***************************************************************************** * 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: St001464 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. ----------------------------------------------------------------------------- References: [1] Ardila, F., Rincón, F., Williams, L. Positroids and non-crossing partitions [[arXiv:1308.2698]] ----------------------------------------------------------------------------- Code: def i_less(a, b, i): """ Return whether a < b for i < i+1 < ... < n < 1 < ... < i-1. """ if min(a, b) >= i or max(a, b) < i: return a < b return a >= i > b def Grassmann_necklace(pi): """ Return the Grassmann necklace corresponding to pi. sage: pi = Permutation([3,4,2,1]) sage: Grassmann_necklace(pi) [{1, 2}, {2, 4}, {3, 4}, {1, 4}] """ pi = Permutation(pi) N = [] n = len(pi) for i in range(1,n+1): iWEX = [j for j in range(1,n+1) if j == pi(j) or i_less(j, pi(j), i)] N.append(set(iWEX)) return N def Gale_less(S, T, i): from functools import cmp_to_key key = cmp_to_key(lambda a,b: 0 if a == b else int(-1) if i_less(a,b,i) else int(1)) S_sorted = sorted(S, key=key) T_sorted = sorted(T, key=key) return all(s == t or i_less(s, t, i) for s,t in zip(S_sorted, T_sorted)) def positroid(N): """ Return the positroid corresponding to the Grassmann necklace. sage: pi = Permutation([3,4,2,1]) sage: N = Grassmann_necklace(pi) sage: positroid(N) [{1, 2}, {1, 3}, {1, 4}, {2, 4}, {3, 4}] sage: [set([len(positroid(Grassmann_necklace(p))) for p in orbit(pi)]) for pi in Permutations(4)] """ n = len(N) d = len(N[0]) result = [] for B in Subsets(range(1,n+1), d): if all(B == N[j] or Gale_less(N[j], B, j+1) for j in range(n)): result.append(B) return result def statistic(pi): return len(positroid(Grassmann_necklace(pi))) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 1 [2,1] => 2 [1,2,3] => 1 [1,3,2] => 2 [2,1,3] => 2 [2,3,1] => 3 [3,1,2] => 3 [3,2,1] => 2 [1,2,3,4] => 1 [1,2,4,3] => 2 [1,3,2,4] => 2 [1,3,4,2] => 3 [1,4,2,3] => 3 [1,4,3,2] => 2 [2,1,3,4] => 2 [2,1,4,3] => 4 [2,3,1,4] => 3 [2,3,4,1] => 4 [2,4,1,3] => 5 [2,4,3,1] => 3 [3,1,2,4] => 3 [3,1,4,2] => 5 [3,2,1,4] => 2 [3,2,4,1] => 3 [3,4,1,2] => 6 [3,4,2,1] => 5 [4,1,2,3] => 4 [4,1,3,2] => 3 [4,2,1,3] => 3 [4,2,3,1] => 2 [4,3,1,2] => 5 [4,3,2,1] => 4 [1,2,3,4,5] => 1 [1,2,3,5,4] => 2 [1,2,4,3,5] => 2 [1,2,4,5,3] => 3 [1,2,5,3,4] => 3 [1,2,5,4,3] => 2 [1,3,2,4,5] => 2 [1,3,2,5,4] => 4 [1,3,4,2,5] => 3 [1,3,4,5,2] => 4 [1,3,5,2,4] => 5 [1,3,5,4,2] => 3 [1,4,2,3,5] => 3 [1,4,2,5,3] => 5 [1,4,3,2,5] => 2 [1,4,3,5,2] => 3 [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] => 5 [1,5,4,3,2] => 4 [2,1,3,4,5] => 2 [2,1,3,5,4] => 4 [2,1,4,3,5] => 4 [2,1,4,5,3] => 6 [2,1,5,3,4] => 6 [2,1,5,4,3] => 4 [2,3,1,4,5] => 3 [2,3,1,5,4] => 6 [2,3,4,1,5] => 4 [2,3,4,5,1] => 5 [2,3,5,1,4] => 7 [2,3,5,4,1] => 4 [2,4,1,3,5] => 5 [2,4,1,5,3] => 8 [2,4,3,1,5] => 3 [2,4,3,5,1] => 4 [2,4,5,1,3] => 9 [2,4,5,3,1] => 7 [2,5,1,3,4] => 7 [2,5,1,4,3] => 5 [2,5,3,1,4] => 5 [2,5,3,4,1] => 3 [2,5,4,1,3] => 8 [2,5,4,3,1] => 6 [3,1,2,4,5] => 3 [3,1,2,5,4] => 6 [3,1,4,2,5] => 5 [3,1,4,5,2] => 7 [3,1,5,2,4] => 8 [3,1,5,4,2] => 5 [3,2,1,4,5] => 2 [3,2,1,5,4] => 4 [3,2,4,1,5] => 3 [3,2,4,5,1] => 4 [3,2,5,1,4] => 5 [3,2,5,4,1] => 3 [3,4,1,2,5] => 6 [3,4,1,5,2] => 9 [3,4,2,1,5] => 5 [3,4,2,5,1] => 7 [3,4,5,1,2] => 10 [3,4,5,2,1] => 9 [3,5,1,2,4] => 9 [3,5,1,4,2] => 6 [3,5,2,1,4] => 8 [3,5,2,4,1] => 5 [3,5,4,1,2] => 9 [3,5,4,2,1] => 8 [4,1,2,3,5] => 4 [4,1,2,5,3] => 7 [4,1,3,2,5] => 3 [4,1,3,5,2] => 5 [4,1,5,2,3] => 9 [4,1,5,3,2] => 8 [4,2,1,3,5] => 3 [4,2,1,5,3] => 5 [4,2,3,1,5] => 2 [4,2,3,5,1] => 3 [4,2,5,1,3] => 6 [4,2,5,3,1] => 5 [4,3,1,2,5] => 5 [4,3,1,5,2] => 8 [4,3,2,1,5] => 4 [4,3,2,5,1] => 6 [4,3,5,1,2] => 9 [4,3,5,2,1] => 8 [4,5,1,2,3] => 10 [4,5,1,3,2] => 9 [4,5,2,1,3] => 9 [4,5,2,3,1] => 7 [4,5,3,1,2] => 6 [4,5,3,2,1] => 5 [5,1,2,3,4] => 5 [5,1,2,4,3] => 4 [5,1,3,2,4] => 4 [5,1,3,4,2] => 3 [5,1,4,2,3] => 7 [5,1,4,3,2] => 6 [5,2,1,3,4] => 4 [5,2,1,4,3] => 3 [5,2,3,1,4] => 3 [5,2,3,4,1] => 2 [5,2,4,1,3] => 5 [5,2,4,3,1] => 4 [5,3,1,2,4] => 7 [5,3,1,4,2] => 5 [5,3,2,1,4] => 6 [5,3,2,4,1] => 4 [5,3,4,1,2] => 7 [5,3,4,2,1] => 6 [5,4,1,2,3] => 9 [5,4,1,3,2] => 8 [5,4,2,1,3] => 8 [5,4,2,3,1] => 6 [5,4,3,1,2] => 5 [5,4,3,2,1] => 4 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 2 [1,2,3,5,4,6] => 2 [1,2,3,5,6,4] => 3 [1,2,3,6,4,5] => 3 [1,2,3,6,5,4] => 2 [1,2,4,3,5,6] => 2 [1,2,4,3,6,5] => 4 [1,2,4,5,3,6] => 3 [1,2,4,5,6,3] => 4 [1,2,4,6,3,5] => 5 [1,2,4,6,5,3] => 3 [1,2,5,3,4,6] => 3 [1,2,5,3,6,4] => 5 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 3 [1,2,5,6,3,4] => 6 [1,2,5,6,4,3] => 5 [1,2,6,3,4,5] => 4 [1,2,6,3,5,4] => 3 [1,2,6,4,3,5] => 3 [1,2,6,4,5,3] => 2 [1,2,6,5,3,4] => 5 [1,2,6,5,4,3] => 4 [1,3,2,4,5,6] => 2 [1,3,2,4,6,5] => 4 [1,3,2,5,4,6] => 4 [1,3,2,5,6,4] => 6 [1,3,2,6,4,5] => 6 [1,3,2,6,5,4] => 4 [1,3,4,2,5,6] => 3 [1,3,4,2,6,5] => 6 [1,3,4,5,2,6] => 4 [1,3,4,5,6,2] => 5 [1,3,4,6,2,5] => 7 [1,3,4,6,5,2] => 4 [1,3,5,2,4,6] => 5 [1,3,5,2,6,4] => 8 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 4 [1,3,5,6,2,4] => 9 [1,3,5,6,4,2] => 7 [1,3,6,2,4,5] => 7 [1,3,6,2,5,4] => 5 [1,3,6,4,2,5] => 5 [1,3,6,4,5,2] => 3 [1,3,6,5,2,4] => 8 [1,3,6,5,4,2] => 6 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 6 [1,4,2,5,3,6] => 5 [1,4,2,5,6,3] => 7 [1,4,2,6,3,5] => 8 [1,4,2,6,5,3] => 5 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 4 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 4 [1,4,3,6,2,5] => 5 [1,4,3,6,5,2] => 3 [1,4,5,2,3,6] => 6 [1,4,5,2,6,3] => 9 [1,4,5,3,2,6] => 5 [1,4,5,3,6,2] => 7 [1,4,5,6,2,3] => 10 [1,4,5,6,3,2] => 9 [1,4,6,2,3,5] => 9 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 8 [1,4,6,3,5,2] => 5 [1,4,6,5,2,3] => 9 [1,4,6,5,3,2] => 8 [1,5,2,3,4,6] => 4 [1,5,2,3,6,4] => 7 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 5 [1,5,2,6,3,4] => 9 [1,5,2,6,4,3] => 8 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 5 [1,5,3,4,2,6] => 2 [1,5,3,4,6,2] => 3 [1,5,3,6,2,4] => 6 [1,5,3,6,4,2] => 5 [1,5,4,2,3,6] => 5 [1,5,4,2,6,3] => 8 [1,5,4,3,2,6] => 4 [1,5,4,3,6,2] => 6 [1,5,4,6,2,3] => 9 [1,5,4,6,3,2] => 8 [1,5,6,2,3,4] => 10 [1,5,6,2,4,3] => 9 [1,5,6,3,2,4] => 9 [1,5,6,3,4,2] => 7 [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] => 7 [1,6,2,5,4,3] => 6 [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] => 5 [1,6,3,5,4,2] => 4 [1,6,4,2,3,5] => 7 [1,6,4,2,5,3] => 5 [1,6,4,3,2,5] => 6 [1,6,4,3,5,2] => 4 [1,6,4,5,2,3] => 7 [1,6,4,5,3,2] => 6 [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] => 6 [1,6,5,4,2,3] => 5 [1,6,5,4,3,2] => 4 [2,1,3,4,5,6] => 2 [2,1,3,4,6,5] => 4 [2,1,3,5,4,6] => 4 [2,1,3,5,6,4] => 6 [2,1,3,6,4,5] => 6 [2,1,3,6,5,4] => 4 [2,1,4,3,5,6] => 4 [2,1,4,3,6,5] => 8 [2,1,4,5,3,6] => 6 [2,1,4,5,6,3] => 8 [2,1,4,6,3,5] => 10 [2,1,4,6,5,3] => 6 [2,1,5,3,4,6] => 6 [2,1,5,3,6,4] => 10 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 6 [2,1,5,6,3,4] => 12 [2,1,5,6,4,3] => 10 [2,1,6,3,4,5] => 8 [2,1,6,3,5,4] => 6 [2,1,6,4,3,5] => 6 [2,1,6,4,5,3] => 4 [2,1,6,5,3,4] => 10 [2,1,6,5,4,3] => 8 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 6 [2,3,1,5,4,6] => 6 [2,3,1,5,6,4] => 9 [2,3,1,6,4,5] => 9 [2,3,1,6,5,4] => 6 [2,3,4,1,5,6] => 4 [2,3,4,1,6,5] => 8 [2,3,4,5,1,6] => 5 [2,3,4,5,6,1] => 6 [2,3,4,6,1,5] => 9 [2,3,4,6,5,1] => 5 [2,3,5,1,4,6] => 7 [2,3,5,1,6,4] => 11 [2,3,5,4,1,6] => 4 [2,3,5,4,6,1] => 5 [2,3,5,6,1,4] => 12 [2,3,5,6,4,1] => 9 [2,3,6,1,4,5] => 10 [2,3,6,1,5,4] => 7 [2,3,6,4,1,5] => 7 [2,3,6,4,5,1] => 4 [2,3,6,5,1,4] => 11 [2,3,6,5,4,1] => 8 [2,4,1,3,5,6] => 5 [2,4,1,3,6,5] => 10 [2,4,1,5,3,6] => 8 [2,4,1,5,6,3] => 11 [2,4,1,6,3,5] => 13 [2,4,1,6,5,3] => 8 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 6 [2,4,3,5,1,6] => 4 [2,4,3,5,6,1] => 5 [2,4,3,6,1,5] => 7 [2,4,3,6,5,1] => 4 [2,4,5,1,3,6] => 9 [2,4,5,1,6,3] => 13 [2,4,5,3,1,6] => 7 [2,4,5,3,6,1] => 9 [2,4,5,6,1,3] => 14 [2,4,5,6,3,1] => 12 [2,4,6,1,3,5] => 14 [2,4,6,1,5,3] => 9 [2,4,6,3,1,5] => 12 [2,4,6,3,5,1] => 7 [2,4,6,5,1,3] => 13 [2,4,6,5,3,1] => 11 [2,5,1,3,4,6] => 7 [2,5,1,3,6,4] => 12 [2,5,1,4,3,6] => 5 [2,5,1,4,6,3] => 8 [2,5,1,6,3,4] => 15 [2,5,1,6,4,3] => 13 [2,5,3,1,4,6] => 5 [2,5,3,1,6,4] => 8 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 4 [2,5,3,6,1,4] => 9 [2,5,3,6,4,1] => 7 [2,5,4,1,3,6] => 8 [2,5,4,1,6,3] => 12 [2,5,4,3,1,6] => 6 [2,5,4,3,6,1] => 8 [2,5,4,6,1,3] => 13 [2,5,4,6,3,1] => 11 [2,5,6,1,3,4] => 16 [2,5,6,1,4,3] => 14 [2,5,6,3,1,4] => 14 [2,5,6,3,4,1] => 10 [2,5,6,4,1,3] => 9 [2,5,6,4,3,1] => 7 [2,6,1,3,4,5] => 9 [2,6,1,3,5,4] => 7 [2,6,1,4,3,5] => 7 [2,6,1,4,5,3] => 5 [2,6,1,5,3,4] => 12 [2,6,1,5,4,3] => 10 [2,6,3,1,4,5] => 7 [2,6,3,1,5,4] => 5 [2,6,3,4,1,5] => 5 [2,6,3,4,5,1] => 3 [2,6,3,5,1,4] => 8 [2,6,3,5,4,1] => 6 [2,6,4,1,3,5] => 12 [2,6,4,1,5,3] => 8 [2,6,4,3,1,5] => 10 [2,6,4,3,5,1] => 6 [2,6,4,5,1,3] => 11 [2,6,4,5,3,1] => 9 [2,6,5,1,3,4] => 15 [2,6,5,1,4,3] => 13 [2,6,5,3,1,4] => 13 [2,6,5,3,4,1] => 9 [2,6,5,4,1,3] => 8 [2,6,5,4,3,1] => 6 [3,1,2,4,5,6] => 3 [3,1,2,4,6,5] => 6 [3,1,2,5,4,6] => 6 [3,1,2,5,6,4] => 9 [3,1,2,6,4,5] => 9 [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] => 7 [3,1,4,5,6,2] => 9 [3,1,4,6,2,5] => 12 [3,1,4,6,5,2] => 7 [3,1,5,2,4,6] => 8 [3,1,5,2,6,4] => 13 [3,1,5,4,2,6] => 5 [3,1,5,4,6,2] => 7 [3,1,5,6,2,4] => 15 [3,1,5,6,4,2] => 12 [3,1,6,2,4,5] => 11 [3,1,6,2,5,4] => 8 [3,1,6,4,2,5] => 8 [3,1,6,4,5,2] => 5 [3,1,6,5,2,4] => 13 [3,1,6,5,4,2] => 10 [3,2,1,4,5,6] => 2 [3,2,1,4,6,5] => 4 [3,2,1,5,4,6] => 4 [3,2,1,5,6,4] => 6 [3,2,1,6,4,5] => 6 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 3 [3,2,4,1,6,5] => 6 [3,2,4,5,1,6] => 4 [3,2,4,5,6,1] => 5 [3,2,4,6,1,5] => 7 [3,2,4,6,5,1] => 4 [3,2,5,1,4,6] => 5 [3,2,5,1,6,4] => 8 [3,2,5,4,1,6] => 3 [3,2,5,4,6,1] => 4 [3,2,5,6,1,4] => 9 [3,2,5,6,4,1] => 7 [3,2,6,1,4,5] => 7 [3,2,6,1,5,4] => 5 [3,2,6,4,1,5] => 5 [3,2,6,4,5,1] => 3 [3,2,6,5,1,4] => 8 [3,2,6,5,4,1] => 6 [3,4,1,2,5,6] => 6 [3,4,1,2,6,5] => 12 [3,4,1,5,2,6] => 9 [3,4,1,5,6,2] => 12 [3,4,1,6,2,5] => 15 [3,4,1,6,5,2] => 9 [3,4,2,1,5,6] => 5 [3,4,2,1,6,5] => 10 [3,4,2,5,1,6] => 7 [3,4,2,5,6,1] => 9 [3,4,2,6,1,5] => 12 [3,4,2,6,5,1] => 7 [3,4,5,1,2,6] => 10 [3,4,5,1,6,2] => 14 [3,4,5,2,1,6] => 9 [3,4,5,2,6,1] => 12 [3,4,5,6,1,2] => 15 [3,4,5,6,2,1] => 14 [3,4,6,1,2,5] => 16 [3,4,6,1,5,2] => 10 [3,4,6,2,1,5] => 15 [3,4,6,2,5,1] => 9 [3,4,6,5,1,2] => 14 [3,4,6,5,2,1] => 13 [3,5,1,2,4,6] => 9 [3,5,1,2,6,4] => 15 [3,5,1,4,2,6] => 6 [3,5,1,4,6,2] => 9 [3,5,1,6,2,4] => 18 [3,5,1,6,4,2] => 15 [3,5,2,1,4,6] => 8 [3,5,2,1,6,4] => 13 [3,5,2,4,1,6] => 5 [3,5,2,4,6,1] => 7 [3,5,2,6,1,4] => 15 [3,5,2,6,4,1] => 12 [3,5,4,1,2,6] => 9 [3,5,4,1,6,2] => 13 [3,5,4,2,1,6] => 8 [3,5,4,2,6,1] => 11 [3,5,4,6,1,2] => 14 [3,5,4,6,2,1] => 13 [3,5,6,1,2,4] => 19 [3,5,6,1,4,2] => 16 [3,5,6,2,1,4] => 18 [3,5,6,2,4,1] => 14 [3,5,6,4,1,2] => 10 [3,5,6,4,2,1] => 9 [3,6,1,2,4,5] => 12 [3,6,1,2,5,4] => 9 [3,6,1,4,2,5] => 9 [3,6,1,4,5,2] => 6 [3,6,1,5,2,4] => 15 [3,6,1,5,4,2] => 12 [3,6,2,1,4,5] => 11 [3,6,2,1,5,4] => 8 [3,6,2,4,1,5] => 8 [3,6,2,4,5,1] => 5 [3,6,2,5,1,4] => 13 [3,6,2,5,4,1] => 10 [3,6,4,1,2,5] => 14 [3,6,4,1,5,2] => 9 [3,6,4,2,1,5] => 13 [3,6,4,2,5,1] => 8 [3,6,4,5,1,2] => 12 [3,6,4,5,2,1] => 11 [3,6,5,1,2,4] => 18 [3,6,5,1,4,2] => 15 [3,6,5,2,1,4] => 17 [3,6,5,2,4,1] => 13 [3,6,5,4,1,2] => 9 [3,6,5,4,2,1] => 8 [4,1,2,3,5,6] => 4 [4,1,2,3,6,5] => 8 [4,1,2,5,3,6] => 7 [4,1,2,5,6,3] => 10 [4,1,2,6,3,5] => 11 [4,1,2,6,5,3] => 7 [4,1,3,2,5,6] => 3 [4,1,3,2,6,5] => 6 [4,1,3,5,2,6] => 5 [4,1,3,5,6,2] => 7 [4,1,3,6,2,5] => 8 [4,1,3,6,5,2] => 5 [4,1,5,2,3,6] => 9 [4,1,5,2,6,3] => 14 [4,1,5,3,2,6] => 8 [4,1,5,3,6,2] => 12 [4,1,5,6,2,3] => 16 [4,1,5,6,3,2] => 15 [4,1,6,2,3,5] => 13 [4,1,6,2,5,3] => 9 [4,1,6,3,2,5] => 12 [4,1,6,3,5,2] => 8 [4,1,6,5,2,3] => 14 [4,1,6,5,3,2] => 13 [4,2,1,3,5,6] => 3 [4,2,1,3,6,5] => 6 [4,2,1,5,3,6] => 5 [4,2,1,5,6,3] => 7 [4,2,1,6,3,5] => 8 [4,2,1,6,5,3] => 5 [4,2,3,1,5,6] => 2 [4,2,3,1,6,5] => 4 [4,2,3,5,1,6] => 3 [4,2,3,5,6,1] => 4 [4,2,3,6,1,5] => 5 [4,2,3,6,5,1] => 3 [4,2,5,1,3,6] => 6 [4,2,5,1,6,3] => 9 [4,2,5,3,1,6] => 5 [4,2,5,3,6,1] => 7 [4,2,5,6,1,3] => 10 [4,2,5,6,3,1] => 9 [4,2,6,1,3,5] => 9 [4,2,6,1,5,3] => 6 [4,2,6,3,1,5] => 8 [4,2,6,3,5,1] => 5 [4,2,6,5,1,3] => 9 [4,2,6,5,3,1] => 8 [4,3,1,2,5,6] => 5 [4,3,1,2,6,5] => 10 [4,3,1,5,2,6] => 8 [4,3,1,5,6,2] => 11 [4,3,1,6,2,5] => 13 [4,3,1,6,5,2] => 8 [4,3,2,1,5,6] => 4 [4,3,2,1,6,5] => 8 [4,3,2,5,1,6] => 6 [4,3,2,5,6,1] => 8 [4,3,2,6,1,5] => 10 [4,3,2,6,5,1] => 6 [4,3,5,1,2,6] => 9 [4,3,5,1,6,2] => 13 [4,3,5,2,1,6] => 8 [4,3,5,2,6,1] => 11 [4,3,5,6,1,2] => 14 [4,3,5,6,2,1] => 13 [4,3,6,1,2,5] => 14 [4,3,6,1,5,2] => 9 [4,3,6,2,1,5] => 13 [4,3,6,2,5,1] => 8 [4,3,6,5,1,2] => 13 [4,3,6,5,2,1] => 12 [4,5,1,2,3,6] => 10 [4,5,1,2,6,3] => 16 [4,5,1,3,2,6] => 9 [4,5,1,3,6,2] => 14 [4,5,1,6,2,3] => 19 [4,5,1,6,3,2] => 18 [4,5,2,1,3,6] => 9 [4,5,2,1,6,3] => 14 [4,5,2,3,1,6] => 7 [4,5,2,3,6,1] => 10 [4,5,2,6,1,3] => 16 [4,5,2,6,3,1] => 14 [4,5,3,1,2,6] => 6 [4,5,3,1,6,2] => 9 [4,5,3,2,1,6] => 5 [4,5,3,2,6,1] => 7 [4,5,3,6,1,2] => 10 [4,5,3,6,2,1] => 9 [4,5,6,1,2,3] => 20 [4,5,6,1,3,2] => 19 [4,5,6,2,1,3] => 19 [4,5,6,2,3,1] => 16 [4,5,6,3,1,2] => 16 [4,5,6,3,2,1] => 14 [4,6,1,2,3,5] => 14 [4,6,1,2,5,3] => 10 [4,6,1,3,2,5] => 13 [4,6,1,3,5,2] => 9 [4,6,1,5,2,3] => 16 [4,6,1,5,3,2] => 15 [4,6,2,1,3,5] => 13 [4,6,2,1,5,3] => 9 [4,6,2,3,1,5] => 11 [4,6,2,3,5,1] => 7 [4,6,2,5,1,3] => 14 [4,6,2,5,3,1] => 12 [4,6,3,1,2,5] => 9 [4,6,3,1,5,2] => 6 [4,6,3,2,1,5] => 8 [4,6,3,2,5,1] => 5 [4,6,3,5,1,2] => 9 [4,6,3,5,2,1] => 8 [4,6,5,1,2,3] => 19 [4,6,5,1,3,2] => 18 [4,6,5,2,1,3] => 18 [4,6,5,2,3,1] => 15 [4,6,5,3,1,2] => 15 [4,6,5,3,2,1] => 13 [5,1,2,3,4,6] => 5 [5,1,2,3,6,4] => 9 [5,1,2,4,3,6] => 4 [5,1,2,4,6,3] => 7 [5,1,2,6,3,4] => 12 [5,1,2,6,4,3] => 11 [5,1,3,2,4,6] => 4 [5,1,3,2,6,4] => 7 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 5 [5,1,3,6,2,4] => 9 [5,1,3,6,4,2] => 8 [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] => 10 [5,1,4,6,2,3] => 14 [5,1,4,6,3,2] => 13 [5,1,6,2,3,4] => 14 [5,1,6,2,4,3] => 13 [5,1,6,3,2,4] => 13 [5,1,6,3,4,2] => 11 [5,1,6,4,2,3] => 9 [5,1,6,4,3,2] => 8 [5,2,1,3,4,6] => 4 [5,2,1,3,6,4] => 7 [5,2,1,4,3,6] => 3 [5,2,1,4,6,3] => 5 [5,2,1,6,3,4] => 9 [5,2,1,6,4,3] => 8 [5,2,3,1,4,6] => 3 [5,2,3,1,6,4] => 5 [5,2,3,4,1,6] => 2 [5,2,3,4,6,1] => 3 [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] => 8 [5,2,4,3,1,6] => 4 [5,2,4,3,6,1] => 6 [5,2,4,6,1,3] => 9 [5,2,4,6,3,1] => 8 [5,2,6,1,3,4] => 10 [5,2,6,1,4,3] => 9 [5,2,6,3,1,4] => 9 [5,2,6,3,4,1] => 7 [5,2,6,4,1,3] => 6 [5,2,6,4,3,1] => 5 [5,3,1,2,4,6] => 7 [5,3,1,2,6,4] => 12 [5,3,1,4,2,6] => 5 [5,3,1,4,6,2] => 8 [5,3,1,6,2,4] => 15 [5,3,1,6,4,2] => 13 [5,3,2,1,4,6] => 6 [5,3,2,1,6,4] => 10 [5,3,2,4,1,6] => 4 [5,3,2,4,6,1] => 6 [5,3,2,6,1,4] => 12 [5,3,2,6,4,1] => 10 [5,3,4,1,2,6] => 7 [5,3,4,1,6,2] => 11 [5,3,4,2,1,6] => 6 [5,3,4,2,6,1] => 9 [5,3,4,6,1,2] => 12 [5,3,4,6,2,1] => 11 [5,3,6,1,2,4] => 16 [5,3,6,1,4,2] => 14 [5,3,6,2,1,4] => 15 [5,3,6,2,4,1] => 12 [5,3,6,4,1,2] => 9 [5,3,6,4,2,1] => 8 [5,4,1,2,3,6] => 9 [5,4,1,2,6,3] => 15 [5,4,1,3,2,6] => 8 [5,4,1,3,6,2] => 13 [5,4,1,6,2,3] => 18 [5,4,1,6,3,2] => 17 [5,4,2,1,3,6] => 8 [5,4,2,1,6,3] => 13 [5,4,2,3,1,6] => 6 [5,4,2,3,6,1] => 9 [5,4,2,6,1,3] => 15 [5,4,2,6,3,1] => 13 [5,4,3,1,2,6] => 5 [5,4,3,1,6,2] => 8 [5,4,3,2,1,6] => 4 [5,4,3,2,6,1] => 6 [5,4,3,6,1,2] => 9 [5,4,3,6,2,1] => 8 [5,4,6,1,2,3] => 19 [5,4,6,1,3,2] => 18 [5,4,6,2,1,3] => 18 [5,4,6,2,3,1] => 15 [5,4,6,3,1,2] => 15 [5,4,6,3,2,1] => 13 [5,6,1,2,3,4] => 15 [5,6,1,2,4,3] => 14 [5,6,1,3,2,4] => 14 [5,6,1,3,4,2] => 12 [5,6,1,4,2,3] => 10 [5,6,1,4,3,2] => 9 [5,6,2,1,3,4] => 14 [5,6,2,1,4,3] => 13 [5,6,2,3,1,4] => 12 [5,6,2,3,4,1] => 9 [5,6,2,4,1,3] => 9 [5,6,2,4,3,1] => 7 [5,6,3,1,2,4] => 10 [5,6,3,1,4,2] => 9 [5,6,3,2,1,4] => 9 [5,6,3,2,4,1] => 7 [5,6,3,4,1,2] => 6 [5,6,3,4,2,1] => 5 [5,6,4,1,2,3] => 16 [5,6,4,1,3,2] => 15 [5,6,4,2,1,3] => 15 [5,6,4,2,3,1] => 12 [5,6,4,3,1,2] => 12 [5,6,4,3,2,1] => 10 [6,1,2,3,4,5] => 6 [6,1,2,3,5,4] => 5 [6,1,2,4,3,5] => 5 [6,1,2,4,5,3] => 4 [6,1,2,5,3,4] => 9 [6,1,2,5,4,3] => 8 [6,1,3,2,4,5] => 5 [6,1,3,2,5,4] => 4 [6,1,3,4,2,5] => 4 [6,1,3,4,5,2] => 3 [6,1,3,5,2,4] => 7 [6,1,3,5,4,2] => 6 [6,1,4,2,3,5] => 9 [6,1,4,2,5,3] => 7 [6,1,4,3,2,5] => 8 [6,1,4,3,5,2] => 6 [6,1,4,5,2,3] => 10 [6,1,4,5,3,2] => 9 [6,1,5,2,3,4] => 12 [6,1,5,2,4,3] => 11 [6,1,5,3,2,4] => 11 [6,1,5,3,4,2] => 9 [6,1,5,4,2,3] => 7 [6,1,5,4,3,2] => 6 [6,2,1,3,4,5] => 5 [6,2,1,3,5,4] => 4 [6,2,1,4,3,5] => 4 [6,2,1,4,5,3] => 3 [6,2,1,5,3,4] => 7 [6,2,1,5,4,3] => 6 [6,2,3,1,4,5] => 4 [6,2,3,1,5,4] => 3 [6,2,3,4,1,5] => 3 [6,2,3,4,5,1] => 2 [6,2,3,5,1,4] => 5 [6,2,3,5,4,1] => 4 [6,2,4,1,3,5] => 7 [6,2,4,1,5,3] => 5 [6,2,4,3,1,5] => 6 [6,2,4,3,5,1] => 4 [6,2,4,5,1,3] => 7 [6,2,4,5,3,1] => 6 [6,2,5,1,3,4] => 9 [6,2,5,1,4,3] => 8 [6,2,5,3,1,4] => 8 [6,2,5,3,4,1] => 6 [6,2,5,4,1,3] => 5 [6,2,5,4,3,1] => 4 [6,3,1,2,4,5] => 9 [6,3,1,2,5,4] => 7 [6,3,1,4,2,5] => 7 [6,3,1,4,5,2] => 5 [6,3,1,5,2,4] => 12 [6,3,1,5,4,2] => 10 [6,3,2,1,4,5] => 8 [6,3,2,1,5,4] => 6 [6,3,2,4,1,5] => 6 [6,3,2,4,5,1] => 4 [6,3,2,5,1,4] => 10 [6,3,2,5,4,1] => 8 [6,3,4,1,2,5] => 10 [6,3,4,1,5,2] => 7 [6,3,4,2,1,5] => 9 [6,3,4,2,5,1] => 6 [6,3,4,5,1,2] => 9 [6,3,4,5,2,1] => 8 [6,3,5,1,2,4] => 14 [6,3,5,1,4,2] => 12 [6,3,5,2,1,4] => 13 [6,3,5,2,4,1] => 10 [6,3,5,4,1,2] => 7 [6,3,5,4,2,1] => 6 [6,4,1,2,3,5] => 12 [6,4,1,2,5,3] => 9 [6,4,1,3,2,5] => 11 [6,4,1,3,5,2] => 8 [6,4,1,5,2,3] => 14 [6,4,1,5,3,2] => 13 [6,4,2,1,3,5] => 11 [6,4,2,1,5,3] => 8 [6,4,2,3,1,5] => 9 [6,4,2,3,5,1] => 6 [6,4,2,5,1,3] => 12 [6,4,2,5,3,1] => 10 [6,4,3,1,2,5] => 7 [6,4,3,1,5,2] => 5 [6,4,3,2,1,5] => 6 [6,4,3,2,5,1] => 4 [6,4,3,5,1,2] => 7 [6,4,3,5,2,1] => 6 [6,4,5,1,2,3] => 16 [6,4,5,1,3,2] => 15 [6,4,5,2,1,3] => 15 [6,4,5,2,3,1] => 12 [6,4,5,3,1,2] => 12 [6,4,5,3,2,1] => 10 [6,5,1,2,3,4] => 14 [6,5,1,2,4,3] => 13 [6,5,1,3,2,4] => 13 [6,5,1,3,4,2] => 11 [6,5,1,4,2,3] => 9 [6,5,1,4,3,2] => 8 [6,5,2,1,3,4] => 13 [6,5,2,1,4,3] => 12 [6,5,2,3,1,4] => 11 [6,5,2,3,4,1] => 8 [6,5,2,4,1,3] => 8 [6,5,2,4,3,1] => 6 [6,5,3,1,2,4] => 9 [6,5,3,1,4,2] => 8 [6,5,3,2,1,4] => 8 [6,5,3,2,4,1] => 6 [6,5,3,4,1,2] => 5 [6,5,3,4,2,1] => 4 [6,5,4,1,2,3] => 14 [6,5,4,1,3,2] => 13 [6,5,4,2,1,3] => 13 [6,5,4,2,3,1] => 10 [6,5,4,3,1,2] => 10 [6,5,4,3,2,1] => 8 [1,2,3,4,5,6,7] => 1 [1,2,3,4,5,7,6] => 2 [1,2,3,4,6,5,7] => 2 [1,2,3,4,6,7,5] => 3 [1,2,3,4,7,5,6] => 3 [1,2,3,4,7,6,5] => 2 [1,2,3,5,4,6,7] => 2 [1,2,3,5,4,7,6] => 4 [1,2,3,5,6,4,7] => 3 [1,2,3,5,6,7,4] => 4 [1,2,3,5,7,4,6] => 5 [1,2,3,5,7,6,4] => 3 [1,2,3,6,4,5,7] => 3 [1,2,3,6,4,7,5] => 5 [1,2,3,6,5,4,7] => 2 [1,2,3,6,5,7,4] => 3 [1,2,3,6,7,4,5] => 6 [1,2,3,6,7,5,4] => 5 [1,2,3,7,4,5,6] => 4 [1,2,3,7,4,6,5] => 3 [1,2,3,7,5,4,6] => 3 [1,2,3,7,5,6,4] => 2 [1,2,3,7,6,4,5] => 5 [1,2,3,7,6,5,4] => 4 [1,2,4,3,5,6,7] => 2 [1,2,4,3,5,7,6] => 4 [1,2,4,3,6,5,7] => 4 [1,2,4,3,6,7,5] => 6 [1,2,4,3,7,5,6] => 6 [1,2,4,3,7,6,5] => 4 [1,2,4,5,3,6,7] => 3 [1,2,4,5,3,7,6] => 6 [1,2,4,5,6,3,7] => 4 [1,2,4,5,6,7,3] => 5 [1,2,4,5,7,3,6] => 7 [1,2,4,5,7,6,3] => 4 [1,2,4,6,3,5,7] => 5 [1,2,4,6,3,7,5] => 8 [1,2,4,6,5,3,7] => 3 [1,2,4,6,5,7,3] => 4 [1,2,4,6,7,3,5] => 9 [1,2,4,6,7,5,3] => 7 [1,2,4,7,3,5,6] => 7 [1,2,4,7,3,6,5] => 5 [1,2,4,7,5,3,6] => 5 [1,2,4,7,5,6,3] => 3 [1,2,4,7,6,3,5] => 8 [1,2,4,7,6,5,3] => 6 [1,2,5,3,4,6,7] => 3 [1,2,5,3,4,7,6] => 6 [1,2,5,3,6,4,7] => 5 [1,2,5,3,6,7,4] => 7 [1,2,5,3,7,4,6] => 8 [1,2,5,3,7,6,4] => 5 [1,2,5,4,3,6,7] => 2 [1,2,5,4,3,7,6] => 4 [1,2,5,4,6,3,7] => 3 [1,2,5,4,6,7,3] => 4 [1,2,5,4,7,3,6] => 5 [1,2,5,4,7,6,3] => 3 [1,2,5,6,3,4,7] => 6 [1,2,5,6,3,7,4] => 9 [1,2,5,6,4,3,7] => 5 [1,2,5,6,4,7,3] => 7 [1,2,5,6,7,3,4] => 10 [1,2,5,6,7,4,3] => 9 [1,2,5,7,3,4,6] => 9 [1,2,5,7,3,6,4] => 6 [1,2,5,7,4,3,6] => 8 [1,2,5,7,4,6,3] => 5 [1,2,5,7,6,3,4] => 9 [1,2,5,7,6,4,3] => 8 [1,2,6,3,4,5,7] => 4 [1,2,6,3,4,7,5] => 7 [1,2,6,3,5,4,7] => 3 [1,2,6,3,5,7,4] => 5 [1,2,6,3,7,4,5] => 9 [1,2,6,3,7,5,4] => 8 [1,2,6,4,3,5,7] => 3 [1,2,6,4,3,7,5] => 5 [1,2,6,4,5,3,7] => 2 [1,2,6,4,5,7,3] => 3 [1,2,6,4,7,3,5] => 6 [1,2,6,4,7,5,3] => 5 [1,2,6,5,3,4,7] => 5 [1,2,6,5,3,7,4] => 8 [1,2,6,5,4,3,7] => 4 [1,2,6,5,4,7,3] => 6 [1,2,6,5,7,3,4] => 9 [1,2,6,5,7,4,3] => 8 [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] => 7 [1,2,6,7,5,3,4] => 6 [1,2,6,7,5,4,3] => 5 [1,2,7,3,4,5,6] => 5 [1,2,7,3,4,6,5] => 4 [1,2,7,3,5,4,6] => 4 [1,2,7,3,5,6,4] => 3 [1,2,7,3,6,4,5] => 7 [1,2,7,3,6,5,4] => 6 [1,2,7,4,3,5,6] => 4 [1,2,7,4,3,6,5] => 3 [1,2,7,4,5,3,6] => 3 [1,2,7,4,5,6,3] => 2 [1,2,7,4,6,3,5] => 5 [1,2,7,4,6,5,3] => 4 [1,2,7,5,3,4,6] => 7 [1,2,7,5,3,6,4] => 5 [1,2,7,5,4,3,6] => 6 [1,2,7,5,4,6,3] => 4 [1,2,7,5,6,3,4] => 7 [1,2,7,5,6,4,3] => 6 [1,2,7,6,3,4,5] => 9 [1,2,7,6,3,5,4] => 8 [1,2,7,6,4,3,5] => 8 [1,2,7,6,4,5,3] => 6 [1,2,7,6,5,3,4] => 5 [1,2,7,6,5,4,3] => 4 [1,3,2,4,5,6,7] => 2 [1,3,2,4,5,7,6] => 4 [1,3,2,4,6,5,7] => 4 [1,3,2,4,6,7,5] => 6 [1,3,2,4,7,5,6] => 6 [1,3,2,4,7,6,5] => 4 [1,3,2,5,4,6,7] => 4 [1,3,2,5,4,7,6] => 8 [1,3,2,5,6,4,7] => 6 [1,3,2,5,6,7,4] => 8 [1,3,2,5,7,4,6] => 10 [1,3,2,5,7,6,4] => 6 [1,3,2,6,4,5,7] => 6 [1,3,2,6,4,7,5] => 10 [1,3,2,6,5,4,7] => 4 [1,3,2,6,5,7,4] => 6 [1,3,2,6,7,4,5] => 12 [1,3,2,6,7,5,4] => 10 [1,3,2,7,4,5,6] => 8 [1,3,2,7,4,6,5] => 6 [1,3,2,7,5,4,6] => 6 [1,3,2,7,5,6,4] => 4 [1,3,2,7,6,4,5] => 10 [1,3,2,7,6,5,4] => 8 [1,3,4,2,5,6,7] => 3 [1,3,4,2,5,7,6] => 6 [1,3,4,2,6,5,7] => 6 [1,3,4,2,6,7,5] => 9 [1,3,4,2,7,5,6] => 9 [1,3,4,2,7,6,5] => 6 [1,3,4,5,2,6,7] => 4 [1,3,4,5,2,7,6] => 8 [1,3,4,5,6,2,7] => 5 [1,3,4,5,6,7,2] => 6 [1,3,4,5,7,2,6] => 9 [1,3,4,5,7,6,2] => 5 [1,3,4,6,2,5,7] => 7 [1,3,4,6,2,7,5] => 11 [1,3,4,6,5,2,7] => 4 [1,3,4,6,5,7,2] => 5 [1,3,4,6,7,2,5] => 12 [1,3,4,6,7,5,2] => 9 [1,3,4,7,2,5,6] => 10 [1,3,4,7,2,6,5] => 7 [1,3,4,7,5,2,6] => 7 [1,3,4,7,5,6,2] => 4 [1,3,4,7,6,2,5] => 11 [1,3,4,7,6,5,2] => 8 [1,3,5,2,4,6,7] => 5 [1,3,5,2,4,7,6] => 10 [1,3,5,2,6,4,7] => 8 [1,3,5,2,6,7,4] => 11 [1,3,5,2,7,4,6] => 13 [1,3,5,2,7,6,4] => 8 [1,3,5,4,2,6,7] => 3 [1,3,5,4,2,7,6] => 6 [1,3,5,4,6,2,7] => 4 [1,3,5,4,6,7,2] => 5 [1,3,5,4,7,2,6] => 7 [1,3,5,4,7,6,2] => 4 [1,3,5,6,2,4,7] => 9 [1,3,5,6,2,7,4] => 13 [1,3,5,6,4,2,7] => 7 [1,3,5,6,4,7,2] => 9 [1,3,5,6,7,2,4] => 14 [1,3,5,6,7,4,2] => 12 [1,3,5,7,2,4,6] => 14 [1,3,5,7,2,6,4] => 9 [1,3,5,7,4,2,6] => 12 [1,3,5,7,4,6,2] => 7 [1,3,5,7,6,2,4] => 13 [1,3,5,7,6,4,2] => 11 [1,3,6,2,4,5,7] => 7 [1,3,6,2,4,7,5] => 12 [1,3,6,2,5,4,7] => 5 [1,3,6,2,5,7,4] => 8 [1,3,6,2,7,4,5] => 15 [1,3,6,2,7,5,4] => 13 [1,3,6,4,2,5,7] => 5 [1,3,6,4,2,7,5] => 8 [1,3,6,4,5,2,7] => 3 [1,3,6,4,5,7,2] => 4 [1,3,6,4,7,2,5] => 9 [1,3,6,4,7,5,2] => 7 [1,3,6,5,2,4,7] => 8 [1,3,6,5,2,7,4] => 12 [1,3,6,5,4,2,7] => 6 [1,3,6,5,4,7,2] => 8 [1,3,6,5,7,2,4] => 13 [1,3,6,5,7,4,2] => 11 [1,3,6,7,2,4,5] => 16 [1,3,6,7,2,5,4] => 14 [1,3,6,7,4,2,5] => 14 [1,3,6,7,4,5,2] => 10 [1,3,6,7,5,2,4] => 9 [1,3,6,7,5,4,2] => 7 [1,3,7,2,4,5,6] => 9 [1,3,7,2,4,6,5] => 7 [1,3,7,2,5,4,6] => 7 [1,3,7,2,5,6,4] => 5 [1,3,7,2,6,4,5] => 12 [1,3,7,2,6,5,4] => 10 [1,3,7,4,2,5,6] => 7 [1,3,7,4,2,6,5] => 5 [1,3,7,4,5,2,6] => 5 [1,3,7,4,5,6,2] => 3 [1,3,7,4,6,2,5] => 8 [1,3,7,4,6,5,2] => 6 [1,3,7,5,2,4,6] => 12 [1,3,7,5,2,6,4] => 8 [1,3,7,5,4,2,6] => 10 [1,3,7,5,4,6,2] => 6 [1,3,7,5,6,2,4] => 11 [1,3,7,5,6,4,2] => 9 [1,3,7,6,2,4,5] => 15 [1,3,7,6,2,5,4] => 13 [1,3,7,6,4,2,5] => 13 [1,3,7,6,4,5,2] => 9 [1,3,7,6,5,2,4] => 8 [1,3,7,6,5,4,2] => 6 [1,4,2,3,5,6,7] => 3 [1,4,2,3,5,7,6] => 6 [1,4,2,3,6,5,7] => 6 [1,4,2,3,6,7,5] => 9 [1,4,2,3,7,5,6] => 9 [1,4,2,3,7,6,5] => 6 [1,4,2,5,3,6,7] => 5 [1,4,2,5,3,7,6] => 10 [1,4,2,5,6,3,7] => 7 [1,4,2,5,6,7,3] => 9 [1,4,2,5,7,3,6] => 12 [1,4,2,5,7,6,3] => 7 [1,4,2,6,3,5,7] => 8 [1,4,2,6,3,7,5] => 13 [1,4,2,6,5,3,7] => 5 [1,4,2,6,5,7,3] => 7 [1,4,2,6,7,3,5] => 15 [1,4,2,6,7,5,3] => 12 [1,4,2,7,3,5,6] => 11 [1,4,2,7,3,6,5] => 8 [1,4,2,7,5,3,6] => 8 [1,4,2,7,5,6,3] => 5 [1,4,2,7,6,3,5] => 13 [1,4,2,7,6,5,3] => 10 [1,4,3,2,5,6,7] => 2 [1,4,3,2,5,7,6] => 4 [1,4,3,2,6,5,7] => 4 [1,4,3,2,6,7,5] => 6 [1,4,3,2,7,5,6] => 6 [1,4,3,2,7,6,5] => 4 [1,4,3,5,2,6,7] => 3 [1,4,3,5,2,7,6] => 6 [1,4,3,5,6,2,7] => 4 [1,4,3,5,6,7,2] => 5 [1,4,3,5,7,2,6] => 7 [1,4,3,5,7,6,2] => 4 [1,4,3,6,2,5,7] => 5 [1,4,3,6,2,7,5] => 8 [1,4,3,6,5,2,7] => 3 [1,4,3,6,5,7,2] => 4 [1,4,3,6,7,2,5] => 9 [1,4,3,6,7,5,2] => 7 [1,4,3,7,2,5,6] => 7 [1,4,3,7,2,6,5] => 5 [1,4,3,7,5,2,6] => 5 [1,4,3,7,5,6,2] => 3 [1,4,3,7,6,2,5] => 8 [1,4,3,7,6,5,2] => 6 [1,4,5,2,3,6,7] => 6 [1,4,5,2,3,7,6] => 12 [1,4,5,2,6,3,7] => 9 [1,4,5,2,6,7,3] => 12 [1,4,5,2,7,3,6] => 15 [1,4,5,2,7,6,3] => 9 [1,4,5,3,2,6,7] => 5 [1,4,5,3,2,7,6] => 10 [1,4,5,3,6,2,7] => 7 [1,4,5,3,6,7,2] => 9 [1,4,5,3,7,2,6] => 12 [1,4,5,3,7,6,2] => 7 [1,4,5,6,2,3,7] => 10 [1,4,5,6,2,7,3] => 14 [1,4,5,6,3,2,7] => 9 [1,4,5,6,3,7,2] => 12 [1,4,5,6,7,2,3] => 15 [1,4,5,6,7,3,2] => 14 [1,4,5,7,2,3,6] => 16 [1,4,5,7,2,6,3] => 10 [1,4,5,7,3,2,6] => 15 [1,4,5,7,3,6,2] => 9 [1,4,5,7,6,2,3] => 14 [1,4,5,7,6,3,2] => 13 [1,4,6,2,3,5,7] => 9 [1,4,6,2,3,7,5] => 15 [1,4,6,2,5,3,7] => 6 [1,4,6,2,5,7,3] => 9 [1,4,6,2,7,3,5] => 18 [1,4,6,2,7,5,3] => 15 [1,4,6,3,2,5,7] => 8 [1,4,6,3,2,7,5] => 13 [1,4,6,3,5,2,7] => 5 [1,4,6,3,5,7,2] => 7 [1,4,6,3,7,2,5] => 15 [1,4,6,3,7,5,2] => 12 [1,4,6,5,2,3,7] => 9 [1,4,6,5,2,7,3] => 13 [1,4,6,5,3,2,7] => 8 ----------------------------------------------------------------------------- Created: Aug 12, 2019 at 16:34 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 09, 2023 at 15:54 by Tilman Möller