************************************************************************ * 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: Mp00299 ------------------------------------------------------------------------ Map name: ones to leading ------------------------------------------------------------------------ Domain: Parking functions ------------------------------------------------------------------------ Codomain: Parking functions ------------------------------------------------------------------------ Description: The unique parking function obtained by applying the Foata-Riordan map to obtain a Prüfer code, then prepending 0 and cyclically shifting. Let $c_1,\dots,c_{n-1}$ be the Prüfer code obtained via the Foata-Riordan map described in [1, eq (1.2)] and let $c_0=0$. This map returns the a unique parking function $(q_1,\dots,q_n)$ such that $q_i-c_{i-1}$ is constant modulo $n+1$, see [2, sec 4]. This map sends the number of ones to the number of occurrences of the first element. ------------------------------------------------------------------------ References: [1] (service unreachable) [[MathSciNet:0335294]] ------------------------------------------------------------------------ Code: def mapping(p): if not p: return p return pruefer_to_parking_circular(parking_to_pruefer_foata_riordan(p)) def pruefer_to_parking_circular(c): pc = [0] + list(c) n = len(pc) P = ParkingFunctions(n) for i in range(n): if pc in P: break pc = [(e + 1) % (n+1) for e in pc] return ParkingFunction(pc) def parking_to_pruefer_foata_riordan(p): n = len(p) tau = Permutation([sum(1 for j in range(n) if p[j] < p[i] or (p[j] == p[i] and j <= i)) for i in range(n)]) pi = tau.inverse() E = [(0, i) if c == 1 else (i, pi(c-1)) for i, c in enumerate(p, 1)] V = list(range(n+1)) G = Graph([V, E]) c = [] for _ in range(n-1): for u in V: if G.degree(u) == 1: c.append(G[u][0]) G.delete_vertex(u) V.remove(u) break return c ------------------------------------------------------------------------ Map images: [1] => [1] [1,1] => [1,1] [1,2] => [1,2] [2,1] => [2,1] [1,1,1] => [1,1,1] [1,1,2] => [1,1,2] [1,2,1] => [1,2,1] [2,1,1] => [1,3,1] [1,1,3] => [1,1,3] [1,3,1] => [2,2,1] [3,1,1] => [2,1,2] [1,2,2] => [1,2,2] [2,1,2] => [3,1,1] [2,2,1] => [2,1,1] [1,2,3] => [1,2,3] [1,3,2] => [2,3,1] [2,1,3] => [1,3,2] [2,3,1] => [2,1,3] [3,1,2] => [3,1,2] [3,2,1] => [3,2,1] [1,1,1,1] => [1,1,1,1] [1,1,1,2] => [1,1,1,2] [1,1,2,1] => [1,1,2,1] [1,2,1,1] => [1,2,1,1] [2,1,1,1] => [1,3,1,1] [1,1,1,3] => [1,1,1,3] [1,1,3,1] => [1,1,3,1] [1,3,1,1] => [1,1,4,1] [3,1,1,1] => [1,4,1,1] [1,1,1,4] => [1,1,1,4] [1,1,4,1] => [2,2,2,1] [1,4,1,1] => [2,2,1,2] [4,1,1,1] => [2,1,2,2] [1,1,2,2] => [1,1,2,2] [1,2,1,2] => [1,2,1,2] [1,2,2,1] => [1,2,2,1] [2,1,1,2] => [1,3,1,3] [2,1,2,1] => [1,3,3,1] [2,2,1,1] => [3,1,1,3] [1,1,2,3] => [1,2,1,3] [1,1,3,2] => [1,3,1,2] [1,2,1,3] => [1,2,1,4] [1,2,3,1] => [2,3,2,1] [1,3,1,2] => [1,4,1,2] [1,3,2,1] => [2,1,3,2] [2,1,1,3] => [1,3,1,4] [2,1,3,1] => [2,4,2,1] [2,3,1,1] => [3,1,2,3] [3,1,1,2] => [1,4,1,3] [3,1,2,1] => [2,1,4,2] [3,2,1,1] => [3,2,1,3] [1,1,2,4] => [1,1,2,4] [1,1,4,2] => [2,2,3,1] [1,2,1,4] => [1,1,2,3] [1,2,4,1] => [1,3,2,1] [1,4,1,2] => [2,1,2,3] [1,4,2,1] => [1,4,2,1] [2,1,1,4] => [1,1,3,2] [2,1,4,1] => [1,2,3,1] [2,4,1,1] => [1,2,4,1] [4,1,1,2] => [2,1,2,4] [4,1,2,1] => [1,4,3,1] [4,2,1,1] => [1,3,4,1] [1,1,3,3] => [1,1,3,3] [1,3,1,3] => [3,3,1,1] [1,3,3,1] => [2,2,1,1] [3,1,1,3] => [3,1,3,1] [3,1,3,1] => [2,1,2,1] [3,3,1,1] => [2,1,1,2] [1,1,3,4] => [1,1,3,4] [1,1,4,3] => [2,2,4,1] [1,3,1,4] => [1,1,4,3] [1,3,4,1] => [2,2,1,4] [1,4,1,3] => [3,3,1,2] [1,4,3,1] => [3,3,2,1] [3,1,1,4] => [1,1,4,2] [3,1,4,1] => [2,2,1,3] [3,4,1,1] => [2,3,1,2] [4,1,1,3] => [3,2,3,1] [4,1,3,1] => [3,1,3,2] [4,3,1,1] => [2,4,1,2] [1,2,2,2] => [1,2,2,2] [2,1,2,2] => [4,1,1,1] [2,2,1,2] => [3,1,1,1] [2,2,2,1] => [2,1,1,1] [1,2,2,3] => [1,2,2,3] [1,2,3,2] => [1,2,3,2] [1,3,2,2] => [1,2,4,2] [2,1,2,3] => [1,3,3,2] [2,1,3,2] => [1,3,2,3] [2,2,1,3] => [3,1,1,4] [2,2,3,1] => [2,1,1,3] [2,3,1,2] => [3,1,4,1] [2,3,2,1] => [2,1,3,1] [3,1,2,2] => [4,1,2,1] [3,2,1,2] => [4,2,1,2] [3,2,2,1] => [2,1,4,1] [1,2,2,4] => [1,2,2,4] [1,2,4,2] => [2,3,3,1] [1,4,2,2] => [2,3,1,3] [2,1,2,4] => [4,1,1,2] [2,1,4,2] => [4,1,1,3] [2,2,1,4] => [4,2,2,1] [2,2,4,1] => [2,1,1,4] [2,4,1,2] => [3,1,1,2] [2,4,2,1] => [3,2,2,1] [4,1,2,2] => [4,1,3,1] [4,2,1,2] => [3,1,2,1] [4,2,2,1] => [3,2,1,2] [1,2,3,3] => [1,2,3,3] [1,3,2,3] => [3,4,1,1] [1,3,3,2] => [2,3,1,1] [2,1,3,3] => [1,3,2,2] [2,3,1,3] => [1,4,2,2] [2,3,3,1] => [2,1,3,3] [3,1,2,3] => [4,1,2,2] [3,1,3,2] => [2,4,1,1] [3,2,1,3] => [4,2,1,1] [3,2,3,1] => [4,3,1,1] [3,3,1,2] => [3,1,2,2] [3,3,2,1] => [3,2,1,1] [1,2,3,4] => [1,2,3,4] [1,2,4,3] => [2,3,4,1] [1,3,2,4] => [1,2,4,3] [1,3,4,2] => [2,3,1,4] [1,4,2,3] => [3,4,1,2] [1,4,3,2] => [3,4,2,1] [2,1,3,4] => [1,3,2,4] [2,1,4,3] => [2,4,3,1] [2,3,1,4] => [1,4,2,3] [2,3,4,1] => [2,1,4,3] [2,4,1,3] => [3,1,2,4] [2,4,3,1] => [3,2,1,4] [3,1,2,4] => [1,3,4,2] [3,1,4,2] => [2,4,1,3] [3,2,1,4] => [1,4,3,2] [3,2,4,1] => [2,1,3,4] [3,4,1,2] => [3,1,4,2] [3,4,2,1] => [3,2,4,1] [4,1,2,3] => [4,1,3,2] [4,1,3,2] => [4,1,2,3] [4,2,1,3] => [4,2,3,1] [4,2,3,1] => [4,3,2,1] [4,3,1,2] => [4,2,1,3] [4,3,2,1] => [4,3,1,2] [1,1,1,1,1] => [1,1,1,1,1] [1,1,1,1,2] => [1,1,1,1,2] [1,1,1,2,1] => [1,1,1,2,1] [1,1,2,1,1] => [1,1,2,1,1] [1,2,1,1,1] => [1,2,1,1,1] [2,1,1,1,1] => [1,3,1,1,1] [1,1,1,1,3] => [1,1,1,1,3] [1,1,1,3,1] => [1,1,1,3,1] [1,1,3,1,1] => [1,1,3,1,1] [1,3,1,1,1] => [1,1,4,1,1] [3,1,1,1,1] => [1,4,1,1,1] [1,1,1,1,4] => [1,1,1,1,4] [1,1,1,4,1] => [1,1,1,4,1] [1,1,4,1,1] => [1,1,1,5,1] [1,4,1,1,1] => [1,1,5,1,1] [4,1,1,1,1] => [1,5,1,1,1] [1,1,1,1,5] => [1,1,1,1,5] [1,1,1,5,1] => [2,2,2,2,1] [1,1,5,1,1] => [2,2,2,1,2] [1,5,1,1,1] => [2,2,1,2,2] [5,1,1,1,1] => [2,1,2,2,2] [1,1,1,2,2] => [1,1,1,2,2] [1,1,2,1,2] => [1,1,2,1,2] [1,1,2,2,1] => [1,1,2,2,1] [1,2,1,1,2] => [1,2,1,1,2] [1,2,1,2,1] => [1,2,1,2,1] [1,2,2,1,1] => [1,2,2,1,1] [2,1,1,1,2] => [1,3,1,1,3] [2,1,1,2,1] => [1,3,1,3,1] [2,1,2,1,1] => [1,3,3,1,1] [2,2,1,1,1] => [1,4,4,1,1] [1,1,1,2,3] => [1,1,2,1,3] [1,1,1,3,2] => [1,1,3,1,2] [1,1,2,1,3] => [1,2,1,1,3] [1,1,2,3,1] => [1,2,1,3,1] [1,1,3,1,2] => [1,3,1,1,2] [1,1,3,2,1] => [1,3,1,2,1] [1,2,1,1,3] => [1,2,1,1,4] [1,2,1,3,1] => [1,2,1,4,1] [1,2,3,1,1] => [1,2,1,5,1] [1,3,1,1,2] => [1,4,1,1,2] [1,3,1,2,1] => [1,4,1,2,1] [1,3,2,1,1] => [1,5,2,1,1] [2,1,1,1,3] => [1,3,1,1,4] [2,1,1,3,1] => [1,3,1,4,1] [2,1,3,1,1] => [1,3,1,5,1] [2,3,1,1,1] => [1,4,5,1,1] [3,1,1,1,2] => [1,4,1,1,3] [3,1,1,2,1] => [1,4,1,3,1] [3,1,2,1,1] => [1,5,3,1,1] [3,2,1,1,1] => [1,5,4,1,1] [1,1,1,2,4] => [1,1,2,1,4] [1,1,1,4,2] => [1,1,4,1,2] [1,1,2,1,4] => [1,1,2,1,5] [1,1,2,4,1] => [2,2,3,2,1] [1,1,4,1,2] => [1,1,5,1,2] [1,1,4,2,1] => [2,2,1,3,2] [1,2,1,1,4] => [1,2,1,1,5] [1,2,1,4,1] => [2,3,2,2,1] [1,2,4,1,1] => [2,3,2,1,2] [1,4,1,1,2] => [1,5,1,1,2] [1,4,1,2,1] => [2,1,2,3,2] [1,4,2,1,1] => [2,1,3,2,2] [2,1,1,1,4] => [1,3,1,1,5] [2,1,1,4,1] => [2,4,2,2,1] [2,1,4,1,1] => [2,4,2,1,2] [2,4,1,1,1] => [2,5,1,2,2] [4,1,1,1,2] => [1,5,1,1,3] [4,1,1,2,1] => [2,1,2,4,2] [4,1,2,1,1] => [2,1,4,2,2] [4,2,1,1,1] => [2,1,5,2,2] [1,1,1,2,5] => [1,1,1,2,5] [1,1,1,5,2] => [2,2,2,3,1] [1,1,2,1,5] => [1,1,1,2,4] [1,1,2,5,1] => [1,1,4,2,1] [1,1,5,1,2] => [2,2,1,2,3] [1,1,5,2,1] => [1,1,5,2,1] [1,2,1,1,5] => [1,1,1,2,3] [1,2,1,5,1] => [1,1,3,2,1] [1,2,5,1,1] => [1,3,2,1,1] [1,5,1,1,2] => [2,1,2,2,3] [1,5,1,2,1] => [1,5,1,2,1] [1,5,2,1,1] => [1,4,2,1,1] [2,1,1,1,5] => [1,1,1,3,2] [2,1,1,5,1] => [1,1,2,3,1] [2,1,5,1,1] => [1,2,3,1,1] [2,5,1,1,1] => [1,2,4,1,1] [5,1,1,1,2] => [2,1,2,2,4] [5,1,1,2,1] => [1,5,1,3,1] [5,1,2,1,1] => [1,4,3,1,1] [5,2,1,1,1] => [1,3,4,1,1] [1,1,1,3,3] => [1,1,1,3,3] [1,1,3,1,3] => [1,1,3,1,3] [1,1,3,3,1] => [1,1,3,3,1] [1,3,1,1,3] => [1,1,4,1,4] [1,3,1,3,1] => [1,1,4,4,1] [1,3,3,1,1] => [3,3,1,1,3] [3,1,1,1,3] => [1,4,1,1,4] [3,1,1,3,1] => [1,4,1,4,1] [3,1,3,1,1] => [3,1,3,1,3] [3,3,1,1,1] => [3,1,1,3,3] [1,1,1,3,4] => [1,1,3,1,4] [1,1,1,4,3] => [1,1,4,1,3] [1,1,3,1,4] => [1,1,3,1,5] [1,1,3,4,1] => [2,2,4,2,1] [1,1,4,1,3] => [1,1,5,1,3] [1,1,4,3,1] => [2,2,1,4,2] [1,3,1,1,4] => [1,1,4,1,5] [1,3,1,4,1] => [2,2,5,2,1] [1,3,4,1,1] => [3,3,1,2,3] [1,4,1,1,3] => [1,1,5,1,4] [1,4,1,3,1] => [2,2,1,5,2] [1,4,3,1,1] => [3,3,2,1,3] [3,1,1,1,4] => [1,4,1,1,5] [3,1,1,4,1] => [2,5,2,2,1] [3,1,4,1,1] => [3,1,3,2,3] [3,4,1,1,1] => [3,1,2,3,3] [4,1,1,1,3] => [1,5,1,1,4] [4,1,1,3,1] => [2,1,2,5,2] [4,1,3,1,1] => [3,2,3,1,3] [4,3,1,1,1] => [3,2,1,3,3] [1,1,1,3,5] => [1,1,1,3,5] [1,1,1,5,3] => [2,2,2,4,1] [1,1,3,1,5] => [1,1,1,3,4] [1,1,3,5,1] => [1,1,4,3,1] [1,1,5,1,3] => [2,2,1,2,4] [1,1,5,3,1] => [1,1,5,3,1] [1,3,1,1,5] => [1,1,1,4,3] [1,3,1,5,1] => [1,1,3,4,1] [1,3,5,1,1] => [1,1,3,5,1] [1,5,1,1,3] => [2,2,1,2,5] [1,5,1,3,1] => [1,1,5,4,1] [1,5,3,1,1] => [1,1,4,5,1] [3,1,1,1,5] => [1,1,1,4,2] [3,1,1,5,1] => [1,1,2,4,1] [3,1,5,1,1] => [1,1,2,5,1] [3,5,1,1,1] => [1,2,5,1,1] [5,1,1,1,3] => [2,1,2,2,5] [5,1,1,3,1] => [1,5,1,4,1] [5,1,3,1,1] => [1,4,1,5,1] [5,3,1,1,1] => [1,3,5,1,1] [1,1,1,4,4] => [1,1,1,4,4] [1,1,4,1,4] => [3,3,3,1,1] [1,1,4,4,1] => [2,2,2,1,1] [1,4,1,1,4] => [3,3,1,3,1] [1,4,1,4,1] => [2,2,1,2,1] [1,4,4,1,1] => [2,2,1,1,2] [4,1,1,1,4] => [3,1,3,3,1] [4,1,1,4,1] => [2,1,2,2,1] [4,1,4,1,1] => [2,1,2,1,2] [4,4,1,1,1] => [2,1,1,2,2] [1,1,1,4,5] => [1,1,1,4,5] [1,1,1,5,4] => [2,2,2,5,1] [1,1,4,1,5] => [1,1,1,5,4] [1,1,4,5,1] => [2,2,2,1,5] [1,1,5,1,4] => [3,3,3,1,2] [1,1,5,4,1] => [3,3,3,2,1] [1,4,1,1,5] => [1,1,1,5,3] [1,4,1,5,1] => [2,2,2,1,4] [1,4,5,1,1] => [2,2,4,1,2] [1,5,1,1,4] => [3,3,2,3,1] [1,5,1,4,1] => [3,3,1,3,2] [1,5,4,1,1] => [2,2,5,1,2] [4,1,1,1,5] => [1,1,1,5,2] [4,1,1,5,1] => [2,2,2,1,3] [4,1,5,1,1] => [2,2,3,1,2] [4,5,1,1,1] => [2,3,1,2,2] [5,1,1,1,4] => [3,2,3,3,1] [5,1,1,4,1] => [3,1,3,3,2] [5,1,4,1,1] => [2,5,2,1,2] [5,4,1,1,1] => [2,4,1,2,2] [1,1,2,2,2] => [1,1,2,2,2] [1,2,1,2,2] => [1,2,1,2,2] [1,2,2,1,2] => [1,2,2,1,2] [1,2,2,2,1] => [1,2,2,2,1] [2,1,1,2,2] => [1,3,1,3,3] [2,1,2,1,2] => [1,3,3,1,3] [2,1,2,2,1] => [1,3,3,3,1] [2,2,1,1,2] => [4,1,1,4,1] [2,2,1,2,1] => [4,1,1,1,4] [2,2,2,1,1] => [3,1,1,1,3] [1,1,2,2,3] => [1,2,2,1,3] [1,1,2,3,2] => [1,2,3,1,2] [1,1,3,2,2] => [1,3,1,2,2] [1,2,1,2,3] => [1,2,2,1,4] [1,2,1,3,2] => [1,2,4,1,2] [1,2,2,1,3] => [1,2,2,1,5] [1,2,2,3,1] => [2,3,3,2,1] [1,2,3,1,2] => [1,2,5,1,2] [1,2,3,2,1] => [2,3,1,3,2] [1,3,1,2,2] => [1,4,1,2,2] [1,3,2,1,2] => [1,5,2,1,2] [1,3,2,2,1] => [2,1,3,3,2] [2,1,1,2,3] => [1,3,3,1,4] [2,1,1,3,2] => [1,3,4,1,3] [2,1,2,1,3] => [1,3,3,1,5] [2,1,2,3,1] => [2,4,4,2,1] [2,1,3,1,2] => [1,3,5,1,3] [2,1,3,2,1] => [2,4,1,4,2] [2,2,1,1,3] => [4,1,1,4,2] [2,2,1,3,1] => [4,1,1,4,3] [2,2,3,1,1] => [3,1,1,2,3] [2,3,1,1,2] => [4,1,2,4,1] [2,3,1,2,1] => [4,1,3,1,4] [2,3,2,1,1] => [3,1,2,1,3] [3,1,1,2,2] => [1,4,1,3,3] [3,1,2,1,2] => [1,5,3,1,3] [3,1,2,2,1] => [2,1,4,4,2] [3,2,1,1,2] => [4,2,1,4,1] [3,2,1,2,1] => [4,3,1,1,4] [3,2,2,1,1] => [3,2,1,1,3] [1,1,2,2,4] => [1,1,2,2,4] [1,1,2,4,2] => [1,1,2,4,2] [1,1,4,2,2] => [1,1,2,5,2] [1,2,1,2,4] => [1,1,2,2,3] [1,2,1,4,2] => [1,1,2,3,2] [1,2,2,1,4] => [1,2,1,2,3] [1,2,2,4,1] => [1,2,3,2,1] [1,2,4,1,2] => [1,3,2,1,2] [1,2,4,2,1] => [1,3,2,2,1] [1,4,1,2,2] => [1,5,1,2,2] [1,4,2,1,2] => [1,4,2,1,2] [1,4,2,2,1] => [1,4,2,2,1] [2,1,1,2,4] => [1,1,3,3,2] [2,1,1,4,2] => [1,1,3,2,3] [2,1,2,1,4] => [1,3,1,3,2] [2,1,2,4,1] => [1,3,2,3,1] [2,1,4,1,2] => [1,2,3,1,3] [2,1,4,2,1] => [1,2,3,3,1] [2,2,1,1,4] => [1,4,1,4,2] [2,2,1,4,1] => [1,4,2,4,1] [2,2,4,1,1] => [3,1,4,1,3] [2,4,1,1,2] => [1,2,4,1,4] [2,4,1,2,1] => [1,2,4,4,1] [2,4,2,1,1] => [3,4,1,1,3] [4,1,1,2,2] => [1,5,1,3,3] [4,1,2,1,2] => [1,4,3,1,3] [4,1,2,2,1] => [1,4,3,3,1] [4,2,1,1,2] => [1,3,4,1,4] [4,2,1,2,1] => [1,3,4,4,1] [4,2,2,1,1] => [3,5,1,1,3] [1,1,2,2,5] => [1,1,2,2,5] [1,1,2,5,2] => [2,2,3,3,1] [1,1,5,2,2] => [2,2,3,1,3] [1,2,1,2,5] => [1,2,1,2,5] [1,2,1,5,2] => [2,3,2,3,1] [1,2,2,1,5] => [1,2,1,2,4] [1,2,2,5,1] => [1,2,4,2,1] [1,2,5,1,2] => [2,3,1,2,3] [1,2,5,2,1] => [1,2,5,2,1] [1,5,1,2,2] => [2,1,2,3,3] [1,5,2,1,2] => [2,1,3,2,3] [1,5,2,2,1] => [1,5,2,2,1] [2,1,1,2,5] => [1,3,1,3,5] [2,1,1,5,2] => [2,4,2,4,1] [2,1,2,1,5] => [1,3,1,3,4] [2,1,2,5,1] => [1,3,4,3,1] [2,1,5,1,2] => [2,4,1,2,4] [2,1,5,2,1] => [1,3,5,3,1] [2,2,1,1,5] => [1,4,1,4,3] [2,2,1,5,1] => [1,4,3,4,1] [2,2,5,1,1] => [3,1,5,1,3] [2,5,1,1,2] => [4,1,3,4,1] [2,5,1,2,1] => [4,1,2,1,4] [2,5,2,1,1] => [4,2,1,2,4] [5,1,1,2,2] => [2,1,2,4,4] [5,1,2,1,2] => [2,1,4,2,4] [5,1,2,2,1] => [1,5,3,3,1] [5,2,1,1,2] => [4,3,1,4,1] [5,2,1,2,1] => [4,2,1,1,4] [5,2,2,1,1] => [4,1,2,2,4] [1,1,2,3,3] => [1,2,1,3,3] [1,1,3,2,3] => [1,3,2,1,3] [1,1,3,3,2] => [1,3,3,1,2] [1,2,1,3,3] => [1,2,1,4,4] [1,2,3,1,3] => [3,4,3,1,1] [1,2,3,3,1] => [2,3,2,1,1] [1,3,1,2,3] => [1,4,2,1,4] [1,3,1,3,2] => [1,4,4,1,2] [1,3,2,1,3] => [3,1,4,3,1] [1,3,2,3,1] => [2,1,3,2,1] [1,3,3,1,2] => [3,1,1,3,4] [1,3,3,2,1] => [2,1,1,3,2] [2,1,1,3,3] => [1,3,1,4,4] [2,1,3,1,3] => [3,5,3,1,1] [2,1,3,3,1] => [2,4,2,1,1] [2,3,1,1,3] => [4,1,2,4,2] [2,3,1,3,1] => [2,5,1,2,1] [2,3,3,1,1] => [3,1,2,2,3] [3,1,1,2,3] => [1,4,3,1,4] [3,1,1,3,2] => [1,4,4,1,3] [3,1,2,1,3] => [3,1,5,3,1] [3,1,2,3,1] => [2,1,4,2,1] [3,1,3,1,2] => [3,1,1,3,5] [3,1,3,2,1] => [2,1,1,4,2] [3,2,1,1,3] => [4,2,1,4,2] [3,2,1,3,1] => [2,1,5,2,1] [3,2,3,1,1] => [3,2,1,2,3] [3,3,1,1,2] => [4,2,2,4,1] [3,3,1,2,1] => [2,1,1,5,2] [3,3,2,1,1] => [3,2,2,1,3] [1,1,2,3,4] => [1,3,1,2,4] [1,1,2,4,3] => [1,4,2,1,3] [1,1,3,2,4] => [1,3,1,2,5] [1,1,3,4,2] => [2,4,2,3,1] [1,1,4,2,3] => [1,5,2,1,3] [1,1,4,3,2] => [2,1,4,2,3] [1,2,1,3,4] => [1,4,1,2,3] [1,2,1,4,3] => [1,3,2,1,4] [1,2,3,1,4] => [1,5,1,2,3] [1,2,3,4,1] => [2,1,4,3,2] [1,2,4,1,3] => [1,3,2,1,5] [1,2,4,3,1] => [2,4,3,2,1] [1,3,1,2,4] => [1,4,1,2,5] [1,3,1,4,2] => [2,5,2,3,1] [1,3,2,1,4] => [1,5,1,2,4] [1,3,2,4,1] => [2,1,5,3,2] [1,3,4,1,2] => [3,1,2,3,4] [1,3,4,2,1] => [3,2,1,4,3] [1,4,1,2,3] => [1,5,2,1,4] [1,4,1,3,2] => [2,1,5,2,3] [1,4,2,1,3] => [1,4,2,1,5] [1,4,2,3,1] => [2,5,3,2,1] [1,4,3,1,2] => [3,2,1,3,4] [1,4,3,2,1] => [3,1,2,4,3] [2,1,1,3,4] => [1,4,1,3,2] [2,1,1,4,3] => [1,2,3,1,4] [2,1,3,1,4] => [1,5,1,3,2] [2,1,3,4,1] => [2,1,3,4,2] [2,1,4,1,3] => [1,2,3,1,5] [2,1,4,3,1] => [2,3,4,2,1] [2,3,1,1,4] => [1,5,1,4,2] [2,3,1,4,1] => [2,1,3,5,2] [2,3,4,1,1] => [3,2,4,1,3] [2,4,1,1,3] => [1,2,4,1,5] [2,4,1,3,1] => [2,3,5,2,1] [2,4,3,1,1] => [3,4,1,2,3] [3,1,1,2,4] => [1,4,1,3,5] [3,1,1,4,2] => [2,5,2,4,1] [3,1,2,1,4] => [1,5,1,3,4] [3,1,2,4,1] => [2,1,5,4,2] [3,1,4,1,2] => [3,1,2,3,5] [3,1,4,2,1] => [3,2,1,5,3] [3,2,1,1,4] => [1,5,1,4,3] [3,2,1,4,1] => [2,1,4,5,2] [3,2,4,1,1] => [3,2,5,1,3] [3,4,1,1,2] => [4,2,3,4,1] [3,4,1,2,1] => [4,3,2,1,4] [3,4,2,1,1] => [4,3,1,2,4] [4,1,1,2,3] => [1,5,3,1,4] [4,1,1,3,2] => [2,1,5,2,4] [4,1,2,1,3] => [1,4,3,1,5] [4,1,2,3,1] => [2,5,4,2,1] [4,1,3,1,2] => [3,2,1,3,5] [4,1,3,2,1] => [3,1,2,5,3] [4,2,1,1,3] => [1,3,4,1,5] [4,2,1,3,1] => [2,4,5,2,1] [4,2,3,1,1] => [3,5,1,2,3] [4,3,1,1,2] => [4,3,2,4,1] [4,3,1,2,1] => [4,2,3,1,4] [4,3,2,1,1] => [4,1,3,2,4] [1,1,2,3,5] => [1,2,1,3,5] [1,1,2,5,3] => [2,3,2,4,1] [1,1,3,2,5] => [1,2,1,3,4] [1,1,3,5,2] => [1,4,3,1,2] [1,1,5,2,3] => [2,1,3,2,4] [1,1,5,3,2] => [1,5,3,1,2] [1,2,1,3,5] => [1,2,1,4,5] [1,2,1,5,3] => [2,3,2,5,1] [1,2,3,1,5] => [1,2,1,5,4] [1,2,3,5,1] => [2,3,2,1,5] [1,2,5,1,3] => [3,4,3,1,2] [1,2,5,3,1] => [3,4,3,2,1] [1,3,1,2,5] => [1,2,1,4,3] [1,3,1,5,2] => [1,3,4,1,2] [1,3,2,1,5] => [1,2,1,5,3] [1,3,2,5,1] => [2,3,2,1,4] [1,3,5,1,2] => [1,3,5,1,2] [1,3,5,2,1] => [2,4,1,3,2] [1,5,1,2,3] => [2,1,3,2,5] [1,5,1,3,2] => [1,5,4,1,2] [1,5,2,1,3] => [3,2,4,3,1] [1,5,2,3,1] => [3,1,4,3,2] [1,5,3,1,2] => [1,4,5,1,2] [1,5,3,2,1] => [2,5,1,3,2] [2,1,1,3,5] => [1,3,1,4,5] [2,1,1,5,3] => [2,4,2,5,1] [2,1,3,1,5] => [1,3,1,5,4] [2,1,3,5,1] => [2,4,2,1,5] [2,1,5,1,3] => [3,5,3,1,2] [2,1,5,3,1] => [3,5,3,2,1] [2,3,1,1,5] => [1,4,1,5,3] [2,3,1,5,1] => [2,5,2,1,4] [2,3,5,1,1] => [3,1,5,2,3] [2,5,1,1,3] => [4,1,3,4,2] [2,5,1,3,1] => [4,1,2,4,3] [2,5,3,1,1] => [4,2,1,3,4] [3,1,1,2,5] => [1,3,1,4,2] [3,1,1,5,2] => [1,2,4,1,3] [3,1,2,1,5] => [1,3,1,5,2] [3,1,2,5,1] => [2,4,2,1,3] [3,1,5,1,2] => [1,2,5,1,3] [3,1,5,2,1] => [2,3,1,4,2] [3,2,1,1,5] => [1,4,1,5,2] [3,2,1,5,1] => [2,5,2,1,3] [3,2,5,1,1] => [3,1,4,2,3] [3,5,1,1,2] => [1,2,5,1,4] [3,5,1,2,1] => [2,3,1,5,2] [3,5,2,1,1] => [3,4,2,1,3] [5,1,1,2,3] => [2,1,4,2,5] [5,1,1,3,2] => [1,5,4,1,3] [5,1,2,1,3] => [3,2,5,3,1] [5,1,2,3,1] => [3,1,5,3,2] [5,1,3,1,2] => [1,4,5,1,3] [5,1,3,2,1] => [2,5,1,4,2] [5,2,1,1,3] => [4,3,1,4,2] [5,2,1,3,1] => [4,2,1,4,3] [5,2,3,1,1] => [4,1,2,3,4] [5,3,1,1,2] => [1,3,5,1,4] [5,3,1,2,1] => [2,4,1,5,2] [5,3,2,1,1] => [3,5,2,1,3] [1,1,2,4,4] => [1,1,2,4,4] [1,1,4,2,4] => [3,3,4,1,1] [1,1,4,4,2] => [2,2,3,1,1] [1,2,1,4,4] => [1,1,2,3,3] [1,2,4,1,4] => [1,3,1,2,3] [1,2,4,4,1] => [1,3,3,2,1] [1,4,1,2,4] => [3,1,3,4,1] [1,4,1,4,2] => [2,1,2,3,1] [1,4,2,1,4] => [1,4,1,2,4] [1,4,2,4,1] => [1,4,4,2,1] [1,4,4,1,2] => [2,1,1,2,3] [1,4,4,2,1] => [3,1,1,4,3] [2,1,1,4,4] => [1,1,3,2,2] [2,1,4,1,4] => [1,2,1,3,2] [2,1,4,4,1] => [1,2,2,3,1] [2,4,1,1,4] => [1,2,1,4,2] [2,4,1,4,1] => [1,2,2,4,1] [2,4,4,1,1] => [1,2,2,5,1] [4,1,1,2,4] => [3,1,3,5,1] [4,1,1,4,2] => [2,1,2,4,1] [4,1,2,1,4] => [1,4,1,3,4] [4,1,2,4,1] => [1,4,4,3,1] [4,1,4,1,2] => [2,1,1,2,4] [4,1,4,2,1] => [3,1,1,5,3] [4,2,1,1,4] => [1,3,1,4,3] [4,2,1,4,1] => [1,3,3,4,1] [4,2,4,1,1] => [1,3,3,5,1] [4,4,1,1,2] => [2,1,1,2,5] [4,4,1,2,1] => [4,2,2,1,4] [4,4,2,1,1] => [4,1,1,2,4] [1,1,2,4,5] => [1,1,2,4,5] [1,1,2,5,4] => [2,2,3,5,1] [1,1,4,2,5] => [1,1,2,5,4] [1,1,4,5,2] => [2,2,3,1,5] [1,1,5,2,4] => [3,3,4,1,2] [1,1,5,4,2] => [3,3,4,2,1] [1,2,1,4,5] => [1,1,2,3,5] [1,2,1,5,4] => [2,2,3,4,1] [1,2,4,1,5] => [1,1,2,3,4] [1,2,4,5,1] => [1,4,3,2,1] [1,2,5,1,4] => [2,1,2,3,4] [1,2,5,4,1] => [1,5,3,2,1] [1,4,1,2,5] => [1,1,2,5,3] [1,4,1,5,2] => [2,2,3,1,4] [1,4,2,1,5] => [1,1,2,4,3] [1,4,2,5,1] => [1,3,4,2,1] [1,4,5,1,2] => [2,4,1,2,3] [1,4,5,2,1] => [1,3,5,2,1] [1,5,1,2,4] => [3,2,3,4,1] [1,5,1,4,2] => [3,1,3,4,2] [1,5,2,1,4] => [2,1,2,3,5] [1,5,2,4,1] => [1,5,4,2,1] [1,5,4,1,2] => [2,5,1,2,3] [1,5,4,2,1] => [1,4,5,2,1] [2,1,1,4,5] => [1,1,3,2,5] [2,1,1,5,4] => [2,2,4,3,1] [2,1,4,1,5] => [1,1,3,2,4] [2,1,4,5,1] => [1,4,2,3,1] [2,1,5,1,4] => [2,1,2,4,3] [2,1,5,4,1] => [1,5,2,3,1] [2,4,1,1,5] => [1,1,4,2,3] [2,4,1,5,1] => [1,3,2,4,1] [2,4,5,1,1] => [1,3,2,5,1] [2,5,1,1,4] => [2,1,2,5,3] [2,5,1,4,1] => [1,5,2,4,1] [2,5,4,1,1] => [1,4,2,5,1] [4,1,1,2,5] => [1,1,3,5,2] [4,1,1,5,2] => [2,2,4,1,3] [4,1,2,1,5] => [1,1,3,4,2] [4,1,2,5,1] => [1,2,4,3,1] [4,1,5,1,2] => [2,3,1,2,4] [4,1,5,2,1] => [1,2,5,3,1] [4,2,1,1,5] => [1,1,4,3,2] [4,2,1,5,1] => [1,2,3,4,1] [4,2,5,1,1] => [1,2,3,5,1] [4,5,1,1,2] => [2,3,1,2,5] [4,5,1,2,1] => [1,2,5,4,1] [4,5,2,1,1] => [1,2,4,5,1] [5,1,1,2,4] => [3,2,3,5,1] [5,1,1,4,2] => [3,1,3,5,2] [5,1,2,1,4] => [2,1,2,4,5] [5,1,2,4,1] => [1,5,4,3,1] [5,1,4,1,2] => [2,5,1,2,4] [5,1,4,2,1] => [1,4,5,3,1] [5,2,1,1,4] => [2,1,2,5,4] [5,2,1,4,1] => [1,5,3,4,1] [5,2,4,1,1] => [1,4,3,5,1] [5,4,1,1,2] => [2,4,1,2,5] [5,4,1,2,1] => [1,3,5,4,1] [5,4,2,1,1] => [1,3,4,5,1] [1,1,3,3,3] => [1,1,3,3,3] [1,3,1,3,3] => [4,4,1,1,1] [1,3,3,1,3] => [3,3,1,1,1] [1,3,3,3,1] => [2,2,1,1,1] [3,1,1,3,3] => [4,1,4,1,1] [3,1,3,1,3] => [3,1,3,1,1] [3,1,3,3,1] => [2,1,2,1,1] [3,3,1,1,3] => [3,1,1,3,1] [3,3,1,3,1] => [2,1,1,2,1] [3,3,3,1,1] => [2,1,1,1,2] [1,1,3,3,4] => [1,1,3,3,4] [1,1,3,4,3] => [1,1,3,4,3] [1,1,4,3,3] => [1,1,3,5,3] [1,3,1,3,4] => [1,1,4,4,3] [1,3,1,4,3] => [1,1,4,3,4] [1,3,3,1,4] => [3,3,1,1,5] [1,3,3,4,1] => [2,2,1,1,4] [1,3,4,1,3] => [3,3,1,5,1] [1,3,4,3,1] => [2,2,1,4,1] [1,4,1,3,3] => [4,4,1,2,1] [1,4,3,1,3] => [4,4,2,1,2] [1,4,3,3,1] => [2,2,1,5,1] [3,1,1,3,4] => [1,1,4,4,2] [3,1,1,4,3] => [1,1,4,2,4] [3,1,3,1,4] => [3,3,1,1,4] [3,1,3,4,1] => [2,2,1,1,3] [3,1,4,1,3] => [3,3,1,4,1] [3,1,4,3,1] => [2,2,1,3,1] [3,3,1,1,4] => [3,1,3,1,4] [3,3,1,4,1] => [2,1,2,1,3] [3,3,4,1,1] => [2,1,3,1,2] [3,4,1,1,3] => [3,4,1,3,1] [3,4,1,3,1] => [2,3,1,2,1] [3,4,3,1,1] => [2,3,1,1,2] [4,1,1,3,3] => [4,2,4,1,1] [4,1,3,1,3] => [4,1,4,2,2] [4,1,3,3,1] => [2,5,2,1,1] [4,3,1,1,3] => [3,5,1,3,1] [4,3,1,3,1] => [2,4,1,2,1] [4,3,3,1,1] => [2,4,1,1,2] [1,1,3,3,5] => [1,1,3,3,5] [1,1,3,5,3] => [2,2,4,4,1] [1,1,5,3,3] => [2,2,4,1,4] [1,3,1,3,5] => [4,4,1,1,2] [1,3,1,5,3] => [4,4,1,1,3] [1,3,3,1,5] => [4,4,2,2,1] [1,3,3,5,1] => [2,2,1,1,5] [1,3,5,1,3] => [3,3,1,1,2] [1,3,5,3,1] => [3,3,2,2,1] [1,5,1,3,3] => [4,4,1,3,1] [1,5,3,1,3] => [3,3,1,2,1] [1,5,3,3,1] => [3,3,2,1,2] [3,1,1,3,5] => [4,1,4,1,2] [3,1,1,5,3] => [4,1,4,1,3] [3,1,3,1,5] => [4,2,4,2,1] [3,1,3,5,1] => [2,1,2,1,5] [3,1,5,1,3] => [3,1,3,1,2] [3,1,5,3,1] => [3,2,3,2,1] [3,3,1,1,5] => [3,1,3,1,5] [3,3,1,5,1] => [2,1,2,1,4] [3,3,5,1,1] => [2,1,4,1,2] [3,5,1,1,3] => [3,1,2,3,1] [3,5,1,3,1] => [3,2,1,3,2] [3,5,3,1,1] => [2,1,5,1,2] [5,1,1,3,3] => [4,3,4,1,1] [5,1,3,1,3] => [3,2,3,1,1] [5,1,3,3,1] => [3,1,3,2,2] [5,3,1,1,3] => [3,2,1,3,1] [5,3,1,3,1] => [3,1,2,3,2] [5,3,3,1,1] => [2,5,1,1,2] [1,1,3,4,4] => [1,1,3,4,4] [1,1,4,3,4] => [3,3,5,1,1] [1,1,4,4,3] => [2,2,4,1,1] [1,3,1,4,4] => [1,1,4,3,3] [1,3,4,1,4] => [1,1,5,3,3] [1,3,4,4,1] => [2,2,1,4,4] [1,4,1,3,4] => [4,4,1,2,2] [1,4,1,4,3] => [2,2,5,1,1] [1,4,3,1,4] => [4,4,2,1,1] [1,4,3,4,1] => [4,4,3,1,1] [1,4,4,1,3] => [3,3,1,2,2] [1,4,4,3,1] => [3,3,2,1,1] [3,1,1,4,4] => [1,1,4,2,2] [3,1,4,1,4] => [1,1,5,2,2] [3,1,4,4,1] => [2,2,1,3,3] [3,4,1,1,4] => [1,2,1,5,2] [3,4,1,4,1] => [2,3,2,1,3] [3,4,4,1,1] => [2,3,3,1,2] [4,1,1,3,4] => [4,2,4,1,2] [4,1,1,4,3] => [2,1,2,5,1] [4,1,3,1,4] => [4,1,4,2,1] [4,1,3,4,1] => [4,1,4,3,1] [4,1,4,1,3] => [3,2,3,1,2] [4,1,4,3,1] => [3,1,3,2,1] [4,3,1,1,4] => [1,3,1,5,3] [4,3,1,4,1] => [2,4,2,1,4] [4,3,4,1,1] => [2,4,4,1,2] [4,4,1,1,3] => [3,2,2,3,1] [4,4,1,3,1] => [3,1,1,3,2] [4,4,3,1,1] => [4,1,1,3,4] [1,1,3,4,5] => [1,1,3,4,5] [1,1,3,5,4] => [2,2,4,5,1] [1,1,4,3,5] => [1,1,3,5,4] [1,1,4,5,3] => [2,2,4,1,5] [1,1,5,3,4] => [3,3,5,1,2] [1,1,5,4,3] => [3,3,5,2,1] [1,3,1,4,5] => [1,1,4,3,5] [1,3,1,5,4] => [2,2,5,4,1] [1,3,4,1,5] => [1,1,5,3,4] [1,3,4,5,1] => [2,2,1,5,4] [1,3,5,1,4] => [3,3,1,2,5] [1,3,5,4,1] => [3,3,2,1,5] [1,4,1,3,5] => [1,1,4,5,3] [1,4,1,5,3] => [2,2,5,1,4] [1,4,3,1,5] => [1,1,5,4,3] [1,4,3,5,1] => [2,2,1,4,5] [1,4,5,1,3] => [3,3,1,5,2] [1,4,5,3,1] => [3,3,2,5,1] [1,5,1,3,4] => [4,4,1,3,2] [1,5,1,4,3] => [4,4,1,2,3] [1,5,3,1,4] => [4,4,2,3,1] [1,5,3,4,1] => [4,4,3,2,1] [1,5,4,1,3] => [4,4,2,1,3] [1,5,4,3,1] => [4,4,3,1,2] [3,1,1,4,5] => [1,1,4,2,5] [3,1,1,5,4] => [2,2,5,3,1] [3,1,4,1,5] => [1,1,5,2,4] [3,1,4,5,1] => [2,2,1,5,3] [3,1,5,1,4] => [3,3,1,2,4] [3,1,5,4,1] => [3,3,2,1,4] [3,4,1,1,5] => [1,1,5,2,3] [3,4,1,5,1] => [2,2,1,4,3] [3,4,5,1,1] => [2,4,3,1,2] [3,5,1,1,4] => [3,2,3,1,4] [3,5,1,4,1] => [3,1,3,2,4] [3,5,4,1,1] => [2,5,3,1,2] [4,1,1,3,5] => [1,1,4,5,2] [4,1,1,5,3] => [2,2,5,1,3] [4,1,3,1,5] => [1,1,5,4,2] [4,1,3,5,1] => [2,2,1,3,5] [4,1,5,1,3] => [3,3,1,4,2] [4,1,5,3,1] => [3,3,2,4,1] [4,3,1,1,5] => [1,1,5,3,2] [4,3,1,5,1] => [2,2,1,3,4] [4,3,5,1,1] => [2,3,4,1,2] [4,5,1,1,3] => [3,4,2,3,1] [4,5,1,3,1] => [3,4,1,3,2] [4,5,3,1,1] => [2,3,5,1,2] [5,1,1,3,4] => [4,3,4,1,2] [5,1,1,4,3] => [4,2,4,1,3] [5,1,3,1,4] => [4,3,4,2,1] [5,1,3,4,1] => [4,2,4,3,1] [5,1,4,1,3] => [4,1,4,2,3] [5,1,4,3,1] => [4,1,4,3,2] [5,3,1,1,4] => [3,2,3,1,5] [5,3,1,4,1] => [3,1,3,2,5] [5,3,4,1,1] => [2,5,4,1,2] [5,4,1,1,3] => [3,5,2,3,1] [5,4,1,3,1] => [3,5,1,3,2] [5,4,3,1,1] => [2,4,5,1,2] [1,2,2,2,2] => [1,2,2,2,2] [2,1,2,2,2] => [5,1,1,1,1] [2,2,1,2,2] => [4,1,1,1,1] [2,2,2,1,2] => [3,1,1,1,1] [2,2,2,2,1] => [2,1,1,1,1] [1,2,2,2,3] => [1,2,2,2,3] [1,2,2,3,2] => [1,2,2,3,2] [1,2,3,2,2] => [1,2,3,2,2] [1,3,2,2,2] => [1,2,4,2,2] [2,1,2,2,3] => [1,3,3,3,2] [2,1,2,3,2] => [1,3,3,2,3] [2,1,3,2,2] => [1,3,2,3,3] [2,2,1,2,3] => [4,1,1,1,5] [2,2,1,3,2] => [4,1,1,5,1] [2,2,2,1,3] => [3,1,1,1,4] [2,2,2,3,1] => [2,1,1,1,3] [2,2,3,1,2] => [3,1,1,4,1] [2,2,3,2,1] => [2,1,1,3,1] [2,3,1,2,2] => [4,1,5,1,1] [2,3,2,1,2] => [3,1,4,1,1] [2,3,2,2,1] => [2,1,3,1,1] [3,1,2,2,2] => [5,1,2,1,1] [3,2,1,2,2] => [5,2,1,2,2] [3,2,2,1,2] => [3,1,5,1,1] [3,2,2,2,1] => [2,1,4,1,1] [1,2,2,2,4] => [1,2,2,2,4] [1,2,2,4,2] => [1,2,2,4,2] [1,2,4,2,2] => [1,2,2,5,2] [1,4,2,2,2] => [1,2,5,2,2] [2,1,2,2,4] => [5,1,1,1,2] [2,1,2,4,2] => [5,1,1,2,1] [2,1,4,2,2] => [5,1,1,3,1] [2,2,1,2,4] => [5,2,2,2,1] [2,2,1,4,2] => [5,2,2,1,2] [2,2,2,1,4] => [3,1,1,1,5] [2,2,2,4,1] => [2,1,1,1,4] [2,2,4,1,2] => [3,1,1,5,1] [2,2,4,2,1] => [2,1,1,4,1] [2,4,1,2,2] => [4,1,1,2,1] [2,4,2,1,2] => [4,2,2,1,2] [2,4,2,2,1] => [2,1,1,5,1] [4,1,2,2,2] => [5,1,3,1,1] [4,2,1,2,2] => [4,1,2,1,1] [4,2,2,1,2] => [4,2,1,2,2] [4,2,2,2,1] => [2,1,5,1,1] [1,2,2,2,5] => [1,2,2,2,5] [1,2,2,5,2] => [2,3,3,3,1] [1,2,5,2,2] => [2,3,3,1,3] [1,5,2,2,2] => [2,3,1,3,3] [2,1,2,2,5] => [5,1,1,1,3] [2,1,2,5,2] => [5,1,1,1,4] [2,1,5,2,2] => [5,1,1,4,1] [2,2,1,2,5] => [4,1,1,1,2] [2,2,1,5,2] => [4,1,1,1,3] [2,2,2,1,5] => [4,2,2,2,1] [2,2,2,5,1] => [2,1,1,1,5] [2,2,5,1,2] => [3,1,1,1,2] [2,2,5,2,1] => [3,2,2,2,1] [2,5,1,2,2] => [4,1,1,3,1] [2,5,2,1,2] => [3,1,1,2,1] [2,5,2,2,1] => [3,2,2,1,2] [5,1,2,2,2] => [5,1,4,1,1] [5,2,1,2,2] => [4,1,3,1,1] [5,2,2,1,2] => [3,1,2,1,1] [5,2,2,2,1] => [3,2,1,2,2] [1,2,2,3,3] => [1,2,2,3,3] [1,2,3,2,3] => [1,2,3,2,3] [1,2,3,3,2] => [1,2,3,3,2] [1,3,2,2,3] => [1,2,4,2,4] [1,3,2,3,2] => [1,2,4,4,2] [1,3,3,2,2] => [3,4,1,1,4] [2,1,2,3,3] => [1,3,3,2,2] [2,1,3,2,3] => [1,3,2,3,2] [2,1,3,3,2] => [1,3,2,2,3] [2,2,1,3,3] => [1,4,4,2,2] [2,2,3,1,3] => [3,1,1,4,4] [2,2,3,3,1] => [2,1,1,3,3] [2,3,1,2,3] => [1,4,2,4,2] [2,3,1,3,2] => [1,4,2,2,4] [2,3,2,1,3] => [3,1,4,1,4] [2,3,2,3,1] => [2,1,3,1,3] [2,3,3,1,2] => [3,1,4,4,1] [2,3,3,2,1] => [2,1,3,3,1] [3,1,2,2,3] => [5,1,2,1,2] [3,1,2,3,2] => [5,1,2,2,1] [3,1,3,2,2] => [5,1,3,3,1] [3,2,1,2,3] => [5,2,1,2,1] [3,2,1,3,2] => [5,2,1,1,2] [3,2,2,1,3] => [5,3,1,3,1] [3,2,2,3,1] => [2,1,4,1,4] [3,2,3,1,2] => [5,3,1,1,3] [3,2,3,2,1] => [2,1,4,4,1] [3,3,1,2,2] => [4,1,2,2,1] [3,3,2,1,2] => [4,2,1,1,2] [3,3,2,2,1] => [4,3,1,1,3] [1,2,2,3,4] => [1,2,3,2,4] [1,2,2,4,3] => [1,2,4,2,3] [1,2,3,2,4] => [1,2,3,2,5] [1,2,3,4,2] => [2,3,4,3,1] [1,2,4,2,3] => [1,2,5,2,3] [1,2,4,3,2] => [2,3,1,4,3] [1,3,2,2,4] => [1,2,4,2,5] [1,3,2,4,2] => [2,3,5,3,1] [1,3,4,2,2] => [3,4,1,2,4] [1,4,2,2,3] => [1,2,5,2,4] [1,4,2,3,2] => [2,3,1,5,3] [1,4,3,2,2] => [3,4,2,1,4] [2,1,2,3,4] => [1,3,2,3,4] [2,1,2,4,3] => [1,3,4,3,2] [2,1,3,2,4] => [1,3,2,3,5] [2,1,3,4,2] => [2,4,3,4,1] [2,1,4,2,3] => [1,3,5,3,2] [2,1,4,3,2] => [2,4,1,3,4] [2,2,1,3,4] => [1,4,2,4,3] [2,2,1,4,3] => [1,4,3,4,2] [2,2,3,1,4] => [3,1,4,1,5] [2,2,3,4,1] => [2,1,3,1,4] [2,2,4,1,3] => [3,1,5,1,4] [2,2,4,3,1] => [2,1,4,1,3] [2,3,1,2,4] => [4,1,5,1,2] [2,3,1,4,2] => [4,1,5,1,3] [2,3,2,1,4] => [4,2,5,2,1] [2,3,2,4,1] => [2,1,3,1,5] [2,3,4,1,2] => [3,1,4,1,2] [2,3,4,2,1] => [3,2,4,2,1] [2,4,1,2,3] => [4,1,2,1,5] [2,4,1,3,2] => [4,1,3,5,1] [2,4,2,1,3] => [4,2,1,2,5] [2,4,2,3,1] => [2,1,5,1,3] [2,4,3,1,2] => [3,1,2,4,1] [2,4,3,2,1] => [3,2,1,4,2] [3,1,2,2,4] => [5,1,2,1,3] [3,1,2,4,2] => [5,1,2,1,4] [3,1,4,2,2] => [5,1,3,4,1] [3,2,1,2,4] => [5,2,1,2,3] [3,2,1,4,2] => [5,2,1,2,4] [3,2,2,1,4] => [5,3,1,3,2] [3,2,2,4,1] => [2,1,4,1,5] [3,2,4,1,2] => [3,1,5,1,2] [3,2,4,2,1] => [3,2,5,2,1] [3,4,1,2,2] => [4,1,2,3,1] [3,4,2,1,2] => [4,2,1,3,2] [3,4,2,2,1] => [4,3,1,2,3] [4,1,2,2,3] => [5,1,3,1,2] [4,1,2,3,2] => [5,1,4,2,1] [4,1,3,2,2] => [5,1,4,3,1] [4,2,1,2,3] => [5,2,3,2,1] [4,2,1,3,2] => [5,2,4,1,2] [4,2,2,1,3] => [5,3,2,3,1] [4,2,2,3,1] => [2,1,5,1,4] [4,2,3,1,2] => [3,1,2,5,1] [4,2,3,2,1] => [3,2,1,5,2] [4,3,1,2,2] => [4,1,3,2,1] [4,3,2,1,2] => [4,2,3,1,2] [4,3,2,2,1] => [4,3,2,1,3] [1,2,2,3,5] => [1,2,2,3,5] [1,2,2,5,3] => [2,3,3,4,1] [1,2,3,2,5] => [1,2,2,3,4] [1,2,3,5,2] => [1,2,4,3,2] [1,2,5,2,3] => [2,3,1,3,4] [1,2,5,3,2] => [1,2,5,3,2] [1,3,2,2,5] => [1,2,2,4,3] [1,3,2,5,2] => [1,2,3,4,2] [1,3,5,2,2] => [1,2,3,5,2] [1,5,2,2,3] => [2,3,1,3,5] [1,5,2,3,2] => [1,2,5,4,2] [1,5,3,2,2] => [1,2,4,5,2] [2,1,2,3,5] => [1,3,3,2,5] [2,1,2,5,3] => [2,4,4,3,1] [2,1,3,2,5] => [1,3,3,2,4] [2,1,3,5,2] => [1,3,4,2,3] [2,1,5,2,3] => [2,4,1,4,3] [2,1,5,3,2] => [1,3,5,2,3] [2,2,1,3,5] => [4,1,1,5,2] [2,2,1,5,3] => [4,1,1,5,3] [2,2,3,1,5] => [4,2,2,5,1] [2,2,3,5,1] => [2,1,1,5,3] [2,2,5,1,3] => [3,1,1,2,4] [2,2,5,3,1] => [3,2,2,1,4] [2,3,1,2,5] => [1,4,4,2,3] [2,3,1,5,2] => [1,4,3,2,4] [2,3,2,1,5] => [3,1,1,4,5] [2,3,2,5,1] => [2,1,1,4,3] [2,3,5,1,2] => [3,1,5,4,1] [2,3,5,2,1] => [2,1,4,3,1] [2,5,1,2,3] => [4,1,3,1,5] [2,5,1,3,2] => [4,1,2,5,1] [2,5,2,1,3] => [3,1,2,1,4] [2,5,2,3,1] => [3,2,1,2,4] [2,5,3,1,2] => [4,2,1,5,2] [2,5,3,2,1] => [2,1,5,3,1] [3,1,2,2,5] => [1,3,3,4,2] [3,1,2,5,2] => [1,3,2,4,3] [3,1,5,2,2] => [1,3,2,5,3] [3,2,1,2,5] => [1,4,4,3,2] [3,2,1,5,2] => [1,4,2,3,4] [3,2,2,1,5] => [3,1,1,5,4] [3,2,2,5,1] => [2,1,1,3,4] [3,2,5,1,2] => [3,1,4,5,1] [3,2,5,2,1] => [2,1,3,4,1] [3,5,1,2,2] => [4,1,5,2,1] [3,5,2,1,2] => [4,2,5,1,2] [3,5,2,2,1] => [2,1,3,5,1] [5,1,2,2,3] => [5,1,4,1,2] [5,1,2,3,2] => [5,1,3,2,1] [5,1,3,2,2] => [5,1,2,3,1] [5,2,1,2,3] => [5,2,4,2,1] [5,2,1,3,2] => [5,2,3,1,2] [5,2,2,1,3] => [3,1,2,1,5] [5,2,2,3,1] => [3,2,1,2,5] [5,2,3,1,2] => [5,3,2,1,3] [5,2,3,2,1] => [2,1,5,4,1] [5,3,1,2,2] => [5,2,1,3,2] [5,3,2,1,2] => [5,3,1,2,3] [5,3,2,2,1] => [2,1,4,5,1] [1,2,2,4,4] => [1,2,2,4,4] [1,2,4,2,4] => [3,4,4,1,1] [1,2,4,4,2] => [2,3,3,1,1] [1,4,2,2,4] => [3,4,1,4,1] [1,4,2,4,2] => [2,3,1,3,1] [1,4,4,2,2] => [2,3,1,1,3] [2,1,2,4,4] => [5,1,1,2,2] [2,1,4,2,4] => [5,1,1,3,3] [2,1,4,4,2] => [2,4,4,1,1] [2,2,1,4,4] => [5,2,2,1,1] [2,2,4,1,4] => [5,3,3,1,1] [2,2,4,4,1] => [2,1,1,4,4] [2,4,1,2,4] => [4,1,1,2,2] [2,4,1,4,2] => [4,1,1,3,3] [2,4,2,1,4] => [4,2,2,1,1] [2,4,2,4,1] => [4,3,3,1,1] [2,4,4,1,2] => [3,1,1,2,2] [2,4,4,2,1] => [3,2,2,1,1] [4,1,2,2,4] => [5,1,3,1,3] [4,1,2,4,2] => [2,4,1,4,1] [4,1,4,2,2] => [2,4,1,1,4] [4,2,1,2,4] => [4,1,2,1,2] [4,2,1,4,2] => [4,1,3,1,3] [4,2,2,1,4] => [4,2,1,2,1] [4,2,2,4,1] => [4,3,1,3,1] [4,2,4,1,2] => [3,1,2,1,2] [4,2,4,2,1] => [3,2,1,2,1] [4,4,1,2,2] => [4,1,3,3,1] [4,4,2,1,2] => [3,1,2,2,1] [4,4,2,2,1] => [3,2,1,1,2] [1,2,2,4,5] => [1,2,2,4,5] [1,2,2,5,4] => [2,3,3,5,1] [1,2,4,2,5] => [1,2,2,5,4] [1,2,4,5,2] => [2,3,3,1,5] [1,2,5,2,4] => [3,4,4,1,2] [1,2,5,4,2] => [3,4,4,2,1] [1,4,2,2,5] => [1,2,2,5,3] [1,4,2,5,2] => [2,3,3,1,4] [1,4,5,2,2] => [2,3,4,1,3] [1,5,2,2,4] => [3,4,2,4,1] [1,5,2,4,2] => [3,4,1,4,2] [1,5,4,2,2] => [2,3,5,1,3] [2,1,2,4,5] => [5,1,1,2,3] [2,1,2,5,4] => [5,1,1,2,4] [2,1,4,2,5] => [5,1,1,3,2] [2,1,4,5,2] => [5,1,1,4,2] [2,1,5,2,4] => [5,1,1,3,4] [2,1,5,4,2] => [5,1,1,4,3] [2,2,1,4,5] => [5,2,2,1,3] [2,2,1,5,4] => [5,2,2,1,4] [2,2,4,1,5] => [5,3,3,1,2] [2,2,4,5,1] => [2,1,1,5,4] [2,2,5,1,4] => [3,1,1,2,5] [2,2,5,4,1] => [3,2,2,1,5] [2,4,1,2,5] => [5,2,2,3,1] [2,4,1,5,2] => [5,2,2,4,1] [2,4,2,1,5] => [5,3,3,2,1] [2,4,2,5,1] => [2,1,1,4,5] [2,4,5,1,2] => [3,1,1,5,2] [2,4,5,2,1] => [3,2,2,5,1] [2,5,1,2,4] => [4,1,1,3,2] [2,5,1,4,2] => [4,1,1,2,3] [2,5,2,1,4] => [4,2,2,3,1] [2,5,2,4,1] => [4,3,3,2,1] [2,5,4,1,2] => [4,2,2,1,3] [2,5,4,2,1] => [4,3,3,1,2] [4,1,2,2,5] => [1,3,3,5,2] [4,1,2,5,2] => [2,4,4,1,3] [4,1,5,2,2] => [2,4,3,1,4] [4,2,1,2,5] => [4,1,1,2,5] [4,2,1,5,2] => [4,1,1,3,5] [4,2,2,1,5] => [4,2,2,1,5] [4,2,2,5,1] => [2,1,1,3,5] [4,2,5,1,2] => [3,1,1,4,2] [4,2,5,2,1] => [3,2,2,4,1] [4,5,1,2,2] => [4,1,5,3,1] [4,5,2,1,2] => [3,1,4,2,1] [4,5,2,2,1] => [3,2,4,1,2] [5,1,2,2,4] => [5,1,4,1,3] [5,1,2,4,2] => [5,1,3,1,4] [5,1,4,2,2] => [5,1,2,4,1] [5,2,1,2,4] => [4,1,3,1,2] [5,2,1,4,2] => [4,1,2,1,3] [5,2,2,1,4] => [4,2,3,2,1] [5,2,2,4,1] => [4,3,2,3,1] [5,2,4,1,2] => [4,2,1,2,3] [5,2,4,2,1] => [4,3,1,3,2] [5,4,1,2,2] => [5,2,1,4,2] [5,4,2,1,2] => [3,1,5,2,1] [5,4,2,2,1] => [3,2,5,1,2] [1,2,3,3,3] => [1,2,3,3,3] [1,3,2,3,3] => [4,5,1,1,1] [1,3,3,2,3] => [3,4,1,1,1] [1,3,3,3,2] => [2,3,1,1,1] [2,1,3,3,3] => [1,3,2,2,2] [2,3,1,3,3] => [1,4,2,2,2] [2,3,3,1,3] => [1,5,2,2,2] [2,3,3,3,1] => [2,1,3,3,3] [3,1,2,3,3] => [5,1,2,2,2] [3,1,3,2,3] => [3,5,1,1,1] [3,1,3,3,2] => [2,4,1,1,1] [3,2,1,3,3] => [5,2,1,1,1] [3,2,3,1,3] => [5,3,1,1,1] [3,2,3,3,1] => [5,4,1,1,1] [3,3,1,2,3] => [4,1,2,2,2] [3,3,1,3,2] => [2,5,1,1,1] [3,3,2,1,3] => [4,2,1,1,1] [3,3,2,3,1] => [4,3,1,1,1] [3,3,3,1,2] => [3,1,2,2,2] [3,3,3,2,1] => [3,2,1,1,1] [1,2,3,3,4] => [1,2,3,3,4] [1,2,3,4,3] => [1,2,3,4,3] [1,2,4,3,3] => [1,2,3,5,3] [1,3,2,3,4] => [1,2,4,4,3] [1,3,2,4,3] => [1,2,4,3,4] [1,3,3,2,4] => [3,4,1,1,5] [1,3,3,4,2] => [2,3,1,1,4] [1,3,4,2,3] => [3,4,1,5,1] [1,3,4,3,2] => [2,3,1,4,1] [1,4,2,3,3] => [4,5,1,2,1] [1,4,3,2,3] => [4,5,2,1,2] [1,4,3,3,2] => [2,3,1,5,1] [2,1,3,3,4] => [1,3,2,2,4] [2,1,3,4,3] => [1,3,2,4,2] [2,1,4,3,3] => [1,3,2,5,2] [2,3,1,3,4] => [1,4,2,2,3] [2,3,1,4,3] => [1,4,2,3,2] [2,3,3,1,4] => [1,5,2,2,3] [2,3,3,4,1] => [2,1,3,4,3] [2,3,4,1,3] => [1,5,3,2,2] [2,3,4,3,1] => [2,1,4,3,3] [2,4,1,3,3] => [1,4,5,2,2] [2,4,3,1,3] => [1,5,4,2,2] [2,4,3,3,1] => [2,1,5,3,3] [3,1,2,3,4] => [1,3,4,4,2] [3,1,2,4,3] => [1,3,4,2,4] [3,1,3,2,4] => [3,5,1,1,4] [3,1,3,4,2] => [2,4,1,1,3] [3,1,4,2,3] => [3,5,1,4,1] [3,1,4,3,2] => [2,4,1,3,1] [3,2,1,3,4] => [1,4,3,3,2] [3,2,1,4,3] => [1,4,3,2,3] [3,2,3,1,4] => [1,5,3,3,2] [3,2,3,4,1] => [2,1,4,3,4] [3,2,4,1,3] => [1,5,2,3,3] [3,2,4,3,1] => [2,1,3,4,4] [3,3,1,2,4] => [4,1,2,2,5] [3,3,1,4,2] => [2,5,1,1,3] [3,3,2,1,4] => [4,2,1,1,5] [3,3,2,4,1] => [4,3,1,5,1] [3,3,4,1,2] => [3,1,2,4,2] [3,3,4,2,1] => [3,2,1,4,1] [3,4,1,2,3] => [4,1,5,2,2] [3,4,1,3,2] => [2,5,3,1,1] [3,4,2,1,3] => [4,2,5,1,1] [3,4,2,3,1] => [4,3,5,1,1] [3,4,3,1,2] => [3,1,4,2,2] [3,4,3,2,1] => [3,2,4,1,1] [4,1,2,3,3] => [5,1,3,2,2] [4,1,3,2,3] => [5,1,2,3,3] [4,1,3,3,2] => [2,4,5,1,1] [4,2,1,3,3] => [5,2,3,1,1] [4,2,3,1,3] => [5,3,2,1,1] [4,2,3,3,1] => [5,4,2,1,1] [4,3,1,2,3] => [5,2,1,3,3] [4,3,1,3,2] => [2,5,4,1,1] [4,3,2,1,3] => [5,3,1,2,2] [4,3,2,3,1] => [5,4,1,2,2] [4,3,3,1,2] => [3,1,5,2,2] ----------------------------------------------------------------------------- Created: Jun 16, 2023 at 15:26 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 16, 2023 at 15:26 by Martin Rubey