***************************************************************************** * 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: St000530 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of permutations with the same descent word as the given permutation. The descent word of a permutation is the binary word given by [[Mp00109]]. For a given permutation, this statistic is the number of permutations with the same descent word, so the number of elements in the fiber of the map [[Mp00109]] containing a given permutation. This statistic appears as ''up-down analysis'' in statistical applications in genetics, see [1] and the references therein. ----------------------------------------------------------------------------- References: [1] Morton, J., Pachter, L., Shiu, A., Sturmfels, B., Wienand, O. Convex rank tests and semigraphoids [[MathSciNet:2538642]] ----------------------------------------------------------------------------- Code: from collections import defaultdict def word(pi): w = [0]*(len(pi)-1) for i in pi.descents(from_zero=True): w[i] = 1 return Words([0,1])(w) @cached_function def preimages(n): D = defaultdict(int) for pi in Permutations(n): D[word(pi)] += 1 return D def statistic(pi): return preimages(len(pi))[word(pi)] ----------------------------------------------------------------------------- Statistic values: [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 2 [2,1,3] => 2 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 1 [1,2,4,3] => 3 [1,3,2,4] => 5 [1,3,4,2] => 3 [1,4,2,3] => 5 [1,4,3,2] => 3 [2,1,3,4] => 3 [2,1,4,3] => 5 [2,3,1,4] => 5 [2,3,4,1] => 3 [2,4,1,3] => 5 [2,4,3,1] => 3 [3,1,2,4] => 3 [3,1,4,2] => 5 [3,2,1,4] => 3 [3,2,4,1] => 5 [3,4,1,2] => 5 [3,4,2,1] => 3 [4,1,2,3] => 3 [4,1,3,2] => 5 [4,2,1,3] => 3 [4,2,3,1] => 5 [4,3,1,2] => 3 [4,3,2,1] => 1 [1,2,3,4,5] => 1 [1,2,3,5,4] => 4 [1,2,4,3,5] => 9 [1,2,4,5,3] => 4 [1,2,5,3,4] => 9 [1,2,5,4,3] => 6 [1,3,2,4,5] => 9 [1,3,2,5,4] => 16 [1,3,4,2,5] => 9 [1,3,4,5,2] => 4 [1,3,5,2,4] => 9 [1,3,5,4,2] => 6 [1,4,2,3,5] => 9 [1,4,2,5,3] => 16 [1,4,3,2,5] => 11 [1,4,3,5,2] => 16 [1,4,5,2,3] => 9 [1,4,5,3,2] => 6 [1,5,2,3,4] => 9 [1,5,2,4,3] => 16 [1,5,3,2,4] => 11 [1,5,3,4,2] => 16 [1,5,4,2,3] => 11 [1,5,4,3,2] => 4 [2,1,3,4,5] => 4 [2,1,3,5,4] => 11 [2,1,4,3,5] => 16 [2,1,4,5,3] => 11 [2,1,5,3,4] => 16 [2,1,5,4,3] => 9 [2,3,1,4,5] => 9 [2,3,1,5,4] => 16 [2,3,4,1,5] => 9 [2,3,4,5,1] => 4 [2,3,5,1,4] => 9 [2,3,5,4,1] => 6 [2,4,1,3,5] => 9 [2,4,1,5,3] => 16 [2,4,3,1,5] => 11 [2,4,3,5,1] => 16 [2,4,5,1,3] => 9 [2,4,5,3,1] => 6 [2,5,1,3,4] => 9 [2,5,1,4,3] => 16 [2,5,3,1,4] => 11 [2,5,3,4,1] => 16 [2,5,4,1,3] => 11 [2,5,4,3,1] => 4 [3,1,2,4,5] => 4 [3,1,2,5,4] => 11 [3,1,4,2,5] => 16 [3,1,4,5,2] => 11 [3,1,5,2,4] => 16 [3,1,5,4,2] => 9 [3,2,1,4,5] => 6 [3,2,1,5,4] => 9 [3,2,4,1,5] => 16 [3,2,4,5,1] => 11 [3,2,5,1,4] => 16 [3,2,5,4,1] => 9 [3,4,1,2,5] => 9 [3,4,1,5,2] => 16 [3,4,2,1,5] => 11 [3,4,2,5,1] => 16 [3,4,5,1,2] => 9 [3,4,5,2,1] => 6 [3,5,1,2,4] => 9 [3,5,1,4,2] => 16 [3,5,2,1,4] => 11 [3,5,2,4,1] => 16 [3,5,4,1,2] => 11 [3,5,4,2,1] => 4 [4,1,2,3,5] => 4 [4,1,2,5,3] => 11 [4,1,3,2,5] => 16 [4,1,3,5,2] => 11 [4,1,5,2,3] => 16 [4,1,5,3,2] => 9 [4,2,1,3,5] => 6 [4,2,1,5,3] => 9 [4,2,3,1,5] => 16 [4,2,3,5,1] => 11 [4,2,5,1,3] => 16 [4,2,5,3,1] => 9 [4,3,1,2,5] => 6 [4,3,1,5,2] => 9 [4,3,2,1,5] => 4 [4,3,2,5,1] => 9 [4,3,5,1,2] => 16 [4,3,5,2,1] => 9 [4,5,1,2,3] => 9 [4,5,1,3,2] => 16 [4,5,2,1,3] => 11 [4,5,2,3,1] => 16 [4,5,3,1,2] => 11 [4,5,3,2,1] => 4 [5,1,2,3,4] => 4 [5,1,2,4,3] => 11 [5,1,3,2,4] => 16 [5,1,3,4,2] => 11 [5,1,4,2,3] => 16 [5,1,4,3,2] => 9 [5,2,1,3,4] => 6 [5,2,1,4,3] => 9 [5,2,3,1,4] => 16 [5,2,3,4,1] => 11 [5,2,4,1,3] => 16 [5,2,4,3,1] => 9 [5,3,1,2,4] => 6 [5,3,1,4,2] => 9 [5,3,2,1,4] => 4 [5,3,2,4,1] => 9 [5,3,4,1,2] => 16 [5,3,4,2,1] => 9 [5,4,1,2,3] => 6 [5,4,1,3,2] => 9 [5,4,2,1,3] => 4 [5,4,2,3,1] => 9 [5,4,3,1,2] => 4 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 5 [1,2,3,5,4,6] => 14 [1,2,3,5,6,4] => 5 [1,2,3,6,4,5] => 14 [1,2,3,6,5,4] => 10 [1,2,4,3,5,6] => 19 [1,2,4,3,6,5] => 35 [1,2,4,5,3,6] => 14 [1,2,4,5,6,3] => 5 [1,2,4,6,3,5] => 14 [1,2,4,6,5,3] => 10 [1,2,5,3,4,6] => 19 [1,2,5,3,6,4] => 35 [1,2,5,4,3,6] => 26 [1,2,5,4,6,3] => 35 [1,2,5,6,3,4] => 14 [1,2,5,6,4,3] => 10 [1,2,6,3,4,5] => 19 [1,2,6,3,5,4] => 35 [1,2,6,4,3,5] => 26 [1,2,6,4,5,3] => 35 [1,2,6,5,3,4] => 26 [1,2,6,5,4,3] => 10 [1,3,2,4,5,6] => 14 [1,3,2,4,6,5] => 40 [1,3,2,5,4,6] => 61 [1,3,2,5,6,4] => 40 [1,3,2,6,4,5] => 61 [1,3,2,6,5,4] => 35 [1,3,4,2,5,6] => 19 [1,3,4,2,6,5] => 35 [1,3,4,5,2,6] => 14 [1,3,4,5,6,2] => 5 [1,3,4,6,2,5] => 14 [1,3,4,6,5,2] => 10 [1,3,5,2,4,6] => 19 [1,3,5,2,6,4] => 35 [1,3,5,4,2,6] => 26 [1,3,5,4,6,2] => 35 [1,3,5,6,2,4] => 14 [1,3,5,6,4,2] => 10 [1,3,6,2,4,5] => 19 [1,3,6,2,5,4] => 35 [1,3,6,4,2,5] => 26 [1,3,6,4,5,2] => 35 [1,3,6,5,2,4] => 26 [1,3,6,5,4,2] => 10 [1,4,2,3,5,6] => 14 [1,4,2,3,6,5] => 40 [1,4,2,5,3,6] => 61 [1,4,2,5,6,3] => 40 [1,4,2,6,3,5] => 61 [1,4,2,6,5,3] => 35 [1,4,3,2,5,6] => 26 [1,4,3,2,6,5] => 40 [1,4,3,5,2,6] => 61 [1,4,3,5,6,2] => 40 [1,4,3,6,2,5] => 61 [1,4,3,6,5,2] => 35 [1,4,5,2,3,6] => 19 [1,4,5,2,6,3] => 35 [1,4,5,3,2,6] => 26 [1,4,5,3,6,2] => 35 [1,4,5,6,2,3] => 14 [1,4,5,6,3,2] => 10 [1,4,6,2,3,5] => 19 [1,4,6,2,5,3] => 35 [1,4,6,3,2,5] => 26 [1,4,6,3,5,2] => 35 [1,4,6,5,2,3] => 26 [1,4,6,5,3,2] => 10 [1,5,2,3,4,6] => 14 [1,5,2,3,6,4] => 40 [1,5,2,4,3,6] => 61 [1,5,2,4,6,3] => 40 [1,5,2,6,3,4] => 61 [1,5,2,6,4,3] => 35 [1,5,3,2,4,6] => 26 [1,5,3,2,6,4] => 40 [1,5,3,4,2,6] => 61 [1,5,3,4,6,2] => 40 [1,5,3,6,2,4] => 61 [1,5,3,6,4,2] => 35 [1,5,4,2,3,6] => 26 [1,5,4,2,6,3] => 40 [1,5,4,3,2,6] => 19 [1,5,4,3,6,2] => 40 [1,5,4,6,2,3] => 61 [1,5,4,6,3,2] => 35 [1,5,6,2,3,4] => 19 [1,5,6,2,4,3] => 35 [1,5,6,3,2,4] => 26 [1,5,6,3,4,2] => 35 [1,5,6,4,2,3] => 26 [1,5,6,4,3,2] => 10 [1,6,2,3,4,5] => 14 [1,6,2,3,5,4] => 40 [1,6,2,4,3,5] => 61 [1,6,2,4,5,3] => 40 [1,6,2,5,3,4] => 61 [1,6,2,5,4,3] => 35 [1,6,3,2,4,5] => 26 [1,6,3,2,5,4] => 40 [1,6,3,4,2,5] => 61 [1,6,3,4,5,2] => 40 [1,6,3,5,2,4] => 61 [1,6,3,5,4,2] => 35 [1,6,4,2,3,5] => 26 [1,6,4,2,5,3] => 40 [1,6,4,3,2,5] => 19 [1,6,4,3,5,2] => 40 [1,6,4,5,2,3] => 61 [1,6,4,5,3,2] => 35 [1,6,5,2,3,4] => 26 [1,6,5,2,4,3] => 40 [1,6,5,3,2,4] => 19 [1,6,5,3,4,2] => 40 [1,6,5,4,2,3] => 19 [1,6,5,4,3,2] => 5 [2,1,3,4,5,6] => 5 [2,1,3,4,6,5] => 19 [2,1,3,5,4,6] => 40 [2,1,3,5,6,4] => 19 [2,1,3,6,4,5] => 40 [2,1,3,6,5,4] => 26 [2,1,4,3,5,6] => 35 [2,1,4,3,6,5] => 61 [2,1,4,5,3,6] => 40 [2,1,4,5,6,3] => 19 [2,1,4,6,3,5] => 40 [2,1,4,6,5,3] => 26 [2,1,5,3,4,6] => 35 [2,1,5,3,6,4] => 61 [2,1,5,4,3,6] => 40 [2,1,5,4,6,3] => 61 [2,1,5,6,3,4] => 40 [2,1,5,6,4,3] => 26 [2,1,6,3,4,5] => 35 [2,1,6,3,5,4] => 61 [2,1,6,4,3,5] => 40 [2,1,6,4,5,3] => 61 [2,1,6,5,3,4] => 40 [2,1,6,5,4,3] => 14 [2,3,1,4,5,6] => 14 [2,3,1,4,6,5] => 40 [2,3,1,5,4,6] => 61 [2,3,1,5,6,4] => 40 [2,3,1,6,4,5] => 61 [2,3,1,6,5,4] => 35 [2,3,4,1,5,6] => 19 [2,3,4,1,6,5] => 35 [2,3,4,5,1,6] => 14 [2,3,4,5,6,1] => 5 [2,3,4,6,1,5] => 14 [2,3,4,6,5,1] => 10 [2,3,5,1,4,6] => 19 [2,3,5,1,6,4] => 35 [2,3,5,4,1,6] => 26 [2,3,5,4,6,1] => 35 [2,3,5,6,1,4] => 14 [2,3,5,6,4,1] => 10 [2,3,6,1,4,5] => 19 [2,3,6,1,5,4] => 35 [2,3,6,4,1,5] => 26 [2,3,6,4,5,1] => 35 [2,3,6,5,1,4] => 26 [2,3,6,5,4,1] => 10 [2,4,1,3,5,6] => 14 [2,4,1,3,6,5] => 40 [2,4,1,5,3,6] => 61 [2,4,1,5,6,3] => 40 [2,4,1,6,3,5] => 61 [2,4,1,6,5,3] => 35 [2,4,3,1,5,6] => 26 [2,4,3,1,6,5] => 40 [2,4,3,5,1,6] => 61 [2,4,3,5,6,1] => 40 [2,4,3,6,1,5] => 61 [2,4,3,6,5,1] => 35 [2,4,5,1,3,6] => 19 [2,4,5,1,6,3] => 35 [2,4,5,3,1,6] => 26 [2,4,5,3,6,1] => 35 [2,4,5,6,1,3] => 14 [2,4,5,6,3,1] => 10 [2,4,6,1,3,5] => 19 [2,4,6,1,5,3] => 35 [2,4,6,3,1,5] => 26 [2,4,6,3,5,1] => 35 [2,4,6,5,1,3] => 26 [2,4,6,5,3,1] => 10 [2,5,1,3,4,6] => 14 [2,5,1,3,6,4] => 40 [2,5,1,4,3,6] => 61 [2,5,1,4,6,3] => 40 [2,5,1,6,3,4] => 61 [2,5,1,6,4,3] => 35 [2,5,3,1,4,6] => 26 [2,5,3,1,6,4] => 40 [2,5,3,4,1,6] => 61 [2,5,3,4,6,1] => 40 [2,5,3,6,1,4] => 61 [2,5,3,6,4,1] => 35 [2,5,4,1,3,6] => 26 [2,5,4,1,6,3] => 40 [2,5,4,3,1,6] => 19 [2,5,4,3,6,1] => 40 [2,5,4,6,1,3] => 61 [2,5,4,6,3,1] => 35 [2,5,6,1,3,4] => 19 [2,5,6,1,4,3] => 35 [2,5,6,3,1,4] => 26 [2,5,6,3,4,1] => 35 [2,5,6,4,1,3] => 26 [2,5,6,4,3,1] => 10 [2,6,1,3,4,5] => 14 [2,6,1,3,5,4] => 40 [2,6,1,4,3,5] => 61 [2,6,1,4,5,3] => 40 [2,6,1,5,3,4] => 61 [2,6,1,5,4,3] => 35 [2,6,3,1,4,5] => 26 [2,6,3,1,5,4] => 40 [2,6,3,4,1,5] => 61 [2,6,3,4,5,1] => 40 [2,6,3,5,1,4] => 61 [2,6,3,5,4,1] => 35 [2,6,4,1,3,5] => 26 [2,6,4,1,5,3] => 40 [2,6,4,3,1,5] => 19 [2,6,4,3,5,1] => 40 [2,6,4,5,1,3] => 61 [2,6,4,5,3,1] => 35 [2,6,5,1,3,4] => 26 [2,6,5,1,4,3] => 40 [2,6,5,3,1,4] => 19 [2,6,5,3,4,1] => 40 [2,6,5,4,1,3] => 19 [2,6,5,4,3,1] => 5 [3,1,2,4,5,6] => 5 [3,1,2,4,6,5] => 19 [3,1,2,5,4,6] => 40 [3,1,2,5,6,4] => 19 [3,1,2,6,4,5] => 40 [3,1,2,6,5,4] => 26 [3,1,4,2,5,6] => 35 [3,1,4,2,6,5] => 61 [3,1,4,5,2,6] => 40 [3,1,4,5,6,2] => 19 [3,1,4,6,2,5] => 40 [3,1,4,6,5,2] => 26 [3,1,5,2,4,6] => 35 [3,1,5,2,6,4] => 61 [3,1,5,4,2,6] => 40 [3,1,5,4,6,2] => 61 [3,1,5,6,2,4] => 40 [3,1,5,6,4,2] => 26 [3,1,6,2,4,5] => 35 [3,1,6,2,5,4] => 61 [3,1,6,4,2,5] => 40 [3,1,6,4,5,2] => 61 [3,1,6,5,2,4] => 40 [3,1,6,5,4,2] => 14 [3,2,1,4,5,6] => 10 [3,2,1,4,6,5] => 26 [3,2,1,5,4,6] => 35 [3,2,1,5,6,4] => 26 [3,2,1,6,4,5] => 35 [3,2,1,6,5,4] => 19 [3,2,4,1,5,6] => 35 [3,2,4,1,6,5] => 61 [3,2,4,5,1,6] => 40 [3,2,4,5,6,1] => 19 [3,2,4,6,1,5] => 40 [3,2,4,6,5,1] => 26 [3,2,5,1,4,6] => 35 [3,2,5,1,6,4] => 61 [3,2,5,4,1,6] => 40 [3,2,5,4,6,1] => 61 [3,2,5,6,1,4] => 40 [3,2,5,6,4,1] => 26 [3,2,6,1,4,5] => 35 [3,2,6,1,5,4] => 61 [3,2,6,4,1,5] => 40 [3,2,6,4,5,1] => 61 [3,2,6,5,1,4] => 40 [3,2,6,5,4,1] => 14 [3,4,1,2,5,6] => 14 [3,4,1,2,6,5] => 40 [3,4,1,5,2,6] => 61 [3,4,1,5,6,2] => 40 [3,4,1,6,2,5] => 61 [3,4,1,6,5,2] => 35 [3,4,2,1,5,6] => 26 [3,4,2,1,6,5] => 40 [3,4,2,5,1,6] => 61 [3,4,2,5,6,1] => 40 [3,4,2,6,1,5] => 61 [3,4,2,6,5,1] => 35 [3,4,5,1,2,6] => 19 [3,4,5,1,6,2] => 35 [3,4,5,2,1,6] => 26 [3,4,5,2,6,1] => 35 [3,4,5,6,1,2] => 14 [3,4,5,6,2,1] => 10 [3,4,6,1,2,5] => 19 [3,4,6,1,5,2] => 35 [3,4,6,2,1,5] => 26 [3,4,6,2,5,1] => 35 [3,4,6,5,1,2] => 26 [3,4,6,5,2,1] => 10 [3,5,1,2,4,6] => 14 [3,5,1,2,6,4] => 40 [3,5,1,4,2,6] => 61 [3,5,1,4,6,2] => 40 [3,5,1,6,2,4] => 61 [3,5,1,6,4,2] => 35 [3,5,2,1,4,6] => 26 [3,5,2,1,6,4] => 40 [3,5,2,4,1,6] => 61 [3,5,2,4,6,1] => 40 [3,5,2,6,1,4] => 61 [3,5,2,6,4,1] => 35 [3,5,4,1,2,6] => 26 [3,5,4,1,6,2] => 40 [3,5,4,2,1,6] => 19 [3,5,4,2,6,1] => 40 [3,5,4,6,1,2] => 61 [3,5,4,6,2,1] => 35 [3,5,6,1,2,4] => 19 [3,5,6,1,4,2] => 35 [3,5,6,2,1,4] => 26 [3,5,6,2,4,1] => 35 [3,5,6,4,1,2] => 26 [3,5,6,4,2,1] => 10 [3,6,1,2,4,5] => 14 [3,6,1,2,5,4] => 40 [3,6,1,4,2,5] => 61 [3,6,1,4,5,2] => 40 [3,6,1,5,2,4] => 61 [3,6,1,5,4,2] => 35 [3,6,2,1,4,5] => 26 [3,6,2,1,5,4] => 40 [3,6,2,4,1,5] => 61 [3,6,2,4,5,1] => 40 [3,6,2,5,1,4] => 61 [3,6,2,5,4,1] => 35 [3,6,4,1,2,5] => 26 [3,6,4,1,5,2] => 40 [3,6,4,2,1,5] => 19 [3,6,4,2,5,1] => 40 [3,6,4,5,1,2] => 61 [3,6,4,5,2,1] => 35 [3,6,5,1,2,4] => 26 [3,6,5,1,4,2] => 40 [3,6,5,2,1,4] => 19 [3,6,5,2,4,1] => 40 [3,6,5,4,1,2] => 19 [3,6,5,4,2,1] => 5 [4,1,2,3,5,6] => 5 [4,1,2,3,6,5] => 19 [4,1,2,5,3,6] => 40 [4,1,2,5,6,3] => 19 [4,1,2,6,3,5] => 40 [4,1,2,6,5,3] => 26 [4,1,3,2,5,6] => 35 [4,1,3,2,6,5] => 61 [4,1,3,5,2,6] => 40 [4,1,3,5,6,2] => 19 [4,1,3,6,2,5] => 40 [4,1,3,6,5,2] => 26 [4,1,5,2,3,6] => 35 [4,1,5,2,6,3] => 61 [4,1,5,3,2,6] => 40 [4,1,5,3,6,2] => 61 [4,1,5,6,2,3] => 40 [4,1,5,6,3,2] => 26 [4,1,6,2,3,5] => 35 [4,1,6,2,5,3] => 61 [4,1,6,3,2,5] => 40 [4,1,6,3,5,2] => 61 [4,1,6,5,2,3] => 40 [4,1,6,5,3,2] => 14 [4,2,1,3,5,6] => 10 [4,2,1,3,6,5] => 26 [4,2,1,5,3,6] => 35 [4,2,1,5,6,3] => 26 [4,2,1,6,3,5] => 35 [4,2,1,6,5,3] => 19 [4,2,3,1,5,6] => 35 [4,2,3,1,6,5] => 61 [4,2,3,5,1,6] => 40 [4,2,3,5,6,1] => 19 [4,2,3,6,1,5] => 40 [4,2,3,6,5,1] => 26 [4,2,5,1,3,6] => 35 [4,2,5,1,6,3] => 61 [4,2,5,3,1,6] => 40 [4,2,5,3,6,1] => 61 [4,2,5,6,1,3] => 40 [4,2,5,6,3,1] => 26 [4,2,6,1,3,5] => 35 [4,2,6,1,5,3] => 61 [4,2,6,3,1,5] => 40 [4,2,6,3,5,1] => 61 [4,2,6,5,1,3] => 40 [4,2,6,5,3,1] => 14 [4,3,1,2,5,6] => 10 [4,3,1,2,6,5] => 26 [4,3,1,5,2,6] => 35 [4,3,1,5,6,2] => 26 [4,3,1,6,2,5] => 35 [4,3,1,6,5,2] => 19 [4,3,2,1,5,6] => 10 [4,3,2,1,6,5] => 14 [4,3,2,5,1,6] => 35 [4,3,2,5,6,1] => 26 [4,3,2,6,1,5] => 35 [4,3,2,6,5,1] => 19 [4,3,5,1,2,6] => 35 [4,3,5,1,6,2] => 61 [4,3,5,2,1,6] => 40 [4,3,5,2,6,1] => 61 [4,3,5,6,1,2] => 40 [4,3,5,6,2,1] => 26 [4,3,6,1,2,5] => 35 [4,3,6,1,5,2] => 61 [4,3,6,2,1,5] => 40 [4,3,6,2,5,1] => 61 [4,3,6,5,1,2] => 40 [4,3,6,5,2,1] => 14 [4,5,1,2,3,6] => 14 [4,5,1,2,6,3] => 40 [4,5,1,3,2,6] => 61 [4,5,1,3,6,2] => 40 [4,5,1,6,2,3] => 61 [4,5,1,6,3,2] => 35 [4,5,2,1,3,6] => 26 [4,5,2,1,6,3] => 40 [4,5,2,3,1,6] => 61 [4,5,2,3,6,1] => 40 [4,5,2,6,1,3] => 61 [4,5,2,6,3,1] => 35 [4,5,3,1,2,6] => 26 [4,5,3,1,6,2] => 40 [4,5,3,2,1,6] => 19 [4,5,3,2,6,1] => 40 [4,5,3,6,1,2] => 61 [4,5,3,6,2,1] => 35 [4,5,6,1,2,3] => 19 [4,5,6,1,3,2] => 35 [4,5,6,2,1,3] => 26 [4,5,6,2,3,1] => 35 [4,5,6,3,1,2] => 26 [4,5,6,3,2,1] => 10 [4,6,1,2,3,5] => 14 [4,6,1,2,5,3] => 40 [4,6,1,3,2,5] => 61 [4,6,1,3,5,2] => 40 [4,6,1,5,2,3] => 61 [4,6,1,5,3,2] => 35 [4,6,2,1,3,5] => 26 [4,6,2,1,5,3] => 40 [4,6,2,3,1,5] => 61 [4,6,2,3,5,1] => 40 [4,6,2,5,1,3] => 61 [4,6,2,5,3,1] => 35 [4,6,3,1,2,5] => 26 [4,6,3,1,5,2] => 40 [4,6,3,2,1,5] => 19 [4,6,3,2,5,1] => 40 [4,6,3,5,1,2] => 61 [4,6,3,5,2,1] => 35 [4,6,5,1,2,3] => 26 [4,6,5,1,3,2] => 40 [4,6,5,2,1,3] => 19 [4,6,5,2,3,1] => 40 [4,6,5,3,1,2] => 19 [4,6,5,3,2,1] => 5 [5,1,2,3,4,6] => 5 [5,1,2,3,6,4] => 19 [5,1,2,4,3,6] => 40 [5,1,2,4,6,3] => 19 [5,1,2,6,3,4] => 40 [5,1,2,6,4,3] => 26 [5,1,3,2,4,6] => 35 [5,1,3,2,6,4] => 61 [5,1,3,4,2,6] => 40 [5,1,3,4,6,2] => 19 [5,1,3,6,2,4] => 40 [5,1,3,6,4,2] => 26 [5,1,4,2,3,6] => 35 [5,1,4,2,6,3] => 61 [5,1,4,3,2,6] => 40 [5,1,4,3,6,2] => 61 [5,1,4,6,2,3] => 40 [5,1,4,6,3,2] => 26 [5,1,6,2,3,4] => 35 [5,1,6,2,4,3] => 61 [5,1,6,3,2,4] => 40 [5,1,6,3,4,2] => 61 [5,1,6,4,2,3] => 40 [5,1,6,4,3,2] => 14 [5,2,1,3,4,6] => 10 [5,2,1,3,6,4] => 26 [5,2,1,4,3,6] => 35 [5,2,1,4,6,3] => 26 [5,2,1,6,3,4] => 35 [5,2,1,6,4,3] => 19 [5,2,3,1,4,6] => 35 [5,2,3,1,6,4] => 61 [5,2,3,4,1,6] => 40 [5,2,3,4,6,1] => 19 [5,2,3,6,1,4] => 40 [5,2,3,6,4,1] => 26 [5,2,4,1,3,6] => 35 [5,2,4,1,6,3] => 61 [5,2,4,3,1,6] => 40 [5,2,4,3,6,1] => 61 [5,2,4,6,1,3] => 40 [5,2,4,6,3,1] => 26 [5,2,6,1,3,4] => 35 [5,2,6,1,4,3] => 61 [5,2,6,3,1,4] => 40 [5,2,6,3,4,1] => 61 [5,2,6,4,1,3] => 40 [5,2,6,4,3,1] => 14 [5,3,1,2,4,6] => 10 [5,3,1,2,6,4] => 26 [5,3,1,4,2,6] => 35 [5,3,1,4,6,2] => 26 [5,3,1,6,2,4] => 35 [5,3,1,6,4,2] => 19 [5,3,2,1,4,6] => 10 [5,3,2,1,6,4] => 14 [5,3,2,4,1,6] => 35 [5,3,2,4,6,1] => 26 [5,3,2,6,1,4] => 35 [5,3,2,6,4,1] => 19 [5,3,4,1,2,6] => 35 [5,3,4,1,6,2] => 61 [5,3,4,2,1,6] => 40 [5,3,4,2,6,1] => 61 [5,3,4,6,1,2] => 40 [5,3,4,6,2,1] => 26 [5,3,6,1,2,4] => 35 [5,3,6,1,4,2] => 61 [5,3,6,2,1,4] => 40 [5,3,6,2,4,1] => 61 [5,3,6,4,1,2] => 40 [5,3,6,4,2,1] => 14 [5,4,1,2,3,6] => 10 [5,4,1,2,6,3] => 26 [5,4,1,3,2,6] => 35 [5,4,1,3,6,2] => 26 [5,4,1,6,2,3] => 35 [5,4,1,6,3,2] => 19 [5,4,2,1,3,6] => 10 [5,4,2,1,6,3] => 14 [5,4,2,3,1,6] => 35 [5,4,2,3,6,1] => 26 [5,4,2,6,1,3] => 35 [5,4,2,6,3,1] => 19 [5,4,3,1,2,6] => 10 [5,4,3,1,6,2] => 14 [5,4,3,2,1,6] => 5 [5,4,3,2,6,1] => 14 [5,4,3,6,1,2] => 35 [5,4,3,6,2,1] => 19 [5,4,6,1,2,3] => 35 [5,4,6,1,3,2] => 61 [5,4,6,2,1,3] => 40 [5,4,6,2,3,1] => 61 [5,4,6,3,1,2] => 40 [5,4,6,3,2,1] => 14 [5,6,1,2,3,4] => 14 [5,6,1,2,4,3] => 40 [5,6,1,3,2,4] => 61 [5,6,1,3,4,2] => 40 [5,6,1,4,2,3] => 61 [5,6,1,4,3,2] => 35 [5,6,2,1,3,4] => 26 [5,6,2,1,4,3] => 40 [5,6,2,3,1,4] => 61 [5,6,2,3,4,1] => 40 [5,6,2,4,1,3] => 61 [5,6,2,4,3,1] => 35 [5,6,3,1,2,4] => 26 [5,6,3,1,4,2] => 40 [5,6,3,2,1,4] => 19 [5,6,3,2,4,1] => 40 [5,6,3,4,1,2] => 61 [5,6,3,4,2,1] => 35 [5,6,4,1,2,3] => 26 [5,6,4,1,3,2] => 40 [5,6,4,2,1,3] => 19 [5,6,4,2,3,1] => 40 [5,6,4,3,1,2] => 19 [5,6,4,3,2,1] => 5 [6,1,2,3,4,5] => 5 [6,1,2,3,5,4] => 19 [6,1,2,4,3,5] => 40 [6,1,2,4,5,3] => 19 [6,1,2,5,3,4] => 40 [6,1,2,5,4,3] => 26 [6,1,3,2,4,5] => 35 [6,1,3,2,5,4] => 61 [6,1,3,4,2,5] => 40 [6,1,3,4,5,2] => 19 [6,1,3,5,2,4] => 40 [6,1,3,5,4,2] => 26 [6,1,4,2,3,5] => 35 [6,1,4,2,5,3] => 61 [6,1,4,3,2,5] => 40 [6,1,4,3,5,2] => 61 [6,1,4,5,2,3] => 40 [6,1,4,5,3,2] => 26 [6,1,5,2,3,4] => 35 [6,1,5,2,4,3] => 61 [6,1,5,3,2,4] => 40 [6,1,5,3,4,2] => 61 [6,1,5,4,2,3] => 40 [6,1,5,4,3,2] => 14 [6,2,1,3,4,5] => 10 [6,2,1,3,5,4] => 26 [6,2,1,4,3,5] => 35 [6,2,1,4,5,3] => 26 [6,2,1,5,3,4] => 35 [6,2,1,5,4,3] => 19 [6,2,3,1,4,5] => 35 [6,2,3,1,5,4] => 61 [6,2,3,4,1,5] => 40 [6,2,3,4,5,1] => 19 [6,2,3,5,1,4] => 40 [6,2,3,5,4,1] => 26 [6,2,4,1,3,5] => 35 [6,2,4,1,5,3] => 61 [6,2,4,3,1,5] => 40 [6,2,4,3,5,1] => 61 [6,2,4,5,1,3] => 40 [6,2,4,5,3,1] => 26 [6,2,5,1,3,4] => 35 [6,2,5,1,4,3] => 61 [6,2,5,3,1,4] => 40 [6,2,5,3,4,1] => 61 [6,2,5,4,1,3] => 40 [6,2,5,4,3,1] => 14 [6,3,1,2,4,5] => 10 [6,3,1,2,5,4] => 26 [6,3,1,4,2,5] => 35 [6,3,1,4,5,2] => 26 [6,3,1,5,2,4] => 35 [6,3,1,5,4,2] => 19 [6,3,2,1,4,5] => 10 [6,3,2,1,5,4] => 14 [6,3,2,4,1,5] => 35 [6,3,2,4,5,1] => 26 [6,3,2,5,1,4] => 35 [6,3,2,5,4,1] => 19 [6,3,4,1,2,5] => 35 [6,3,4,1,5,2] => 61 [6,3,4,2,1,5] => 40 [6,3,4,2,5,1] => 61 [6,3,4,5,1,2] => 40 [6,3,4,5,2,1] => 26 [6,3,5,1,2,4] => 35 [6,3,5,1,4,2] => 61 [6,3,5,2,1,4] => 40 [6,3,5,2,4,1] => 61 [6,3,5,4,1,2] => 40 [6,3,5,4,2,1] => 14 [6,4,1,2,3,5] => 10 [6,4,1,2,5,3] => 26 [6,4,1,3,2,5] => 35 [6,4,1,3,5,2] => 26 [6,4,1,5,2,3] => 35 [6,4,1,5,3,2] => 19 [6,4,2,1,3,5] => 10 [6,4,2,1,5,3] => 14 [6,4,2,3,1,5] => 35 [6,4,2,3,5,1] => 26 [6,4,2,5,1,3] => 35 [6,4,2,5,3,1] => 19 [6,4,3,1,2,5] => 10 [6,4,3,1,5,2] => 14 [6,4,3,2,1,5] => 5 [6,4,3,2,5,1] => 14 [6,4,3,5,1,2] => 35 [6,4,3,5,2,1] => 19 [6,4,5,1,2,3] => 35 [6,4,5,1,3,2] => 61 [6,4,5,2,1,3] => 40 [6,4,5,2,3,1] => 61 [6,4,5,3,1,2] => 40 [6,4,5,3,2,1] => 14 [6,5,1,2,3,4] => 10 [6,5,1,2,4,3] => 26 [6,5,1,3,2,4] => 35 [6,5,1,3,4,2] => 26 [6,5,1,4,2,3] => 35 [6,5,1,4,3,2] => 19 [6,5,2,1,3,4] => 10 [6,5,2,1,4,3] => 14 [6,5,2,3,1,4] => 35 [6,5,2,3,4,1] => 26 [6,5,2,4,1,3] => 35 [6,5,2,4,3,1] => 19 [6,5,3,1,2,4] => 10 [6,5,3,1,4,2] => 14 [6,5,3,2,1,4] => 5 [6,5,3,2,4,1] => 14 [6,5,3,4,1,2] => 35 [6,5,3,4,2,1] => 19 [6,5,4,1,2,3] => 10 [6,5,4,1,3,2] => 14 [6,5,4,2,1,3] => 5 [6,5,4,2,3,1] => 14 [6,5,4,3,1,2] => 5 [6,5,4,3,2,1] => 1 [1,2,3,4,5,6,7] => 1 [1,2,3,4,5,7,6] => 6 [1,2,3,4,6,5,7] => 20 [1,2,3,4,6,7,5] => 6 [1,2,3,4,7,5,6] => 20 [1,2,3,4,7,6,5] => 15 [1,2,3,5,4,6,7] => 34 [1,2,3,5,4,7,6] => 64 [1,2,3,5,6,4,7] => 20 [1,2,3,5,6,7,4] => 6 [1,2,3,5,7,4,6] => 20 [1,2,3,5,7,6,4] => 15 [1,2,3,6,4,5,7] => 34 [1,2,3,6,4,7,5] => 64 [1,2,3,6,5,4,7] => 50 [1,2,3,6,5,7,4] => 64 [1,2,3,6,7,4,5] => 20 [1,2,3,6,7,5,4] => 15 [1,2,3,7,4,5,6] => 34 [1,2,3,7,4,6,5] => 64 [1,2,3,7,5,4,6] => 50 [1,2,3,7,5,6,4] => 64 [1,2,3,7,6,4,5] => 50 [1,2,3,7,6,5,4] => 20 [1,2,4,3,5,6,7] => 34 [1,2,4,3,5,7,6] => 99 [1,2,4,3,6,5,7] => 155 [1,2,4,3,6,7,5] => 99 [1,2,4,3,7,5,6] => 155 [1,2,4,3,7,6,5] => 90 [1,2,4,5,3,6,7] => 34 [1,2,4,5,3,7,6] => 64 [1,2,4,5,6,3,7] => 20 [1,2,4,5,6,7,3] => 6 [1,2,4,5,7,3,6] => 20 [1,2,4,5,7,6,3] => 15 [1,2,4,6,3,5,7] => 34 [1,2,4,6,3,7,5] => 64 [1,2,4,6,5,3,7] => 50 [1,2,4,6,5,7,3] => 64 [1,2,4,6,7,3,5] => 20 [1,2,4,6,7,5,3] => 15 [1,2,4,7,3,5,6] => 34 [1,2,4,7,3,6,5] => 64 [1,2,4,7,5,3,6] => 50 [1,2,4,7,5,6,3] => 64 [1,2,4,7,6,3,5] => 50 [1,2,4,7,6,5,3] => 20 [1,2,5,3,4,6,7] => 34 [1,2,5,3,4,7,6] => 99 [1,2,5,3,6,4,7] => 155 [1,2,5,3,6,7,4] => 99 [1,2,5,3,7,4,6] => 155 [1,2,5,3,7,6,4] => 90 [1,2,5,4,3,6,7] => 71 [1,2,5,4,3,7,6] => 111 [1,2,5,4,6,3,7] => 155 [1,2,5,4,6,7,3] => 99 [1,2,5,4,7,3,6] => 155 [1,2,5,4,7,6,3] => 90 [1,2,5,6,3,4,7] => 34 [1,2,5,6,3,7,4] => 64 [1,2,5,6,4,3,7] => 50 [1,2,5,6,4,7,3] => 64 [1,2,5,6,7,3,4] => 20 [1,2,5,6,7,4,3] => 15 [1,2,5,7,3,4,6] => 34 [1,2,5,7,3,6,4] => 64 [1,2,5,7,4,3,6] => 50 [1,2,5,7,4,6,3] => 64 [1,2,5,7,6,3,4] => 50 [1,2,5,7,6,4,3] => 20 [1,2,6,3,4,5,7] => 34 [1,2,6,3,4,7,5] => 99 [1,2,6,3,5,4,7] => 155 [1,2,6,3,5,7,4] => 99 [1,2,6,3,7,4,5] => 155 [1,2,6,3,7,5,4] => 90 [1,2,6,4,3,5,7] => 71 [1,2,6,4,3,7,5] => 111 [1,2,6,4,5,3,7] => 155 [1,2,6,4,5,7,3] => 99 [1,2,6,4,7,3,5] => 155 [1,2,6,4,7,5,3] => 90 [1,2,6,5,3,4,7] => 71 [1,2,6,5,3,7,4] => 111 [1,2,6,5,4,3,7] => 55 [1,2,6,5,4,7,3] => 111 [1,2,6,5,7,3,4] => 155 [1,2,6,5,7,4,3] => 90 [1,2,6,7,3,4,5] => 34 [1,2,6,7,3,5,4] => 64 [1,2,6,7,4,3,5] => 50 [1,2,6,7,4,5,3] => 64 [1,2,6,7,5,3,4] => 50 [1,2,6,7,5,4,3] => 20 [1,2,7,3,4,5,6] => 34 [1,2,7,3,4,6,5] => 99 [1,2,7,3,5,4,6] => 155 [1,2,7,3,5,6,4] => 99 [1,2,7,3,6,4,5] => 155 [1,2,7,3,6,5,4] => 90 [1,2,7,4,3,5,6] => 71 [1,2,7,4,3,6,5] => 111 [1,2,7,4,5,3,6] => 155 [1,2,7,4,5,6,3] => 99 [1,2,7,4,6,3,5] => 155 [1,2,7,4,6,5,3] => 90 [1,2,7,5,3,4,6] => 71 [1,2,7,5,3,6,4] => 111 [1,2,7,5,4,3,6] => 55 [1,2,7,5,4,6,3] => 111 [1,2,7,5,6,3,4] => 155 [1,2,7,5,6,4,3] => 90 [1,2,7,6,3,4,5] => 71 [1,2,7,6,3,5,4] => 111 [1,2,7,6,4,3,5] => 55 [1,2,7,6,4,5,3] => 111 [1,2,7,6,5,3,4] => 55 [1,2,7,6,5,4,3] => 15 [1,3,2,4,5,6,7] => 20 [1,3,2,4,5,7,6] => 78 [1,3,2,4,6,5,7] => 169 [1,3,2,4,6,7,5] => 78 [1,3,2,4,7,5,6] => 169 [1,3,2,4,7,6,5] => 111 [1,3,2,5,4,6,7] => 155 [1,3,2,5,4,7,6] => 272 [1,3,2,5,6,4,7] => 169 [1,3,2,5,6,7,4] => 78 [1,3,2,5,7,4,6] => 169 [1,3,2,5,7,6,4] => 111 [1,3,2,6,4,5,7] => 155 [1,3,2,6,4,7,5] => 272 [1,3,2,6,5,4,7] => 181 [1,3,2,6,5,7,4] => 272 [1,3,2,6,7,4,5] => 169 [1,3,2,6,7,5,4] => 111 [1,3,2,7,4,5,6] => 155 [1,3,2,7,4,6,5] => 272 [1,3,2,7,5,4,6] => 181 [1,3,2,7,5,6,4] => 272 [1,3,2,7,6,4,5] => 181 [1,3,2,7,6,5,4] => 64 [1,3,4,2,5,6,7] => 34 [1,3,4,2,5,7,6] => 99 [1,3,4,2,6,5,7] => 155 [1,3,4,2,6,7,5] => 99 [1,3,4,2,7,5,6] => 155 [1,3,4,2,7,6,5] => 90 [1,3,4,5,2,6,7] => 34 [1,3,4,5,2,7,6] => 64 [1,3,4,5,6,2,7] => 20 [1,3,4,5,6,7,2] => 6 [1,3,4,5,7,2,6] => 20 [1,3,4,5,7,6,2] => 15 [1,3,4,6,2,5,7] => 34 [1,3,4,6,2,7,5] => 64 [1,3,4,6,5,2,7] => 50 [1,3,4,6,5,7,2] => 64 [1,3,4,6,7,2,5] => 20 [1,3,4,6,7,5,2] => 15 [1,3,4,7,2,5,6] => 34 [1,3,4,7,2,6,5] => 64 [1,3,4,7,5,2,6] => 50 [1,3,4,7,5,6,2] => 64 [1,3,4,7,6,2,5] => 50 [1,3,4,7,6,5,2] => 20 [1,3,5,2,4,6,7] => 34 [1,3,5,2,4,7,6] => 99 [1,3,5,2,6,4,7] => 155 [1,3,5,2,6,7,4] => 99 [1,3,5,2,7,4,6] => 155 [1,3,5,2,7,6,4] => 90 [1,3,5,4,2,6,7] => 71 [1,3,5,4,2,7,6] => 111 [1,3,5,4,6,2,7] => 155 [1,3,5,4,6,7,2] => 99 [1,3,5,4,7,2,6] => 155 [1,3,5,4,7,6,2] => 90 [1,3,5,6,2,4,7] => 34 [1,3,5,6,2,7,4] => 64 [1,3,5,6,4,2,7] => 50 [1,3,5,6,4,7,2] => 64 [1,3,5,6,7,2,4] => 20 [1,3,5,6,7,4,2] => 15 [1,3,5,7,2,4,6] => 34 [1,3,5,7,2,6,4] => 64 [1,3,5,7,4,2,6] => 50 [1,3,5,7,4,6,2] => 64 [1,3,5,7,6,2,4] => 50 [1,3,5,7,6,4,2] => 20 [1,3,6,2,4,5,7] => 34 [1,3,6,2,4,7,5] => 99 [1,3,6,2,5,4,7] => 155 [1,3,6,2,5,7,4] => 99 [1,3,6,2,7,4,5] => 155 [1,3,6,2,7,5,4] => 90 [1,3,6,4,2,5,7] => 71 [1,3,6,4,2,7,5] => 111 [1,3,6,4,5,2,7] => 155 [1,3,6,4,5,7,2] => 99 [1,3,6,4,7,2,5] => 155 [1,3,6,4,7,5,2] => 90 [1,3,6,5,2,4,7] => 71 [1,3,6,5,2,7,4] => 111 [1,3,6,5,4,2,7] => 55 [1,3,6,5,4,7,2] => 111 [1,3,6,5,7,2,4] => 155 [1,3,6,5,7,4,2] => 90 [1,3,6,7,2,4,5] => 34 [1,3,6,7,2,5,4] => 64 [1,3,6,7,4,2,5] => 50 [1,3,6,7,4,5,2] => 64 [1,3,6,7,5,2,4] => 50 [1,3,6,7,5,4,2] => 20 [1,3,7,2,4,5,6] => 34 [1,3,7,2,4,6,5] => 99 [1,3,7,2,5,4,6] => 155 [1,3,7,2,5,6,4] => 99 [1,3,7,2,6,4,5] => 155 [1,3,7,2,6,5,4] => 90 [1,3,7,4,2,5,6] => 71 [1,3,7,4,2,6,5] => 111 [1,3,7,4,5,2,6] => 155 [1,3,7,4,5,6,2] => 99 [1,3,7,4,6,2,5] => 155 [1,3,7,4,6,5,2] => 90 [1,3,7,5,2,4,6] => 71 [1,3,7,5,2,6,4] => 111 [1,3,7,5,4,2,6] => 55 [1,3,7,5,4,6,2] => 111 [1,3,7,5,6,2,4] => 155 [1,3,7,5,6,4,2] => 90 [1,3,7,6,2,4,5] => 71 [1,3,7,6,2,5,4] => 111 [1,3,7,6,4,2,5] => 55 [1,3,7,6,4,5,2] => 111 [1,3,7,6,5,2,4] => 55 [1,3,7,6,5,4,2] => 15 [1,4,2,3,5,6,7] => 20 [1,4,2,3,5,7,6] => 78 [1,4,2,3,6,5,7] => 169 [1,4,2,3,6,7,5] => 78 [1,4,2,3,7,5,6] => 169 [1,4,2,3,7,6,5] => 111 [1,4,2,5,3,6,7] => 155 [1,4,2,5,3,7,6] => 272 [1,4,2,5,6,3,7] => 169 [1,4,2,5,6,7,3] => 78 [1,4,2,5,7,3,6] => 169 [1,4,2,5,7,6,3] => 111 [1,4,2,6,3,5,7] => 155 [1,4,2,6,3,7,5] => 272 [1,4,2,6,5,3,7] => 181 [1,4,2,6,5,7,3] => 272 [1,4,2,6,7,3,5] => 169 [1,4,2,6,7,5,3] => 111 [1,4,2,7,3,5,6] => 155 [1,4,2,7,3,6,5] => 272 [1,4,2,7,5,3,6] => 181 [1,4,2,7,5,6,3] => 272 [1,4,2,7,6,3,5] => 181 [1,4,2,7,6,5,3] => 64 [1,4,3,2,5,6,7] => 50 [1,4,3,2,5,7,6] => 132 [1,4,3,2,6,5,7] => 181 [1,4,3,2,6,7,5] => 132 [1,4,3,2,7,5,6] => 181 [1,4,3,2,7,6,5] => 99 [1,4,3,5,2,6,7] => 155 [1,4,3,5,2,7,6] => 272 [1,4,3,5,6,2,7] => 169 [1,4,3,5,6,7,2] => 78 [1,4,3,5,7,2,6] => 169 [1,4,3,5,7,6,2] => 111 [1,4,3,6,2,5,7] => 155 [1,4,3,6,2,7,5] => 272 [1,4,3,6,5,2,7] => 181 [1,4,3,6,5,7,2] => 272 [1,4,3,6,7,2,5] => 169 [1,4,3,6,7,5,2] => 111 [1,4,3,7,2,5,6] => 155 [1,4,3,7,2,6,5] => 272 [1,4,3,7,5,2,6] => 181 [1,4,3,7,5,6,2] => 272 [1,4,3,7,6,2,5] => 181 [1,4,3,7,6,5,2] => 64 [1,4,5,2,3,6,7] => 34 [1,4,5,2,3,7,6] => 99 [1,4,5,2,6,3,7] => 155 [1,4,5,2,6,7,3] => 99 [1,4,5,2,7,3,6] => 155 [1,4,5,2,7,6,3] => 90 [1,4,5,3,2,6,7] => 71 [1,4,5,3,2,7,6] => 111 [1,4,5,3,6,2,7] => 155 [1,4,5,3,6,7,2] => 99 [1,4,5,3,7,2,6] => 155 [1,4,5,3,7,6,2] => 90 [1,4,5,6,2,3,7] => 34 [1,4,5,6,2,7,3] => 64 [1,4,5,6,3,2,7] => 50 [1,4,5,6,3,7,2] => 64 [1,4,5,6,7,2,3] => 20 [1,4,5,6,7,3,2] => 15 [1,4,5,7,2,3,6] => 34 [1,4,5,7,2,6,3] => 64 [1,4,5,7,3,2,6] => 50 [1,4,5,7,3,6,2] => 64 [1,4,5,7,6,2,3] => 50 [1,4,5,7,6,3,2] => 20 [1,4,6,2,3,5,7] => 34 [1,4,6,2,3,7,5] => 99 [1,4,6,2,5,3,7] => 155 [1,4,6,2,5,7,3] => 99 [1,4,6,2,7,3,5] => 155 [1,4,6,2,7,5,3] => 90 [1,4,6,3,2,5,7] => 71 [1,4,6,3,2,7,5] => 111 [1,4,6,3,5,2,7] => 155 [1,4,6,3,5,7,2] => 99 [1,4,6,3,7,2,5] => 155 [1,4,6,3,7,5,2] => 90 [1,4,6,5,2,3,7] => 71 [1,4,6,5,2,7,3] => 111 [1,4,6,5,3,2,7] => 55 [1,4,6,5,3,7,2] => 111 ----------------------------------------------------------------------------- Created: Jun 10, 2016 at 08:54 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Jan 15, 2018 at 08:00 by Martin Rubey