***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001271 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The competition number of a graph. The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x, v)$ and $(y, v)$ are arcs of $D$. For any graph, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ is the smallest number of such isolated vertices. ----------------------------------------------------------------------------- References: [1] Kim, S.-R., Yeun Lee, J., Park, B., Sano, Y. The competition number of a graph and the dimension of its hole space [[arXiv:1103.1028]] [2] Kim, S.-R., Roberts, F. S. Competition numbers of graphs with a small number of triangles [[MathSciNet:1475823]] [3] Li, B.-J., Chang, G. J. Competition numbers of complete $r$-partite graphs [[MathSciNet:2954768]] ----------------------------------------------------------------------------- Code: N_vertices = 7 # 8 takes a long time (perhaps an hour) def is_complete_tripartite(G): """ Return n1 <= n2 <= n3 or False. """ deg = G.degree() degs = set(deg) if len(degs) > 3: return False elif len(degs) == 3: n1, n2, n3 = [deg.count(d) for d in degs] if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])): return tuple(sorted((n1, n2, n3))) elif len(degs) == 2: N1, N2 = [deg.count(d) for d in sorted(degs)] n1 = N1 n2 = n3 = N2 // 2 if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])): return tuple(sorted((n1, n2, n3))) n1 = N2 n2 = n3 = N1 // 2 if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])): return tuple(sorted((n1, n2, n3))) elif len(degs) == 1: n1 = n2 = n3 = G.num_verts() // 3 if G.is_isomorphic(graphs.CompleteMultipartiteGraph([n1, n2, n3])): return tuple(sorted((n1, n2, n3))) return False def competition_graph(D): """ Return the competition graph of a DAG. """ n = D.num_verts() G = Graph(n) for i in range(1,n): for j in range(i): if set(D.neighbors_out(i)).intersection(D.neighbors_out(j)): G.add_edge(i,j) return G.canonical_label().copy(immutable=True) @cached_function def competition_graphs(n): """ sage: [len(competition_graphs(n)) for n in range(8)] [1, 1, 1, 2, 4, 10, 29, 116] """ return set(competition_graph(D) for D in digraphs(n, property = lambda g: g.is_directed_acyclic())) def competition_number_naive(G, N): """ sage: [(G, competition_number_brute(G, N_vertices-G.num_verts())) for n in range(1, 6) for G in graphs(n)] """ n = G.num_verts() H = G.copy() if H.canonical_label().copy(immutable=True) in competition_graphs(H.num_verts()): return 0 for i in range(1, N): H.add_vertex() if H.canonical_label().copy(immutable=True) in competition_graphs(H.num_verts()): return i def statistic(G): """special cases due to * [1] Suh-Ryung Kim, Fred S. Roberts, "Competition numbers of graphs with a small number of triangles", DISCRETE APPLIED MATHEMATICS 153-162 * [2] Suh-Ryung Kim, Yoshio Sano, Discrete Applied Mathematics, Volume 156, Issue 18, 28 November 2008, The competition numbers of complete tripartite graphs * [3] Li, Bo-Jr, and Gerard J. Chang. "Competition numbers of complete r-partite graphs." Discrete Applied Mathematics 160.15 (2012): 2271-2276. """ k = competition_number_naive(G, N_vertices-G.num_verts()) if k is not None: return k if G.is_chordal() and min(G.degree()) > 0: # [2] return 1 if not G.is_connected(): return n = G.num_verts() # [3], Theorem 5 N = is_complete_tripartite(G) if N: n1, n2, n3 = N if n2 >= n3 + 2: return n1*n2 - n + 2 elif n2 == n3 + 1 or n2 == n3 == 1: return n1*n2 - n + 3 elif n2 == n3 >= 2: return n1*n2 - n + 4 t = G.triangles_count() if t == 0: # [1] return G.num_edges() - G.num_verts() + 2 if t == 1: # [1] if G.is_even_hole_free() and G.is_odd_hole_free(): return G.num_edges() - G.num_verts() + 1 return ----------------------------------------------------------------------------- Statistic values: ([],1) => 0 ([],2) => 0 ([(0,1)],2) => 1 ([],3) => 0 ([(1,2)],3) => 0 ([(0,2),(1,2)],3) => 1 ([(0,1),(0,2),(1,2)],3) => 1 ([],4) => 0 ([(2,3)],4) => 0 ([(1,3),(2,3)],4) => 0 ([(0,3),(1,3),(2,3)],4) => 1 ([(0,3),(1,2)],4) => 1 ([(0,3),(1,2),(2,3)],4) => 1 ([(1,2),(1,3),(2,3)],4) => 0 ([(0,3),(1,2),(1,3),(2,3)],4) => 1 ([(0,2),(0,3),(1,2),(1,3)],4) => 2 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1 ([],5) => 0 ([(3,4)],5) => 0 ([(2,4),(3,4)],5) => 0 ([(1,4),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,4),(3,4)],5) => 1 ([(1,4),(2,3)],5) => 0 ([(1,4),(2,3),(3,4)],5) => 0 ([(0,1),(2,4),(3,4)],5) => 1 ([(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(3,4)],5) => 1 ([(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(1,3),(1,4),(2,3),(2,4)],5) => 1 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,3),(2,3),(2,4)],5) => 1 ([(0,1),(2,3),(2,4),(3,4)],5) => 1 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 1 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 2 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([],6) => 0 ([(4,5)],6) => 0 ([(3,5),(4,5)],6) => 0 ([(2,5),(3,5),(4,5)],6) => 0 ([(1,5),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1 ([(2,5),(3,4)],6) => 0 ([(2,5),(3,4),(4,5)],6) => 0 ([(1,2),(3,5),(4,5)],6) => 0 ([(3,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,5),(3,4),(4,5)],6) => 0 ([(0,1),(2,5),(3,5),(4,5)],6) => 1 ([(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4)],6) => 1 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3)],6) => 1 ([(1,5),(2,4),(3,4),(3,5)],6) => 0 ([(0,1),(2,5),(3,4),(4,5)],6) => 1 ([(1,2),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 2 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 1 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 1 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 1 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 2 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 3 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 5 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 1 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 1 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([],7) => 0 ([(5,6)],7) => 0 ([(4,6),(5,6)],7) => 0 ([(3,6),(4,6),(5,6)],7) => 0 ([(2,6),(3,6),(4,6),(5,6)],7) => 0 ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1 ([(3,6),(4,5)],7) => 0 ([(3,6),(4,5),(5,6)],7) => 0 ([(2,3),(4,6),(5,6)],7) => 0 ([(4,5),(4,6),(5,6)],7) => 0 ([(2,6),(3,6),(4,5),(5,6)],7) => 0 ([(1,2),(3,6),(4,6),(5,6)],7) => 0 ([(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 0 ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 1 ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1 ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(3,5),(3,6),(4,5),(4,6)],7) => 0 ([(1,6),(2,6),(3,5),(4,5)],7) => 0 ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1 ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1 ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1 ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1 ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 5 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,5),(3,4)],7) => 0 ([(2,6),(3,5),(4,5),(4,6)],7) => 0 ([(1,2),(3,6),(4,5),(5,6)],7) => 0 ([(0,3),(1,2),(4,6),(5,6)],7) => 1 ([(2,3),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0 ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1 ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 0 ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1 ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0 ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 0 ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 1 ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 2 ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 2 ([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => 1 ([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 0 ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 0 ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1 ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 0 ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1 ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => 0 ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1 ([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 0 ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 2 ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 0 ([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => 1 ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 1 ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 1 ([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 3 ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => 1 ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3 ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0 ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => 2 ([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => 0 ([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 2 ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0 ([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 0 ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 3 ([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0 ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0 ([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 2 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => 1 ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => 1 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 2 ([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => 3 ([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => 1 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4 ([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 3 ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 4 ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 4 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 5 ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 5 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 5 ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6 ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 7 ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => 1 ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 1 ([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 1 ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 1 ([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => 1 ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 2 ([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2 ([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => 1 ([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => 1 ([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 0 ([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => 0 ([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 0 ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => 1 ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 1 ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 3 ([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => 0 ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 0 ([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => 1 ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 1 ([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 2 ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 3 ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => 3 ([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 1 ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 3 ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 4 ([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0 ([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 3 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4 ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,4),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => 1 ([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) => 1 ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => 1 ([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 5 ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 1 ([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 1 ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 4 ([(0,4),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) => 0 ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => 1 ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0 ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1 ----------------------------------------------------------------------------- Created: Oct 12, 2018 at 07:59 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 29, 2018 at 22:55 by Martin Rubey