***************************************************************************** * 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: St001399 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The distinguishing number of a poset. This is the minimal number of colours needed to colour the vertices of a poset, such that only the trivial automorphism of the poset preserves the colouring. See also [[St000469]], which is the same concept for graphs. ----------------------------------------------------------------------------- References: [1] [[arXiv 1905.09858]] ----------------------------------------------------------------------------- Code: def statistic(P): G = P.hasse_diagram() for c in range(G.num_verts()+1): # try to find a colouring V = G.vertices() # partition the set of edges into c parts for colouring in SetPartitions(V, c): if G.automorphism_group(map(list, colouring), return_group=False, order=True) == 1: return c ----------------------------------------------------------------------------- Statistic values: ([],1) => 1 ([],2) => 2 ([(0,1)],2) => 1 ([],3) => 3 ([(1,2)],3) => 1 ([(0,1),(0,2)],3) => 2 ([(0,2),(2,1)],3) => 1 ([(0,2),(1,2)],3) => 2 ([],4) => 4 ([(2,3)],4) => 2 ([(1,2),(1,3)],4) => 2 ([(0,1),(0,2),(0,3)],4) => 3 ([(0,2),(0,3),(3,1)],4) => 1 ([(0,1),(0,2),(1,3),(2,3)],4) => 2 ([(1,2),(2,3)],4) => 1 ([(0,3),(3,1),(3,2)],4) => 2 ([(1,3),(2,3)],4) => 2 ([(0,3),(1,3),(3,2)],4) => 2 ([(0,3),(1,3),(2,3)],4) => 3 ([(0,3),(1,2)],4) => 2 ([(0,3),(1,2),(1,3)],4) => 1 ([(0,2),(0,3),(1,2),(1,3)],4) => 2 ([(0,3),(2,1),(3,2)],4) => 1 ([(0,3),(1,2),(2,3)],4) => 1 ([],5) => 5 ([(3,4)],5) => 3 ([(2,3),(2,4)],5) => 2 ([(1,2),(1,3),(1,4)],5) => 3 ([(0,1),(0,2),(0,3),(0,4)],5) => 4 ([(0,2),(0,3),(0,4),(4,1)],5) => 2 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 2 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 3 ([(1,3),(1,4),(4,2)],5) => 1 ([(0,3),(0,4),(4,1),(4,2)],5) => 2 ([(1,2),(1,3),(2,4),(3,4)],5) => 2 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2 ([(0,3),(0,4),(3,2),(4,1)],5) => 2 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(2,3),(3,4)],5) => 2 ([(1,4),(4,2),(4,3)],5) => 2 ([(0,4),(4,1),(4,2),(4,3)],5) => 3 ([(2,4),(3,4)],5) => 2 ([(1,4),(2,4),(4,3)],5) => 2 ([(0,4),(1,4),(4,2),(4,3)],5) => 2 ([(1,4),(2,4),(3,4)],5) => 3 ([(0,4),(1,4),(2,4),(4,3)],5) => 3 ([(0,4),(1,4),(2,4),(3,4)],5) => 4 ([(0,4),(1,4),(2,3)],5) => 2 ([(0,4),(1,3),(2,3),(2,4)],5) => 2 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3 ([(0,4),(1,4),(2,3),(4,2)],5) => 2 ([(0,4),(1,3),(2,3),(3,4)],5) => 2 ([(0,4),(1,4),(2,3),(2,4)],5) => 2 ([(0,4),(1,4),(2,3),(3,4)],5) => 2 ([(1,4),(2,3)],5) => 2 ([(1,4),(2,3),(2,4)],5) => 1 ([(0,4),(1,2),(1,4),(2,3)],5) => 1 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1 ([(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2 ([(0,4),(1,2),(1,4),(4,3)],5) => 1 ([(0,4),(1,2),(1,3)],5) => 2 ([(0,4),(1,2),(1,3),(1,4)],5) => 2 ([(0,2),(0,4),(3,1),(4,3)],5) => 1 ([(0,4),(1,2),(1,3),(3,4)],5) => 1 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 1 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 3 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 1 ([(0,3),(1,2),(1,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2 ([(1,4),(3,2),(4,3)],5) => 1 ([(0,3),(3,4),(4,1),(4,2)],5) => 2 ([(1,4),(2,3),(3,4)],5) => 1 ([(0,4),(1,2),(2,4),(4,3)],5) => 1 ([(0,3),(1,4),(4,2)],5) => 1 ([(0,4),(3,2),(4,1),(4,3)],5) => 1 ([(0,4),(1,2),(2,3),(2,4)],5) => 1 ([(0,4),(2,3),(3,1),(4,2)],5) => 1 ([(0,3),(1,2),(2,4),(3,4)],5) => 2 ([(0,4),(1,2),(2,3),(3,4)],5) => 1 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2 ([],6) => 6 ([(4,5)],6) => 4 ([(3,4),(3,5)],6) => 3 ([(2,3),(2,4),(2,5)],6) => 3 ([(1,2),(1,3),(1,4),(1,5)],6) => 4 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 5 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 3 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 2 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 3 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 4 ([(1,3),(1,4),(1,5),(5,2)],6) => 2 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 2 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 3 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 3 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 2 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 2 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 2 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 1 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(2,3),(2,4),(4,5)],6) => 2 ([(1,4),(1,5),(5,2),(5,3)],6) => 2 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 3 ([(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 2 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 2 ([(1,4),(1,5),(4,3),(5,2)],6) => 2 ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 1 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 2 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 1 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 2 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 2 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 2 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3 ([(3,4),(4,5)],6) => 3 ([(2,3),(3,4),(3,5)],6) => 2 ([(1,5),(5,2),(5,3),(5,4)],6) => 3 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 4 ([(2,3),(3,5),(5,4)],6) => 2 ([(1,4),(4,5),(5,2),(5,3)],6) => 2 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 3 ([(3,5),(4,5)],6) => 3 ([(2,5),(3,5),(5,4)],6) => 2 ([(1,5),(2,5),(5,3),(5,4)],6) => 2 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 3 ([(2,5),(3,5),(4,5)],6) => 3 ([(1,5),(2,5),(3,5),(5,4)],6) => 3 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 3 ([(1,5),(2,5),(3,5),(4,5)],6) => 4 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 4 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5 ([(0,5),(1,5),(2,5),(3,4)],6) => 3 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 3 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 3 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 3 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3 ([(1,5),(2,5),(3,4)],6) => 2 ([(1,5),(2,4),(3,4),(3,5)],6) => 2 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 1 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 2 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 3 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 3 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 2 ([(1,5),(2,5),(3,4),(5,3)],6) => 2 ([(1,5),(2,4),(3,4),(4,5)],6) => 2 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2 ([(0,5),(1,5),(2,3),(5,4)],6) => 2 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 2 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 2 ([(1,5),(2,5),(3,4),(3,5)],6) => 2 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 2 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 2 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2 ([(0,5),(1,5),(2,3),(2,4)],6) => 2 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 2 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 2 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 1 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 2 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 2 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 1 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 2 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,5),(3,4),(4,5)],6) => 2 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2 ([(0,5),(1,5),(2,3),(3,4)],6) => 2 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 1 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 2 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 2 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 2 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 3 ([(0,5),(1,5),(2,4),(3,4)],6) => 2 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 2 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(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 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 2 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 2 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2 ([(2,5),(3,4)],6) => 2 ([(2,5),(3,4),(3,5)],6) => 2 ([(1,5),(2,3),(2,5),(3,4)],6) => 1 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 2 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 2 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 1 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 1 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 1 ([(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 2 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 2 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 2 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 2 ([(1,5),(2,3),(2,5),(5,4)],6) => 1 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 2 ([(1,5),(2,3),(2,4)],6) => 2 ([(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 1 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 2 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 2 ([(0,5),(1,2),(1,3),(1,4)],6) => 3 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 3 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 2 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 2 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 1 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 2 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 3 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 2 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 2 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3 ([(1,3),(1,5),(4,2),(5,4)],6) => 1 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 2 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 1 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 1 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 1 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 1 ([(1,5),(2,3),(2,4),(4,5)],6) => 1 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 1 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 1 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 1 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 2 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 1 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 1 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 1 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 1 ([(0,4),(1,3),(1,5),(5,2)],6) => 1 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 1 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 1 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 1 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 1 ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 2 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 2 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 2 ([(1,4),(1,5),(2,3),(2,5)],6) => 2 ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 1 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 2 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 2 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 2 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 2 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 1 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 2 ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 1 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 1 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 1 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 1 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 1 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 1 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 2 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 2 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 2 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 3 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 4 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 2 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 1 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 2 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 2 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 2 ([(1,4),(2,3),(2,5),(4,5)],6) => 1 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 1 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 2 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 1 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 1 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 1 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,3),(1,4),(5,2)],6) => 2 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 1 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 2 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 2 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 1 ([(2,5),(3,4),(4,5)],6) => 2 ([(1,5),(2,3),(3,5),(5,4)],6) => 1 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 2 ([(1,3),(2,4),(4,5)],6) => 1 ([(1,5),(4,3),(5,2),(5,4)],6) => 1 ([(1,5),(2,3),(3,4),(3,5)],6) => 1 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 1 ([(0,4),(1,5),(5,2),(5,3)],6) => 2 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 2 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 2 ([(1,5),(3,4),(4,2),(5,3)],6) => 1 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 2 ([(1,4),(2,3),(3,5),(4,5)],6) => 2 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 2 ([(0,5),(1,4),(4,2),(5,3)],6) => 2 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 1 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 1 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(1,5),(2,3),(3,4),(4,5)],6) => 1 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 2 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1 ([(0,5),(1,4),(2,3)],6) => 2 ([(0,5),(1,3),(2,4),(2,5)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 2 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 1 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 1 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 1 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 2 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 1 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 1 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 1 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 2 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 2 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 1 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 1 ([(0,5),(1,3),(4,2),(5,4)],6) => 1 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 2 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 1 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 1 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 1 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 1 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1 ([(0,5),(1,3),(2,4),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 2 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 2 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 1 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 1 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2 ([],7) => 7 ([(5,6)],7) => 5 ([(4,5),(4,6)],7) => 4 ([(3,4),(3,5),(3,6)],7) => 3 ([(2,3),(2,4),(2,5),(2,6)],7) => 4 ([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 5 ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 6 ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 4 ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => 3 ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => 3 ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => 4 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5 ([(1,3),(1,4),(1,5),(1,6),(6,2)],7) => 3 ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 3 ([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 2 ([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 3 ([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 4 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 4 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7) => 3 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => 3 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 3 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => 3 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => 2 ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 2 ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => 2 ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(2,4),(2,5),(2,6),(6,3)],7) => 2 ([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => 2 ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 3 ([(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 2 ([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 3 ([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 3 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => 3 ([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 2 ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 2 ([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 3 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 3 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7) => 2 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => 1 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 2 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7) => 2 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7) => 2 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 2 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7) => 2 ([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 2 ([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7) => 2 ([(1,4),(1,5),(1,6),(5,3),(6,2)],7) => 2 ([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 1 ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => 2 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7) => 2 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 2 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7) => 1 ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 2 ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => 2 ([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 2 ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3 ([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => 2 ([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7) => 1 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7) => 2 ([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7) => 1 ([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 2 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 1 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 1 ([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 1 ([(3,4),(3,5),(5,6)],7) => 3 ([(2,5),(2,6),(6,3),(6,4)],7) => 2 ([(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 3 ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 4 ([(3,4),(3,5),(4,6),(5,6)],7) => 3 ([(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 2 ([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => 2 ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => 3 ([(2,5),(2,6),(5,4),(6,3)],7) => 2 ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 2 ([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => 2 ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => 2 ([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 2 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => 2 ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => 2 ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => 2 ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) => 1 ([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7) => 2 ([(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 2 ([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7) => 2 ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7) => 2 ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 3 ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => 3 ([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => 2 ([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) => 2 ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3 ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => 2 ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 2 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 3 ([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7) => 1 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7) => 2 ([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => 2 ([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7) => 2 ([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7) => 2 ([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 2 ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => 3 ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 4 ([(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 2 ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => 1 ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 2 ([(4,5),(5,6)],7) => 4 ([(3,4),(4,5),(4,6)],7) => 3 ([(2,6),(6,3),(6,4),(6,5)],7) => 3 ([(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 4 ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 5 ([(3,4),(4,6),(6,5)],7) => 3 ([(2,5),(5,6),(6,3),(6,4)],7) => 2 ([(1,5),(5,6),(6,2),(6,3),(6,4)],7) => 3 ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 4 ([(4,6),(5,6)],7) => 4 ([(3,6),(4,6),(6,5)],7) => 3 ([(2,6),(3,6),(6,4),(6,5)],7) => 2 ([(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 3 ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 4 ([(3,6),(4,6),(5,6)],7) => 3 ([(2,6),(3,6),(4,6),(6,5)],7) => 3 ([(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 3 ([(2,6),(3,6),(4,6),(5,6)],7) => 4 ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 4 ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 4 ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5 ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6 ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 4 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 4 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 4 ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 4 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 4 ([(1,6),(2,6),(3,6),(4,5)],7) => 3 ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 3 ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 3 ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 3 ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 3 ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 2 ([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 2 ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 3 ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 3 ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(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 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 5 ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 3 ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 2 ([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 2 ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 3 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 3 ([(2,6),(3,6),(4,5)],7) => 2 ([(2,6),(3,5),(4,5),(4,6)],7) => 2 ([(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 1 ([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7) => 2 ([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7) => 2 ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 1 ([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7) => 2 ([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 2 ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 3 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => 3 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 3 ([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7) => 2 ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => 2 ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7) => 2 ([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) => 2 ([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 2 ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7) => 2 ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 2 ([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => 1 ([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7) => 1 ([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 1 ([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 2 ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 1 ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7) => 1 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 1 ([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 1 ([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 2 ([(2,6),(3,6),(4,5),(6,4)],7) => 2 ([(2,6),(3,5),(4,5),(5,6)],7) => 2 ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 2 ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 2 ([(1,6),(2,6),(3,4),(6,5)],7) => 2 ([(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 2 ([(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 2 ([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) => 2 ([(0,6),(1,6),(2,3),(6,4),(6,5)],7) => 2 ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => 2 ([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7) => 2 ([(2,6),(3,6),(4,5),(4,6)],7) => 2 ([(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 2 ([(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 2 ([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7) => 2 ([(1,6),(2,6),(3,4),(3,5)],7) => 2 ([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 2 ([(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 2 ([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 2 ([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(6,5)],7) => 2 ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 2 ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 2 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => 3 ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => 3 ([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7) => 2 ([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 3 ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 3 ([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 2 ([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 1 ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 3 ([(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7) => 2 ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 2 ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 2 ([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7) => 2 ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 2 ([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) => 2 ([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7) => 1 ([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 2 ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 1 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 1 ([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => 1 ([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7) => 2 ([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7) => 1 ([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 1 ([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 2 ([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7) => 2 ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 2 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 1 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => 1 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 1 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => 2 ([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7) => 1 ([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 3 ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => 2 ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => 2 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7) => 2 ([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 3 ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => 2 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 2 ([(2,6),(3,6),(4,5),(5,6)],7) => 2 ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => 2 ([(1,6),(2,6),(3,4),(4,5)],7) => 2 ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 2 ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 2 ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 2 ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 2 ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 2 ([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7) => 2 ([(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7) => 2 ([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7) => 2 ([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) => 2 ([(0,3),(1,6),(2,6),(3,4),(3,5)],7) => 2 ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => 2 ([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7) => 2 ([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) => 2 ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 2 ([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 2 ([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 2 ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 3 ([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 3 ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 4 ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 1 ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 1 ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 2 ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2 ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2 ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 2 ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 2 ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2 ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 2 ([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => 1 ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 2 ([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7) => 2 ([(1,6),(2,6),(3,5),(4,5)],7) => 2 ([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7) => 2 ([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7) => 2 ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 2 ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 2 ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 2 ([(1,6),(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),(5,4)],7) => 3 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 3 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 3 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 4 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 4 ([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 2 ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 2 ([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 2 ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => 2 ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 2 ([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7) => 2 ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7) => 2 ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,4)],7) => 2 ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 2 ([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => 2 ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 2 ([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 2 ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 2 ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) => 2 ([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => 2 ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7) => 2 ([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 2 ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 2 ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => 2 ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1 ([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 1 ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 1 ([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => 2 ([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 2 ([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 2 ([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7) => 2 ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => 2 ([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7) => 2 ([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 2 ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => 1 ([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => 2 ([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 2 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3 ([(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) => 4 ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7) => 2 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => 2 ([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 2 ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7) => 1 ([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7) => 2 ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 2 ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2 ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 2 ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 2 ([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) => 2 ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7) => 2 ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 1 ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 2 ([(3,6),(4,5)],7) => 3 ([(3,6),(4,5),(4,6)],7) => 3 ([(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 2 ([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7) => 3 ([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7) => 2 ([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 3 ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 1 ([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => 1 ([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7) => 2 ([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7) => 1 ([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) => 2 ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => 1 ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => 2 ([(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 1 ([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7) => 1 ([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7) => 2 ([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7) => 2 ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 1 ([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 1 ([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => 1 ([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => 1 ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => 1 ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => 1 ([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7) => 2 ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => 1 ([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 3 ([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 2 ([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 3 ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 2 ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 2 ([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 1 ([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 1 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2 ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 2 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 2 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => 2 ([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 2 ([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 2 ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 2 ([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7) => 2 ([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7) => 2 ([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => 2 ([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => 2 ([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7) => 2 ([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7) => 2 ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 2 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7) => 2 ([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7) => 2 ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7) => 2 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => 2 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 2 ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7) => 2 ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 2 ([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7) => 2 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7) => 2 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 2 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => 2 ([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7) => 1 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) => 2 ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7) => 2 ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 2 ([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 1 ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 2 ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 2 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 3 ([(2,6),(3,4),(3,6),(6,5)],7) => 2 ([(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 2 ([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) => 3 ([(2,6),(3,4),(3,5)],7) => 2 ([(2,6),(3,4),(3,5),(3,6)],7) => 2 ([(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 1 ([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => 1 ([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 1 ([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) => 1 ([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7) => 1 ([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7) => 1 ([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 2 ([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2 ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7) => 2 ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7) => 2 ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) => 2 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => 2 ([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7) => 1 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => 1 ([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1 ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7) => 1 ([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 2 ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 2 ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 1 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7) => 2 ([(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 2 ([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7) => 2 ([(1,6),(2,3),(2,4),(2,5)],7) => 3 ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 3 ([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7) => 2 ([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7) => 2 ([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7) => 2 ([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 2 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) => 3 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 3 ([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7) => 3 ([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => 4 ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 4 ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 3 ([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => 3 ([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => 2 ([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 2 ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => 2 ([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 3 ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 3 ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 4 ([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7) => 3 ([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7) => 2 ([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7) => 3 ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 4 ([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => 2 ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 2 ([(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 2 ([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7) => 2 ([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 1 ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 1 ([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 2 ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 2 ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 2 ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 2 ([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 3 ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 3 ([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 2 ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => 2 ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 2 ([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 2 ([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7) => 1 ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) => 1 ([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7) => 1 ([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 1 ----------------------------------------------------------------------------- Created: May 27, 2019 at 06:59 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 27, 2019 at 06:59 by Martin Rubey