5,3,4] => 5 [2,1,5,4,3] => 4 [2,3,1,4,5] => 3 [2,3,1,5,4] => 7 [2,3,4,1,5] => 6 [2,3,4,5,1] => 10 [2,3,5,1,4] => 7 [2,3,5,4,1] => 6 [2,4,1,3,5] => 4 [2,4,1,5,3] => 8 [2,4,3,1,5] => 3 [2,4,3,5,1] => 7 [2,4,5,1,3] => 7 [2,4,5,3,1] => 6 [2,5,1,3,4] => 5 [2,5,1,4,3] => 4 [2,5,3,1,4] => 4 [2,5,3,4,1] => 3 [2,5,4,1,3] => 8 [2,5,4,3,1] => 7 [3,1,2,4,5] => 2 [3,1,2,5,4] => 6 [3,1,4,2,5] => 5 [3,1,4,5,2] => 9 [3,1,5,2,4] => 6 [3,1,5,4,2] => 5 [3,2,1,4,5] => 1 [3,2,1,5,4] => 5 [3,2,4,1,5] => 4 [3,2,4,5,1] => 8 [3,2,5,1,4] => 5 [3,2,5,4,1] => 4 [3,4,1,2,5] => 4 [3,4,1,5,2] => 8 [3,4,2,1,5] => 3 [3,4,2,5,1] => 7 [3,4,5,1,2] => 7 [3,4,5,2,1] => 6 [3,5,1,2,4] => 5 [3,5,1,4,2] => 4 [3,5,2,1,4] => 4 [3,5,2,4,1] => 3 [3,5,4,1,2] => 8 [3,5,4,2,1] => 7 [4,1,2,3,5] => 3 [4,1,2,5,3] => 7 [4,1,3,2,5] => 2 [4,1,3,5,2] => 6 [4,1,5,2,3] => 6 [4,1,5,3,2] => 5 [4,2,1,3,5] => 2 [4,2,1,5,3] => 6 [4,2,3,1,5] => 1 [4,2,3,5,1] => 5 [4,2,5,1,3] => 5 [4,2,5,3,1] => 4 [4,3,1,2,5] => 5 [4,3,1,5,2] => 9 [4,3,2,1,5] => 4 [4,3,2,5,1] => 8 [4,3,5,1,2] => 8 [4,3,5,2,1] => 7 [4,5,1,2,3] => 6 [4,5,1,3,2] => 5 [4,5,2,1,3] => 5 [4,5,2,3,1] => 4 [4,5,3,1,2] => 4 [4,5,3,2,1] => 3 [5,1,2,3,4] => 4 [5,1,2,4,3] => 3 [5,1,3,2,4] => 3 [5,1,3,4,2] => 2 [5,1,4,2,3] => 7 [5,1,4,3,2] => 6 [5,2,1,3,4] => 3 [5,2,1,4,3] => 2 [5,2,3,1,4] => 2 [5,2,3,4,1] => 1 [5,2,4,1,3] => 6 [5,2,4,3,1] => 5 [5,3,1,2,4] => 6 [5,3,1,4,2] => 5 [5,3,2,1,4] => 5 [5,3,2,4,1] => 4 [5,3,4,1,2] => 9 [5,3,4,2,1] => 8 [5,4,1,2,3] => 7 [5,4,1,3,2] => 6 [5,4,2,1,3] => 6 [5,4,2,3,1] => 5 [5,4,3,1,2] => 5 [5,4,3,2,1] => 4 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 5 [1,2,3,5,4,6] => 4 [1,2,3,5,6,4] => 9 [1,2,3,6,4,5] => 5 [1,2,3,6,5,4] => 4 [1,2,4,3,5,6] => 3 [1,2,4,3,6,5] => 8 [1,2,4,5,3,6] => 7 [1,2,4,5,6,3] => 12 [1,2,4,6,3,5] => 8 [1,2,4,6,5,3] => 7 [1,2,5,3,4,6] => 4 [1,2,5,3,6,4] => 9 [1,2,5,4,3,6] => 3 [1,2,5,4,6,3] => 8 [1,2,5,6,3,4] => 8 [1,2,5,6,4,3] => 7 [1,2,6,3,4,5] => 5 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 4 [1,2,6,4,5,3] => 3 [1,2,6,5,3,4] => 9 [1,2,6,5,4,3] => 8 [1,3,2,4,5,6] => 2 [1,3,2,4,6,5] => 7 [1,3,2,5,4,6] => 6 [1,3,2,5,6,4] => 11 [1,3,2,6,4,5] => 7 [1,3,2,6,5,4] => 6 [1,3,4,2,5,6] => 5 [1,3,4,2,6,5] => 10 [1,3,4,5,2,6] => 9 [1,3,4,5,6,2] => 14 [1,3,4,6,2,5] => 10 [1,3,4,6,5,2] => 9 [1,3,5,2,4,6] => 6 [1,3,5,2,6,4] => 11 [1,3,5,4,2,6] => 5 [1,3,5,4,6,2] => 10 [1,3,5,6,2,4] => 10 [1,3,5,6,4,2] => 9 [1,3,6,2,4,5] => 7 [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] => 11 [1,3,6,5,4,2] => 10 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 8 [1,4,2,5,3,6] => 7 [1,4,2,5,6,3] => 12 [1,4,2,6,3,5] => 8 [1,4,2,6,5,3] => 7 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 7 [1,4,3,5,2,6] => 6 [1,4,3,5,6,2] => 11 [1,4,3,6,2,5] => 7 [1,4,3,6,5,2] => 6 [1,4,5,2,3,6] => 6 [1,4,5,2,6,3] => 11 [1,4,5,3,2,6] => 5 [1,4,5,3,6,2] => 10 [1,4,5,6,2,3] => 10 [1,4,5,6,3,2] => 9 [1,4,6,2,3,5] => 7 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 6 [1,4,6,3,5,2] => 5 [1,4,6,5,2,3] => 11 [1,4,6,5,3,2] => 10 [1,5,2,3,4,6] => 4 [1,5,2,3,6,4] => 9 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 8 [1,5,2,6,3,4] => 8 [1,5,2,6,4,3] => 7 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 8 [1,5,3,4,2,6] => 2 [1,5,3,4,6,2] => 7 [1,5,3,6,2,4] => 7 [1,5,3,6,4,2] => 6 [1,5,4,2,3,6] => 7 [1,5,4,2,6,3] => 12 [1,5,4,3,2,6] => 6 [1,5,4,3,6,2] => 11 [1,5,4,6,2,3] => 11 [1,5,4,6,3,2] => 10 [1,5,6,2,3,4] => 8 [1,5,6,2,4,3] => 7 [1,5,6,3,2,4] => 7 [1,5,6,3,4,2] => 6 [1,5,6,4,2,3] => 6 [1,5,6,4,3,2] => 5 [1,6,2,3,4,5] => 5 [1,6,2,3,5,4] => 4 [1,6,2,4,3,5] => 4 [1,6,2,4,5,3] => 3 [1,6,2,5,3,4] => 9 [1,6,2,5,4,3] => 8 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 3 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 2 [1,6,3,5,2,4] => 8 [1,6,3,5,4,2] => 7 [1,6,4,2,3,5] => 8 [1,6,4,2,5,3] => 7 [1,6,4,3,2,5] => 7 [1,6,4,3,5,2] => 6 [1,6,4,5,2,3] => 12 [1,6,4,5,3,2] => 11 [1,6,5,2,3,4] => 9 [1,6,5,2,4,3] => 8 [1,6,5,3,2,4] => 8 [1,6,5,3,4,2] => 7 [1,6,5,4,2,3] => 7 [1,6,5,4,3,2] => 6 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 6 [2,1,3,5,4,6] => 5 [2,1,3,5,6,4] => 10 [2,1,3,6,4,5] => 6 [2,1,3,6,5,4] => 5 [2,1,4,3,5,6] => 4 [2,1,4,3,6,5] => 9 [2,1,4,5,3,6] => 8 [2,1,4,5,6,3] => 13 [2,1,4,6,3,5] => 9 [2,1,4,6,5,3] => 8 [2,1,5,3,4,6] => 5 [2,1,5,3,6,4] => 10 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 9 [2,1,5,6,3,4] => 9 [2,1,5,6,4,3] => 8 [2,1,6,3,4,5] => 6 [2,1,6,3,5,4] => 5 [2,1,6,4,3,5] => 5 [2,1,6,4,5,3] => 4 [2,1,6,5,3,4] => 10 [2,1,6,5,4,3] => 9 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 8 [2,3,1,5,4,6] => 7 [2,3,1,5,6,4] => 12 [2,3,1,6,4,5] => 8 [2,3,1,6,5,4] => 7 [2,3,4,1,5,6] => 6 [2,3,4,1,6,5] => 11 [2,3,4,5,1,6] => 10 [2,3,4,5,6,1] => 15 [2,3,4,6,1,5] => 11 [2,3,4,6,5,1] => 10 [2,3,5,1,4,6] => 7 [2,3,5,1,6,4] => 12 [2,3,5,4,1,6] => 6 [2,3,5,4,6,1] => 11 [2,3,5,6,1,4] => 11 [2,3,5,6,4,1] => 10 [2,3,6,1,4,5] => 8 [2,3,6,1,5,4] => 7 [2,3,6,4,1,5] => 7 [2,3,6,4,5,1] => 6 [2,3,6,5,1,4] => 12 [2,3,6,5,4,1] => 11 [2,4,1,3,5,6] => 4 [2,4,1,3,6,5] => 9 [2,4,1,5,3,6] => 8 [2,4,1,5,6,3] => 13 [2,4,1,6,3,5] => 9 [2,4,1,6,5,3] => 8 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 8 [2,4,3,5,1,6] => 7 [2,4,3,5,6,1] => 12 [2,4,3,6,1,5] => 8 [2,4,3,6,5,1] => 7 [2,4,5,1,3,6] => 7 [2,4,5,1,6,3] => 12 [2,4,5,3,1,6] => 6 [2,4,5,3,6,1] => 11 [2,4,5,6,1,3] => 11 [2,4,5,6,3,1] => 10 [2,4,6,1,3,5] => 8 [2,4,6,1,5,3] => 7 [2,4,6,3,1,5] => 7 [2,4,6,3,5,1] => 6 [2,4,6,5,1,3] => 12 [2,4,6,5,3,1] => 11 [2,5,1,3,4,6] => 5 [2,5,1,3,6,4] => 10 [2,5,1,4,3,6] => 4 [2,5,1,4,6,3] => 9 [2,5,1,6,3,4] => 9 [2,5,1,6,4,3] => 8 [2,5,3,1,4,6] => 4 [2,5,3,1,6,4] => 9 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 8 [2,5,3,6,1,4] => 8 [2,5,3,6,4,1] => 7 [2,5,4,1,3,6] => 8 [2,5,4,1,6,3] => 13 [2,5,4,3,1,6] => 7 [2,5,4,3,6,1] => 12 [2,5,4,6,1,3] => 12 [2,5,4,6,3,1] => 11 [2,5,6,1,3,4] => 9 [2,5,6,1,4,3] => 8 [2,5,6,3,1,4] => 8 [2,5,6,3,4,1] => 7 [2,5,6,4,1,3] => 7 [2,5,6,4,3,1] => 6 [2,6,1,3,4,5] => 6 [2,6,1,3,5,4] => 5 [2,6,1,4,3,5] => 5 [2,6,1,4,5,3] => 4 [2,6,1,5,3,4] => 10 [2,6,1,5,4,3] => 9 [2,6,3,1,4,5] => 5 [2,6,3,1,5,4] => 4 [2,6,3,4,1,5] => 4 [2,6,3,4,5,1] => 3 [2,6,3,5,1,4] => 9 [2,6,3,5,4,1] => 8 [2,6,4,1,3,5] => 9 [2,6,4,1,5,3] => 8 [2,6,4,3,1,5] => 8 [2,6,4,3,5,1] => 7 [2,6,4,5,1,3] => 13 [2,6,4,5,3,1] => 12 [2,6,5,1,3,4] => 10 [2,6,5,1,4,3] => 9 [2,6,5,3,1,4] => 9 [2,6,5,3,4,1] => 8 [2,6,5,4,1,3] => 8 [2,6,5,4,3,1] => 7 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 7 [3,1,2,5,4,6] => 6 [3,1,2,5,6,4] => 11 [3,1,2,6,4,5] => 7 [3,1,2,6,5,4] => 6 [3,1,4,2,5,6] => 5 [3,1,4,2,6,5] => 10 [3,1,4,5,2,6] => 9 [3,1,4,5,6,2] => 14 [3,1,4,6,2,5] => 10 [3,1,4,6,5,2] => 9 [3,1,5,2,4,6] => 6 [3,1,5,2,6,4] => 11 [3,1,5,4,2,6] => 5 [3,1,5,4,6,2] => 10 [3,1,5,6,2,4] => 10 [3,1,5,6,4,2] => 9 [3,1,6,2,4,5] => 7 [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] => 11 [3,1,6,5,4,2] => 10 [3,2,1,4,5,6] => 1 [3,2,1,4,6,5] => 6 [3,2,1,5,4,6] => 5 [3,2,1,5,6,4] => 10 [3,2,1,6,4,5] => 6 [3,2,1,6,5,4] => 5 [3,2,4,1,5,6] => 4 [3,2,4,1,6,5] => 9 [3,2,4,5,1,6] => 8 [3,2,4,5,6,1] => 13 [3,2,4,6,1,5] => 9 [3,2,4,6,5,1] => 8 [3,2,5,1,4,6] => 5 [3,2,5,1,6,4] => 10 [3,2,5,4,1,6] => 4 [3,2,5,4,6,1] => 9 [3,2,5,6,1,4] => 9 [3,2,5,6,4,1] => 8 [3,2,6,1,4,5] => 6 [3,2,6,1,5,4] => 5 [3,2,6,4,1,5] => 5 [3,2,6,4,5,1] => 4 [3,2,6,5,1,4] => 10 [3,2,6,5,4,1] => 9 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 9 [3,4,1,5,2,6] => 8 [3,4,1,5,6,2] => 13 [3,4,1,6,2,5] => 9 [3,4,1,6,5,2] => 8 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 8 [3,4,2,5,1,6] => 7 [3,4,2,5,6,1] => 12 [3,4,2,6,1,5] => 8 [3,4,2,6,5,1] => 7 [3,4,5,1,2,6] => 7 [3,4,5,1,6,2] => 12 [3,4,5,2,1,6] => 6 [3,4,5,2,6,1] => 11 [3,4,5,6,1,2] => 11 [3,4,5,6,2,1] => 10 [3,4,6,1,2,5] => 8 [3,4,6,1,5,2] => 7 [3,4,6,2,1,5] => 7 [3,4,6,2,5,1] => 6 [3,4,6,5,1,2] => 12 [3,4,6,5,2,1] => 11 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 10 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 9 [3,5,1,6,2,4] => 9 [3,5,1,6,4,2] => 8 [3,5,2,1,4,6] => 4 [3,5,2,1,6,4] => 9 [3,5,2,4,1,6] => 3 [3,5,2,4,6,1] => 8 [3,5,2,6,1,4] => 8 [3,5,2,6,4,1] => 7 [3,5,4,1,2,6] => 8 [3,5,4,1,6,2] => 13 [3,5,4,2,1,6] => 7 [3,5,4,2,6,1] => 12 [3,5,4,6,1,2] => 12 [3,5,4,6,2,1] => 11 [3,5,6,1,2,4] => 9 [3,5,6,1,4,2] => 8 [3,5,6,2,1,4] => 8 [3,5,6,2,4,1] => 7 [3,5,6,4,1,2] => 7 [3,5,6,4,2,1] => 6 [3,6,1,2,4,5] => 6 [3,6,1,2,5,4] => 5 [3,6,1,4,2,5] => 5 [3,6,1,4,5,2] => 4 [3,6,1,5,2,4] => 10 [3,6,1,5,4,2] => 9 [3,6,2,1,4,5] => 5 [3,6,2,1,5,4] => 4 [3,6,2,4,1,5] => 4 [3,6,2,4,5,1] => 3 [3,6,2,5,1,4] => 9 [3,6,2,5,4,1] => 8 [3,6,4,1,2,5] => 9 [3,6,4,1,5,2] => 8 [3,6,4,2,1,5] => 8 [3,6,4,2,5,1] => 7 [3,6,4,5,1,2] => 13 [3,6,4,5,2,1] => 12 [3,6,5,1,2,4] => 10 [3,6,5,1,4,2] => 9 [3,6,5,2,1,4] => 9 [3,6,5,2,4,1] => 8 [3,6,5,4,1,2] => 8 [3,6,5,4,2,1] => 7 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 8 [4,1,2,5,3,6] => 7 [4,1,2,5,6,3] => 12 [4,1,2,6,3,5] => 8 [4,1,2,6,5,3] => 7 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 7 [4,1,3,5,2,6] => 6 [4,1,3,5,6,2] => 11 [4,1,3,6,2,5] => 7 [4,1,3,6,5,2] => 6 [4,1,5,2,3,6] => 6 [4,1,5,2,6,3] => 11 [4,1,5,3,2,6] => 5 [4,1,5,3,6,2] => 10 [4,1,5,6,2,3] => 10 [4,1,5,6,3,2] => 9 [4,1,6,2,3,5] => 7 [4,1,6,2,5,3] => 6 [4,1,6,3,2,5] => 6 [4,1,6,3,5,2] => 5 [4,1,6,5,2,3] => 11 [4,1,6,5,3,2] => 10 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 7 [4,2,1,5,3,6] => 6 [4,2,1,5,6,3] => 11 [4,2,1,6,3,5] => 7 [4,2,1,6,5,3] => 6 [4,2,3,1,5,6] => 1 [4,2,3,1,6,5] => 6 [4,2,3,5,1,6] => 5 [4,2,3,5,6,1] => 10 [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] => 10 [4,2,5,3,1,6] => 4 [4,2,5,3,6,1] => 9 [4,2,5,6,1,3] => 9 [4,2,5,6,3,1] => 8 [4,2,6,1,3,5] => 6 [4,2,6,1,5,3] => 5 [4,2,6,3,1,5] => 5 [4,2,6,3,5,1] => 4 [4,2,6,5,1,3] => 10 [4,2,6,5,3,1] => 9 [4,3,1,2,5,6] => 5 [4,3,1,2,6,5] => 10 [4,3,1,5,2,6] => 9 [4,3,1,5,6,2] => 14 [4,3,1,6,2,5] => 10 [4,3,1,6,5,2] => 9 [4,3,2,1,5,6] => 4 [4,3,2,1,6,5] => 9 [4,3,2,5,1,6] => 8 [4,3,2,5,6,1] => 13 [4,3,2,6,1,5] => 9 [4,3,2,6,5,1] => 8 [4,3,5,1,2,6] => 8 [4,3,5,1,6,2] => 13 [4,3,5,2,1,6] => 7 [4,3,5,2,6,1] => 12 [4,3,5,6,1,2] => 12 [4,3,5,6,2,1] => 11 [4,3,6,1,2,5] => 9 [4,3,6,1,5,2] => 8 [4,3,6,2,1,5] => 8 [4,3,6,2,5,1] => 7 [4,3,6,5,1,2] => 13 [4,3,6,5,2,1] => 12 [4,5,1,2,3,6] => 6 [4,5,1,2,6,3] => 11 [4,5,1,3,2,6] => 5 [4,5,1,3,6,2] => 10 [4,5,1,6,2,3] => 10 [4,5,1,6,3,2] => 9 [4,5,2,1,3,6] => 5 [4,5,2,1,6,3] => 10 [4,5,2,3,1,6] => 4 [4,5,2,3,6,1] => 9 [4,5,2,6,1,3] => 9 [4,5,2,6,3,1] => 8 [4,5,3,1,2,6] => 4 [4,5,3,1,6,2] => 9 [4,5,3,2,1,6] => 3 [4,5,3,2,6,1] => 8 [4,5,3,6,1,2] => 8 [4,5,3,6,2,1] => 7 [4,5,6,1,2,3] => 9 [4,5,6,1,3,2] => 8 [4,5,6,2,1,3] => 8 [4,5,6,2,3,1] => 7 [4,5,6,3,1,2] => 7 [4,5,6,3,2,1] => 6 [4,6,1,2,3,5] => 7 [4,6,1,2,5,3] => 6 [4,6,1,3,2,5] => 6 [4,6,1,3,5,2] => 5 [4,6,1,5,2,3] => 11 [4,6,1,5,3,2] => 10 [4,6,2,1,3,5] => 6 [4,6,2,1,5,3] => 5 [4,6,2,3,1,5] => 5 [4,6,2,3,5,1] => 4 [4,6,2,5,1,3] => 10 [4,6,2,5,3,1] => 9 [4,6,3,1,2,5] => 5 [4,6,3,1,5,2] => 4 [4,6,3,2,1,5] => 4 [4,6,3,2,5,1] => 3 [4,6,3,5,1,2] => 9 [4,6,3,5,2,1] => 8 [4,6,5,1,2,3] => 10 [4,6,5,1,3,2] => 9 [4,6,5,2,1,3] => 9 [4,6,5,2,3,1] => 8 [4,6,5,3,1,2] => 8 [4,6,5,3,2,1] => 7 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 9 [5,1,2,4,3,6] => 3 [5,1,2,4,6,3] => 8 [5,1,2,6,3,4] => 8 [5,1,2,6,4,3] => 7 [5,1,3,2,4,6] => 3 [5,1,3,2,6,4] => 8 [5,1,3,4,2,6] => 2 [5,1,3,4,6,2] => 7 [5,1,3,6,2,4] => 7 [5,1,3,6,4,2] => 6 [5,1,4,2,3,6] => 7 [5,1,4,2,6,3] => 12 [5,1,4,3,2,6] => 6 [5,1,4,3,6,2] => 11 [5,1,4,6,2,3] => 11 [5,1,4,6,3,2] => 10 [5,1,6,2,3,4] => 8 [5,1,6,2,4,3] => 7 [5,1,6,3,2,4] => 7 [5,1,6,3,4,2] => 6 [5,1,6,4,2,3] => 6 [5,1,6,4,3,2] => 5 [5,2,1,3,4,6] => 3 [5,2,1,3,6,4] => 8 [5,2,1,4,3,6] => 2 [5,2,1,4,6,3] => 7 [5,2,1,6,3,4] => 7 [5,2,1,6,4,3] => 6 [5,2,3,1,4,6] => 2 [5,2,3,1,6,4] => 7 [5,2,3,4,1,6] => 1 [5,2,3,4,6,1] => 6 [5,2,3,6,1,4] => 6 [5,2,3,6,4,1] => 5 [5,2,4,1,3,6] => 6 [5,2,4,1,6,3] => 11 [5,2,4,3,1,6] => 5 [5,2,4,3,6,1] => 10 [5,2,4,6,1,3] => 10 [5,2,4,6,3,1] => 9 [5,2,6,1,3,4] => 7 [5,2,6,1,4,3] => 6 [5,2,6,3,1,4] => 6 [5,2,6,3,4,1] => 5 [5,2,6,4,1,3] => 5 [5,2,6,4,3,1] => 4 [5,3,1,2,4,6] => 6 [5,3,1,2,6,4] => 11 [5,3,1,4,2,6] => 5 [5,3,1,4,6,2] => 10 [5,3,1,6,2,4] => 10 [5,3,1,6,4,2] => 9 [5,3,2,1,4,6] => 5 [5,3,2,1,6,4] => 10 [5,3,2,4,1,6] => 4 [5,3,2,4,6,1] => 9 [5,3,2,6,1,4] => 9 [5,3,2,6,4,1] => 8 [5,3,4,1,2,6] => 9 [5,3,4,1,6,2] => 14 [5,3,4,2,1,6] => 8 [5,3,4,2,6,1] => 13 [5,3,4,6,1,2] => 13 [5,3,4,6,2,1] => 12 [5,3,6,1,2,4] => 10 [5,3,6,1,4,2] => 9 [5,3,6,2,1,4] => 9 [5,3,6,2,4,1] => 8 [5,3,6,4,1,2] => 8 [5,3,6,4,2,1] => 7 [5,4,1,2,3,6] => 7 [5,4,1,2,6,3] => 12 [5,4,1,3,2,6] => 6 [5,4,1,3,6,2] => 11 [5,4,1,6,2,3] => 11 [5,4,1,6,3,2] => 10 [5,4,2,1,3,6] => 6 [5,4,2,1,6,3] => 11 [5,4,2,3,1,6] => 5 [5,4,2,3,6,1] => 10 [5,4,2,6,1,3] => 10 [5,4,2,6,3,1] => 9 [5,4,3,1,2,6] => 5 [5,4,3,1,6,2] => 10 [5,4,3,2,1,6] => 4 [5,4,3,2,6,1] => 9 [5,4,3,6,1,2] => 9 [5,4,3,6,2,1] => 8 [5,4,6,1,2,3] => 10 [5,4,6,1,3,2] => 9 [5,4,6,2,1,3] => 9 [5,4,6,2,3,1] => 8 [5,4,6,3,1,2] => 8 [5,4,6,3,2,1] => 7 [5,6,1,2,3,4] => 8 [5,6,1,2,4,3] => 7 [5,6,1,3,2,4] => 7 [5,6,1,3,4,2] => 6 [5,6,1,4,2,3] => 6 [5,6,1,4,3,2] => 5 [5,6,2,1,3,4] => 7 [5,6,2,1,4,3] => 6 [5,6,2,3,1,4] => 6 [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] => 6 [5,6,3,1,4,2] => 5 [5,6,3,2,1,4] => 5 [5,6,3,2,4,1] => 4 [5,6,3,4,1,2] => 4 [5,6,3,4,2,1] => 3 [5,6,4,1,2,3] => 11 [5,6,4,1,3,2] => 10 [5,6,4,2,1,3] => 10 [5,6,4,2,3,1] => 9 [5,6,4,3,1,2] => 9 [5,6,4,3,2,1] => 8 [6,1,2,3,4,5] => 5 [6,1,2,3,5,4] => 4 [6,1,2,4,3,5] => 4 [6,1,2,4,5,3] => 3 [6,1,2,5,3,4] => 9 [6,1,2,5,4,3] => 8 [6,1,3,2,4,5] => 4 [6,1,3,2,5,4] => 3 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 2 [6,1,3,5,2,4] => 8 [6,1,3,5,4,2] => 7 [6,1,4,2,3,5] => 8 [6,1,4,2,5,3] => 7 [6,1,4,3,2,5] => 7 [6,1,4,3,5,2] => 6 [6,1,4,5,2,3] => 12 [6,1,4,5,3,2] => 11 [6,1,5,2,3,4] => 9 [6,1,5,2,4,3] => 8 [6,1,5,3,2,4] => 8 [6,1,5,3,4,2] => 7 [6,1,5,4,2,3] => 7 [6,1,5,4,3,2] => 6 [6,2,1,3,4,5] => 4 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 2 [6,2,1,5,3,4] => 8 [6,2,1,5,4,3] => 7 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 2 [6,2,3,4,1,5] => 2 [6,2,3,4,5,1] => 1 [6,2,3,5,1,4] => 7 [6,2,3,5,4,1] => 6 [6,2,4,1,3,5] => 7 [6,2,4,1,5,3] => 6 [6,2,4,3,1,5] => 6 [6,2,4,3,5,1] => 5 [6,2,4,5,1,3] => 11 [6,2,4,5,3,1] => 10 [6,2,5,1,3,4] => 8 [6,2,5,1,4,3] => 7 [6,2,5,3,1,4] => 7 [6,2,5,3,4,1] => 6 [6,2,5,4,1,3] => 6 [6,2,5,4,3,1] => 5 [6,3,1,2,4,5] => 7 [6,3,1,2,5,4] => 6 [6,3,1,4,2,5] => 6 [6,3,1,4,5,2] => 5 [6,3,1,5,2,4] => 11 [6,3,1,5,4,2] => 10 [6,3,2,1,4,5] => 6 [6,3,2,1,5,4] => 5 [6,3,2,4,1,5] => 5 [6,3,2,4,5,1] => 4 [6,3,2,5,1,4] => 10 [6,3,2,5,4,1] => 9 [6,3,4,1,2,5] => 10 [6,3,4,1,5,2] => 9 [6,3,4,2,1,5] => 9 [6,3,4,2,5,1] => 8 [6,3,4,5,1,2] => 14 [6,3,4,5,2,1] => 13 [6,3,5,1,2,4] => 11 [6,3,5,1,4,2] => 10 [6,3,5,2,1,4] => 10 [6,3,5,2,4,1] => 9 [6,3,5,4,1,2] => 9 [6,3,5,4,2,1] => 8 [6,4,1,2,3,5] => 8 [6,4,1,2,5,3] => 7 [6,4,1,3,2,5] => 7 [6,4,1,3,5,2] => 6 [6,4,1,5,2,3] => 12 [6,4,1,5,3,2] => 11 [6,4,2,1,3,5] => 7 [6,4,2,1,5,3] => 6 [6,4,2,3,1,5] => 6 [6,4,2,3,5,1] => 5 [6,4,2,5,1,3] => 11 [6,4,2,5,3,1] => 10 [6,4,3,1,2,5] => 6 [6,4,3,1,5,2] => 5 [6,4,3,2,1,5] => 5 [6,4,3,2,5,1] => 4 [6,4,3,5,1,2] => 10 [6,4,3,5,2,1] => 9 [6,4,5,1,2,3] => 11 [6,4,5,1,3,2] => 10 [6,4,5,2,1,3] => 10 [6,4,5,2,3,1] => 9 [6,4,5,3,1,2] => 9 [6,4,5,3,2,1] => 8 [6,5,1,2,3,4] => 9 [6,5,1,2,4,3] => 8 [6,5,1,3,2,4] => 8 [6,5,1,3,4,2] => 7 [6,5,1,4,2,3] => 7 [6,5,1,4,3,2] => 6 [6,5,2,1,3,4] => 8 [6,5,2,1,4,3] => 7 [6,5,2,3,1,4] => 7 [6,5,2,3,4,1] => 6 [6,5,2,4,1,3] => 6 [6,5,2,4,3,1] => 5 [6,5,3,1,2,4] => 7 [6,5,3,1,4,2] => 6 [6,5,3,2,1,4] => 6 [6,5,3,2,4,1] => 5 [6,5,3,4,1,2] => 5 [6,5,3,4,2,1] => 4 [6,5,4,1,2,3] => 12 [6,5,4,1,3,2] => 11 [6,5,4,2,1,3] => 11 [6,5,4,2,3,1] => 10 [6,5,4,3,1,2] => 10 [6,5,4,3,2,1] => 9 [1,2,3,4,5,6,7] => 0 [1,2,3,4,5,7,6] => 6 [1,2,3,4,6,5,7] => 5 [1,2,3,4,6,7,5] => 11 [1,2,3,4,7,5,6] => 6 [1,2,3,4,7,6,5] => 5 [1,2,3,5,4,6,7] => 4 [1,2,3,5,4,7,6] => 10 [1,2,3,5,6,4,7] => 9 [1,2,3,5,6,7,4] => 15 [1,2,3,5,7,4,6] => 10 [1,2,3,5,7,6,4] => 9 [1,2,3,6,4,5,7] => 5 [1,2,3,6,4,7,5] => 11 [1,2,3,6,5,4,7] => 4 [1,2,3,6,5,7,4] => 10 [1,2,3,6,7,4,5] => 10 [1,2,3,6,7,5,4] => 9 [1,2,3,7,4,5,6] => 6 [1,2,3,7,4,6,5] => 5 [1,2,3,7,5,4,6] => 5 [1,2,3,7,5,6,4] => 4 [1,2,3,7,6,4,5] => 11 [1,2,3,7,6,5,4] => 10 [1,2,4,3,5,6,7] => 3 [1,2,4,3,5,7,6] => 9 [1,2,4,3,6,5,7] => 8 [1,2,4,3,6,7,5] => 14 [1,2,4,3,7,5,6] => 9 [1,2,4,3,7,6,5] => 8 [1,2,4,5,3,6,7] => 7 [1,2,4,5,3,7,6] => 13 [1,2,4,5,6,3,7] => 12 [1,2,4,5,6,7,3] => 18 [1,2,4,5,7,3,6] => 13 [1,2,4,5,7,6,3] => 12 [1,2,4,6,3,5,7] => 8 [1,2,4,6,3,7,5] => 14 [1,2,4,6,5,3,7] => 7 [1,2,4,6,5,7,3] => 13 [1,2,4,6,7,3,5] => 13 [1,2,4,6,7,5,3] => 12 [1,2,4,7,3,5,6] => 9 [1,2,4,7,3,6,5] => 8 [1,2,4,7,5,3,6] => 8 [1,2,4,7,5,6,3] => 7 [1,2,4,7,6,3,5] => 14 [1,2,4,7,6,5,3] => 13 [1,2,5,3,4,6,7] => 4 [1,2,5,3,4,7,6] => 10 [1,2,5,3,6,4,7] => 9 [1,2,5,3,6,7,4] => 15 [1,2,5,3,7,4,6] => 10 [1,2,5,3,7,6,4] => 9 [1,2,5,4,3,6,7] => 3 [1,2,5,4,3,7,6] => 9 [1,2,5,4,6,3,7] => 8 [1,2,5,4,6,7,3] => 14 [1,2,5,4,7,3,6] => 9 [1,2,5,4,7,6,3] => 8 [1,2,5,6,3,4,7] => 8 [1,2,5,6,3,7,4] => 14 [1,2,5,6,4,3,7] => 7 [1,2,5,6,4,7,3] => 13 [1,2,5,6,7,3,4] => 13 [1,2,5,6,7,4,3] => 12 [1,2,5,7,3,4,6] => 9 [1,2,5,7,3,6,4] => 8 [1,2,5,7,4,3,6] => 8 [1,2,5,7,4,6,3] => 7 [1,2,5,7,6,3,4] => 14 [1,2,5,7,6,4,3] => 13 [1,2,6,3,4,5,7] => 5 [1,2,6,3,4,7,5] => 11 [1,2,6,3,5,4,7] => 4 [1,2,6,3,5,7,4] => 10 [1,2,6,3,7,4,5] => 10 [1,2,6,3,7,5,4] => 9 [1,2,6,4,3,5,7] => 4 [1,2,6,4,3,7,5] => 10 [1,2,6,4,5,3,7] => 3 [1,2,6,4,5,7,3] => 9 [1,2,6,4,7,3,5] => 9 [1,2,6,4,7,5,3] => 8 [1,2,6,5,3,4,7] => 9 [1,2,6,5,3,7,4] => 15 [1,2,6,5,4,3,7] => 8 [1,2,6,5,4,7,3] => 14 [1,2,6,5,7,3,4] => 14 [1,2,6,5,7,4,3] => 13 [1,2,6,7,3,4,5] => 10 [1,2,6,7,3,5,4] => 9 [1,2,6,7,4,3,5] => 9 [1,2,6,7,4,5,3] => 8 [1,2,6,7,5,3,4] => 8 [1,2,6,7,5,4,3] => 7 [1,2,7,3,4,5,6] => 6 [1,2,7,3,4,6,5] => 5 [1,2,7,3,5,4,6] => 5 [1,2,7,3,5,6,4] => 4 [1,2,7,3,6,4,5] => 11 [1,2,7,3,6,5,4] => 10 [1,2,7,4,3,5,6] => 5 [1,2,7,4,3,6,5] => 4 [1,2,7,4,5,3,6] => 4 [1,2,7,4,5,6,3] => 3 [1,2,7,4,6,3,5] => 10 [1,2,7,4,6,5,3] => 9 [1,2,7,5,3,4,6] => 10 [1,2,7,5,3,6,4] => 9 [1,2,7,5,4,3,6] => 9 [1,2,7,5,4,6,3] => 8 [1,2,7,5,6,3,4] => 15 [1,2,7,5,6,4,3] => 14 [1,2,7,6,3,4,5] => 11 [1,2,7,6,3,5,4] => 10 [1,2,7,6,4,3,5] => 10 [1,2,7,6,4,5,3] => 9 [1,2,7,6,5,3,4] => 9 [1,2,7,6,5,4,3] => 8 [1,3,2,4,5,6,7] => 2 [1,3,2,4,5,7,6] => 8 [1,3,2,4,6,5,7] => 7 [1,3,2,4,6,7,5] => 13 [1,3,2,4,7,5,6] => 8 [1,3,2,4,7,6,5] => 7 [1,3,2,5,4,6,7] => 6 [1,3,2,5,4,7,6] => 12 [1,3,2,5,6,4,7] => 11 [1,3,2,5,6,7,4] => 17 [1,3,2,5,7,4,6] => 12 [1,3,2,5,7,6,4] => 11 [1,3,2,6,4,5,7] => 7 [1,3,2,6,4,7,5] => 13 [1,3,2,6,5,4,7] => 6 [1,3,2,6,5,7,4] => 12 [1,3,2,6,7,4,5] => 12 [1,3,2,6,7,5,4] => 11 [1,3,2,7,4,5,6] => 8 [1,3,2,7,4,6,5] => 7 [1,3,2,7,5,4,6] => 7 [1,3,2,7,5,6,4] => 6 [1,3,2,7,6,4,5] => 13 [1,3,2,7,6,5,4] => 12 [1,3,4,2,5,6,7] => 5 [1,3,4,2,5,7,6] => 11 [1,3,4,2,6,5,7] => 10 [1,3,4,2,6,7,5] => 16 [1,3,4,2,7,5,6] => 11 [1,3,4,2,7,6,5] => 10 [1,3,4,5,2,6,7] => 9 [1,3,4,5,2,7,6] => 15 [1,3,4,5,6,2,7] => 14 [1,3,4,5,6,7,2] => 20 [1,3,4,5,7,2,6] => 15 [1,3,4,5,7,6,2] => 14 [1,3,4,6,2,5,7] => 10 [1,3,4,6,2,7,5] => 16 [1,3,4,6,5,2,7] => 9 [1,3,4,6,5,7,2] => 15 [1,3,4,6,7,2,5] => 15 [1,3,4,6,7,5,2] => 14 [1,3,4,7,2,5,6] => 11 [1,3,4,7,2,6,5] => 10 [1,3,4,7,5,2,6] => 10 [1,3,4,7,5,6,2] => 9 [1,3,4,7,6,2,5] => 16 [1,3,4,7,6,5,2] => 15 [1,3,5,2,4,6,7] => 6 [1,3,5,2,4,7,6] => 12 [1,3,5,2,6,4,7] => 11 [1,3,5,2,6,7,4] => 17 [1,3,5,2,7,4,6] => 12 [1,3,5,2,7,6,4] => 11 [1,3,5,4,2,6,7] => 5 [1,3,5,4,2,7,6] => 11 [1,3,5,4,6,2,7] => 10 [1,3,5,4,6,7,2] => 16 [1,3,5,4,7,2,6] => 11 [1,3,5,4,7,6,2] => 10 [1,3,5,6,2,4,7] => 10 [1,3,5,6,2,7,4] => 16 [1,3,5,6,4,2,7] => 9 [1,3,5,6,4,7,2] => 15 [1,3,5,6,7,2,4] => 15 [1,3,5,6,7,4,2] => 14 [1,3,5,7,2,4,6] => 11 [1,3,5,7,2,6,4] => 10 [1,3,5,7,4,2,6] => 10 [1,3,5,7,4,6,2] => 9 [1,3,5,7,6,2,4] => 16 [1,3,5,7,6,4,2] => 15 [1,3,6,2,4,5,7] => 7 [1,3,6,2,4,7,5] => 13 [1,3,6,2,5,4,7] => 6 [1,3,6,2,5,7,4] => 12 [1,3,6,2,7,4,5] => 12 [1,3,6,2,7,5,4] => 11 [1,3,6,4,2,5,7] => 6 [1,3,6,4,2,7,5] => 12 [1,3,6,4,5,2,7] => 5 [1,3,6,4,5,7,2] => 11 [1,3,6,4,7,2,5] => 11 [1,3,6,4,7,5,2] => 10 [1,3,6,5,2,4,7] => 11 [1,3,6,5,2,7,4] => 17 [1,3,6,5,4,2,7] => 10 [1,3,6,5,4,7,2] => 16 [1,3,6,5,7,2,4] => 16 [1,3,6,5,7,4,2] => 15 [1,3,6,7,2,4,5] => 12 [1,3,6,7,2,5,4] => 11 [1,3,6,7,4,2,5] => 11 [1,3,6,7,4,5,2] => 10 [1,3,6,7,5,2,4] => 10 [1,3,6,7,5,4,2] => 9 [1,3,7,2,4,5,6] => 8 [1,3,7,2,4,6,5] => 7 [1,3,7,2,5,4,6] => 7 [1,3,7,2,5,6,4] => 6 [1,3,7,2,6,4,5] => 13 [1,3,7,2,6,5,4] => 12 [1,3,7,4,2,5,6] => 7 [1,3,7,4,2,6,5] => 6 [1,3,7,4,5,2,6] => 6 [1,3,7,4,5,6,2] => 5 [1,3,7,4,6,2,5] => 12 [1,3,7,4,6,5,2] => 11 [1,3,7,5,2,4,6] => 12 [1,3,7,5,2,6,4] => 11 [1,3,7,5,4,2,6] => 11 [1,3,7,5,4,6,2] => 10 [1,3,7,5,6,2,4] => 17 [1,3,7,5,6,4,2] => 16 [1,3,7,6,2,4,5] => 13 [1,3,7,6,2,5,4] => 12 [1,3,7,6,4,2,5] => 12 [1,3,7,6,4,5,2] => 11 [1,3,7,6,5,2,4] => 11 [1,3,7,6,5,4,2] => 10 [1,4,2,3,5,6,7] => 3 [1,4,2,3,5,7,6] => 9 [1,4,2,3,6,5,7] => 8 [1,4,2,3,6,7,5] => 14 [1,4,2,3,7,5,6] => 9 [1,4,2,3,7,6,5] => 8 [1,4,2,5,3,6,7] => 7 [1,4,2,5,3,7,6] => 13 [1,4,2,5,6,3,7] => 12 [1,4,2,5,6,7,3] => 18 [1,4,2,5,7,3,6] => 13 [1,4,2,5,7,6,3] => 12 [1,4,2,6,3,5,7] => 8 [1,4,2,6,3,7,5] => 14 [1,4,2,6,5,3,7] => 7 [1,4,2,6,5,7,3] => 13 [1,4,2,6,7,3,5] => 13 [1,4,2,6,7,5,3] => 12 [1,4,2,7,3,5,6] => 9 [1,4,2,7,3,6,5] => 8 [1,4,2,7,5,3,6] => 8 [1,4,2,7,5,6,3] => 7 [1,4,2,7,6,3,5] => 14 [1,4,2,7,6,5,3] => 13 [1,4,3,2,5,6,7] => 2 [1,4,3,2,5,7,6] => 8 [1,4,3,2,6,5,7] => 7 [1,4,3,2,6,7,5] => 13 [1,4,3,2,7,5,6] => 8 [1,4,3,2,7,6,5] => 7 [1,4,3,5,2,6,7] => 6 [1,4,3,5,2,7,6] => 12 [1,4,3,5,6,2,7] => 11 [1,4,3,5,6,7,2] => 17 [1,4,3,5,7,2,6] => 12 [1,4,3,5,7,6,2] => 11 [1,4,3,6,2,5,7] => 7 [1,4,3,6,2,7,5] => 13 [1,4,3,6,5,2,7] => 6 [1,4,3,6,5,7,2] => 12 [1,4,3,6,7,2,5] => 12 [1,4,3,6,7,5,2] => 11 [1,4,3,7,2,5,6] => 8 [1,4,3,7,2,6,5] => 7 [1,4,3,7,5,2,6] => 7 [1,4,3,7,5,6,2] => 6 [1,4,3,7,6,2,5] => 13 [1,4,3,7,6,5,2] => 12 [1,4,5,2,3,6,7] => 6 [1,4,5,2,3,7,6] => 12 [1,4,5,2,6,3,7] => 11 [1,4,5,2,6,7,3] => 17 [1,4,5,2,7,3,6] => 12 [1,4,5,2,7,6,3] => 11 [1,4,5,3,2,6,7] => 5 [1,4,5,3,2,7,6] => 11 [1,4,5,3,6,2,7] => 10 [1,4,5,3,6,7,2] => 16 [1,4,5,3,7,2,6] => 11 [1,4,5,3,7,6,2] => 10 [1,4,5,6,2,3,7] => 10 [1,4,5,6,2,7,3] => 16 [1,4,5,6,3,2,7] => 9 [1,4,5,6,3,7,2] => 15 [1,4,5,6,7,2,3] => 15 [1,4,5,6,7,3,2] => 14 [1,4,5,7,2,3,6] => 11 [1,4,5,7,2,6,3] => 10 [1,4,5,7,3,2,6] => 10 [1,4,5,7,3,6,2] => 9 [1,4,5,7,6,2,3] => 16 [1,4,5,7,6,3,2] => 15 [1,4,6,2,3,5,7] => 7 [1,4,6,2,3,7,5] => 13 [1,4,6,2,5,3,7] => 6 [1,4,6,2,5,7,3] => 12 [1,4,6,2,7,3,5] => 12 [1,4,6,2,7,5,3] => 11 [1,4,6,3,2,5,7] => 6 [1,4,6,3,2,7,5] => 12 [1,4,6,3,5,2,7] => 5 [1,4,6,3,5,7,2] => 11 [1,4,6,3,7,2,5] => 11 [1,4,6,3,7,5,2] => 10 [1,4,6,5,2,3,7] => 11 [1,4,6,5,2,7,3] => 17 [1,4,6,5,3,2,7] => 10 ----------------------------------------------------------------------------- Created: Jan 18, 2021 at 19:10 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 18, 2021 at 19:10 by Martin Rubey