************************************************************************ * 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: Mp00300 ------------------------------------------------------------------------ Map name: leading to ones ------------------------------------------------------------------------ Domain: Parking functions ------------------------------------------------------------------------ Codomain: Parking functions ------------------------------------------------------------------------ Description: The unique parking function obtained by subtracting the first entry from all others to obtain a Prüfer code and then applying the inverse of the Foata-Riordan map. This map is the inverse of [[Mp00299]]. ------------------------------------------------------------------------ References: [1] (service unreachable) [[MathSciNet:0335294]] ------------------------------------------------------------------------ Code: def mapping(p): if not p: return p return pruefer_to_parking_foata_riordan(parking_to_pruefer_circular(p)) def parking_to_pruefer_circular(p): n = len(p) d = p[0] return [(p[i] - d) % (n+1) for i in range(1, n)] def pruefer_to_tree(c): c = list(c) n = len(c) V = list(range(n+2)) G = Graph([V, []]) for _ in range(n): i, u = next((i, u) for i, u in enumerate(V) if u not in c) del V[i] v = c.pop(0) G.add_edge(u, v) G.add_edge(V) return to_tree(G, 0) def to_tree(G, r): if not G: return LabelledRootedTree([], r) roots = G[r] G.delete_vertex(r) return LabelledOrderedTree([to_tree(G.subgraph(G.connected_component_containing_vertex(u)), u) for u in roots], r) def pruefer_to_parking_foata_riordan(c): t = pruefer_to_tree(c) n = len(c) + 2 labels = [] f = [None]*(n-1) def action(u): i = u.label() labels.append(i) for c in u: f[c.label()-1] = i t.breadth_first_order_traversal(action) sigma = Permutation(labels[1:]).inverse() g = [] for e in f: if e: g.append(1 + sigma(e)) else: g.append(1) return ParkingFunction(g) ------------------------------------------------------------------------ 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] => [2,2,1] [1,1,3] => [1,1,3] [1,3,1] => [2,1,1] [3,1,1] => [2,1,2] [1,2,2] => [1,2,2] [2,1,2] => [3,1,1] [2,2,1] => [1,3,1] [1,2,3] => [1,2,3] [1,3,2] => [2,1,3] [2,1,3] => [2,3,1] [2,3,1] => [1,3,2] [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] => [2,2,2,1] [1,1,1,3] => [1,1,1,3] [1,1,3,1] => [1,1,3,1] [1,3,1,1] => [2,1,1,1] [3,1,1,1] => [2,2,1,2] [1,1,1,4] => [1,1,1,4] [1,1,4,1] => [1,3,1,1] [1,4,1,1] => [3,1,1,1] [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] => [3,3,1,1] [2,1,2,1] => [3,1,3,1] [2,2,1,1] => [1,3,3,1] [1,1,2,3] => [1,2,1,4] [1,1,3,2] => [2,1,1,4] [1,2,1,3] => [1,1,2,3] [1,2,3,1] => [2,1,4,1] [1,3,1,2] => [1,1,3,2] [1,3,2,1] => [1,2,4,1] [2,1,1,3] => [2,2,3,1] [2,1,3,1] => [2,3,2,1] [2,3,1,1] => [1,3,3,2] [3,1,1,2] => [2,4,1,2] [3,1,2,1] => [4,2,1,2] [3,2,1,1] => [3,3,2,1] [1,1,2,4] => [1,1,2,4] [1,1,4,2] => [3,1,1,4] [1,2,1,4] => [1,2,1,3] [1,2,4,1] => [2,4,1,1] [1,4,1,2] => [1,3,1,2] [1,4,2,1] => [1,4,2,1] [2,1,1,4] => [2,2,4,1] [2,1,4,1] => [3,2,2,1] [2,4,1,1] => [3,1,3,2] [4,1,1,2] => [2,1,2,4] [4,1,2,1] => [3,1,2,2] [4,2,1,1] => [3,2,1,3] [1,1,3,3] => [1,1,3,3] [1,3,1,3] => [2,1,1,2] [1,3,3,1] => [2,1,2,1] [3,1,1,3] => [2,2,1,1] [3,1,3,1] => [3,1,1,3] [3,3,1,1] => [1,3,1,3] [1,1,3,4] => [1,1,3,4] [1,1,4,3] => [1,3,1,4] [1,3,1,4] => [2,1,1,3] [1,3,4,1] => [4,2,1,1] [1,4,1,3] => [3,1,1,2] [1,4,3,1] => [4,1,2,1] [3,1,1,4] => [2,2,1,3] [3,1,4,1] => [2,3,1,2] [3,4,1,1] => [1,3,2,3] [4,1,1,3] => [2,1,4,2] [4,1,3,1] => [4,1,2,2] [4,3,1,1] => [3,2,3,1] [1,2,2,2] => [1,2,2,2] [2,1,2,2] => [4,1,1,1] [2,2,1,2] => [1,4,1,1] [2,2,2,1] => [1,1,4,1] [1,2,2,3] => [1,2,2,3] [1,2,3,2] => [1,2,3,2] [1,3,2,2] => [2,1,3,3] [2,1,2,3] => [1,4,1,2] [2,1,3,2] => [1,3,2,1] [2,2,1,3] => [3,1,4,1] [2,2,3,1] => [1,1,4,2] [2,3,1,2] => [3,4,1,1] [2,3,2,1] => [1,2,3,1] [3,1,2,2] => [3,3,1,2] [3,2,1,2] => [4,2,2,1] [3,2,2,1] => [2,4,2,1] [1,2,2,4] => [1,2,2,4] [1,2,4,2] => [1,3,2,2] [1,4,2,2] => [2,3,1,3] [2,1,2,4] => [4,1,1,2] [2,1,4,2] => [3,1,2,1] [2,2,1,4] => [1,3,4,1] [2,2,4,1] => [1,1,4,3] [2,4,1,2] => [4,3,1,1] [2,4,2,1] => [2,1,3,1] [4,1,2,2] => [3,1,2,3] [4,2,1,2] => [3,2,1,2] [4,2,2,1] => [2,2,1,4] [1,2,3,3] => [1,2,3,3] [1,3,2,3] => [2,1,3,2] [1,3,3,2] => [2,1,2,3] [2,1,3,3] => [2,3,3,1] [2,3,1,3] => [1,4,2,2] [2,3,3,1] => [1,2,4,2] [3,1,2,3] => [2,3,1,1] [3,1,3,2] => [4,1,3,1] [3,2,1,3] => [3,2,1,1] [3,2,3,1] => [4,1,1,3] [3,3,1,2] => [1,4,1,3] [3,3,2,1] => [1,4,3,1] [1,2,3,4] => [1,2,3,4] [1,2,4,3] => [1,3,2,4] [1,3,2,4] => [2,1,3,4] [1,3,4,2] => [3,1,2,4] [1,4,2,3] => [2,3,1,4] [1,4,3,2] => [3,2,1,4] [2,1,3,4] => [3,2,4,1] [2,1,4,3] => [2,3,4,1] [2,3,1,4] => [1,3,4,2] [2,3,4,1] => [1,2,4,3] [2,4,1,3] => [3,1,4,2] [2,4,3,1] => [2,1,4,3] [3,1,2,4] => [2,4,1,3] [3,1,4,2] => [3,4,1,2] [3,2,1,4] => [2,4,3,1] [3,2,4,1] => [3,4,2,1] [3,4,1,2] => [1,4,2,3] [3,4,2,1] => [1,4,3,2] [4,1,2,3] => [4,1,3,2] [4,1,3,2] => [4,1,2,3] [4,2,1,3] => [4,3,1,2] [4,2,3,1] => [4,2,1,3] [4,3,1,2] => [4,3,2,1] [4,3,2,1] => [4,2,3,1] [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] => [2,2,2,2,1] [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] => [2,1,1,1,1] [3,1,1,1,1] => [2,2,2,1,2] [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] => [1,3,1,1,1] [1,4,1,1,1] => [3,1,1,1,1] [4,1,1,1,1] => [2,2,1,2,2] [1,1,1,1,5] => [1,1,1,1,5] [1,1,1,5,1] => [1,1,4,1,1] [1,1,5,1,1] => [1,4,1,1,1] [1,5,1,1,1] => [4,1,1,1,1] [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] => [3,3,3,1,1] [2,1,1,2,1] => [3,3,1,3,1] [2,1,2,1,1] => [3,1,3,3,1] [2,2,1,1,1] => [1,3,3,3,1] [1,1,1,2,3] => [1,2,1,1,5] [1,1,1,3,2] => [2,1,1,1,5] [1,1,2,1,3] => [1,1,1,2,3] [1,1,2,3,1] => [2,1,1,5,1] [1,1,3,1,2] => [1,1,1,3,2] [1,1,3,2,1] => [1,2,1,5,1] [1,2,1,1,3] => [1,1,2,1,3] [1,2,1,3,1] => [1,1,2,3,1] [1,2,3,1,1] => [2,1,5,1,1] [1,3,1,1,2] => [1,1,3,1,2] [1,3,1,2,1] => [1,1,3,2,1] [1,3,2,1,1] => [1,2,5,1,1] [2,1,1,1,3] => [2,2,2,3,1] [2,1,1,3,1] => [2,2,3,2,1] [2,1,3,1,1] => [2,3,2,2,1] [2,3,1,1,1] => [1,3,3,3,2] [3,1,1,1,2] => [2,2,5,1,2] [3,1,1,2,1] => [2,5,2,1,2] [3,1,2,1,1] => [5,2,2,1,2] [3,2,1,1,1] => [3,3,3,2,1] [1,1,1,2,4] => [1,1,2,1,5] [1,1,1,4,2] => [3,1,1,1,5] [1,1,2,1,4] => [1,1,1,2,4] [1,1,2,4,1] => [3,1,1,5,1] [1,1,4,1,2] => [1,1,1,4,2] [1,1,4,2,1] => [1,1,2,5,1] [1,2,1,1,4] => [1,2,1,1,3] [1,2,1,4,1] => [1,2,1,3,1] [1,2,4,1,1] => [2,5,1,1,1] [1,4,1,1,2] => [1,3,1,1,2] [1,4,1,2,1] => [1,3,1,2,1] [1,4,2,1,1] => [1,5,2,1,1] [2,1,1,1,4] => [2,2,2,4,1] [2,1,1,4,1] => [2,2,4,2,1] [2,1,4,1,1] => [3,2,2,2,1] [2,4,1,1,1] => [3,1,3,3,2] [4,1,1,1,2] => [2,2,1,2,5] [4,1,1,2,1] => [2,4,1,2,2] [4,1,2,1,1] => [4,2,1,2,2] [4,2,1,1,1] => [3,3,2,1,3] [1,1,1,2,5] => [1,1,1,2,5] [1,1,1,5,2] => [4,1,1,1,5] [1,1,2,1,5] => [1,1,2,1,4] [1,1,2,5,1] => [3,1,5,1,1] [1,1,5,1,2] => [1,1,4,1,2] [1,1,5,2,1] => [1,1,5,2,1] [1,2,1,1,5] => [1,2,1,1,4] [1,2,1,5,1] => [1,2,3,1,1] [1,2,5,1,1] => [3,5,1,1,1] [1,5,1,1,2] => [1,4,1,1,2] [1,5,1,2,1] => [1,5,1,2,1] [1,5,2,1,1] => [1,3,2,1,1] [2,1,1,1,5] => [2,2,2,5,1] [2,1,1,5,1] => [2,4,2,2,1] [2,1,5,1,1] => [4,2,2,2,1] [2,5,1,1,1] => [3,3,1,3,2] [5,1,1,1,2] => [2,1,2,2,4] [5,1,1,2,1] => [2,1,2,4,2] [5,1,2,1,1] => [3,1,2,2,2] [5,2,1,1,1] => [3,2,1,3,3] [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] => [2,1,1,1,2] [1,3,1,3,1] => [2,1,1,2,1] [1,3,3,1,1] => [2,1,2,1,1] [3,1,1,1,3] => [2,2,2,1,1] [3,1,1,3,1] => [3,3,1,1,3] [3,1,3,1,1] => [3,1,3,1,3] [3,3,1,1,1] => [1,3,3,1,3] [1,1,1,3,4] => [1,1,3,1,5] [1,1,1,4,3] => [1,3,1,1,5] [1,1,3,1,4] => [1,1,1,3,4] [1,1,3,4,1] => [1,3,1,5,1] [1,1,4,1,3] => [1,1,1,4,3] [1,1,4,3,1] => [1,1,3,5,1] [1,3,1,1,4] => [2,1,1,1,3] [1,3,1,4,1] => [2,1,1,3,1] [1,3,4,1,1] => [5,2,1,1,1] [1,4,1,1,3] => [3,1,1,1,2] [1,4,1,3,1] => [3,1,1,2,1] [1,4,3,1,1] => [5,1,2,1,1] [3,1,1,1,4] => [2,2,2,1,3] [3,1,1,4,1] => [2,2,3,1,2] [3,1,4,1,1] => [2,3,2,1,2] [3,4,1,1,1] => [1,3,3,2,3] [4,1,1,1,3] => [2,2,1,5,2] [4,1,1,3,1] => [2,5,1,2,2] [4,1,3,1,1] => [5,2,1,2,2] [4,3,1,1,1] => [3,3,2,3,1] [1,1,1,3,5] => [1,1,1,3,5] [1,1,1,5,3] => [1,4,1,1,5] [1,1,3,1,5] => [1,1,3,1,4] [1,1,3,5,1] => [1,3,5,1,1] [1,1,5,1,3] => [1,1,4,1,3] [1,1,5,3,1] => [1,1,5,3,1] [1,3,1,1,5] => [2,1,1,1,4] [1,3,1,5,1] => [2,1,3,1,1] [1,3,5,1,1] => [5,3,1,1,1] [1,5,1,1,3] => [4,1,1,1,2] [1,5,1,3,1] => [5,1,1,2,1] [1,5,3,1,1] => [3,1,2,1,1] [3,1,1,1,5] => [2,2,2,1,4] [3,1,1,5,1] => [2,2,4,1,2] [3,1,5,1,1] => [3,2,2,1,2] [3,5,1,1,1] => [3,1,3,2,3] [5,1,1,1,3] => [2,1,2,2,5] [5,1,1,3,1] => [2,1,4,2,2] [5,1,3,1,1] => [4,1,2,2,2] [5,3,1,1,1] => [3,2,3,1,3] [1,1,1,4,4] => [1,1,1,4,4] [1,1,4,1,4] => [1,3,1,1,3] [1,1,4,4,1] => [1,3,1,3,1] [1,4,1,1,4] => [3,1,1,1,3] [1,4,1,4,1] => [3,1,1,3,1] [1,4,4,1,1] => [2,2,1,1,1] [4,1,1,1,4] => [2,2,1,2,1] [4,1,1,4,1] => [2,2,1,1,2] [4,1,4,1,1] => [3,1,1,3,3] [4,4,1,1,1] => [1,3,1,3,3] [1,1,1,4,5] => [1,1,1,4,5] [1,1,1,5,4] => [1,1,4,1,5] [1,1,4,1,5] => [1,3,1,1,4] [1,1,4,5,1] => [1,5,3,1,1] [1,1,5,1,4] => [1,4,1,1,3] [1,1,5,4,1] => [1,5,1,3,1] [1,4,1,1,5] => [3,1,1,1,4] [1,4,1,5,1] => [5,1,3,1,1] [1,4,5,1,1] => [2,3,1,1,1] [1,5,1,1,4] => [4,1,1,1,3] [1,5,1,4,1] => [5,1,1,3,1] [1,5,4,1,1] => [3,2,1,1,1] [4,1,1,1,5] => [2,2,1,2,3] [4,1,1,5,1] => [2,2,1,3,2] [4,1,5,1,1] => [2,3,1,2,2] [4,5,1,1,1] => [1,3,2,3,3] [5,1,1,1,4] => [2,1,2,5,2] [5,1,1,4,1] => [2,1,5,2,2] [5,1,4,1,1] => [5,1,2,2,2] [5,4,1,1,1] => [3,2,3,3,1] [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] => [4,4,1,1,1] [2,1,2,1,2] => [4,1,4,1,1] [2,1,2,2,1] => [4,1,1,4,1] [2,2,1,1,2] => [1,4,4,1,1] [2,2,1,2,1] => [1,4,1,4,1] [2,2,2,1,1] => [1,1,4,4,1] [1,1,2,2,3] => [1,2,1,2,4] [1,1,2,3,2] => [1,2,1,4,2] [1,1,3,2,2] => [2,1,1,4,4] [1,2,1,2,3] => [1,2,2,1,4] [1,2,1,3,2] => [2,1,4,1,4] [1,2,2,1,3] => [1,1,2,2,3] [1,2,2,3,1] => [2,1,4,4,1] [1,2,3,1,2] => [1,1,2,3,2] [1,2,3,2,1] => [1,2,2,4,1] [1,3,1,2,2] => [1,1,3,2,2] [1,3,2,1,2] => [1,2,4,1,2] [1,3,2,2,1] => [1,2,4,2,1] [2,1,1,2,3] => [1,4,4,1,2] [2,1,1,3,2] => [1,3,3,2,1] [2,1,2,1,3] => [3,3,1,4,1] [2,1,2,3,1] => [1,4,1,4,2] [2,1,3,1,2] => [3,3,4,1,1] [2,1,3,2,1] => [1,3,2,3,1] [2,2,1,1,3] => [3,1,3,4,1] [2,2,1,3,1] => [3,1,4,3,1] [2,2,3,1,1] => [1,1,4,4,2] [2,3,1,1,2] => [3,4,3,1,1] [2,3,1,2,1] => [3,4,1,3,1] [2,3,2,1,1] => [1,2,3,3,1] [3,1,1,2,2] => [2,4,4,1,2] [3,1,2,1,2] => [4,2,4,1,2] [3,1,2,2,1] => [4,4,2,1,2] [3,2,1,1,2] => [4,4,2,2,1] [3,2,1,2,1] => [4,2,4,2,1] [3,2,2,1,1] => [2,4,4,2,1] [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] => [3,1,1,4,4] [1,2,1,2,4] => [1,2,2,1,5] [1,2,1,4,2] => [2,4,1,1,4] [1,2,2,1,4] => [1,2,1,2,3] [1,2,2,4,1] => [2,4,1,4,1] [1,2,4,1,2] => [1,2,1,3,2] [1,2,4,2,1] => [1,2,2,5,1] [1,4,1,2,2] => [1,3,1,2,2] [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] => [4,1,4,1,2] [2,1,1,4,2] => [3,1,3,2,1] [2,1,2,1,4] => [3,3,1,5,1] [2,1,2,4,1] => [4,1,1,4,2] [2,1,4,1,2] => [3,3,5,1,1] [2,1,4,2,1] => [3,1,2,3,1] [2,2,1,1,4] => [1,3,3,4,1] [2,2,1,4,1] => [1,3,4,3,1] [2,2,4,1,1] => [1,1,4,4,3] [2,4,1,1,2] => [4,3,3,1,1] [2,4,1,2,1] => [4,3,1,3,1] [2,4,2,1,1] => [2,1,3,3,1] [4,1,1,2,2] => [2,4,1,2,4] [4,1,2,1,2] => [4,2,1,2,4] [4,1,2,2,1] => [3,3,1,2,2] [4,2,1,1,2] => [3,3,2,1,2] [4,2,1,2,1] => [4,2,2,1,4] [4,2,2,1,1] => [2,4,2,1,4] [1,1,2,2,5] => [1,1,2,2,5] [1,1,2,5,2] => [1,1,4,2,2] [1,1,5,2,2] => [3,1,4,1,4] [1,2,1,2,5] => [1,2,1,2,5] [1,2,1,5,2] => [3,4,1,1,4] [1,2,2,1,5] => [1,2,2,1,3] [1,2,2,5,1] => [2,4,4,1,1] [1,2,5,1,2] => [1,2,3,1,2] [1,2,5,2,1] => [1,2,5,2,1] [1,5,1,2,2] => [1,4,1,2,2] [1,5,2,1,2] => [1,3,2,1,2] [1,5,2,2,1] => [1,5,2,2,1] [2,1,1,2,5] => [4,4,1,1,2] [2,1,1,5,2] => [3,3,1,2,1] [2,1,2,1,5] => [3,1,3,5,1] [2,1,2,5,1] => [4,1,1,4,3] [2,1,5,1,2] => [3,5,3,1,1] [2,1,5,2,1] => [3,2,1,3,1] [2,2,1,1,5] => [1,3,3,5,1] [2,2,1,5,1] => [1,4,3,3,1] [2,2,5,1,1] => [1,4,1,4,3] [2,5,1,1,2] => [5,3,3,1,1] [2,5,1,2,1] => [2,3,1,3,1] [2,5,2,1,1] => [4,1,3,3,1] [5,1,1,2,2] => [2,1,2,4,4] [5,1,2,1,2] => [3,1,2,2,3] [5,1,2,2,1] => [3,1,2,3,2] [5,2,1,1,2] => [3,2,1,3,2] [5,2,1,2,1] => [3,2,1,2,3] [5,2,2,1,1] => [2,2,1,4,4] [1,1,2,3,3] => [1,2,1,4,4] [1,1,3,2,3] => [2,1,1,4,2] [1,1,3,3,2] => [2,1,1,2,4] [1,2,1,3,3] => [1,1,2,3,3] [1,2,3,1,3] => [2,1,4,1,2] [1,2,3,3,1] => [2,1,4,2,1] [1,3,1,2,3] => [1,2,4,1,4] [1,3,1,3,2] => [2,1,2,1,4] [1,3,2,1,3] => [1,1,3,2,3] [1,3,2,3,1] => [2,1,2,4,1] [1,3,3,1,2] => [1,1,3,3,2] [1,3,3,2,1] => [1,2,4,4,1] [2,1,1,3,3] => [2,2,3,3,1] [2,1,3,1,3] => [2,3,2,3,1] [2,1,3,3,1] => [2,3,3,2,1] [2,3,1,1,3] => [1,4,4,2,2] [2,3,1,3,1] => [1,4,2,4,2] [2,3,3,1,1] => [1,2,4,4,2] [3,1,1,2,3] => [2,2,3,1,1] [3,1,1,3,2] => [4,4,1,3,1] [3,1,2,1,3] => [2,3,2,1,1] [3,1,2,3,1] => [3,5,1,1,3] [3,1,3,1,2] => [3,1,5,1,3] [3,1,3,2,1] => [4,1,4,3,1] [3,2,1,1,3] => [3,2,2,1,1] [3,2,1,3,1] => [5,3,1,1,3] [3,2,3,1,1] => [5,1,3,1,3] [3,3,1,1,2] => [1,3,5,1,3] [3,3,1,2,1] => [1,5,3,1,3] [3,3,2,1,1] => [1,4,4,3,1] [1,1,2,3,4] => [1,2,4,1,5] [1,1,2,4,3] => [1,4,2,1,5] [1,1,3,2,4] => [2,1,4,1,5] [1,1,3,4,2] => [4,1,2,1,5] [1,1,4,2,3] => [2,4,1,1,5] [1,1,4,3,2] => [4,2,1,1,5] [1,2,1,3,4] => [1,1,3,2,5] [1,2,1,4,3] => [1,3,1,2,5] [1,2,3,1,4] => [2,1,1,4,3] [1,2,3,4,1] => [4,2,1,5,1] [1,2,4,1,3] => [3,1,1,5,2] [1,2,4,3,1] => [4,1,2,5,1] [1,3,1,2,4] => [1,1,2,3,4] [1,3,1,4,2] => [3,1,1,2,5] [1,3,2,1,4] => [1,2,1,4,3] [1,3,2,4,1] => [2,4,1,5,1] [1,3,4,1,2] => [1,3,1,5,2] [1,3,4,2,1] => [1,4,2,5,1] [1,4,1,2,3] => [1,2,1,3,4] [1,4,1,3,2] => [2,1,1,3,4] [1,4,2,1,3] => [1,1,2,4,3] [1,4,2,3,1] => [2,1,4,5,1] [1,4,3,1,2] => [1,1,3,5,2] [1,4,3,2,1] => [1,2,4,5,1] [2,1,1,3,4] => [3,2,2,5,1] [2,1,1,4,3] => [2,3,2,5,1] [2,1,3,1,4] => [2,2,3,4,1] [2,1,3,4,1] => [3,2,5,2,1] [2,1,4,1,3] => [2,2,4,3,1] [2,1,4,3,1] => [2,3,5,2,1] [2,3,1,1,4] => [1,3,3,4,2] [2,3,1,4,1] => [1,3,4,3,2] [2,3,4,1,1] => [1,2,4,4,3] [2,4,1,1,3] => [3,1,3,4,2] [2,4,1,3,1] => [3,1,4,3,2] [2,4,3,1,1] => [2,1,4,4,3] [3,1,1,2,4] => [2,2,5,1,3] [3,1,1,4,2] => [4,2,5,1,2] [3,1,2,1,4] => [2,5,2,1,3] [3,1,2,4,1] => [2,4,3,1,2] [3,1,4,1,2] => [2,3,4,1,2] [3,1,4,2,1] => [4,5,2,1,2] [3,2,1,1,4] => [2,4,4,3,1] [3,2,1,4,1] => [3,3,4,2,1] [3,2,4,1,1] => [3,4,3,2,1] [3,4,1,1,2] => [1,3,5,2,3] [3,4,1,2,1] => [1,5,3,2,3] [3,4,2,1,1] => [1,4,4,3,2] [4,1,1,2,3] => [2,5,1,4,2] [4,1,1,3,2] => [2,5,1,2,4] [4,1,2,1,3] => [5,2,1,4,2] [4,1,2,3,1] => [3,4,1,2,2] [4,1,3,1,2] => [5,2,1,2,4] [4,1,3,2,1] => [4,3,1,2,2] [4,2,1,1,3] => [4,4,3,1,2] [4,2,1,3,1] => [3,5,2,1,3] [4,2,3,1,1] => [5,3,2,1,3] [4,3,1,1,2] => [4,4,3,2,1] [4,3,1,2,1] => [3,5,2,3,1] [4,3,2,1,1] => [5,3,2,3,1] [1,1,2,3,5] => [1,2,1,4,5] [1,1,2,5,3] => [1,4,1,2,5] [1,1,3,2,5] => [2,1,1,4,5] [1,1,3,5,2] => [4,1,1,2,5] [1,1,5,2,3] => [3,4,1,1,5] [1,1,5,3,2] => [4,3,1,1,5] [1,2,1,3,5] => [1,1,2,3,5] [1,2,1,5,3] => [1,3,2,1,5] [1,2,3,1,5] => [2,1,4,1,3] [1,2,3,5,1] => [4,2,5,1,1] [1,2,5,1,3] => [3,1,5,1,2] [1,2,5,3,1] => [4,1,5,2,1] [1,3,1,2,5] => [1,1,3,2,4] [1,3,1,5,2] => [3,1,2,1,5] [1,3,2,1,5] => [1,2,4,1,3] [1,3,2,5,1] => [2,4,5,1,1] [1,3,5,1,2] => [1,3,5,1,2] [1,3,5,2,1] => [1,4,5,2,1] [1,5,1,2,3] => [1,2,3,1,4] [1,5,1,3,2] => [2,1,3,1,4] [1,5,2,1,3] => [1,1,4,2,3] [1,5,2,3,1] => [2,1,5,4,1] [1,5,3,1,2] => [1,1,5,3,2] [1,5,3,2,1] => [1,2,5,4,1] [2,1,1,3,5] => [4,2,2,5,1] [2,1,1,5,3] => [2,2,3,5,1] [2,1,3,1,5] => [2,3,2,4,1] [2,1,3,5,1] => [3,5,2,2,1] [2,1,5,1,3] => [2,4,2,3,1] [2,1,5,3,1] => [2,5,3,2,1] [2,3,1,1,5] => [1,3,3,5,2] [2,3,1,5,1] => [1,4,3,3,2] [2,3,5,1,1] => [1,4,2,4,3] [2,5,1,1,3] => [3,3,1,4,2] [2,5,1,3,1] => [2,4,1,4,3] [2,5,3,1,1] => [3,4,1,3,2] [3,1,1,2,5] => [2,2,5,1,4] [3,1,1,5,2] => [2,4,5,1,2] [3,1,2,1,5] => [5,2,2,1,3] [3,1,2,5,1] => [4,2,3,1,2] [3,1,5,1,2] => [3,2,4,1,2] [3,1,5,2,1] => [5,4,2,1,2] [3,2,1,1,5] => [4,2,4,3,1] [3,2,1,5,1] => [3,3,5,2,1] [3,2,5,1,1] => [4,3,3,2,1] [3,5,1,1,2] => [3,1,5,2,3] [3,5,1,2,1] => [4,1,4,3,2] [3,5,2,1,1] => [5,1,3,2,3] [5,1,1,2,3] => [2,1,2,4,5] [5,1,1,3,2] => [2,1,4,2,5] [5,1,2,1,3] => [3,1,2,2,4] [5,1,2,3,1] => [5,1,3,2,2] [5,1,3,1,2] => [4,1,2,2,3] [5,1,3,2,1] => [5,1,2,3,2] [5,2,1,1,3] => [3,2,1,3,5] [5,2,1,3,1] => [4,3,1,2,4] [5,2,3,1,1] => [4,2,1,3,3] [5,3,1,1,2] => [3,2,3,1,5] [5,3,1,2,1] => [4,3,2,1,4] [5,3,2,1,1] => [4,2,3,1,3] [1,1,2,4,4] => [1,1,2,4,4] [1,1,4,2,4] => [3,1,1,4,3] [1,1,4,4,2] => [3,1,1,3,4] [1,2,1,4,4] => [1,2,1,3,3] [1,2,4,1,4] => [2,4,1,1,2] [1,2,4,4,1] => [2,4,1,2,1] [1,4,1,2,4] => [1,4,2,1,4] [1,4,1,4,2] => [2,2,1,1,4] [1,4,2,1,4] => [1,3,1,2,3] [1,4,2,4,1] => [2,2,1,4,1] [1,4,4,1,2] => [1,3,1,3,2] [1,4,4,2,1] => [1,4,2,4,1] [2,1,1,4,4] => [2,2,4,4,1] [2,1,4,1,4] => [3,2,2,3,1] [2,1,4,4,1] => [3,2,3,2,1] [2,4,1,1,4] => [4,1,4,2,2] [2,4,1,4,1] => [4,1,2,4,2] [2,4,4,1,1] => [2,1,4,4,2] [4,1,1,2,4] => [4,4,2,1,1] [4,1,1,4,2] => [2,2,1,1,3] [4,1,2,1,4] => [2,5,1,2,1] [4,1,2,4,1] => [2,3,1,1,2] [4,1,4,1,2] => [3,1,1,3,5] [4,1,4,2,1] => [4,1,3,1,4] [4,2,1,1,4] => [5,2,1,2,1] [4,2,1,4,1] => [3,2,1,1,2] [4,2,4,1,1] => [4,1,1,3,3] [4,4,1,1,2] => [1,3,1,3,5] [4,4,1,2,1] => [1,4,1,3,3] [4,4,2,1,1] => [1,4,3,1,4] [1,1,2,4,5] => [1,1,2,4,5] [1,1,2,5,4] => [1,1,4,2,5] [1,1,4,2,5] => [3,1,1,4,5] [1,1,4,5,2] => [4,1,1,3,5] [1,1,5,2,4] => [3,1,4,1,5] [1,1,5,4,2] => [4,1,3,1,5] [1,2,1,4,5] => [1,2,1,3,5] [1,2,1,5,4] => [1,2,3,1,5] [1,2,4,1,5] => [2,4,1,1,3] [1,2,4,5,1] => [4,5,2,1,1] [1,2,5,1,4] => [3,5,1,1,2] [1,2,5,4,1] => [4,5,1,2,1] [1,4,1,2,5] => [1,3,1,2,4] [1,4,1,5,2] => [3,2,1,1,5] [1,4,2,1,5] => [1,4,2,1,3] [1,4,2,5,1] => [2,5,4,1,1] [1,4,5,1,2] => [1,5,3,1,2] [1,4,5,2,1] => [1,5,4,2,1] [1,5,1,2,4] => [1,3,2,1,4] [1,5,1,4,2] => [2,3,1,1,4] [1,5,2,1,4] => [1,4,1,2,3] [1,5,2,4,1] => [2,5,1,4,1] [1,5,4,1,2] => [1,5,1,3,2] [1,5,4,2,1] => [1,5,2,4,1] [2,1,1,4,5] => [2,4,2,5,1] [2,1,1,5,4] => [2,2,4,5,1] [2,1,4,1,5] => [3,2,2,4,1] [2,1,4,5,1] => [5,3,2,2,1] [2,1,5,1,4] => [4,2,2,3,1] [2,1,5,4,1] => [5,2,3,2,1] [2,4,1,1,5] => [3,1,3,5,2] [2,4,1,5,1] => [4,1,2,4,3] [2,4,5,1,1] => [4,1,3,3,2] [2,5,1,1,4] => [3,3,1,5,2] [2,5,1,4,1] => [4,2,1,4,3] [2,5,4,1,1] => [4,3,1,3,2] [4,1,1,2,5] => [4,2,1,2,5] [4,1,1,5,2] => [2,2,1,3,5] [4,1,2,1,5] => [2,4,1,2,3] [4,1,2,5,1] => [2,5,1,3,2] [4,1,5,1,2] => [2,3,1,2,4] [4,1,5,2,1] => [3,5,1,2,2] [4,2,1,1,5] => [3,3,2,1,4] [4,2,1,5,1] => [2,4,3,1,4] [4,2,5,1,1] => [3,4,2,1,3] [4,5,1,1,2] => [1,3,2,3,5] [4,5,1,2,1] => [1,4,2,3,3] [4,5,2,1,1] => [1,4,3,2,4] [5,1,1,2,4] => [2,1,2,5,4] [5,1,1,4,2] => [2,1,4,5,2] [5,1,2,1,4] => [3,1,2,4,2] [5,1,2,4,1] => [5,1,4,2,2] [5,1,4,1,2] => [5,1,2,2,3] [5,1,4,2,1] => [4,1,2,3,2] [5,2,1,1,4] => [3,2,1,5,3] [5,2,1,4,1] => [4,3,1,4,2] [5,2,4,1,1] => [5,2,1,3,3] [5,4,1,1,2] => [4,3,2,4,1] [5,4,1,2,1] => [3,2,3,5,1] [5,4,2,1,1] => [4,2,3,3,1] [1,1,3,3,3] => [1,1,3,3,3] [1,3,1,3,3] => [2,1,1,2,2] [1,3,3,1,3] => [2,1,2,1,2] [1,3,3,3,1] => [2,1,2,2,1] [3,1,1,3,3] => [3,3,1,1,1] [3,1,3,1,3] => [3,1,3,1,1] [3,1,3,3,1] => [4,1,1,1,4] [3,3,1,1,3] => [1,3,3,1,1] [3,3,1,3,1] => [1,4,1,1,4] [3,3,3,1,1] => [1,1,4,1,4] [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] => [1,3,1,4,4] [1,3,1,3,4] => [2,1,2,1,5] [1,3,1,4,3] => [4,2,1,1,4] [1,3,3,1,4] => [2,1,1,2,3] [1,3,3,4,1] => [4,2,1,4,1] [1,3,4,1,3] => [2,1,1,3,2] [1,3,4,3,1] => [2,1,2,5,1] [1,4,1,3,3] => [3,1,1,2,2] [1,4,3,1,3] => [4,1,2,1,2] [1,4,3,3,1] => [4,1,2,2,1] [3,1,1,3,4] => [1,3,3,1,2] [3,1,1,4,3] => [1,4,4,2,1] [3,1,3,1,4] => [3,3,1,1,4] [3,1,3,4,1] => [1,4,1,2,4] [3,1,4,1,3] => [2,2,4,1,1] [3,1,4,3,1] => [1,3,2,1,3] [3,3,1,1,4] => [3,1,3,1,4] [3,3,1,4,1] => [3,1,4,1,3] [3,3,4,1,1] => [1,1,4,2,4] [3,4,1,1,3] => [2,4,2,1,1] [3,4,1,3,1] => [3,4,1,1,3] [3,4,3,1,1] => [1,2,3,1,3] [4,1,1,3,3] => [2,4,1,4,2] [4,1,3,1,3] => [4,2,1,4,2] [4,1,3,3,1] => [4,4,1,2,2] [4,3,1,1,3] => [3,3,2,2,1] [4,3,1,3,1] => [4,2,2,4,1] [4,3,3,1,1] => [2,4,2,4,1] [1,1,3,3,5] => [1,1,3,3,5] [1,1,3,5,3] => [1,1,4,3,3] [1,1,5,3,3] => [1,3,4,1,4] [1,3,1,3,5] => [2,1,1,2,5] [1,3,1,5,3] => [4,3,1,1,4] [1,3,3,1,5] => [2,1,2,1,3] [1,3,3,5,1] => [4,2,4,1,1] [1,3,5,1,3] => [2,1,3,1,2] [1,3,5,3,1] => [2,1,5,2,1] [1,5,1,3,3] => [4,1,1,2,2] [1,5,3,1,3] => [3,1,2,1,2] [1,5,3,3,1] => [5,1,2,2,1] [3,1,1,3,5] => [3,1,3,1,2] [3,1,1,5,3] => [4,1,4,2,1] [3,1,3,1,5] => [3,3,1,1,5] [3,1,3,5,1] => [4,1,1,2,4] [3,1,5,1,3] => [2,2,5,1,1] [3,1,5,3,1] => [3,1,2,1,3] [3,3,1,1,5] => [1,3,3,1,4] [3,3,1,5,1] => [1,3,4,1,3] [3,3,5,1,1] => [1,1,4,3,4] [3,5,1,1,3] => [4,2,2,1,1] [3,5,1,3,1] => [4,3,1,1,3] [3,5,3,1,1] => [2,1,3,1,3] [5,1,1,3,3] => [2,1,4,2,4] [5,1,3,1,3] => [4,1,2,2,4] [5,1,3,3,1] => [3,1,3,2,2] [5,3,1,1,3] => [3,2,3,1,2] [5,3,1,3,1] => [3,2,2,1,3] [5,3,3,1,1] => [2,2,4,1,4] [1,1,3,4,4] => [1,1,3,4,4] [1,1,4,3,4] => [1,3,1,4,3] [1,1,4,4,3] => [1,3,1,3,4] [1,3,1,4,4] => [2,1,1,3,3] [1,3,4,1,4] => [4,2,1,1,2] [1,3,4,4,1] => [4,2,1,2,1] [1,4,1,3,4] => [4,1,2,1,4] [1,4,1,4,3] => [2,2,1,1,5] [1,4,3,1,4] => [3,1,1,2,3] [1,4,3,4,1] => [2,2,1,5,1] [1,4,4,1,3] => [3,1,1,3,2] [1,4,4,3,1] => [4,1,2,4,1] [3,1,1,4,4] => [2,2,3,1,3] [3,1,4,1,4] => [2,3,2,1,3] [3,1,4,4,1] => [2,3,3,1,2] [3,4,1,1,4] => [1,3,3,2,2] [3,4,1,4,1] => [1,4,2,2,4] [3,4,4,1,1] => [1,2,4,2,4] [4,1,1,3,4] => [4,4,3,1,1] [4,1,1,4,3] => [2,2,1,3,1] [4,1,3,1,4] => [2,3,1,2,1] [4,1,3,4,1] => [2,5,1,1,2] [4,1,4,1,3] => [3,1,1,5,3] [4,1,4,3,1] => [4,1,3,4,1] [4,3,1,1,4] => [3,2,1,2,1] [4,3,1,4,1] => [5,2,1,1,2] [4,3,4,1,1] => [5,1,1,3,3] [4,4,1,1,3] => [1,3,1,5,3] [4,4,1,3,1] => [1,5,1,3,3] [4,4,3,1,1] => [1,4,3,4,1] [1,1,3,4,5] => [1,1,3,4,5] [1,1,3,5,4] => [1,1,4,3,5] [1,1,4,3,5] => [1,3,1,4,5] [1,1,4,5,3] => [1,4,1,3,5] [1,1,5,3,4] => [1,3,4,1,5] [1,1,5,4,3] => [1,4,3,1,5] [1,3,1,4,5] => [2,1,1,3,5] [1,3,1,5,4] => [2,1,3,1,5] [1,3,4,1,5] => [4,2,1,1,3] [1,3,4,5,1] => [5,4,2,1,1] [1,3,5,1,4] => [5,3,1,1,2] [1,3,5,4,1] => [5,4,1,2,1] [1,4,1,3,5] => [3,1,1,2,4] [1,4,1,5,3] => [2,3,1,1,5] [1,4,3,1,5] => [4,1,2,1,3] [1,4,3,5,1] => [5,2,4,1,1] [1,4,5,1,3] => [5,1,3,1,2] [1,4,5,3,1] => [5,1,4,2,1] [1,5,1,3,4] => [3,1,2,1,4] [1,5,1,4,3] => [3,2,1,1,4] [1,5,3,1,4] => [4,1,1,2,3] [1,5,3,4,1] => [5,2,1,4,1] [1,5,4,1,3] => [5,1,1,3,2] [1,5,4,3,1] => [5,1,2,4,1] [3,1,1,4,5] => [2,3,2,1,5] [3,1,1,5,4] => [3,2,2,1,5] [3,1,4,1,5] => [2,2,3,1,4] [3,1,4,5,1] => [3,2,5,1,2] [3,1,5,1,4] => [2,2,4,1,3] [3,1,5,4,1] => [2,3,5,1,2] [3,4,1,1,5] => [1,3,3,2,4] [3,4,1,5,1] => [1,3,4,2,3] [3,4,5,1,1] => [1,2,4,3,4] [3,5,1,1,4] => [3,1,3,2,4] [3,5,1,4,1] => [3,1,4,2,3] [3,5,4,1,1] => [2,1,4,3,4] [4,1,1,3,5] => [4,2,1,5,2] [4,1,1,5,3] => [2,2,1,5,3] [4,1,3,1,5] => [2,5,1,2,3] [4,1,3,5,1] => [2,4,1,3,2] [4,1,5,1,3] => [2,3,1,4,2] [4,1,5,3,1] => [4,5,1,2,2] [4,3,1,1,5] => [2,4,3,4,1] [4,3,1,5,1] => [3,3,2,4,1] [4,3,5,1,1] => [3,4,2,3,1] [4,5,1,1,3] => [1,3,2,5,3] [4,5,1,3,1] => [1,5,2,3,3] [4,5,3,1,1] => [1,4,3,4,2] [5,1,1,3,4] => [2,1,5,2,4] [5,1,1,4,3] => [2,1,5,4,2] [5,1,3,1,4] => [5,1,2,4,2] [5,1,3,4,1] => [3,1,4,2,2] [5,1,4,1,3] => [5,1,2,2,4] [5,1,4,3,1] => [4,1,3,2,2] [5,3,1,1,4] => [4,3,4,1,2] [5,3,1,4,1] => [3,2,5,1,3] [5,3,4,1,1] => [5,2,3,1,3] [5,4,1,1,3] => [4,3,4,2,1] [5,4,1,3,1] => [3,2,5,3,1] [5,4,3,1,1] => [5,2,3,3,1] [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] => [1,5,1,1,1] [2,2,2,1,2] => [1,1,5,1,1] [2,2,2,2,1] => [1,1,1,5,1] [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] => [2,1,3,3,3] [2,1,2,2,3] => [1,5,1,1,2] [2,1,2,3,2] => [1,4,1,2,1] [2,1,3,2,2] => [1,4,2,1,1] [2,2,1,2,3] => [1,1,5,1,2] [2,2,1,3,2] => [1,1,4,2,1] [2,2,2,1,3] => [4,1,1,5,1] [2,2,2,3,1] => [1,1,1,5,2] [2,2,3,1,2] => [4,1,5,1,1] [2,2,3,2,1] => [1,1,2,4,1] [2,3,1,2,2] => [4,5,1,1,1] [2,3,2,1,2] => [1,2,4,1,1] [2,3,2,2,1] => [1,2,1,4,1] [3,1,2,2,2] => [3,3,3,1,2] [3,2,1,2,2] => [5,2,2,2,1] [3,2,2,1,2] => [2,5,2,2,1] [3,2,2,2,1] => [2,2,5,2,1] [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] => [1,3,2,2,2] [1,4,2,2,2] => [2,3,1,3,3] [2,1,2,2,4] => [5,1,1,1,2] [2,1,2,4,2] => [4,1,1,2,1] [2,1,4,2,2] => [4,1,2,1,1] [2,2,1,2,4] => [1,1,5,1,3] [2,2,1,4,2] => [1,1,4,3,1] [2,2,2,1,4] => [1,4,1,5,1] [2,2,2,4,1] => [1,1,1,5,3] [2,2,4,1,2] => [1,4,5,1,1] [2,2,4,2,1] => [1,1,3,4,1] [2,4,1,2,2] => [5,4,1,1,1] [2,4,2,1,2] => [2,1,4,1,1] [2,4,2,2,1] => [2,1,1,4,1] [4,1,2,2,2] => [3,3,1,2,3] [4,2,1,2,2] => [4,2,2,1,2] [4,2,2,1,2] => [2,4,2,1,2] [4,2,2,2,1] => [2,2,2,1,5] [1,2,2,2,5] => [1,2,2,2,5] [1,2,2,5,2] => [1,2,4,2,2] [1,2,5,2,2] => [1,4,2,2,2] [1,5,2,2,2] => [2,3,3,1,3] [2,1,2,2,5] => [5,1,1,1,3] [2,1,2,5,2] => [4,1,1,3,1] [2,1,5,2,2] => [4,2,1,1,1] [2,2,1,2,5] => [1,5,1,1,3] [2,2,1,5,2] => [1,4,1,3,1] [2,2,2,1,5] => [1,1,4,5,1] [2,2,2,5,1] => [1,1,1,5,4] [2,2,5,1,2] => [1,5,4,1,1] [2,2,5,2,1] => [1,3,1,4,1] [2,5,1,2,2] => [2,4,1,1,1] [2,5,2,1,2] => [5,1,4,1,1] [2,5,2,2,1] => [3,1,1,4,1] [5,1,2,2,2] => [3,1,2,3,3] [5,2,1,2,2] => [3,2,1,2,2] [5,2,2,1,2] => [2,2,1,4,2] [5,2,2,2,1] => [2,2,1,2,4] [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] => [2,1,3,3,2] [1,3,2,3,2] => [2,1,3,2,3] [1,3,3,2,2] => [2,1,2,3,3] [2,1,2,3,3] => [1,5,1,2,2] [2,1,3,2,3] => [1,5,2,1,2] [2,1,3,3,2] => [1,3,2,2,1] [2,2,1,3,3] => [3,1,4,4,1] [2,2,3,1,3] => [1,1,5,2,2] [2,2,3,3,1] => [1,1,2,5,2] [2,3,1,2,3] => [1,2,5,1,2] [2,3,1,3,2] => [1,2,3,2,1] [2,3,2,1,3] => [3,4,1,4,1] [2,3,2,3,1] => [1,2,1,5,2] [2,3,3,1,2] => [3,4,4,1,1] [2,3,3,2,1] => [1,2,2,3,1] [3,1,2,2,3] => [2,3,3,1,1] [3,1,2,3,2] => [5,3,1,3,1] [3,1,3,2,2] => [5,1,3,3,1] [3,2,1,2,3] => [3,2,3,1,1] [3,2,1,3,2] => [3,5,1,3,1] [3,2,2,1,3] => [3,3,2,1,1] [3,2,2,3,1] => [4,4,1,1,3] [3,2,3,1,2] => [4,1,4,1,3] [3,2,3,2,1] => [3,1,5,3,1] [3,3,1,2,2] => [1,4,4,1,3] [3,3,2,1,2] => [1,5,3,3,1] [3,3,2,2,1] => [1,3,5,3,1] [1,2,2,3,4] => [1,2,3,2,5] [1,2,2,4,3] => [1,3,2,2,5] [1,2,3,2,4] => [1,2,2,3,4] [1,2,3,4,2] => [1,3,2,5,2] [1,2,4,2,3] => [1,2,2,4,3] [1,2,4,3,2] => [1,2,3,5,2] [1,3,2,2,4] => [2,1,3,3,4] [1,3,2,4,2] => [2,1,3,4,3] [1,3,4,2,2] => [3,1,2,4,4] [1,4,2,2,3] => [2,3,1,3,4] [1,4,2,3,2] => [2,3,1,4,3] [1,4,3,2,2] => [3,2,1,4,4] [2,1,2,3,4] => [1,2,5,1,4] [2,1,2,4,3] => [2,1,5,1,4] [2,1,3,2,4] => [1,1,5,2,3] [2,1,3,4,2] => [2,1,3,4,1] [2,1,4,2,3] => [1,1,4,3,2] [2,1,4,3,2] => [1,2,3,4,1] [2,2,1,3,4] => [4,3,1,5,1] [2,2,1,4,3] => [3,4,1,5,1] [2,2,3,1,4] => [1,4,1,5,2] [2,2,3,4,1] => [1,2,1,5,4] [2,2,4,1,3] => [4,1,1,5,2] [2,2,4,3,1] => [2,1,1,5,4] [2,3,1,2,4] => [4,1,5,1,2] [2,3,1,4,2] => [3,1,5,2,1] [2,3,2,1,4] => [1,3,2,5,1] [2,3,2,4,1] => [1,1,2,5,3] [2,3,4,1,2] => [4,3,5,1,1] [2,3,4,2,1] => [2,1,4,3,1] [2,4,1,2,3] => [1,4,5,1,2] [2,4,1,3,2] => [1,3,5,2,1] [2,4,2,1,3] => [3,1,2,5,1] [2,4,2,3,1] => [1,1,3,4,2] [2,4,3,1,2] => [3,4,5,1,1] [2,4,3,2,1] => [1,2,4,3,1] [3,1,2,2,4] => [2,4,4,1,3] [3,1,2,4,2] => [3,3,4,1,2] [3,1,4,2,2] => [3,4,3,1,2] [3,2,1,2,4] => [2,5,2,3,1] [3,2,1,4,2] => [2,4,3,2,1] [3,2,2,1,4] => [2,2,5,3,1] [3,2,2,4,1] => [4,2,5,2,1] [3,2,4,1,2] => [4,5,2,2,1] [3,2,4,2,1] => [2,3,4,2,1] [3,4,1,2,2] => [1,4,4,2,3] [3,4,2,1,2] => [1,5,3,3,2] [3,4,2,2,1] => [1,3,5,3,2] [4,1,2,2,3] => [4,4,1,3,2] [4,1,2,3,2] => [3,5,1,2,3] [4,1,3,2,2] => [5,3,1,2,3] [4,2,1,2,3] => [5,2,4,1,2] [4,2,1,3,2] => [3,4,2,1,2] [4,2,2,1,3] => [2,5,4,1,2] [4,2,2,3,1] => [2,5,2,1,4] [4,2,3,1,2] => [4,3,2,1,2] [4,2,3,2,1] => [5,2,2,1,4] [4,3,1,2,2] => [5,3,3,2,1] [4,3,2,1,2] => [3,5,3,2,1] [4,3,2,2,1] => [4,4,2,3,1] [1,2,2,3,5] => [1,2,2,3,5] [1,2,2,5,3] => [1,4,2,2,5] [1,2,3,2,5] => [1,2,3,2,4] [1,2,3,5,2] => [1,3,5,2,2] [1,2,5,2,3] => [1,2,4,2,3] [1,2,5,3,2] => [1,2,5,3,2] [1,3,2,2,5] => [2,1,3,3,5] [1,3,2,5,2] => [2,1,4,3,3] [1,3,5,2,2] => [3,1,4,2,4] [1,5,2,2,3] => [2,3,3,1,4] [1,5,2,3,2] => [3,2,4,1,4] [1,5,3,2,2] => [2,3,4,1,3] [2,1,2,3,5] => [1,5,2,1,4] [2,1,2,5,3] => [2,5,1,1,4] [2,1,3,2,5] => [1,5,1,2,3] [2,1,3,5,2] => [2,3,1,4,1] [2,1,5,2,3] => [1,4,1,3,2] [2,1,5,3,2] => [1,3,2,4,1] [2,2,1,3,5] => [4,1,3,5,1] [2,2,1,5,3] => [3,1,4,5,1] [2,2,3,1,5] => [1,1,4,5,2] [2,2,3,5,1] => [1,1,2,5,4] [2,2,5,1,3] => [4,1,1,5,3] [2,2,5,3,1] => [3,1,1,5,4] [2,3,1,2,5] => [4,5,1,1,2] [2,3,1,5,2] => [3,5,1,2,1] [2,3,2,1,5] => [1,2,3,5,1] [2,3,2,5,1] => [1,2,1,5,3] [2,3,5,1,2] => [4,5,3,1,1] [2,3,5,2,1] => [2,4,1,3,1] [2,5,1,2,3] => [1,5,4,1,2] [2,5,1,3,2] => [1,5,3,2,1] [2,5,2,1,3] => [3,2,1,5,1] [2,5,2,3,1] => [1,3,1,4,2] [2,5,3,1,2] => [3,5,4,1,1] [2,5,3,2,1] => [1,4,2,3,1] [3,1,2,2,5] => [4,2,4,1,3] [3,1,2,5,2] => [3,3,5,1,2] [3,1,5,2,2] => [4,3,3,1,2] [3,2,1,2,5] => [5,2,2,3,1] [3,2,1,5,2] => [4,2,3,2,1] [3,2,2,1,5] => [2,2,5,4,1] [3,2,2,5,1] => [2,4,5,2,1] [3,2,5,1,2] => [5,4,2,2,1] [3,2,5,2,1] => [3,2,4,2,1] [3,5,1,2,2] => [5,1,3,3,2] [3,5,2,1,2] => [4,1,4,2,3] [3,5,2,2,1] => [3,1,5,3,2] [5,1,2,2,3] => [3,1,2,3,5] [5,1,2,3,2] => [4,1,3,2,4] [5,1,3,2,2] => [4,1,2,3,3] [5,2,1,2,3] => [3,2,1,2,4] [5,2,1,3,2] => [5,3,1,2,2] [5,2,2,1,3] => [2,2,1,4,5] [5,2,2,3,1] => [2,4,1,2,5] [5,2,3,1,2] => [5,2,1,3,2] [5,2,3,2,1] => [4,2,1,2,3] [5,3,1,2,2] => [4,3,2,1,3] [5,3,2,1,2] => [4,2,3,1,4] [5,3,2,2,1] => [3,3,2,1,5] [1,2,2,4,4] => [1,2,2,4,4] [1,2,4,2,4] => [1,3,2,2,3] [1,2,4,4,2] => [1,3,2,3,2] [1,4,2,2,4] => [2,3,1,3,2] [1,4,2,4,2] => [2,3,1,2,3] [1,4,4,2,2] => [2,2,1,3,3] [2,1,2,4,4] => [5,1,1,2,2] [2,1,4,2,4] => [5,1,2,1,2] [2,1,4,4,2] => [3,1,2,2,1] [2,2,1,4,4] => [1,3,4,4,1] [2,2,4,1,4] => [1,1,5,3,3] [2,2,4,4,1] => [1,1,3,5,3] [2,4,1,2,4] => [2,1,5,1,2] [2,4,1,4,2] => [2,1,3,2,1] [2,4,2,1,4] => [4,3,1,4,1] [2,4,2,4,1] => [2,1,1,5,2] [2,4,4,1,2] => [4,3,4,1,1] [2,4,4,2,1] => [2,1,2,3,1] [4,1,2,2,4] => [5,2,2,1,1] [4,1,2,4,2] => [2,3,1,1,3] [4,1,4,2,2] => [4,1,3,1,3] [4,2,1,2,4] => [2,5,2,1,1] [4,2,1,4,2] => [3,2,1,1,3] [4,2,2,1,4] => [4,4,1,2,1] [4,2,2,4,1] => [3,3,1,1,2] [4,2,4,1,2] => [4,1,1,3,4] [4,2,4,2,1] => [3,1,3,1,5] [4,4,1,2,2] => [1,4,1,3,4] [4,4,2,1,2] => [1,4,3,1,3] [4,4,2,2,1] => [1,3,3,1,5] [1,2,2,4,5] => [1,2,2,4,5] [1,2,2,5,4] => [1,2,4,2,5] [1,2,4,2,5] => [1,3,2,2,4] [1,2,4,5,2] => [1,5,3,2,2] [1,2,5,2,4] => [1,4,2,2,3] [1,2,5,4,2] => [1,5,2,3,2] [1,4,2,2,5] => [2,3,1,3,5] [1,4,2,5,2] => [3,4,1,2,4] [1,4,5,2,2] => [2,4,1,3,3] [1,5,2,2,4] => [2,3,3,1,5] [1,5,2,4,2] => [3,4,2,1,4] [1,5,4,2,2] => [2,4,3,1,3] [2,1,2,4,5] => [5,1,2,1,4] [2,1,2,5,4] => [5,2,1,1,4] [2,1,4,2,5] => [5,1,1,2,3] [2,1,4,5,2] => [3,2,1,4,1] [2,1,5,2,4] => [4,1,1,3,2] [2,1,5,4,2] => [3,1,2,4,1] [2,2,1,4,5] => [1,4,3,5,1] [2,2,1,5,4] => [1,3,4,5,1] [2,2,4,1,5] => [1,1,4,5,3] [2,2,4,5,1] => [1,1,3,5,4] [2,2,5,1,4] => [1,4,1,5,3] [2,2,5,4,1] => [1,3,1,5,4] [2,4,1,2,5] => [5,4,1,1,2] [2,4,1,5,2] => [5,3,1,2,1] [2,4,2,1,5] => [2,1,3,5,1] [2,4,2,5,1] => [2,1,1,5,3] [2,4,5,1,2] => [5,4,3,1,1] [2,4,5,2,1] => [4,2,1,3,1] [2,5,1,2,4] => [5,1,4,1,2] [2,5,1,4,2] => [5,1,3,2,1] [2,5,2,1,4] => [2,3,1,5,1] [2,5,2,4,1] => [3,1,1,4,2] [2,5,4,1,2] => [5,3,4,1,1] [2,5,4,2,1] => [4,1,2,3,1] [4,1,2,2,5] => [3,3,1,2,4] [4,1,2,5,2] => [2,4,1,3,4] [4,1,5,2,2] => [3,4,1,2,3] [4,2,1,2,5] => [2,4,2,1,3] [4,2,1,5,2] => [2,5,3,1,2] [4,2,2,1,5] => [4,2,2,1,5] [4,2,2,5,1] => [2,2,3,1,5] [4,2,5,1,2] => [3,5,2,1,2] [4,2,5,2,1] => [2,3,2,1,4] [4,5,1,2,2] => [1,4,2,3,4] [4,5,2,1,2] => [1,4,3,2,3] [4,5,2,2,1] => [1,3,3,2,5] [5,1,2,2,4] => [3,1,2,5,3] [5,1,2,4,2] => [4,1,3,4,2] [5,1,4,2,2] => [5,1,2,3,3] [5,2,1,2,4] => [3,2,1,4,2] [5,2,1,4,2] => [5,4,1,2,2] [5,2,2,1,4] => [2,2,1,5,4] [5,2,2,4,1] => [2,4,1,5,2] [5,2,4,1,2] => [4,2,1,3,2] [5,2,4,2,1] => [5,2,1,2,3] [5,4,1,2,2] => [4,3,2,3,1] [5,4,2,1,2] => [3,3,2,5,1] [5,4,2,2,1] => [4,2,3,4,1] [1,2,3,3,3] => [1,2,3,3,3] [1,3,2,3,3] => [2,1,3,2,2] [1,3,3,2,3] => [2,1,2,3,2] [1,3,3,3,2] => [2,1,2,2,3] [2,1,3,3,3] => [2,3,3,3,1] [2,3,1,3,3] => [1,5,2,2,2] [2,3,3,1,3] => [1,2,5,2,2] [2,3,3,3,1] => [1,2,2,5,2] [3,1,2,3,3] => [3,4,1,1,1] [3,1,3,2,3] => [3,1,4,1,1] [3,1,3,3,2] => [5,1,1,4,1] [3,2,1,3,3] => [4,3,1,1,1] [3,2,3,1,3] => [4,1,3,1,1] [3,2,3,3,1] => [5,1,1,1,4] [3,3,1,2,3] => [1,3,4,1,1] [3,3,1,3,2] => [1,5,1,4,1] [3,3,2,1,3] => [1,4,3,1,1] [3,3,2,3,1] => [1,5,1,1,4] [3,3,3,1,2] => [1,1,5,1,4] [3,3,3,2,1] => [1,1,5,4,1] [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] => [1,3,2,4,4] [1,3,2,3,4] => [2,1,2,3,4] [1,3,2,4,3] => [3,1,2,5,2] [1,3,3,2,4] => [2,1,3,2,5] [1,3,3,4,2] => [3,1,2,2,5] [1,3,4,2,3] => [2,1,3,5,2] [1,3,4,3,2] => [2,1,2,4,3] [1,4,2,3,3] => [2,3,1,4,4] [1,4,3,2,3] => [3,2,1,4,3] [1,4,3,3,2] => [3,2,1,3,4] [2,1,3,3,4] => [3,2,4,4,1] [2,1,3,4,3] => [2,3,3,4,1] [2,1,4,3,3] => [2,3,4,3,1] [2,3,1,3,4] => [1,2,5,2,3] [2,3,1,4,3] => [1,2,4,3,2] [2,3,3,1,4] => [1,4,2,5,2] [2,3,3,4,1] => [1,2,2,5,3] [2,3,4,1,3] => [1,4,5,2,2] [2,3,4,3,1] => [1,2,3,4,2] [2,4,1,3,3] => [3,1,4,4,2] [2,4,3,1,3] => [2,1,5,3,3] [2,4,3,3,1] => [2,1,3,5,3] [3,1,2,3,4] => [1,3,4,1,2] [3,1,2,4,3] => [1,4,3,2,1] [3,1,3,2,4] => [3,5,1,4,1] [3,1,3,4,2] => [1,5,1,4,2] [3,1,4,2,3] => [3,2,5,1,1] [3,1,4,3,2] => [1,5,2,3,1] [3,2,1,3,4] => [1,4,3,1,2] [3,2,1,4,3] => [1,3,4,2,1] [3,2,3,1,4] => [3,5,1,1,4] [3,2,3,4,1] => [1,5,1,2,4] [3,2,4,1,3] => [2,3,4,1,1] [3,2,4,3,1] => [1,5,2,1,3] [3,3,1,2,4] => [3,1,5,1,4] [3,3,1,4,2] => [4,1,5,1,3] [3,3,2,1,4] => [3,1,5,4,1] [3,3,2,4,1] => [4,1,5,3,1] [3,3,4,1,2] => [1,1,5,2,4] [3,3,4,2,1] => [1,1,5,4,2] [3,4,1,2,3] => [2,4,3,1,1] [3,4,1,3,2] => [4,5,1,3,1] [3,4,2,1,3] => [3,5,2,1,1] [3,4,2,3,1] => [4,5,1,1,3] [3,4,3,1,2] => [1,2,5,1,3] [3,4,3,2,1] => [1,2,5,3,1] [4,1,2,3,3] => [5,3,1,3,2] [4,1,3,2,3] => [3,5,1,3,2] [4,1,3,3,2] => [4,4,1,2,3] [4,2,1,3,3] => [5,3,3,1,2] [4,2,3,1,3] => [3,5,3,1,2] [4,2,3,3,1] => [4,4,2,1,3] [4,3,1,2,3] => [3,4,2,2,1] [4,3,1,3,2] => [5,2,4,2,1] [4,3,2,1,3] => [4,3,2,2,1] [4,3,2,3,1] => [5,2,2,4,1] [4,3,3,1,2] => [2,5,4,2,1] ----------------------------------------------------------------------------- Created: Jun 16, 2023 at 22:35 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 16, 2023 at 22:35 by Martin Rubey