***************************************************************************** * 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: St000001 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of reduced words for a permutation. This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$. ----------------------------------------------------------------------------- References: [1] Edelman, P., Greene, C. Balanced tableaux [[MathSciNet:0871081]] [2] Number of simple allowable sequences on 1..n containing the permutation 12...n. [[OEIS:A005118]] [3] Total number of reduced decompositions for all permutations in S_n. [[OEIS:A246865]] ----------------------------------------------------------------------------- Code: def statistic(x): return sum(1 for _ in x.reduced_words_iterator()) ----------------------------------------------------------------------------- Statistic values: [] => 1 [1] => 1 [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 2 [1,2,3,4] => 1 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 1 [1,4,2,3] => 1 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 1 [2,3,4,1] => 1 [2,4,1,3] => 2 [2,4,3,1] => 3 [3,1,2,4] => 1 [3,1,4,2] => 2 [3,2,1,4] => 2 [3,2,4,1] => 3 [3,4,1,2] => 2 [3,4,2,1] => 5 [4,1,2,3] => 1 [4,1,3,2] => 3 [4,2,1,3] => 3 [4,2,3,1] => 6 [4,3,1,2] => 5 [4,3,2,1] => 16 [1,2,3,4,5] => 1 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 1 [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] => 1 [1,3,4,5,2] => 1 [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] => 5 [1,5,2,3,4] => 1 [1,5,2,4,3] => 3 [1,5,3,2,4] => 3 [1,5,3,4,2] => 6 [1,5,4,2,3] => 5 [1,5,4,3,2] => 16 [2,1,3,4,5] => 1 [2,1,3,5,4] => 2 [2,1,4,3,5] => 2 [2,1,4,5,3] => 3 [2,1,5,3,4] => 3 [2,1,5,4,3] => 8 [2,3,1,4,5] => 1 [2,3,1,5,4] => 3 [2,3,4,1,5] => 1 [2,3,4,5,1] => 1 [2,3,5,1,4] => 3 [2,3,5,4,1] => 4 [2,4,1,3,5] => 2 [2,4,1,5,3] => 5 [2,4,3,1,5] => 3 [2,4,3,5,1] => 4 [2,4,5,1,3] => 5 [2,4,5,3,1] => 9 [2,5,1,3,4] => 3 [2,5,1,4,3] => 11 [2,5,3,1,4] => 6 [2,5,3,4,1] => 10 [2,5,4,1,3] => 16 [2,5,4,3,1] => 35 [3,1,2,4,5] => 1 [3,1,2,5,4] => 3 [3,1,4,2,5] => 2 [3,1,4,5,2] => 3 [3,1,5,2,4] => 5 [3,1,5,4,2] => 11 [3,2,1,4,5] => 2 [3,2,1,5,4] => 8 [3,2,4,1,5] => 3 [3,2,4,5,1] => 4 [3,2,5,1,4] => 11 [3,2,5,4,1] => 19 [3,4,1,2,5] => 2 [3,4,1,5,2] => 5 [3,4,2,1,5] => 5 [3,4,2,5,1] => 9 [3,4,5,1,2] => 5 [3,4,5,2,1] => 14 [3,5,1,2,4] => 5 [3,5,1,4,2] => 16 [3,5,2,1,4] => 16 [3,5,2,4,1] => 35 [3,5,4,1,2] => 21 [3,5,4,2,1] => 70 [4,1,2,3,5] => 1 [4,1,2,5,3] => 3 [4,1,3,2,5] => 3 [4,1,3,5,2] => 6 [4,1,5,2,3] => 5 [4,1,5,3,2] => 16 [4,2,1,3,5] => 3 [4,2,1,5,3] => 11 [4,2,3,1,5] => 6 [4,2,3,5,1] => 10 [4,2,5,1,3] => 16 [4,2,5,3,1] => 35 [4,3,1,2,5] => 5 [4,3,1,5,2] => 16 [4,3,2,1,5] => 16 [4,3,2,5,1] => 35 [4,3,5,1,2] => 21 [4,3,5,2,1] => 70 [4,5,1,2,3] => 5 [4,5,1,3,2] => 21 [4,5,2,1,3] => 21 [4,5,2,3,1] => 56 [4,5,3,1,2] => 42 [4,5,3,2,1] => 168 [5,1,2,3,4] => 1 [5,1,2,4,3] => 4 [5,1,3,2,4] => 4 [5,1,3,4,2] => 10 [5,1,4,2,3] => 9 [5,1,4,3,2] => 35 [5,2,1,3,4] => 4 [5,2,1,4,3] => 19 [5,2,3,1,4] => 10 [5,2,3,4,1] => 20 [5,2,4,1,3] => 35 [5,2,4,3,1] => 90 [5,3,1,2,4] => 9 [5,3,1,4,2] => 35 [5,3,2,1,4] => 35 [5,3,2,4,1] => 90 [5,3,4,1,2] => 56 [5,3,4,2,1] => 216 [5,4,1,2,3] => 14 [5,4,1,3,2] => 70 [5,4,2,1,3] => 70 [5,4,2,3,1] => 216 [5,4,3,1,2] => 168 [5,4,3,2,1] => 768 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 1 [1,2,3,5,4,6] => 1 [1,2,3,5,6,4] => 1 [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] => 1 [1,2,4,5,6,3] => 1 [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] => 5 [1,2,6,3,4,5] => 1 [1,2,6,3,5,4] => 3 [1,2,6,4,3,5] => 3 [1,2,6,4,5,3] => 6 [1,2,6,5,3,4] => 5 [1,2,6,5,4,3] => 16 [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] => 3 [1,3,2,6,5,4] => 8 [1,3,4,2,5,6] => 1 [1,3,4,2,6,5] => 3 [1,3,4,5,2,6] => 1 [1,3,4,5,6,2] => 1 [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] => 5 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 4 [1,3,5,6,2,4] => 5 [1,3,5,6,4,2] => 9 [1,3,6,2,4,5] => 3 [1,3,6,2,5,4] => 11 [1,3,6,4,2,5] => 6 [1,3,6,4,5,2] => 10 [1,3,6,5,2,4] => 16 [1,3,6,5,4,2] => 35 [1,4,2,3,5,6] => 1 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 2 [1,4,2,5,6,3] => 3 [1,4,2,6,3,5] => 5 [1,4,2,6,5,3] => 11 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 8 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 4 [1,4,3,6,2,5] => 11 [1,4,3,6,5,2] => 19 [1,4,5,2,3,6] => 2 [1,4,5,2,6,3] => 5 [1,4,5,3,2,6] => 5 [1,4,5,3,6,2] => 9 [1,4,5,6,2,3] => 5 [1,4,5,6,3,2] => 14 [1,4,6,2,3,5] => 5 [1,4,6,2,5,3] => 16 [1,4,6,3,2,5] => 16 [1,4,6,3,5,2] => 35 [1,4,6,5,2,3] => 21 [1,4,6,5,3,2] => 70 [1,5,2,3,4,6] => 1 [1,5,2,3,6,4] => 3 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 6 [1,5,2,6,3,4] => 5 [1,5,2,6,4,3] => 16 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 11 [1,5,3,4,2,6] => 6 [1,5,3,4,6,2] => 10 [1,5,3,6,2,4] => 16 [1,5,3,6,4,2] => 35 [1,5,4,2,3,6] => 5 [1,5,4,2,6,3] => 16 [1,5,4,3,2,6] => 16 [1,5,4,3,6,2] => 35 [1,5,4,6,2,3] => 21 [1,5,4,6,3,2] => 70 [1,5,6,2,3,4] => 5 [1,5,6,2,4,3] => 21 [1,5,6,3,2,4] => 21 [1,5,6,3,4,2] => 56 [1,5,6,4,2,3] => 42 [1,5,6,4,3,2] => 168 [1,6,2,3,4,5] => 1 [1,6,2,3,5,4] => 4 [1,6,2,4,3,5] => 4 [1,6,2,4,5,3] => 10 [1,6,2,5,3,4] => 9 [1,6,2,5,4,3] => 35 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 19 [1,6,3,4,2,5] => 10 [1,6,3,4,5,2] => 20 [1,6,3,5,2,4] => 35 [1,6,3,5,4,2] => 90 [1,6,4,2,3,5] => 9 [1,6,4,2,5,3] => 35 [1,6,4,3,2,5] => 35 [1,6,4,3,5,2] => 90 [1,6,4,5,2,3] => 56 [1,6,4,5,3,2] => 216 [1,6,5,2,3,4] => 14 [1,6,5,2,4,3] => 70 [1,6,5,3,2,4] => 70 [1,6,5,3,4,2] => 216 [1,6,5,4,2,3] => 168 [1,6,5,4,3,2] => 768 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 2 [2,1,3,5,4,6] => 2 [2,1,3,5,6,4] => 3 [2,1,3,6,4,5] => 3 [2,1,3,6,5,4] => 8 [2,1,4,3,5,6] => 2 [2,1,4,3,6,5] => 6 [2,1,4,5,3,6] => 3 [2,1,4,5,6,3] => 4 [2,1,4,6,3,5] => 8 [2,1,4,6,5,3] => 15 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 8 [2,1,5,4,3,6] => 8 [2,1,5,4,6,3] => 15 [2,1,5,6,3,4] => 10 [2,1,5,6,4,3] => 30 [2,1,6,3,4,5] => 4 [2,1,6,3,5,4] => 15 [2,1,6,4,3,5] => 15 [2,1,6,4,5,3] => 36 [2,1,6,5,3,4] => 30 [2,1,6,5,4,3] => 112 [2,3,1,4,5,6] => 1 [2,3,1,4,6,5] => 3 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 6 [2,3,1,6,4,5] => 6 [2,3,1,6,5,4] => 20 [2,3,4,1,5,6] => 1 [2,3,4,1,6,5] => 4 [2,3,4,5,1,6] => 1 [2,3,4,5,6,1] => 1 [2,3,4,6,1,5] => 4 [2,3,4,6,5,1] => 5 [2,3,5,1,4,6] => 3 [2,3,5,1,6,4] => 9 [2,3,5,4,1,6] => 4 [2,3,5,4,6,1] => 5 [2,3,5,6,1,4] => 9 [2,3,5,6,4,1] => 14 [2,3,6,1,4,5] => 6 [2,3,6,1,5,4] => 26 [2,3,6,4,1,5] => 10 [2,3,6,4,5,1] => 15 [2,3,6,5,1,4] => 35 [2,3,6,5,4,1] => 64 [2,4,1,3,5,6] => 2 [2,4,1,3,6,5] => 8 [2,4,1,5,3,6] => 5 [2,4,1,5,6,3] => 9 [2,4,1,6,3,5] => 16 [2,4,1,6,5,3] => 40 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 15 [2,4,3,5,1,6] => 4 [2,4,3,5,6,1] => 5 [2,4,3,6,1,5] => 19 [2,4,3,6,5,1] => 29 [2,4,5,1,3,6] => 5 [2,4,5,1,6,3] => 14 [2,4,5,3,1,6] => 9 [2,4,5,3,6,1] => 14 [2,4,5,6,1,3] => 14 [2,4,5,6,3,1] => 28 [2,4,6,1,3,5] => 16 [2,4,6,1,5,3] => 56 [2,4,6,3,1,5] => 35 [2,4,6,3,5,1] => 64 [2,4,6,5,1,3] => 70 [2,4,6,5,3,1] => 162 [2,5,1,3,4,6] => 3 [2,5,1,3,6,4] => 11 [2,5,1,4,3,6] => 11 [2,5,1,4,6,3] => 26 [2,5,1,6,3,4] => 21 [2,5,1,6,4,3] => 77 [2,5,3,1,4,6] => 6 [2,5,3,1,6,4] => 26 [2,5,3,4,1,6] => 10 [2,5,3,4,6,1] => 15 [2,5,3,6,1,4] => 35 [2,5,3,6,4,1] => 64 [2,5,4,1,3,6] => 16 [2,5,4,1,6,3] => 56 [2,5,4,3,1,6] => 35 [2,5,4,3,6,1] => 64 [2,5,4,6,1,3] => 70 [2,5,4,6,3,1] => 162 [2,5,6,1,3,4] => 21 [2,5,6,1,4,3] => 98 [2,5,6,3,1,4] => 56 [2,5,6,3,4,1] => 120 [2,5,6,4,1,3] => 168 [2,5,6,4,3,1] => 450 [2,6,1,3,4,5] => 4 [2,6,1,3,5,4] => 19 [2,6,1,4,3,5] => 19 [2,6,1,4,5,3] => 55 [2,6,1,5,3,4] => 49 [2,6,1,5,4,3] => 216 [2,6,3,1,4,5] => 10 [2,6,3,1,5,4] => 55 [2,6,3,4,1,5] => 20 [2,6,3,4,5,1] => 35 [2,6,3,5,1,4] => 90 [2,6,3,5,4,1] => 189 [2,6,4,1,3,5] => 35 [2,6,4,1,5,3] => 146 [2,6,4,3,1,5] => 90 [2,6,4,3,5,1] => 189 [2,6,4,5,1,3] => 216 [2,6,4,5,3,1] => 567 [2,6,5,1,3,4] => 70 [2,6,5,1,4,3] => 384 [2,6,5,3,1,4] => 216 [2,6,5,3,4,1] => 525 [2,6,5,4,1,3] => 768 [2,6,5,4,3,1] => 2310 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 3 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 6 [3,1,2,6,4,5] => 6 [3,1,2,6,5,4] => 20 [3,1,4,2,5,6] => 2 [3,1,4,2,6,5] => 8 [3,1,4,5,2,6] => 3 [3,1,4,5,6,2] => 4 [3,1,4,6,2,5] => 11 [3,1,4,6,5,2] => 19 [3,1,5,2,4,6] => 5 [3,1,5,2,6,4] => 16 [3,1,5,4,2,6] => 11 [3,1,5,4,6,2] => 19 [3,1,5,6,2,4] => 21 [3,1,5,6,4,2] => 49 [3,1,6,2,4,5] => 9 [3,1,6,2,5,4] => 40 [3,1,6,4,2,5] => 26 [3,1,6,4,5,2] => 55 [3,1,6,5,2,4] => 77 [3,1,6,5,4,2] => 216 [3,2,1,4,5,6] => 2 [3,2,1,4,6,5] => 8 [3,2,1,5,4,6] => 8 [3,2,1,5,6,4] => 20 [3,2,1,6,4,5] => 20 [3,2,1,6,5,4] => 80 [3,2,4,1,5,6] => 3 [3,2,4,1,6,5] => 15 [3,2,4,5,1,6] => 4 [3,2,4,5,6,1] => 5 [3,2,4,6,1,5] => 19 [3,2,4,6,5,1] => 29 [3,2,5,1,4,6] => 11 [3,2,5,1,6,4] => 40 [3,2,5,4,1,6] => 19 [3,2,5,4,6,1] => 29 [3,2,5,6,1,4] => 49 [3,2,5,6,4,1] => 92 [3,2,6,1,4,5] => 26 [3,2,6,1,5,4] => 132 [3,2,6,4,1,5] => 55 [3,2,6,4,5,1] => 99 [3,2,6,5,1,4] => 216 [3,2,6,5,4,1] => 471 [3,4,1,2,5,6] => 2 [3,4,1,2,6,5] => 10 [3,4,1,5,2,6] => 5 [3,4,1,5,6,2] => 9 [3,4,1,6,2,5] => 21 [3,4,1,6,5,2] => 49 [3,4,2,1,5,6] => 5 [3,4,2,1,6,5] => 30 [3,4,2,5,1,6] => 9 [3,4,2,5,6,1] => 14 [3,4,2,6,1,5] => 49 [3,4,2,6,5,1] => 92 [3,4,5,1,2,6] => 5 [3,4,5,1,6,2] => 14 [3,4,5,2,1,6] => 14 [3,4,5,2,6,1] => 28 [3,4,5,6,1,2] => 14 [3,4,5,6,2,1] => 42 [3,4,6,1,2,5] => 21 [3,4,6,1,5,2] => 70 [3,4,6,2,1,5] => 70 [3,4,6,2,5,1] => 162 [3,4,6,5,1,2] => 84 [3,4,6,5,2,1] => 288 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 21 [3,5,1,4,2,6] => 16 [3,5,1,4,6,2] => 35 [3,5,1,6,2,4] => 42 [3,5,1,6,4,2] => 126 [3,5,2,1,4,6] => 16 [3,5,2,1,6,4] => 77 [3,5,2,4,1,6] => 35 [3,5,2,4,6,1] => 64 [3,5,2,6,1,4] => 126 [3,5,2,6,4,1] => 282 [3,5,4,1,2,6] => 21 [3,5,4,1,6,2] => 70 [3,5,4,2,1,6] => 70 [3,5,4,2,6,1] => 162 [3,5,4,6,1,2] => 84 [3,5,4,6,2,1] => 288 [3,5,6,1,2,4] => 42 [3,5,6,1,4,2] => 168 [3,5,6,2,1,4] => 168 [3,5,6,2,4,1] => 450 [3,5,6,4,1,2] => 252 [3,5,6,4,2,1] => 990 [3,6,1,2,4,5] => 9 [3,6,1,2,5,4] => 49 [3,6,1,4,2,5] => 35 [3,6,1,4,5,2] => 90 [3,6,1,5,2,4] => 126 [3,6,1,5,4,2] => 432 [3,6,2,1,4,5] => 35 [3,6,2,1,5,4] => 216 [3,6,2,4,1,5] => 90 [3,6,2,4,5,1] => 189 [3,6,2,5,1,4] => 432 [3,6,2,5,4,1] => 1092 [3,6,4,1,2,5] => 56 [3,6,4,1,5,2] => 216 [3,6,4,2,1,5] => 216 [3,6,4,2,5,1] => 567 [3,6,4,5,1,2] => 300 [3,6,4,5,2,1] => 1155 [3,6,5,1,2,4] => 168 [3,6,5,1,4,2] => 768 [3,6,5,2,1,4] => 768 [3,6,5,2,4,1] => 2310 [3,6,5,4,1,2] => 1320 [3,6,5,4,2,1] => 5775 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 3 [4,1,2,5,6,3] => 6 [4,1,2,6,3,5] => 9 [4,1,2,6,5,3] => 26 [4,1,3,2,5,6] => 3 [4,1,3,2,6,5] => 15 [4,1,3,5,2,6] => 6 [4,1,3,5,6,2] => 10 [4,1,3,6,2,5] => 26 [4,1,3,6,5,2] => 55 [4,1,5,2,3,6] => 5 [4,1,5,2,6,3] => 16 [4,1,5,3,2,6] => 16 [4,1,5,3,6,2] => 35 [4,1,5,6,2,3] => 21 [4,1,5,6,3,2] => 70 [4,1,6,2,3,5] => 14 [4,1,6,2,5,3] => 56 [4,1,6,3,2,5] => 56 [4,1,6,3,5,2] => 146 [4,1,6,5,2,3] => 98 [4,1,6,5,3,2] => 384 [4,2,1,3,5,6] => 3 [4,2,1,3,6,5] => 15 [4,2,1,5,3,6] => 11 [4,2,1,5,6,3] => 26 [4,2,1,6,3,5] => 40 [4,2,1,6,5,3] => 132 [4,2,3,1,5,6] => 6 [4,2,3,1,6,5] => 36 [4,2,3,5,1,6] => 10 [4,2,3,5,6,1] => 15 [4,2,3,6,1,5] => 55 [4,2,3,6,5,1] => 99 [4,2,5,1,3,6] => 16 [4,2,5,1,6,3] => 56 [4,2,5,3,1,6] => 35 [4,2,5,3,6,1] => 64 [4,2,5,6,1,3] => 70 [4,2,5,6,3,1] => 162 [4,2,6,1,3,5] => 56 [4,2,6,1,5,3] => 244 [4,2,6,3,1,5] => 146 [4,2,6,3,5,1] => 309 [4,2,6,5,1,3] => 384 [4,2,6,5,3,1] => 1017 [4,3,1,2,5,6] => 5 [4,3,1,2,6,5] => 30 [4,3,1,5,2,6] => 16 [4,3,1,5,6,2] => 35 [4,3,1,6,2,5] => 77 [4,3,1,6,5,2] => 216 [4,3,2,1,5,6] => 16 [4,3,2,1,6,5] => 112 [4,3,2,5,1,6] => 35 [4,3,2,5,6,1] => 64 [4,3,2,6,1,5] => 216 [4,3,2,6,5,1] => 471 [4,3,5,1,2,6] => 21 [4,3,5,1,6,2] => 70 [4,3,5,2,1,6] => 70 [4,3,5,2,6,1] => 162 [4,3,5,6,1,2] => 84 [4,3,5,6,2,1] => 288 [4,3,6,1,2,5] => 98 [4,3,6,1,5,2] => 384 [4,3,6,2,1,5] => 384 [4,3,6,2,5,1] => 1017 [4,3,6,5,1,2] => 552 [4,3,6,5,2,1] => 2145 [4,5,1,2,3,6] => 5 [4,5,1,2,6,3] => 21 [4,5,1,3,2,6] => 21 [4,5,1,3,6,2] => 56 [4,5,1,6,2,3] => 42 [4,5,1,6,3,2] => 168 [4,5,2,1,3,6] => 21 [4,5,2,1,6,3] => 98 [4,5,2,3,1,6] => 56 [4,5,2,3,6,1] => 120 [4,5,2,6,1,3] => 168 [4,5,2,6,3,1] => 450 [4,5,3,1,2,6] => 42 [4,5,3,1,6,2] => 168 [4,5,3,2,1,6] => 168 [4,5,3,2,6,1] => 450 [4,5,3,6,1,2] => 252 [4,5,3,6,2,1] => 990 [4,5,6,1,2,3] => 42 [4,5,6,1,3,2] => 210 [4,5,6,2,1,3] => 210 [4,5,6,2,3,1] => 660 [4,5,6,3,1,2] => 462 [4,5,6,3,2,1] => 2112 [4,6,1,2,3,5] => 14 [4,6,1,2,5,3] => 70 [4,6,1,3,2,5] => 70 [4,6,1,3,5,2] => 216 [4,6,1,5,2,3] => 168 [4,6,1,5,3,2] => 768 [4,6,2,1,3,5] => 70 [4,6,2,1,5,3] => 384 [4,6,2,3,1,5] => 216 [4,6,2,3,5,1] => 525 [4,6,2,5,1,3] => 768 [4,6,2,5,3,1] => 2310 [4,6,3,1,2,5] => 168 [4,6,3,1,5,2] => 768 [4,6,3,2,1,5] => 768 [4,6,3,2,5,1] => 2310 [4,6,3,5,1,2] => 1320 [4,6,3,5,2,1] => 5775 [4,6,5,1,2,3] => 210 [4,6,5,1,3,2] => 1188 [4,6,5,2,1,3] => 1188 [4,6,5,2,3,1] => 4158 [4,6,5,3,1,2] => 2970 [4,6,5,3,2,1] => 15015 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 4 [5,1,2,4,3,6] => 4 [5,1,2,4,6,3] => 10 [5,1,2,6,3,4] => 9 [5,1,2,6,4,3] => 35 [5,1,3,2,4,6] => 4 [5,1,3,2,6,4] => 19 [5,1,3,4,2,6] => 10 [5,1,3,4,6,2] => 20 [5,1,3,6,2,4] => 35 [5,1,3,6,4,2] => 90 [5,1,4,2,3,6] => 9 [5,1,4,2,6,3] => 35 [5,1,4,3,2,6] => 35 [5,1,4,3,6,2] => 90 [5,1,4,6,2,3] => 56 [5,1,4,6,3,2] => 216 [5,1,6,2,3,4] => 14 [5,1,6,2,4,3] => 70 [5,1,6,3,2,4] => 70 [5,1,6,3,4,2] => 216 [5,1,6,4,2,3] => 168 [5,1,6,4,3,2] => 768 [5,2,1,3,4,6] => 4 [5,2,1,3,6,4] => 19 [5,2,1,4,3,6] => 19 [5,2,1,4,6,3] => 55 [5,2,1,6,3,4] => 49 [5,2,1,6,4,3] => 216 [5,2,3,1,4,6] => 10 [5,2,3,1,6,4] => 55 [5,2,3,4,1,6] => 20 [5,2,3,4,6,1] => 35 [5,2,3,6,1,4] => 90 [5,2,3,6,4,1] => 189 [5,2,4,1,3,6] => 35 [5,2,4,1,6,3] => 146 [5,2,4,3,1,6] => 90 [5,2,4,3,6,1] => 189 [5,2,4,6,1,3] => 216 [5,2,4,6,3,1] => 567 [5,2,6,1,3,4] => 70 [5,2,6,1,4,3] => 384 [5,2,6,3,1,4] => 216 [5,2,6,3,4,1] => 525 [5,2,6,4,1,3] => 768 [5,2,6,4,3,1] => 2310 [5,3,1,2,4,6] => 9 [5,3,1,2,6,4] => 49 [5,3,1,4,2,6] => 35 [5,3,1,4,6,2] => 90 [5,3,1,6,2,4] => 126 [5,3,1,6,4,2] => 432 [5,3,2,1,4,6] => 35 [5,3,2,1,6,4] => 216 [5,3,2,4,1,6] => 90 [5,3,2,4,6,1] => 189 [5,3,2,6,1,4] => 432 [5,3,2,6,4,1] => 1092 [5,3,4,1,2,6] => 56 [5,3,4,1,6,2] => 216 [5,3,4,2,1,6] => 216 [5,3,4,2,6,1] => 567 [5,3,4,6,1,2] => 300 [5,3,4,6,2,1] => 1155 [5,3,6,1,2,4] => 168 [5,3,6,1,4,2] => 768 [5,3,6,2,1,4] => 768 [5,3,6,2,4,1] => 2310 [5,3,6,4,1,2] => 1320 [5,3,6,4,2,1] => 5775 [5,4,1,2,3,6] => 14 [5,4,1,2,6,3] => 70 [5,4,1,3,2,6] => 70 [5,4,1,3,6,2] => 216 [5,4,1,6,2,3] => 168 [5,4,1,6,3,2] => 768 [5,4,2,1,3,6] => 70 [5,4,2,1,6,3] => 384 [5,4,2,3,1,6] => 216 [5,4,2,3,6,1] => 525 [5,4,2,6,1,3] => 768 [5,4,2,6,3,1] => 2310 [5,4,3,1,2,6] => 168 [5,4,3,1,6,2] => 768 [5,4,3,2,1,6] => 768 [5,4,3,2,6,1] => 2310 [5,4,3,6,1,2] => 1320 [5,4,3,6,2,1] => 5775 [5,4,6,1,2,3] => 210 [5,4,6,1,3,2] => 1188 [5,4,6,2,1,3] => 1188 [5,4,6,2,3,1] => 4158 [5,4,6,3,1,2] => 2970 [5,4,6,3,2,1] => 15015 [5,6,1,2,3,4] => 14 [5,6,1,2,4,3] => 84 [5,6,1,3,2,4] => 84 [5,6,1,3,4,2] => 300 [5,6,1,4,2,3] => 252 [5,6,1,4,3,2] => 1320 [5,6,2,1,3,4] => 84 [5,6,2,1,4,3] => 552 [5,6,2,3,1,4] => 300 [5,6,2,3,4,1] => 825 [5,6,2,4,1,3] => 1320 [5,6,2,4,3,1] => 4455 [5,6,3,1,2,4] => 252 [5,6,3,1,4,2] => 1320 [5,6,3,2,1,4] => 1320 [5,6,3,2,4,1] => 4455 [5,6,3,4,1,2] => 2640 [5,6,3,4,2,1] => 12870 [5,6,4,1,2,3] => 462 [5,6,4,1,3,2] => 2970 [5,6,4,2,1,3] => 2970 [5,6,4,2,3,1] => 11583 [5,6,4,3,1,2] => 8580 [5,6,4,3,2,1] => 48048 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 5 [6,1,2,4,3,5] => 5 [6,1,2,4,5,3] => 15 [6,1,2,5,3,4] => 14 [6,1,2,5,4,3] => 64 [6,1,3,2,4,5] => 5 [6,1,3,2,5,4] => 29 [6,1,3,4,2,5] => 15 [6,1,3,4,5,2] => 35 [6,1,3,5,2,4] => 64 [6,1,3,5,4,2] => 189 [6,1,4,2,3,5] => 14 [6,1,4,2,5,3] => 64 [6,1,4,3,2,5] => 64 [6,1,4,3,5,2] => 189 [6,1,4,5,2,3] => 120 [6,1,4,5,3,2] => 525 [6,1,5,2,3,4] => 28 [6,1,5,2,4,3] => 162 [6,1,5,3,2,4] => 162 [6,1,5,3,4,2] => 567 [6,1,5,4,2,3] => 450 [6,1,5,4,3,2] => 2310 [6,2,1,3,4,5] => 5 [6,2,1,3,5,4] => 29 [6,2,1,4,3,5] => 29 [6,2,1,4,5,3] => 99 [6,2,1,5,3,4] => 92 [6,2,1,5,4,3] => 471 [6,2,3,1,4,5] => 15 [6,2,3,1,5,4] => 99 [6,2,3,4,1,5] => 35 [6,2,3,4,5,1] => 70 [6,2,3,5,1,4] => 189 [6,2,3,5,4,1] => 448 [6,2,4,1,3,5] => 64 [6,2,4,1,5,3] => 309 [6,2,4,3,1,5] => 189 [6,2,4,3,5,1] => 448 [6,2,4,5,1,3] => 525 [6,2,4,5,3,1] => 1540 [6,2,5,1,3,4] => 162 [6,2,5,1,4,3] => 1017 [6,2,5,3,1,4] => 567 [6,2,5,3,4,1] => 1540 [6,2,5,4,1,3] => 2310 [6,2,5,4,3,1] => 7700 [6,3,1,2,4,5] => 14 [6,3,1,2,5,4] => 92 [6,3,1,4,2,5] => 64 [6,3,1,4,5,2] => 189 [6,3,1,5,2,4] => 282 [6,3,1,5,4,2] => 1092 [6,3,2,1,4,5] => 64 [6,3,2,1,5,4] => 471 [6,3,2,4,1,5] => 189 [6,3,2,4,5,1] => 448 [6,3,2,5,1,4] => 1092 [6,3,2,5,4,1] => 3080 [6,3,4,1,2,5] => 120 [6,3,4,1,5,2] => 525 [6,3,4,2,1,5] => 525 [6,3,4,2,5,1] => 1540 [6,3,4,5,1,2] => 825 [6,3,4,5,2,1] => 3520 [6,3,5,1,2,4] => 450 [6,3,5,1,4,2] => 2310 [6,3,5,2,1,4] => 2310 [6,3,5,2,4,1] => 7700 [6,3,5,4,1,2] => 4455 [6,3,5,4,2,1] => 21450 [6,4,1,2,3,5] => 28 [6,4,1,2,5,3] => 162 [6,4,1,3,2,5] => 162 [6,4,1,3,5,2] => 567 [6,4,1,5,2,3] => 450 [6,4,1,5,3,2] => 2310 [6,4,2,1,3,5] => 162 [6,4,2,1,5,3] => 1017 [6,4,2,3,1,5] => 567 [6,4,2,3,5,1] => 1540 [6,4,2,5,1,3] => 2310 [6,4,2,5,3,1] => 7700 [6,4,3,1,2,5] => 450 [6,4,3,1,5,2] => 2310 [6,4,3,2,1,5] => 2310 [6,4,3,2,5,1] => 7700 [6,4,3,5,1,2] => 4455 [6,4,3,5,2,1] => 21450 [6,4,5,1,2,3] => 660 [6,4,5,1,3,2] => 4158 [6,4,5,2,1,3] => 4158 [6,4,5,2,3,1] => 16016 [6,4,5,3,1,2] => 11583 [6,4,5,3,2,1] => 64064 [6,5,1,2,3,4] => 42 [6,5,1,2,4,3] => 288 [6,5,1,3,2,4] => 288 [6,5,1,3,4,2] => 1155 [6,5,1,4,2,3] => 990 [6,5,1,4,3,2] => 5775 [6,5,2,1,3,4] => 288 [6,5,2,1,4,3] => 2145 [6,5,2,3,1,4] => 1155 [6,5,2,3,4,1] => 3520 [6,5,2,4,1,3] => 5775 [6,5,2,4,3,1] => 21450 [6,5,3,1,2,4] => 990 [6,5,3,1,4,2] => 5775 [6,5,3,2,1,4] => 5775 [6,5,3,2,4,1] => 21450 [6,5,3,4,1,2] => 12870 [6,5,3,4,2,1] => 68640 [6,5,4,1,2,3] => 2112 [6,5,4,1,3,2] => 15015 [6,5,4,2,1,3] => 15015 [6,5,4,2,3,1] => 64064 [6,5,4,3,1,2] => 48048 [6,5,4,3,2,1] => 292864 [1,2,3,4,5,6,7] => 1 [1,2,3,4,5,7,6] => 1 [1,2,3,4,6,5,7] => 1 [1,2,3,6,4,7,5] => 2 [1,2,6,3,4,7,5] => 3 [1,3,2,4,5,6,7] => 1 [1,3,7,2,4,5,6] => 4 [1,3,7,6,5,4,2] => 2310 [1,4,6,7,2,3,5] => 42 [1,4,6,7,5,3,2] => 990 [1,4,7,2,3,5,6] => 9 [1,4,7,6,5,3,2] => 5775 [1,5,2,3,4,7,6] => 4 [1,5,2,7,3,4,6] => 14 [1,5,4,7,6,3,2] => 2145 [1,5,6,2,7,3,4] => 42 [1,5,6,4,7,3,2] => 990 [1,5,6,7,2,3,4] => 42 [1,5,6,7,4,3,2] => 2112 [1,5,7,2,3,4,6] => 14 [1,5,7,6,4,3,2] => 15015 [1,6,2,3,4,7,5] => 4 [1,6,2,3,7,4,5] => 9 [1,6,2,7,3,4,5] => 14 [1,6,5,4,3,7,2] => 2310 [1,6,5,4,7,3,2] => 5775 [1,6,5,7,4,3,2] => 15015 [1,6,7,2,3,4,5] => 14 [1,6,7,5,4,3,2] => 48048 [1,7,2,3,4,5,6] => 1 [1,7,3,5,6,4,2] => 1540 [1,7,3,6,5,4,2] => 7700 [1,7,4,3,6,5,2] => 3080 [1,7,4,5,3,6,2] => 1540 [1,7,4,5,6,3,2] => 3520 [1,7,4,6,5,3,2] => 21450 [1,7,5,4,3,6,2] => 7700 [1,7,5,4,6,3,2] => 21450 [1,7,6,4,5,3,2] => 68640 [1,7,6,5,4,3,2] => 292864 [2,1,3,4,5,6,7] => 1 [2,1,3,4,7,5,6] => 3 [2,1,3,7,4,5,6] => 4 [2,1,6,3,4,5,7] => 4 [2,1,7,3,4,5,6] => 5 [2,1,7,6,5,4,3] => 8448 [2,3,1,4,5,6,7] => 1 [2,3,4,1,5,6,7] => 1 [2,3,4,1,5,7,6] => 4 [2,3,4,5,1,6,7] => 1 [2,3,4,5,1,7,6] => 5 [2,3,4,5,6,1,7] => 1 [2,3,4,5,6,7,1] => 1 [2,3,4,5,7,1,6] => 5 [2,3,4,6,1,7,5] => 14 [2,3,4,6,7,1,5] => 14 [2,3,4,7,1,5,6] => 10 [2,3,5,6,7,1,4] => 28 [2,4,1,3,5,6,7] => 2 [2,5,1,3,4,6,7] => 3 [2,5,7,1,3,4,6] => 70 [2,6,1,3,4,5,7] => 4 [2,6,1,7,3,4,5] => 84 [2,6,5,4,3,1,7] => 2310 [2,6,7,1,3,4,5] => 84 [2,7,1,3,4,5,6] => 5 [3,1,2,4,5,6,7] => 1 [3,1,2,4,5,7,6] => 3 [3,2,1,4,5,6,7] => 2 [3,2,4,5,6,7,1] => 6 [3,4,1,2,5,6,7] => 2 [3,4,2,5,6,7,1] => 20 [3,4,5,2,6,7,1] => 48 [3,4,5,6,2,7,1] => 90 [3,4,5,6,7,1,2] => 42 [3,5,6,1,2,4,7] => 42 [3,5,6,4,2,1,7] => 990 [3,6,1,2,4,5,7] => 9 [3,6,5,4,2,1,7] => 5775 [4,1,2,3,5,6,7] => 1 [4,1,2,3,5,7,6] => 4 [4,1,6,2,3,5,7] => 14 [4,2,3,5,6,7,1] => 21 [4,2,5,1,3,6,7] => 16 [4,3,2,1,5,6,7] => 16 [4,3,2,5,6,7,1] => 105 [4,3,5,2,6,7,1] => 315 [4,3,6,5,2,1,7] => 2145 [4,5,1,6,2,3,7] => 42 [4,5,2,3,6,7,1] => 225 [4,5,3,6,2,1,7] => 990 [4,5,6,1,2,3,7] => 42 [4,5,6,3,2,1,7] => 2112 [4,6,1,2,3,5,7] => 14 [4,6,1,2,3,7,5] => 84 [4,6,5,3,2,1,7] => 15015 [5,1,2,3,4,6,7] => 1 [5,1,2,3,4,7,6] => 5 [5,1,2,3,6,4,7] => 4 [5,1,2,3,6,7,4] => 10 [5,1,2,3,7,4,6] => 14 [5,1,2,6,3,4,7] => 9 [5,1,6,2,3,4,7] => 14 [5,1,6,2,3,7,4] => 70 [5,2,3,4,6,7,1] => 56 [5,2,6,7,1,3,4] => 1188 [5,3,2,4,6,7,1] => 350 [5,3,2,6,1,4,7] => 432 [5,3,6,7,1,2,4] => 2970 [5,4,3,2,1,6,7] => 768 [5,4,3,2,1,7,6] => 8448 [5,4,3,2,6,1,7] => 2310 [5,4,3,6,2,1,7] => 5775 [5,4,6,3,2,1,7] => 15015 [5,4,6,7,1,2,3] => 3432 [5,6,1,2,3,4,7] => 14 [5,6,1,2,3,7,4] => 84 [5,6,3,4,1,2,7] => 2640 [5,6,4,3,2,1,7] => 48048 [5,6,7,1,2,3,4] => 462 [6,1,2,3,4,5,7] => 1 [6,1,2,3,4,7,5] => 5 [6,1,2,3,7,4,5] => 14 [6,1,2,7,3,4,5] => 28 [6,2,3,4,5,7,1] => 126 [6,2,4,5,3,1,7] => 1540 [6,2,5,4,3,1,7] => 7700 [6,3,2,5,4,1,7] => 3080 [6,3,4,2,5,1,7] => 1540 [6,3,4,5,2,1,7] => 3520 [6,3,4,7,1,2,5] => 4455 [6,3,5,4,2,1,7] => 21450 [6,4,3,2,5,1,7] => 7700 [6,4,3,2,7,1,5] => 58916 [6,4,3,5,2,1,7] => 21450 [6,4,5,7,1,2,3] => 15015 [6,4,7,2,5,1,3] => 292864 [6,4,7,3,5,1,2] => 640640 [6,5,3,4,2,1,7] => 68640 [6,5,4,3,2,1,7] => 292864 [6,5,7,3,4,1,2] => 1361360 [6,7,1,2,3,4,5] => 42 [6,7,3,4,1,2,5] => 21450 [6,7,4,5,1,2,3] => 171600 [7,1,2,3,4,5,6] => 1 [7,2,1,3,4,5,6] => 6 [7,2,3,1,4,5,6] => 21 [7,2,3,4,1,5,6] => 56 [7,2,3,4,5,1,6] => 126 [7,3,1,2,4,5,6] => 20 [7,3,2,1,4,5,6] => 105 [7,3,2,4,1,5,6] => 350 [7,3,4,1,2,5,6] => 225 [7,4,1,2,3,5,6] => 48 [7,4,2,1,3,5,6] => 315 [7,4,5,6,1,2,3] => 50050 [7,5,1,2,3,4,6] => 90 [7,5,6,1,2,3,4] => 9009 [7,5,6,3,4,1,2] => 6534528 [7,6,1,2,3,4,5] => 132 [7,6,4,5,1,2,3] => 972400 [7,6,5,1,2,3,4] => 30030 [1,2,3,4,5,6,7,8] => 1 [1,7,8,6,5,4,3,2] => 141892608 [1,6,8,7,5,4,3,2] => 34918884 [1,7,6,8,5,4,3,2] => 34918884 [1,6,7,8,5,4,3,2] => 3734016 [1,5,8,7,6,4,3,2] => 10720710 [1,7,6,5,8,4,3,2] => 10720710 [1,3,5,7,8,6,4,2] => 2673 [1,4,3,8,7,6,5,2] => 61204 [1,6,5,4,3,8,7,2] => 61204 [1,4,3,6,5,8,7,2] => 314 [1,2,6,7,8,5,4,3] => 2112 [1,2,3,5,6,7,8,4] => 1 [1,2,3,4,5,6,8,7] => 1 [1,4,3,2,7,6,5,8] => 80 [1,3,4,2,6,7,5,8] => 6 [1,3,2,5,4,7,6,8] => 6 [1,2,3,5,4,7,6,8] => 2 [1,3,2,4,5,7,6,8] => 2 [1,2,3,4,5,7,6,8] => 1 [1,2,4,3,6,5,7,8] => 2 [1,3,2,5,4,6,7,8] => 2 [1,2,3,5,4,6,7,8] => 1 [1,3,2,4,5,6,7,8] => 1 [1,3,2,5,4,8,6,7] => 12 [1,3,5,8,2,4,6,7] => 35 [1,3,5,6,2,7,4,8] => 14 [1,3,2,6,4,7,5,8] => 8 [1,3,2,6,4,8,5,7] => 25 [1,3,2,6,4,5,7,8] => 3 [1,3,2,7,4,8,5,6] => 30 [1,3,2,7,4,5,6,8] => 4 [1,3,2,8,4,5,6,7] => 5 [1,3,2,4,5,8,6,7] => 3 [1,4,2,5,3,7,6,8] => 8 [1,4,2,5,3,8,6,7] => 20 [1,4,2,5,3,6,7,8] => 2 [1,4,5,6,7,2,3,8] => 14 [1,4,2,6,3,7,5,8] => 16 [1,4,2,6,7,8,3,5] => 84 [1,4,2,6,3,8,5,7] => 61 [1,4,2,6,3,5,7,8] => 5 [1,4,2,7,3,8,5,6] => 91 [1,4,2,7,3,5,6,8] => 9 [1,4,2,3,7,5,6,8] => 6 [1,4,2,3,5,7,6,8] => 3 [1,4,2,8,3,5,6,7] => 14 [1,4,2,3,5,8,6,7] => 6 [1,4,2,3,5,6,7,8] => 1 [1,5,2,6,3,7,4,8] => 16 [1,5,2,6,3,8,4,7] => 77 [1,5,2,6,3,4,7,8] => 5 [1,2,5,6,3,4,7,8] => 2 [1,5,2,7,3,8,4,6] => 168 [1,5,2,7,3,4,6,8] => 14 [1,5,2,3,4,7,6,8] => 4 [1,5,2,8,3,4,6,7] => 28 [1,5,8,2,3,4,6,7] => 28 [1,5,2,3,4,8,6,7] => 10 [1,2,3,5,4,8,6,7] => 3 [1,5,2,3,4,6,7,8] => 1 [1,6,2,7,3,8,4,5] => 168 [1,6,7,8,2,3,4,5] => 462 [1,6,2,7,3,4,5,8] => 14 [1,6,7,2,3,4,5,8] => 14 [1,6,2,3,4,7,5,8] => 4 [1,2,3,6,4,7,5,8] => 2 [1,6,2,8,3,4,5,7] => 42 [1,6,8,2,3,4,5,7] => 42 [1,6,2,3,4,8,5,7] => 14 [1,2,3,6,4,8,5,7] => 5 [1,6,2,3,4,5,7,8] => 1 [1,2,3,6,4,5,7,8] => 1 [1,7,2,8,3,4,5,6] => 42 [1,7,8,2,3,4,5,6] => 42 [1,7,2,3,8,4,5,6] => 28 [1,7,2,3,4,8,5,6] => 14 [1,2,3,7,4,8,5,6] => 5 [1,7,2,3,4,5,8,6] => 5 [1,2,7,3,4,5,8,6] => 4 [1,7,2,3,4,5,6,8] => 1 [1,2,3,7,4,5,6,8] => 1 [1,2,3,8,4,5,6,7] => 1 [1,2,3,4,5,8,6,7] => 1 [1,6,7,4,5,2,3,8] => 2640 [1,5,4,7,6,2,3,8] => 552 [1,5,3,7,2,6,4,8] => 244 [1,6,7,3,2,5,4,8] => 552 [1,7,3,4,2,5,8,6] => 99 [1,5,6,3,4,8,7,2] => 2090 [1,7,5,4,8,3,6,2] => 474903 [1,7,6,8,4,3,5,2] => 2362932 [1,6,7,8,3,4,5,2] => 50050 [1,5,7,3,8,4,6,2] => 23452 [1,4,3,7,8,5,6,2] => 2090 [1,5,8,3,7,6,4,2] => 474903 [1,6,8,7,3,5,4,2] => 2362932 [1,7,8,6,5,3,4,2] => 26604864 [1,4,3,8,7,5,6,2] => 11121 [1,4,6,7,3,2,8,5] => 912 [1,7,4,5,3,2,8,6] => 4675 [1,7,4,8,6,3,5,2] => 1153152 [1,7,3,5,6,8,2,4] => 3520 [1,3,6,7,5,8,2,4] => 990 [1,7,2,5,8,6,4,3] => 21450 [1,7,4,8,2,6,5,3] => 132704 [1,7,2,4,3,5,6,8] => 5 [1,6,2,4,3,5,7,8] => 4 [1,5,2,4,3,6,7,8] => 3 [1,6,2,5,3,4,7,8] => 9 [1,7,2,5,3,4,6,8] => 14 [1,7,2,6,3,4,5,8] => 28 [1,7,2,8,3,5,4,6] => 288 [1,6,2,8,3,5,4,7] => 246 [1,5,2,8,3,6,4,7] => 134 [1,4,2,8,3,6,5,7] => 78 [1,3,2,8,4,6,5,7] => 24 [1,2,3,8,4,6,5,7] => 4 [1,2,3,7,4,6,5,8] => 3 [1,3,2,7,4,6,5,8] => 15 [1,4,2,7,3,6,5,8] => 40 [1,5,2,7,3,6,4,8] => 56 [1,6,2,7,3,5,4,8] => 70 [1,7,2,6,3,5,4,8] => 162 [1,7,2,5,3,6,4,8] => 64 [1,6,2,5,3,7,4,8] => 35 [1,5,2,4,3,7,6,8] => 15 [1,6,2,4,3,7,5,8] => 19 [1,7,2,4,3,6,5,8] => 29 [1,7,2,3,4,6,5,8] => 5 [1,7,2,4,3,8,5,6] => 92 [1,6,2,4,3,8,5,7] => 78 [1,5,2,4,3,8,6,7] => 45 [1,6,2,5,3,8,4,7] => 190 [1,7,2,5,3,8,4,6] => 282 [1,7,2,6,3,8,4,5] => 450 [1,2,3,8,4,7,5,6] => 9 [1,3,2,8,4,7,5,6] => 63 [1,4,2,8,3,7,5,6] => 232 [1,5,2,8,3,7,4,6] => 534 [1,6,2,8,3,7,4,5] => 702 [1,7,2,8,3,6,4,5] => 990 [1,7,2,8,5,3,4,6] => 990 [1,2,8,7,6,3,4,5] => 2112 [1,6,7,2,8,4,3,5] => 2970 [1,7,2,8,4,5,3,6] => 1155 [1,2,7,5,8,3,4,6] => 168 [1,6,4,7,5,8,2,3] => 8580 [1,3,7,4,6,8,2,5] => 567 [1,7,6,5,4,8,2,3] => 640640 [1,2,7,6,8,3,4,5] => 210 [1,6,2,5,8,3,4,7] => 288 [1,5,4,2,8,3,6,7] => 232 [1,7,6,8,5,4,2,3] => 5105100 [1,4,8,6,7,5,2,3] => 126126 [1,3,8,7,5,6,2,4] => 68640 [1,5,8,4,3,2,6,7] => 2310 [1,7,4,3,8,5,2,6] => 11220 [1,5,7,3,8,4,2,6] => 8613 [1,6,8,5,3,7,4,2] => 1153152 [1,7,5,6,3,2,8,4] => 27599 [1,2,8,7,4,5,6,3] => 3520 [1,7,8,5,2,6,4,3] => 640640 [1,2,3,4,5,6,7,9,8] => 1 [1,2,3,4,5,6,7,8,9] => 1 [1,7,9,2,3,4,5,6,8] => 132 [1,2,3,4,5,6,7,8,10,9] => 1 [1,2,3,4,5,6,7,8,9,10] => 1 [1,2,3,4,5,6,7,8,9,11,10] => 1 ----------------------------------------------------------------------------- Created: Sep 13, 2011 at 22:02 by Chris Berg ----------------------------------------------------------------------------- Last Updated: May 23, 2019 at 16:07 by Martin Rubey