************************************************************************ * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2013 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. * ************************************************************************ ------------------------------------------------------------------------ Map identifier: Mp00248 ------------------------------------------------------------------------ Map name: DEX composition ------------------------------------------------------------------------ Domain: Permutations ------------------------------------------------------------------------ Codomain: Integer compositions ------------------------------------------------------------------------ Description: The DEX composition of a permutation. Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$. The (quasi)symmetric function $$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$ where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function. ------------------------------------------------------------------------ References: [1] Shareshian, J., Wachs, M. L. Eulerian quasisymmetric functions [[arXiv:0812.0764]] ------------------------------------------------------------------------ Code: def mapping(pi): pi = list(pi) n = len(pi) for i, e in enumerate(pi): if e > i + 1: pi[i] = -n-1+e return Composition(from_subset=([i for i in range(1, len(pi)) if pi[i-1] > pi[i]], n)) ------------------------------------------------------------------------ Map images: [1] => [1] [1,2] => [2] [2,1] => [2] [1,2,3] => [3] [1,3,2] => [1,2] [2,1,3] => [3] [2,3,1] => [3] [3,1,2] => [3] [3,2,1] => [2,1] [1,2,3,4] => [4] [1,2,4,3] => [2,2] [1,3,2,4] => [1,3] [1,3,4,2] => [1,3] [1,4,2,3] => [1,3] [1,4,3,2] => [1,2,1] [2,1,3,4] => [4] [2,1,4,3] => [2,2] [2,3,1,4] => [4] [2,3,4,1] => [4] [2,4,1,3] => [4] [2,4,3,1] => [3,1] [3,1,2,4] => [4] [3,1,4,2] => [2,2] [3,2,1,4] => [2,2] [3,2,4,1] => [2,2] [3,4,1,2] => [4] [3,4,2,1] => [3,1] [4,1,2,3] => [4] [4,1,3,2] => [3,1] [4,2,1,3] => [2,2] [4,2,3,1] => [3,1] [4,3,1,2] => [1,3] [4,3,2,1] => [1,2,1] [1,2,3,4,5] => [5] [1,2,3,5,4] => [3,2] [1,2,4,3,5] => [2,3] [1,2,4,5,3] => [2,3] [1,2,5,3,4] => [2,3] [1,2,5,4,3] => [2,2,1] [1,3,2,4,5] => [1,4] [1,3,2,5,4] => [1,2,2] [1,3,4,2,5] => [1,4] [1,3,4,5,2] => [1,4] [1,3,5,2,4] => [1,4] [1,3,5,4,2] => [1,3,1] [1,4,2,3,5] => [1,4] [1,4,2,5,3] => [1,2,2] [1,4,3,2,5] => [1,2,2] [1,4,3,5,2] => [1,2,2] [1,4,5,2,3] => [1,4] [1,4,5,3,2] => [1,3,1] [1,5,2,3,4] => [1,4] [1,5,2,4,3] => [1,3,1] [1,5,3,2,4] => [1,2,2] [1,5,3,4,2] => [1,3,1] [1,5,4,2,3] => [1,1,3] [1,5,4,3,2] => [1,1,2,1] [2,1,3,4,5] => [5] [2,1,3,5,4] => [3,2] [2,1,4,3,5] => [2,3] [2,1,4,5,3] => [2,3] [2,1,5,3,4] => [2,3] [2,1,5,4,3] => [2,2,1] [2,3,1,4,5] => [5] [2,3,1,5,4] => [3,2] [2,3,4,1,5] => [5] [2,3,4,5,1] => [5] [2,3,5,1,4] => [5] [2,3,5,4,1] => [4,1] [2,4,1,3,5] => [5] [2,4,1,5,3] => [3,2] [2,4,3,1,5] => [3,2] [2,4,3,5,1] => [3,2] [2,4,5,1,3] => [5] [2,4,5,3,1] => [4,1] [2,5,1,3,4] => [5] [2,5,1,4,3] => [4,1] [2,5,3,1,4] => [3,2] [2,5,3,4,1] => [4,1] [2,5,4,1,3] => [2,3] [2,5,4,3,1] => [2,2,1] [3,1,2,4,5] => [5] [3,1,2,5,4] => [3,2] [3,1,4,2,5] => [2,3] [3,1,4,5,2] => [2,3] [3,1,5,2,4] => [2,3] [3,1,5,4,2] => [2,2,1] [3,2,1,4,5] => [2,3] [3,2,1,5,4] => [2,1,2] [3,2,4,1,5] => [2,3] [3,2,4,5,1] => [2,3] [3,2,5,1,4] => [2,3] [3,2,5,4,1] => [2,2,1] [3,4,1,2,5] => [5] [3,4,1,5,2] => [3,2] [3,4,2,1,5] => [3,2] [3,4,2,5,1] => [3,2] [3,4,5,1,2] => [5] [3,4,5,2,1] => [4,1] [3,5,1,2,4] => [5] [3,5,1,4,2] => [4,1] [3,5,2,1,4] => [3,2] [3,5,2,4,1] => [4,1] [3,5,4,1,2] => [2,3] [3,5,4,2,1] => [2,2,1] [4,1,2,3,5] => [5] [4,1,2,5,3] => [3,2] [4,1,3,2,5] => [3,2] [4,1,3,5,2] => [3,2] [4,1,5,2,3] => [2,3] [4,1,5,3,2] => [2,2,1] [4,2,1,3,5] => [2,3] [4,2,1,5,3] => [2,1,2] [4,2,3,1,5] => [3,2] [4,2,3,5,1] => [3,2] [4,2,5,1,3] => [2,3] [4,2,5,3,1] => [2,2,1] [4,3,1,2,5] => [1,4] [4,3,1,5,2] => [1,2,2] [4,3,2,1,5] => [1,2,2] [4,3,2,5,1] => [1,2,2] [4,3,5,1,2] => [1,4] [4,3,5,2,1] => [1,3,1] [4,5,1,2,3] => [5] [4,5,1,3,2] => [4,1] [4,5,2,1,3] => [3,2] [4,5,2,3,1] => [4,1] [4,5,3,1,2] => [3,2] [4,5,3,2,1] => [3,1,1] [5,1,2,3,4] => [5] [5,1,2,4,3] => [4,1] [5,1,3,2,4] => [3,2] [5,1,3,4,2] => [4,1] [5,1,4,2,3] => [2,3] [5,1,4,3,2] => [2,2,1] [5,2,1,3,4] => [2,3] [5,2,1,4,3] => [2,2,1] [5,2,3,1,4] => [3,2] [5,2,3,4,1] => [4,1] [5,2,4,1,3] => [2,3] [5,2,4,3,1] => [2,2,1] [5,3,1,2,4] => [1,4] [5,3,1,4,2] => [1,3,1] [5,3,2,1,4] => [1,2,2] [5,3,2,4,1] => [1,3,1] [5,3,4,1,2] => [1,4] [5,3,4,2,1] => [1,3,1] [5,4,1,2,3] => [1,4] [5,4,1,3,2] => [1,3,1] [5,4,2,1,3] => [1,2,2] [5,4,2,3,1] => [1,3,1] [5,4,3,1,2] => [1,2,2] [5,4,3,2,1] => [1,2,1,1] [1,2,3,4,5,6] => [6] [1,2,3,4,6,5] => [4,2] [1,2,3,5,4,6] => [3,3] [1,2,3,5,6,4] => [3,3] [1,2,3,6,4,5] => [3,3] [1,2,3,6,5,4] => [3,2,1] [1,2,4,3,5,6] => [2,4] [1,2,4,3,6,5] => [2,2,2] [1,2,4,5,3,6] => [2,4] [1,2,4,5,6,3] => [2,4] [1,2,4,6,3,5] => [2,4] [1,2,4,6,5,3] => [2,3,1] [1,2,5,3,4,6] => [2,4] [1,2,5,3,6,4] => [2,2,2] [1,2,5,4,3,6] => [2,2,2] [1,2,5,4,6,3] => [2,2,2] [1,2,5,6,3,4] => [2,4] [1,2,5,6,4,3] => [2,3,1] [1,2,6,3,4,5] => [2,4] [1,2,6,3,5,4] => [2,3,1] [1,2,6,4,3,5] => [2,2,2] [1,2,6,4,5,3] => [2,3,1] [1,2,6,5,3,4] => [2,1,3] [1,2,6,5,4,3] => [2,1,2,1] [1,3,2,4,5,6] => [1,5] [1,3,2,4,6,5] => [1,3,2] [1,3,2,5,4,6] => [1,2,3] [1,3,2,5,6,4] => [1,2,3] [1,3,2,6,4,5] => [1,2,3] [1,3,2,6,5,4] => [1,2,2,1] [1,3,4,2,5,6] => [1,5] [1,3,4,2,6,5] => [1,3,2] [1,3,4,5,2,6] => [1,5] [1,3,4,5,6,2] => [1,5] [1,3,4,6,2,5] => [1,5] [1,3,4,6,5,2] => [1,4,1] [1,3,5,2,4,6] => [1,5] [1,3,5,2,6,4] => [1,3,2] [1,3,5,4,2,6] => [1,3,2] [1,3,5,4,6,2] => [1,3,2] [1,3,5,6,2,4] => [1,5] [1,3,5,6,4,2] => [1,4,1] [1,3,6,2,4,5] => [1,5] [1,3,6,2,5,4] => [1,4,1] [1,3,6,4,2,5] => [1,3,2] [1,3,6,4,5,2] => [1,4,1] [1,3,6,5,2,4] => [1,2,3] [1,3,6,5,4,2] => [1,2,2,1] [1,4,2,3,5,6] => [1,5] [1,4,2,3,6,5] => [1,3,2] [1,4,2,5,3,6] => [1,2,3] [1,4,2,5,6,3] => [1,2,3] [1,4,2,6,3,5] => [1,2,3] [1,4,2,6,5,3] => [1,2,2,1] [1,4,3,2,5,6] => [1,2,3] [1,4,3,2,6,5] => [1,2,1,2] [1,4,3,5,2,6] => [1,2,3] [1,4,3,5,6,2] => [1,2,3] [1,4,3,6,2,5] => [1,2,3] [1,4,3,6,5,2] => [1,2,2,1] [1,4,5,2,3,6] => [1,5] [1,4,5,2,6,3] => [1,3,2] [1,4,5,3,2,6] => [1,3,2] [1,4,5,3,6,2] => [1,3,2] [1,4,5,6,2,3] => [1,5] [1,4,5,6,3,2] => [1,4,1] [1,4,6,2,3,5] => [1,5] [1,4,6,2,5,3] => [1,4,1] [1,4,6,3,2,5] => [1,3,2] [1,4,6,3,5,2] => [1,4,1] [1,4,6,5,2,3] => [1,2,3] [1,4,6,5,3,2] => [1,2,2,1] [1,5,2,3,4,6] => [1,5] [1,5,2,3,6,4] => [1,3,2] [1,5,2,4,3,6] => [1,3,2] [1,5,2,4,6,3] => [1,3,2] [1,5,2,6,3,4] => [1,2,3] [1,5,2,6,4,3] => [1,2,2,1] [1,5,3,2,4,6] => [1,2,3] [1,5,3,2,6,4] => [1,2,1,2] [1,5,3,4,2,6] => [1,3,2] [1,5,3,4,6,2] => [1,3,2] [1,5,3,6,2,4] => [1,2,3] [1,5,3,6,4,2] => [1,2,2,1] [1,5,4,2,3,6] => [1,1,4] [1,5,4,2,6,3] => [1,1,2,2] [1,5,4,3,2,6] => [1,1,2,2] [1,5,4,3,6,2] => [1,1,2,2] [1,5,4,6,2,3] => [1,1,4] [1,5,4,6,3,2] => [1,1,3,1] [1,5,6,2,3,4] => [1,5] [1,5,6,2,4,3] => [1,4,1] [1,5,6,3,2,4] => [1,3,2] [1,5,6,3,4,2] => [1,4,1] [1,5,6,4,2,3] => [1,3,2] [1,5,6,4,3,2] => [1,3,1,1] [1,6,2,3,4,5] => [1,5] [1,6,2,3,5,4] => [1,4,1] [1,6,2,4,3,5] => [1,3,2] [1,6,2,4,5,3] => [1,4,1] [1,6,2,5,3,4] => [1,2,3] [1,6,2,5,4,3] => [1,2,2,1] [1,6,3,2,4,5] => [1,2,3] [1,6,3,2,5,4] => [1,2,2,1] [1,6,3,4,2,5] => [1,3,2] [1,6,3,4,5,2] => [1,4,1] [1,6,3,5,2,4] => [1,2,3] [1,6,3,5,4,2] => [1,2,2,1] [1,6,4,2,3,5] => [1,1,4] [1,6,4,2,5,3] => [1,1,3,1] [1,6,4,3,2,5] => [1,1,2,2] [1,6,4,3,5,2] => [1,1,3,1] [1,6,4,5,2,3] => [1,1,4] [1,6,4,5,3,2] => [1,1,3,1] [1,6,5,2,3,4] => [1,1,4] [1,6,5,2,4,3] => [1,1,3,1] [1,6,5,3,2,4] => [1,1,2,2] [1,6,5,3,4,2] => [1,1,3,1] [1,6,5,4,2,3] => [1,1,2,2] [1,6,5,4,3,2] => [1,1,2,1,1] [2,1,3,4,5,6] => [6] [2,1,3,4,6,5] => [4,2] [2,1,3,5,4,6] => [3,3] [2,1,3,5,6,4] => [3,3] [2,1,3,6,4,5] => [3,3] [2,1,3,6,5,4] => [3,2,1] [2,1,4,3,5,6] => [2,4] [2,1,4,3,6,5] => [2,2,2] [2,1,4,5,3,6] => [2,4] [2,1,4,5,6,3] => [2,4] [2,1,4,6,3,5] => [2,4] [2,1,4,6,5,3] => [2,3,1] [2,1,5,3,4,6] => [2,4] [2,1,5,3,6,4] => [2,2,2] [2,1,5,4,3,6] => [2,2,2] [2,1,5,4,6,3] => [2,2,2] [2,1,5,6,3,4] => [2,4] [2,1,5,6,4,3] => [2,3,1] [2,1,6,3,4,5] => [2,4] [2,1,6,3,5,4] => [2,3,1] [2,1,6,4,3,5] => [2,2,2] [2,1,6,4,5,3] => [2,3,1] [2,1,6,5,3,4] => [2,1,3] [2,1,6,5,4,3] => [2,1,2,1] [2,3,1,4,5,6] => [6] [2,3,1,4,6,5] => [4,2] [2,3,1,5,4,6] => [3,3] [2,3,1,5,6,4] => [3,3] [2,3,1,6,4,5] => [3,3] [2,3,1,6,5,4] => [3,2,1] [2,3,4,1,5,6] => [6] [2,3,4,1,6,5] => [4,2] [2,3,4,5,1,6] => [6] [2,3,4,5,6,1] => [6] [2,3,4,6,1,5] => [6] [2,3,4,6,5,1] => [5,1] [2,3,5,1,4,6] => [6] [2,3,5,1,6,4] => [4,2] [2,3,5,4,1,6] => [4,2] [2,3,5,4,6,1] => [4,2] [2,3,5,6,1,4] => [6] [2,3,5,6,4,1] => [5,1] [2,3,6,1,4,5] => [6] [2,3,6,1,5,4] => [5,1] [2,3,6,4,1,5] => [4,2] [2,3,6,4,5,1] => [5,1] [2,3,6,5,1,4] => [3,3] [2,3,6,5,4,1] => [3,2,1] [2,4,1,3,5,6] => [6] [2,4,1,3,6,5] => [4,2] [2,4,1,5,3,6] => [3,3] [2,4,1,5,6,3] => [3,3] [2,4,1,6,3,5] => [3,3] [2,4,1,6,5,3] => [3,2,1] [2,4,3,1,5,6] => [3,3] [2,4,3,1,6,5] => [3,1,2] [2,4,3,5,1,6] => [3,3] [2,4,3,5,6,1] => [3,3] [2,4,3,6,1,5] => [3,3] [2,4,3,6,5,1] => [3,2,1] [2,4,5,1,3,6] => [6] [2,4,5,1,6,3] => [4,2] [2,4,5,3,1,6] => [4,2] [2,4,5,3,6,1] => [4,2] [2,4,5,6,1,3] => [6] [2,4,5,6,3,1] => [5,1] [2,4,6,1,3,5] => [6] [2,4,6,1,5,3] => [5,1] [2,4,6,3,1,5] => [4,2] [2,4,6,3,5,1] => [5,1] [2,4,6,5,1,3] => [3,3] [2,4,6,5,3,1] => [3,2,1] [2,5,1,3,4,6] => [6] [2,5,1,3,6,4] => [4,2] [2,5,1,4,3,6] => [4,2] [2,5,1,4,6,3] => [4,2] [2,5,1,6,3,4] => [3,3] [2,5,1,6,4,3] => [3,2,1] [2,5,3,1,4,6] => [3,3] [2,5,3,1,6,4] => [3,1,2] [2,5,3,4,1,6] => [4,2] [2,5,3,4,6,1] => [4,2] [2,5,3,6,1,4] => [3,3] [2,5,3,6,4,1] => [3,2,1] [2,5,4,1,3,6] => [2,4] [2,5,4,1,6,3] => [2,2,2] [2,5,4,3,1,6] => [2,2,2] [2,5,4,3,6,1] => [2,2,2] [2,5,4,6,1,3] => [2,4] [2,5,4,6,3,1] => [2,3,1] [2,5,6,1,3,4] => [6] [2,5,6,1,4,3] => [5,1] [2,5,6,3,1,4] => [4,2] [2,5,6,3,4,1] => [5,1] [2,5,6,4,1,3] => [4,2] [2,5,6,4,3,1] => [4,1,1] [2,6,1,3,4,5] => [6] [2,6,1,3,5,4] => [5,1] [2,6,1,4,3,5] => [4,2] [2,6,1,4,5,3] => [5,1] [2,6,1,5,3,4] => [3,3] [2,6,1,5,4,3] => [3,2,1] [2,6,3,1,4,5] => [3,3] [2,6,3,1,5,4] => [3,2,1] [2,6,3,4,1,5] => [4,2] [2,6,3,4,5,1] => [5,1] [2,6,3,5,1,4] => [3,3] [2,6,3,5,4,1] => [3,2,1] [2,6,4,1,3,5] => [2,4] [2,6,4,1,5,3] => [2,3,1] [2,6,4,3,1,5] => [2,2,2] [2,6,4,3,5,1] => [2,3,1] [2,6,4,5,1,3] => [2,4] [2,6,4,5,3,1] => [2,3,1] [2,6,5,1,3,4] => [2,4] [2,6,5,1,4,3] => [2,3,1] [2,6,5,3,1,4] => [2,2,2] [2,6,5,3,4,1] => [2,3,1] [2,6,5,4,1,3] => [2,2,2] [2,6,5,4,3,1] => [2,2,1,1] [3,1,2,4,5,6] => [6] [3,1,2,4,6,5] => [4,2] [3,1,2,5,4,6] => [3,3] [3,1,2,5,6,4] => [3,3] [3,1,2,6,4,5] => [3,3] [3,1,2,6,5,4] => [3,2,1] [3,1,4,2,5,6] => [2,4] [3,1,4,2,6,5] => [2,2,2] [3,1,4,5,2,6] => [2,4] [3,1,4,5,6,2] => [2,4] [3,1,4,6,2,5] => [2,4] [3,1,4,6,5,2] => [2,3,1] [3,1,5,2,4,6] => [2,4] [3,1,5,2,6,4] => [2,2,2] [3,1,5,4,2,6] => [2,2,2] [3,1,5,4,6,2] => [2,2,2] [3,1,5,6,2,4] => [2,4] [3,1,5,6,4,2] => [2,3,1] [3,1,6,2,4,5] => [2,4] [3,1,6,2,5,4] => [2,3,1] [3,1,6,4,2,5] => [2,2,2] [3,1,6,4,5,2] => [2,3,1] [3,1,6,5,2,4] => [2,1,3] [3,1,6,5,4,2] => [2,1,2,1] [3,2,1,4,5,6] => [2,4] [3,2,1,4,6,5] => [2,2,2] [3,2,1,5,4,6] => [2,1,3] [3,2,1,5,6,4] => [2,1,3] [3,2,1,6,4,5] => [2,1,3] [3,2,1,6,5,4] => [2,1,2,1] [3,2,4,1,5,6] => [2,4] [3,2,4,1,6,5] => [2,2,2] [3,2,4,5,1,6] => [2,4] [3,2,4,5,6,1] => [2,4] [3,2,4,6,1,5] => [2,4] [3,2,4,6,5,1] => [2,3,1] [3,2,5,1,4,6] => [2,4] [3,2,5,1,6,4] => [2,2,2] [3,2,5,4,1,6] => [2,2,2] [3,2,5,4,6,1] => [2,2,2] [3,2,5,6,1,4] => [2,4] [3,2,5,6,4,1] => [2,3,1] [3,2,6,1,4,5] => [2,4] [3,2,6,1,5,4] => [2,3,1] [3,2,6,4,1,5] => [2,2,2] [3,2,6,4,5,1] => [2,3,1] [3,2,6,5,1,4] => [2,1,3] [3,2,6,5,4,1] => [2,1,2,1] [3,4,1,2,5,6] => [6] [3,4,1,2,6,5] => [4,2] [3,4,1,5,2,6] => [3,3] [3,4,1,5,6,2] => [3,3] [3,4,1,6,2,5] => [3,3] [3,4,1,6,5,2] => [3,2,1] [3,4,2,1,5,6] => [3,3] [3,4,2,1,6,5] => [3,1,2] [3,4,2,5,1,6] => [3,3] [3,4,2,5,6,1] => [3,3] [3,4,2,6,1,5] => [3,3] [3,4,2,6,5,1] => [3,2,1] [3,4,5,1,2,6] => [6] [3,4,5,1,6,2] => [4,2] [3,4,5,2,1,6] => [4,2] [3,4,5,2,6,1] => [4,2] [3,4,5,6,1,2] => [6] [3,4,5,6,2,1] => [5,1] [3,4,6,1,2,5] => [6] [3,4,6,1,5,2] => [5,1] [3,4,6,2,1,5] => [4,2] [3,4,6,2,5,1] => [5,1] [3,4,6,5,1,2] => [3,3] [3,4,6,5,2,1] => [3,2,1] [3,5,1,2,4,6] => [6] [3,5,1,2,6,4] => [4,2] [3,5,1,4,2,6] => [4,2] [3,5,1,4,6,2] => [4,2] [3,5,1,6,2,4] => [3,3] [3,5,1,6,4,2] => [3,2,1] [3,5,2,1,4,6] => [3,3] [3,5,2,1,6,4] => [3,1,2] [3,5,2,4,1,6] => [4,2] [3,5,2,4,6,1] => [4,2] [3,5,2,6,1,4] => [3,3] [3,5,2,6,4,1] => [3,2,1] [3,5,4,1,2,6] => [2,4] [3,5,4,1,6,2] => [2,2,2] [3,5,4,2,1,6] => [2,2,2] [3,5,4,2,6,1] => [2,2,2] [3,5,4,6,1,2] => [2,4] [3,5,4,6,2,1] => [2,3,1] [3,5,6,1,2,4] => [6] [3,5,6,1,4,2] => [5,1] [3,5,6,2,1,4] => [4,2] [3,5,6,2,4,1] => [5,1] [3,5,6,4,1,2] => [4,2] [3,5,6,4,2,1] => [4,1,1] [3,6,1,2,4,5] => [6] [3,6,1,2,5,4] => [5,1] [3,6,1,4,2,5] => [4,2] [3,6,1,4,5,2] => [5,1] [3,6,1,5,2,4] => [3,3] [3,6,1,5,4,2] => [3,2,1] [3,6,2,1,4,5] => [3,3] [3,6,2,1,5,4] => [3,2,1] [3,6,2,4,1,5] => [4,2] [3,6,2,4,5,1] => [5,1] [3,6,2,5,1,4] => [3,3] [3,6,2,5,4,1] => [3,2,1] [3,6,4,1,2,5] => [2,4] [3,6,4,1,5,2] => [2,3,1] [3,6,4,2,1,5] => [2,2,2] [3,6,4,2,5,1] => [2,3,1] [3,6,4,5,1,2] => [2,4] [3,6,4,5,2,1] => [2,3,1] [3,6,5,1,2,4] => [2,4] [3,6,5,1,4,2] => [2,3,1] [3,6,5,2,1,4] => [2,2,2] [3,6,5,2,4,1] => [2,3,1] [3,6,5,4,1,2] => [2,2,2] [3,6,5,4,2,1] => [2,2,1,1] [4,1,2,3,5,6] => [6] [4,1,2,3,6,5] => [4,2] [4,1,2,5,3,6] => [3,3] [4,1,2,5,6,3] => [3,3] [4,1,2,6,3,5] => [3,3] [4,1,2,6,5,3] => [3,2,1] [4,1,3,2,5,6] => [3,3] [4,1,3,2,6,5] => [3,1,2] [4,1,3,5,2,6] => [3,3] [4,1,3,5,6,2] => [3,3] [4,1,3,6,2,5] => [3,3] [4,1,3,6,5,2] => [3,2,1] [4,1,5,2,3,6] => [2,4] [4,1,5,2,6,3] => [2,2,2] [4,1,5,3,2,6] => [2,2,2] [4,1,5,3,6,2] => [2,2,2] [4,1,5,6,2,3] => [2,4] [4,1,5,6,3,2] => [2,3,1] [4,1,6,2,3,5] => [2,4] [4,1,6,2,5,3] => [2,3,1] [4,1,6,3,2,5] => [2,2,2] [4,1,6,3,5,2] => [2,3,1] [4,1,6,5,2,3] => [2,1,3] [4,1,6,5,3,2] => [2,1,2,1] [4,2,1,3,5,6] => [2,4] [4,2,1,3,6,5] => [2,2,2] [4,2,1,5,3,6] => [2,1,3] [4,2,1,5,6,3] => [2,1,3] [4,2,1,6,3,5] => [2,1,3] [4,2,1,6,5,3] => [2,1,2,1] [4,2,3,1,5,6] => [3,3] [4,2,3,1,6,5] => [3,1,2] [4,2,3,5,1,6] => [3,3] [4,2,3,5,6,1] => [3,3] [4,2,3,6,1,5] => [3,3] [4,2,3,6,5,1] => [3,2,1] [4,2,5,1,3,6] => [2,4] [4,2,5,1,6,3] => [2,2,2] [4,2,5,3,1,6] => [2,2,2] [4,2,5,3,6,1] => [2,2,2] [4,2,5,6,1,3] => [2,4] [4,2,5,6,3,1] => [2,3,1] [4,2,6,1,3,5] => [2,4] [4,2,6,1,5,3] => [2,3,1] [4,2,6,3,1,5] => [2,2,2] [4,2,6,3,5,1] => [2,3,1] [4,2,6,5,1,3] => [2,1,3] [4,2,6,5,3,1] => [2,1,2,1] [4,3,1,2,5,6] => [1,5] [4,3,1,2,6,5] => [1,3,2] [4,3,1,5,2,6] => [1,2,3] [4,3,1,5,6,2] => [1,2,3] [4,3,1,6,2,5] => [1,2,3] [4,3,1,6,5,2] => [1,2,2,1] [4,3,2,1,5,6] => [1,2,3] [4,3,2,1,6,5] => [1,2,1,2] [4,3,2,5,1,6] => [1,2,3] [4,3,2,5,6,1] => [1,2,3] [4,3,2,6,1,5] => [1,2,3] [4,3,2,6,5,1] => [1,2,2,1] [4,3,5,1,2,6] => [1,5] [4,3,5,1,6,2] => [1,3,2] [4,3,5,2,1,6] => [1,3,2] [4,3,5,2,6,1] => [1,3,2] [4,3,5,6,1,2] => [1,5] [4,3,5,6,2,1] => [1,4,1] [4,3,6,1,2,5] => [1,5] [4,3,6,1,5,2] => [1,4,1] [4,3,6,2,1,5] => [1,3,2] [4,3,6,2,5,1] => [1,4,1] [4,3,6,5,1,2] => [1,2,3] [4,3,6,5,2,1] => [1,2,2,1] [4,5,1,2,3,6] => [6] [4,5,1,2,6,3] => [4,2] [4,5,1,3,2,6] => [4,2] [4,5,1,3,6,2] => [4,2] [4,5,1,6,2,3] => [3,3] [4,5,1,6,3,2] => [3,2,1] [4,5,2,1,3,6] => [3,3] [4,5,2,1,6,3] => [3,1,2] [4,5,2,3,1,6] => [4,2] [4,5,2,3,6,1] => [4,2] [4,5,2,6,1,3] => [3,3] [4,5,2,6,3,1] => [3,2,1] [4,5,3,1,2,6] => [3,3] [4,5,3,1,6,2] => [3,1,2] [4,5,3,2,1,6] => [3,1,2] [4,5,3,2,6,1] => [3,1,2] [4,5,3,6,1,2] => [3,3] [4,5,3,6,2,1] => [3,2,1] [4,5,6,1,2,3] => [6] [4,5,6,1,3,2] => [5,1] [4,5,6,2,1,3] => [4,2] [4,5,6,2,3,1] => [5,1] [4,5,6,3,1,2] => [4,2] [4,5,6,3,2,1] => [4,1,1] [4,6,1,2,3,5] => [6] [4,6,1,2,5,3] => [5,1] [4,6,1,3,2,5] => [4,2] [4,6,1,3,5,2] => [5,1] [4,6,1,5,2,3] => [3,3] [4,6,1,5,3,2] => [3,2,1] [4,6,2,1,3,5] => [3,3] [4,6,2,1,5,3] => [3,2,1] [4,6,2,3,1,5] => [4,2] [4,6,2,3,5,1] => [5,1] [4,6,2,5,1,3] => [3,3] [4,6,2,5,3,1] => [3,2,1] [4,6,3,1,2,5] => [3,3] [4,6,3,1,5,2] => [3,2,1] [4,6,3,2,1,5] => [3,1,2] [4,6,3,2,5,1] => [3,2,1] [4,6,3,5,1,2] => [3,3] [4,6,3,5,2,1] => [3,2,1] [4,6,5,1,2,3] => [2,4] [4,6,5,1,3,2] => [2,3,1] [4,6,5,2,1,3] => [2,2,2] [4,6,5,2,3,1] => [2,3,1] [4,6,5,3,1,2] => [2,2,2] [4,6,5,3,2,1] => [2,2,1,1] [5,1,2,3,4,6] => [6] [5,1,2,3,6,4] => [4,2] [5,1,2,4,3,6] => [4,2] [5,1,2,4,6,3] => [4,2] [5,1,2,6,3,4] => [3,3] [5,1,2,6,4,3] => [3,2,1] [5,1,3,2,4,6] => [3,3] [5,1,3,2,6,4] => [3,1,2] [5,1,3,4,2,6] => [4,2] [5,1,3,4,6,2] => [4,2] [5,1,3,6,2,4] => [3,3] [5,1,3,6,4,2] => [3,2,1] [5,1,4,2,3,6] => [2,4] [5,1,4,2,6,3] => [2,2,2] [5,1,4,3,2,6] => [2,2,2] [5,1,4,3,6,2] => [2,2,2] [5,1,4,6,2,3] => [2,4] [5,1,4,6,3,2] => [2,3,1] [5,1,6,2,3,4] => [2,4] [5,1,6,2,4,3] => [2,3,1] [5,1,6,3,2,4] => [2,2,2] [5,1,6,3,4,2] => [2,3,1] [5,1,6,4,2,3] => [2,2,2] [5,1,6,4,3,2] => [2,2,1,1] [5,2,1,3,4,6] => [2,4] [5,2,1,3,6,4] => [2,2,2] [5,2,1,4,3,6] => [2,2,2] [5,2,1,4,6,3] => [2,2,2] [5,2,1,6,3,4] => [2,1,3] [5,2,1,6,4,3] => [2,1,2,1] [5,2,3,1,4,6] => [3,3] [5,2,3,1,6,4] => [3,1,2] [5,2,3,4,1,6] => [4,2] [5,2,3,4,6,1] => [4,2] [5,2,3,6,1,4] => [3,3] [5,2,3,6,4,1] => [3,2,1] [5,2,4,1,3,6] => [2,4] [5,2,4,1,6,3] => [2,2,2] [5,2,4,3,1,6] => [2,2,2] [5,2,4,3,6,1] => [2,2,2] [5,2,4,6,1,3] => [2,4] [5,2,4,6,3,1] => [2,3,1] [5,2,6,1,3,4] => [2,4] [5,2,6,1,4,3] => [2,3,1] [5,2,6,3,1,4] => [2,2,2] [5,2,6,3,4,1] => [2,3,1] [5,2,6,4,1,3] => [2,2,2] [5,2,6,4,3,1] => [2,2,1,1] [5,3,1,2,4,6] => [1,5] [5,3,1,2,6,4] => [1,3,2] [5,3,1,4,2,6] => [1,3,2] [5,3,1,4,6,2] => [1,3,2] [5,3,1,6,2,4] => [1,2,3] [5,3,1,6,4,2] => [1,2,2,1] [5,3,2,1,4,6] => [1,2,3] [5,3,2,1,6,4] => [1,2,1,2] [5,3,2,4,1,6] => [1,3,2] [5,3,2,4,6,1] => [1,3,2] [5,3,2,6,1,4] => [1,2,3] [5,3,2,6,4,1] => [1,2,2,1] [5,3,4,1,2,6] => [1,5] [5,3,4,1,6,2] => [1,3,2] [5,3,4,2,1,6] => [1,3,2] [5,3,4,2,6,1] => [1,3,2] [5,3,4,6,1,2] => [1,5] [5,3,4,6,2,1] => [1,4,1] [5,3,6,1,2,4] => [1,5] [5,3,6,1,4,2] => [1,4,1] [5,3,6,2,1,4] => [1,3,2] [5,3,6,2,4,1] => [1,4,1] [5,3,6,4,1,2] => [1,3,2] [5,3,6,4,2,1] => [1,3,1,1] [5,4,1,2,3,6] => [1,5] [5,4,1,2,6,3] => [1,3,2] [5,4,1,3,2,6] => [1,3,2] [5,4,1,3,6,2] => [1,3,2] [5,4,1,6,2,3] => [1,2,3] [5,4,1,6,3,2] => [1,2,2,1] [5,4,2,1,3,6] => [1,2,3] [5,4,2,1,6,3] => [1,2,1,2] [5,4,2,3,1,6] => [1,3,2] [5,4,2,3,6,1] => [1,3,2] [5,4,2,6,1,3] => [1,2,3] [5,4,2,6,3,1] => [1,2,2,1] [5,4,3,1,2,6] => [1,2,3] [5,4,3,1,6,2] => [1,2,1,2] [5,4,3,2,1,6] => [1,2,1,2] [5,4,3,2,6,1] => [1,2,1,2] [5,4,3,6,1,2] => [1,2,3] [5,4,3,6,2,1] => [1,2,2,1] [5,4,6,1,2,3] => [1,5] [5,4,6,1,3,2] => [1,4,1] [5,4,6,2,1,3] => [1,3,2] [5,4,6,2,3,1] => [1,4,1] [5,4,6,3,1,2] => [1,3,2] [5,4,6,3,2,1] => [1,3,1,1] [5,6,1,2,3,4] => [6] [5,6,1,2,4,3] => [5,1] [5,6,1,3,2,4] => [4,2] [5,6,1,3,4,2] => [5,1] [5,6,1,4,2,3] => [4,2] [5,6,1,4,3,2] => [4,1,1] [5,6,2,1,3,4] => [3,3] [5,6,2,1,4,3] => [3,2,1] [5,6,2,3,1,4] => [4,2] [5,6,2,3,4,1] => [5,1] [5,6,2,4,1,3] => [4,2] [5,6,2,4,3,1] => [4,1,1] [5,6,3,1,2,4] => [3,3] [5,6,3,1,4,2] => [3,2,1] [5,6,3,2,1,4] => [3,1,2] [5,6,3,2,4,1] => [3,2,1] [5,6,3,4,1,2] => [4,2] [5,6,3,4,2,1] => [4,1,1] [5,6,4,1,2,3] => [2,4] [5,6,4,1,3,2] => [2,3,1] [5,6,4,2,1,3] => [2,2,2] [5,6,4,2,3,1] => [2,3,1] [5,6,4,3,1,2] => [2,2,2] [5,6,4,3,2,1] => [2,2,1,1] [6,1,2,3,4,5] => [6] [6,1,2,3,5,4] => [5,1] [6,1,2,4,3,5] => [4,2] [6,1,2,4,5,3] => [5,1] [6,1,2,5,3,4] => [3,3] [6,1,2,5,4,3] => [3,2,1] [6,1,3,2,4,5] => [3,3] [6,1,3,2,5,4] => [3,2,1] [6,1,3,4,2,5] => [4,2] [6,1,3,4,5,2] => [5,1] [6,1,3,5,2,4] => [3,3] [6,1,3,5,4,2] => [3,2,1] [6,1,4,2,3,5] => [2,4] [6,1,4,2,5,3] => [2,3,1] [6,1,4,3,2,5] => [2,2,2] [6,1,4,3,5,2] => [2,3,1] [6,1,4,5,2,3] => [2,4] [6,1,4,5,3,2] => [2,3,1] [6,1,5,2,3,4] => [2,4] [6,1,5,2,4,3] => [2,3,1] [6,1,5,3,2,4] => [2,2,2] [6,1,5,3,4,2] => [2,3,1] [6,1,5,4,2,3] => [2,2,2] [6,1,5,4,3,2] => [2,2,1,1] [6,2,1,3,4,5] => [2,4] [6,2,1,3,5,4] => [2,3,1] [6,2,1,4,3,5] => [2,2,2] [6,2,1,4,5,3] => [2,3,1] [6,2,1,5,3,4] => [2,1,3] [6,2,1,5,4,3] => [2,1,2,1] [6,2,3,1,4,5] => [3,3] [6,2,3,1,5,4] => [3,2,1] [6,2,3,4,1,5] => [4,2] [6,2,3,4,5,1] => [5,1] [6,2,3,5,1,4] => [3,3] [6,2,3,5,4,1] => [3,2,1] [6,2,4,1,3,5] => [2,4] [6,2,4,1,5,3] => [2,3,1] [6,2,4,3,1,5] => [2,2,2] [6,2,4,3,5,1] => [2,3,1] [6,2,4,5,1,3] => [2,4] [6,2,4,5,3,1] => [2,3,1] [6,2,5,1,3,4] => [2,4] [6,2,5,1,4,3] => [2,3,1] [6,2,5,3,1,4] => [2,2,2] [6,2,5,3,4,1] => [2,3,1] [6,2,5,4,1,3] => [2,2,2] [6,2,5,4,3,1] => [2,2,1,1] [6,3,1,2,4,5] => [1,5] [6,3,1,2,5,4] => [1,4,1] [6,3,1,4,2,5] => [1,3,2] [6,3,1,4,5,2] => [1,4,1] [6,3,1,5,2,4] => [1,2,3] [6,3,1,5,4,2] => [1,2,2,1] [6,3,2,1,4,5] => [1,2,3] [6,3,2,1,5,4] => [1,2,2,1] [6,3,2,4,1,5] => [1,3,2] [6,3,2,4,5,1] => [1,4,1] [6,3,2,5,1,4] => [1,2,3] [6,3,2,5,4,1] => [1,2,2,1] [6,3,4,1,2,5] => [1,5] [6,3,4,1,5,2] => [1,4,1] [6,3,4,2,1,5] => [1,3,2] [6,3,4,2,5,1] => [1,4,1] [6,3,4,5,1,2] => [1,5] [6,3,4,5,2,1] => [1,4,1] [6,3,5,1,2,4] => [1,5] [6,3,5,1,4,2] => [1,4,1] [6,3,5,2,1,4] => [1,3,2] [6,3,5,2,4,1] => [1,4,1] [6,3,5,4,1,2] => [1,3,2] [6,3,5,4,2,1] => [1,3,1,1] [6,4,1,2,3,5] => [1,5] [6,4,1,2,5,3] => [1,4,1] [6,4,1,3,2,5] => [1,3,2] [6,4,1,3,5,2] => [1,4,1] [6,4,1,5,2,3] => [1,2,3] [6,4,1,5,3,2] => [1,2,2,1] [6,4,2,1,3,5] => [1,2,3] [6,4,2,1,5,3] => [1,2,2,1] [6,4,2,3,1,5] => [1,3,2] [6,4,2,3,5,1] => [1,4,1] [6,4,2,5,1,3] => [1,2,3] [6,4,2,5,3,1] => [1,2,2,1] [6,4,3,1,2,5] => [1,2,3] [6,4,3,1,5,2] => [1,2,2,1] [6,4,3,2,1,5] => [1,2,1,2] [6,4,3,2,5,1] => [1,2,2,1] [6,4,3,5,1,2] => [1,2,3] [6,4,3,5,2,1] => [1,2,2,1] [6,4,5,1,2,3] => [1,5] [6,4,5,1,3,2] => [1,4,1] [6,4,5,2,1,3] => [1,3,2] [6,4,5,2,3,1] => [1,4,1] [6,4,5,3,1,2] => [1,3,2] [6,4,5,3,2,1] => [1,3,1,1] [6,5,1,2,3,4] => [1,5] [6,5,1,2,4,3] => [1,4,1] [6,5,1,3,2,4] => [1,3,2] [6,5,1,3,4,2] => [1,4,1] [6,5,1,4,2,3] => [1,3,2] [6,5,1,4,3,2] => [1,3,1,1] [6,5,2,1,3,4] => [1,2,3] [6,5,2,1,4,3] => [1,2,2,1] [6,5,2,3,1,4] => [1,3,2] [6,5,2,3,4,1] => [1,4,1] [6,5,2,4,1,3] => [1,3,2] [6,5,2,4,3,1] => [1,3,1,1] [6,5,3,1,2,4] => [1,2,3] [6,5,3,1,4,2] => [1,2,2,1] [6,5,3,2,1,4] => [1,2,1,2] [6,5,3,2,4,1] => [1,2,2,1] [6,5,3,4,1,2] => [1,3,2] [6,5,3,4,2,1] => [1,3,1,1] [6,5,4,1,2,3] => [1,1,4] [6,5,4,1,3,2] => [1,1,3,1] [6,5,4,2,1,3] => [1,1,2,2] [6,5,4,2,3,1] => [1,1,3,1] [6,5,4,3,1,2] => [1,1,2,2] [6,5,4,3,2,1] => [1,1,2,1,1] [1,2,3,4,5,6,7] => [7] [1,2,3,4,5,7,6] => [5,2] [1,2,3,4,6,5,7] => [4,3] [1,2,3,4,6,7,5] => [4,3] [1,2,3,4,7,5,6] => [4,3] [1,2,3,4,7,6,5] => [4,2,1] [1,2,3,5,4,6,7] => [3,4] [1,2,3,5,4,7,6] => [3,2,2] [1,2,3,5,6,4,7] => [3,4] [1,2,3,5,6,7,4] => [3,4] [1,2,3,5,7,4,6] => [3,4] [1,2,3,5,7,6,4] => [3,3,1] [1,2,3,6,4,5,7] => [3,4] [1,2,3,6,4,7,5] => [3,2,2] [1,2,3,6,5,4,7] => [3,2,2] [1,2,3,6,5,7,4] => [3,2,2] [1,2,3,6,7,4,5] => [3,4] [1,2,3,6,7,5,4] => [3,3,1] [1,2,3,7,4,5,6] => [3,4] [1,2,3,7,4,6,5] => [3,3,1] [1,2,3,7,5,4,6] => [3,2,2] [1,2,3,7,5,6,4] => [3,3,1] [1,2,3,7,6,4,5] => [3,1,3] [1,2,3,7,6,5,4] => [3,1,2,1] [1,2,4,3,5,6,7] => [2,5] [1,2,4,3,5,7,6] => [2,3,2] [1,2,4,3,6,5,7] => [2,2,3] [1,2,4,3,6,7,5] => [2,2,3] [1,2,4,3,7,5,6] => [2,2,3] [1,2,4,3,7,6,5] => [2,2,2,1] [1,2,4,5,3,6,7] => [2,5] [1,2,4,5,3,7,6] => [2,3,2] [1,2,4,5,6,3,7] => [2,5] [1,2,4,5,6,7,3] => [2,5] [1,2,4,5,7,3,6] => [2,5] [1,2,4,5,7,6,3] => [2,4,1] [1,2,4,6,3,5,7] => [2,5] [1,2,4,6,3,7,5] => [2,3,2] [1,2,4,6,5,3,7] => [2,3,2] [1,2,4,6,5,7,3] => [2,3,2] [1,2,4,6,7,3,5] => [2,5] [1,2,4,6,7,5,3] => [2,4,1] [1,2,4,7,3,5,6] => [2,5] [1,2,4,7,3,6,5] => [2,4,1] [1,2,4,7,5,3,6] => [2,3,2] [1,2,4,7,5,6,3] => [2,4,1] [1,2,4,7,6,3,5] => [2,2,3] [1,2,4,7,6,5,3] => [2,2,2,1] [1,2,5,3,4,6,7] => [2,5] [1,2,5,3,4,7,6] => [2,3,2] [1,2,5,3,6,4,7] => [2,2,3] [1,2,5,3,6,7,4] => [2,2,3] [1,2,5,3,7,4,6] => [2,2,3] [1,2,5,3,7,6,4] => [2,2,2,1] [1,2,5,4,3,6,7] => [2,2,3] [1,2,5,4,3,7,6] => [2,2,1,2] [1,2,5,4,6,3,7] => [2,2,3] [1,2,5,4,6,7,3] => [2,2,3] [1,2,5,4,7,3,6] => [2,2,3] [1,2,5,4,7,6,3] => [2,2,2,1] [1,2,5,6,3,4,7] => [2,5] [1,2,5,6,3,7,4] => [2,3,2] [1,2,5,6,4,3,7] => [2,3,2] [1,2,5,6,4,7,3] => [2,3,2] [1,2,5,6,7,3,4] => [2,5] [1,2,5,6,7,4,3] => [2,4,1] [1,2,5,7,3,4,6] => [2,5] [1,2,5,7,3,6,4] => [2,4,1] [1,2,5,7,4,3,6] => [2,3,2] [1,2,5,7,4,6,3] => [2,4,1] [1,2,5,7,6,3,4] => [2,2,3] [1,2,5,7,6,4,3] => [2,2,2,1] [1,2,6,3,4,5,7] => [2,5] [1,2,6,3,4,7,5] => [2,3,2] [1,2,6,3,5,4,7] => [2,3,2] [1,2,6,3,5,7,4] => [2,3,2] [1,2,6,3,7,4,5] => [2,2,3] [1,2,6,3,7,5,4] => [2,2,2,1] [1,2,6,4,3,5,7] => [2,2,3] [1,2,6,4,3,7,5] => [2,2,1,2] [1,2,6,4,5,3,7] => [2,3,2] [1,2,6,4,5,7,3] => [2,3,2] [1,2,6,4,7,3,5] => [2,2,3] [1,2,6,4,7,5,3] => [2,2,2,1] [1,2,6,5,3,4,7] => [2,1,4] [1,2,6,5,3,7,4] => [2,1,2,2] [1,2,6,5,4,3,7] => [2,1,2,2] [1,2,6,5,4,7,3] => [2,1,2,2] [1,2,6,5,7,3,4] => [2,1,4] [1,2,6,5,7,4,3] => [2,1,3,1] [1,2,6,7,3,4,5] => [2,5] [1,2,6,7,3,5,4] => [2,4,1] [1,2,6,7,4,3,5] => [2,3,2] [1,2,6,7,4,5,3] => [2,4,1] [1,2,6,7,5,3,4] => [2,3,2] [1,2,6,7,5,4,3] => [2,3,1,1] [1,2,7,3,4,5,6] => [2,5] [1,2,7,3,4,6,5] => [2,4,1] [1,2,7,3,5,4,6] => [2,3,2] [1,2,7,3,5,6,4] => [2,4,1] [1,2,7,3,6,4,5] => [2,2,3] [1,2,7,3,6,5,4] => [2,2,2,1] [1,2,7,4,3,5,6] => [2,2,3] [1,2,7,4,3,6,5] => [2,2,2,1] [1,2,7,4,5,3,6] => [2,3,2] [1,2,7,4,5,6,3] => [2,4,1] [1,2,7,4,6,3,5] => [2,2,3] [1,2,7,4,6,5,3] => [2,2,2,1] [1,2,7,5,3,4,6] => [2,1,4] [1,2,7,5,3,6,4] => [2,1,3,1] [1,2,7,5,4,3,6] => [2,1,2,2] [1,2,7,5,4,6,3] => [2,1,3,1] [1,2,7,5,6,3,4] => [2,1,4] [1,2,7,5,6,4,3] => [2,1,3,1] [1,2,7,6,3,4,5] => [2,1,4] [1,2,7,6,3,5,4] => [2,1,3,1] [1,2,7,6,4,3,5] => [2,1,2,2] [1,2,7,6,4,5,3] => [2,1,3,1] [1,2,7,6,5,3,4] => [2,1,2,2] [1,2,7,6,5,4,3] => [2,1,2,1,1] [1,3,2,4,5,6,7] => [1,6] [1,3,2,4,5,7,6] => [1,4,2] [1,3,2,4,6,5,7] => [1,3,3] [1,3,2,4,6,7,5] => [1,3,3] [1,3,2,4,7,5,6] => [1,3,3] [1,3,2,4,7,6,5] => [1,3,2,1] [1,3,2,5,4,6,7] => [1,2,4] [1,3,2,5,4,7,6] => [1,2,2,2] [1,3,2,5,6,4,7] => [1,2,4] [1,3,2,5,6,7,4] => [1,2,4] [1,3,2,5,7,4,6] => [1,2,4] [1,3,2,5,7,6,4] => [1,2,3,1] [1,3,2,6,4,5,7] => [1,2,4] [1,3,2,6,4,7,5] => [1,2,2,2] [1,3,2,6,5,4,7] => [1,2,2,2] [1,3,2,6,5,7,4] => [1,2,2,2] [1,3,2,6,7,4,5] => [1,2,4] [1,3,2,6,7,5,4] => [1,2,3,1] [1,3,2,7,4,5,6] => [1,2,4] [1,3,2,7,4,6,5] => [1,2,3,1] [1,3,2,7,5,4,6] => [1,2,2,2] [1,3,2,7,5,6,4] => [1,2,3,1] [1,3,2,7,6,4,5] => [1,2,1,3] [1,3,2,7,6,5,4] => [1,2,1,2,1] [1,3,4,2,5,6,7] => [1,6] [1,3,4,2,5,7,6] => [1,4,2] [1,3,4,2,6,5,7] => [1,3,3] [1,3,4,2,6,7,5] => [1,3,3] [1,3,4,2,7,5,6] => [1,3,3] [1,3,4,2,7,6,5] => [1,3,2,1] [1,3,4,5,2,6,7] => [1,6] [1,3,4,5,2,7,6] => [1,4,2] [1,3,4,5,6,2,7] => [1,6] [1,3,4,5,6,7,2] => [1,6] [1,3,4,5,7,2,6] => [1,6] [1,3,4,5,7,6,2] => [1,5,1] [1,3,4,6,2,5,7] => [1,6] [1,3,4,6,2,7,5] => [1,4,2] [1,3,4,6,5,2,7] => [1,4,2] [1,3,4,6,5,7,2] => [1,4,2] [1,3,4,6,7,2,5] => [1,6] [1,3,4,6,7,5,2] => [1,5,1] [1,3,4,7,2,5,6] => [1,6] [1,3,4,7,2,6,5] => [1,5,1] [1,3,4,7,5,2,6] => [1,4,2] [1,3,4,7,5,6,2] => [1,5,1] [1,3,4,7,6,2,5] => [1,3,3] [1,3,4,7,6,5,2] => [1,3,2,1] [1,3,5,2,4,6,7] => [1,6] [1,3,5,2,4,7,6] => [1,4,2] [1,3,5,2,6,4,7] => [1,3,3] [1,3,5,2,6,7,4] => [1,3,3] [1,3,5,2,7,4,6] => [1,3,3] [1,3,5,2,7,6,4] => [1,3,2,1] [1,3,5,4,2,6,7] => [1,3,3] [1,3,5,4,2,7,6] => [1,3,1,2] [1,3,5,4,6,2,7] => [1,3,3] [1,3,5,4,6,7,2] => [1,3,3] [1,3,5,4,7,2,6] => [1,3,3] [1,3,5,4,7,6,2] => [1,3,2,1] [1,3,5,6,2,4,7] => [1,6] [1,3,5,6,2,7,4] => [1,4,2] [1,3,5,6,4,2,7] => [1,4,2] [1,3,5,6,4,7,2] => [1,4,2] [1,3,5,6,7,2,4] => [1,6] [1,3,5,6,7,4,2] => [1,5,1] [1,3,5,7,2,4,6] => [1,6] [1,3,5,7,2,6,4] => [1,5,1] [1,3,5,7,4,2,6] => [1,4,2] [1,3,5,7,4,6,2] => [1,5,1] [1,3,5,7,6,2,4] => [1,3,3] [1,3,5,7,6,4,2] => [1,3,2,1] [1,3,6,2,4,5,7] => [1,6] [1,3,6,2,4,7,5] => [1,4,2] [1,3,6,2,5,4,7] => [1,4,2] [1,3,6,2,5,7,4] => [1,4,2] [1,3,6,2,7,4,5] => [1,3,3] [1,3,6,2,7,5,4] => [1,3,2,1] [1,3,6,4,2,5,7] => [1,3,3] [1,3,6,4,2,7,5] => [1,3,1,2] [1,3,6,4,5,2,7] => [1,4,2] [1,3,6,4,5,7,2] => [1,4,2] [1,3,6,4,7,2,5] => [1,3,3] [1,3,6,4,7,5,2] => [1,3,2,1] [1,3,6,5,2,4,7] => [1,2,4] [1,3,6,5,2,7,4] => [1,2,2,2] [1,3,6,5,4,2,7] => [1,2,2,2] [1,3,6,5,4,7,2] => [1,2,2,2] [1,3,6,5,7,2,4] => [1,2,4] [1,3,6,5,7,4,2] => [1,2,3,1] [1,3,6,7,2,4,5] => [1,6] [1,3,6,7,2,5,4] => [1,5,1] [1,3,6,7,4,2,5] => [1,4,2] [1,3,6,7,4,5,2] => [1,5,1] [1,3,6,7,5,2,4] => [1,4,2] [1,3,6,7,5,4,2] => [1,4,1,1] [1,3,7,2,4,5,6] => [1,6] [1,3,7,2,4,6,5] => [1,5,1] [1,3,7,2,5,4,6] => [1,4,2] [1,3,7,2,5,6,4] => [1,5,1] [1,3,7,2,6,4,5] => [1,3,3] [1,3,7,2,6,5,4] => [1,3,2,1] [1,3,7,4,2,5,6] => [1,3,3] [1,3,7,4,2,6,5] => [1,3,2,1] [1,3,7,4,5,2,6] => [1,4,2] [1,3,7,4,5,6,2] => [1,5,1] [1,3,7,4,6,2,5] => [1,3,3] [1,3,7,4,6,5,2] => [1,3,2,1] [1,3,7,5,2,4,6] => [1,2,4] [1,3,7,5,2,6,4] => [1,2,3,1] [1,3,7,5,4,2,6] => [1,2,2,2] [1,3,7,5,4,6,2] => [1,2,3,1] [1,3,7,5,6,2,4] => [1,2,4] [1,3,7,5,6,4,2] => [1,2,3,1] [1,3,7,6,2,4,5] => [1,2,4] [1,3,7,6,2,5,4] => [1,2,3,1] [1,3,7,6,4,2,5] => [1,2,2,2] [1,3,7,6,4,5,2] => [1,2,3,1] [1,3,7,6,5,2,4] => [1,2,2,2] [1,3,7,6,5,4,2] => [1,2,2,1,1] [1,4,2,3,5,6,7] => [1,6] [1,4,2,3,5,7,6] => [1,4,2] [1,4,2,3,6,5,7] => [1,3,3] [1,4,2,3,6,7,5] => [1,3,3] [1,4,2,3,7,5,6] => [1,3,3] [1,4,2,3,7,6,5] => [1,3,2,1] [1,4,2,5,3,6,7] => [1,2,4] [1,4,2,5,3,7,6] => [1,2,2,2] [1,4,2,5,6,3,7] => [1,2,4] [1,4,2,5,6,7,3] => [1,2,4] [1,4,2,5,7,3,6] => [1,2,4] [1,4,2,5,7,6,3] => [1,2,3,1] [1,4,2,6,3,5,7] => [1,2,4] [1,4,2,6,3,7,5] => [1,2,2,2] [1,4,2,6,5,3,7] => [1,2,2,2] [1,4,2,6,5,7,3] => [1,2,2,2] [1,4,2,6,7,3,5] => [1,2,4] [1,4,2,6,7,5,3] => [1,2,3,1] [1,4,2,7,3,5,6] => [1,2,4] [1,4,2,7,3,6,5] => [1,2,3,1] [1,4,2,7,5,3,6] => [1,2,2,2] [1,4,2,7,5,6,3] => [1,2,3,1] [1,4,2,7,6,3,5] => [1,2,1,3] [1,4,2,7,6,5,3] => [1,2,1,2,1] [1,4,3,2,5,6,7] => [1,2,4] [1,4,3,2,5,7,6] => [1,2,2,2] [1,4,3,2,6,5,7] => [1,2,1,3] [1,4,3,2,6,7,5] => [1,2,1,3] [1,4,3,2,7,5,6] => [1,2,1,3] [1,4,3,2,7,6,5] => [1,2,1,2,1] [1,4,3,5,2,6,7] => [1,2,4] [1,4,3,5,2,7,6] => [1,2,2,2] [1,4,3,5,6,2,7] => [1,2,4] [1,4,3,5,6,7,2] => [1,2,4] [1,4,3,5,7,2,6] => [1,2,4] [1,4,3,5,7,6,2] => [1,2,3,1] [1,4,3,6,2,5,7] => [1,2,4] [1,4,3,6,2,7,5] => [1,2,2,2] [1,4,3,6,5,2,7] => [1,2,2,2] [1,4,3,6,5,7,2] => [1,2,2,2] [1,4,3,6,7,2,5] => [1,2,4] [1,4,3,6,7,5,2] => [1,2,3,1] [1,4,3,7,2,5,6] => [1,2,4] [1,4,3,7,2,6,5] => [1,2,3,1] [1,4,3,7,5,2,6] => [1,2,2,2] [1,4,3,7,5,6,2] => [1,2,3,1] [1,4,3,7,6,2,5] => [1,2,1,3] [1,4,3,7,6,5,2] => [1,2,1,2,1] [1,4,5,2,3,6,7] => [1,6] [1,4,5,2,3,7,6] => [1,4,2] [1,4,5,2,6,3,7] => [1,3,3] [1,4,5,2,6,7,3] => [1,3,3] [1,4,5,2,7,3,6] => [1,3,3] [1,4,5,2,7,6,3] => [1,3,2,1] [1,4,5,3,2,6,7] => [1,3,3] [1,4,5,3,2,7,6] => [1,3,1,2] [1,4,5,3,6,2,7] => [1,3,3] [1,4,5,3,6,7,2] => [1,3,3] [1,4,5,3,7,2,6] => [1,3,3] [1,4,5,3,7,6,2] => [1,3,2,1] [1,4,5,6,2,3,7] => [1,6] [1,4,5,6,2,7,3] => [1,4,2] [1,4,5,6,3,2,7] => [1,4,2] [1,4,5,6,3,7,2] => [1,4,2] [1,4,5,6,7,2,3] => [1,6] [1,4,5,6,7,3,2] => [1,5,1] [1,4,5,7,2,3,6] => [1,6] [1,4,5,7,2,6,3] => [1,5,1] [1,4,5,7,3,2,6] => [1,4,2] [1,4,5,7,3,6,2] => [1,5,1] [1,4,5,7,6,2,3] => [1,3,3] [1,4,5,7,6,3,2] => [1,3,2,1] [1,4,6,2,3,5,7] => [1,6] [1,4,6,2,3,7,5] => [1,4,2] [1,4,6,2,5,3,7] => [1,4,2] [1,4,6,2,5,7,3] => [1,4,2] [1,4,6,2,7,3,5] => [1,3,3] [1,4,6,2,7,5,3] => [1,3,2,1] [1,4,6,3,2,5,7] => [1,3,3] [1,4,6,3,2,7,5] => [1,3,1,2] [1,4,6,3,5,2,7] => [1,4,2] [1,4,6,3,5,7,2] => [1,4,2] [1,4,6,3,7,2,5] => [1,3,3] [1,4,6,3,7,5,2] => [1,3,2,1] [1,4,6,5,2,3,7] => [1,2,4] [1,4,6,5,2,7,3] => [1,2,2,2] [1,4,6,5,3,2,7] => [1,2,2,2] ----------------------------------------------------------------------------- Created: Feb 20, 2022 at 19:42 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 20, 2022 at 19:42 by Martin Rubey