***************************************************************************** * 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: St000479 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The Ramsey number of a graph. This is the smallest integer $n$ such that every two-colouring of the edges of the complete graph $K_n$ contains a (not necessarily induced) monochromatic copy of the given graph. [1] Thus, the Ramsey number of the complete graph $K_n$ is the ordinary Ramsey number $R(n,n)$. Very few of these numbers are known, in particular, it is only known that $43\leq R(5,5)\leq 48$. [2,3,4,5] ----------------------------------------------------------------------------- References: [1] Chvatál, C., Rödl, V., Szemerédi, E., Trotter, Jr., W. T. The Ramsey number of a graph with bounded maximum degree [[MathSciNet:0714447]] [2] Radziszowski, Stanisław P. Small Ramsey numbers [[MathSciNet:1670625]] [3] [[wikipedia:Ramsey's theorem#Ramsey numbers]] [4] Hendry, G. R. T. Ramsey numbers for graphs with five vertices [[MathSciNet:0994745]] [5] Angeltveit, V., McKay, B. D. $R(5,5) \le 48$ [[arXiv:1703.08768]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: ([],0) => 0 ([],1) => 1 ([],2) => 2 ([(0,1)],2) => 2 ([],3) => 3 ([(1,2)],3) => 3 ([(0,2),(1,2)],3) => 3 ([(0,1),(0,2),(1,2)],3) => 6 ([],4) => 4 ([(2,3)],4) => 4 ([(1,3),(2,3)],4) => 4 ([(0,3),(1,3),(2,3)],4) => 6 ([(0,3),(1,2)],4) => 5 ([(0,3),(1,2),(2,3)],4) => 5 ([(1,2),(1,3),(2,3)],4) => 6 ([(0,3),(1,2),(1,3),(2,3)],4) => 7 ([(0,2),(0,3),(1,2),(1,3)],4) => 6 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 10 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 18 ([],5) => 5 ([(3,4)],5) => 5 ([(2,4),(3,4)],5) => 5 ([(1,4),(2,4),(3,4)],5) => 6 ([(0,4),(1,4),(2,4),(3,4)],5) => 7 ([(1,4),(2,3)],5) => 5 ([(1,4),(2,3),(3,4)],5) => 5 ([(0,1),(2,4),(3,4)],5) => 6 ([(2,3),(2,4),(3,4)],5) => 6 ([(0,4),(1,4),(2,3),(3,4)],5) => 6 ([(1,4),(2,3),(2,4),(3,4)],5) => 7 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 9 ([(1,3),(1,4),(2,3),(2,4)],5) => 6 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 6 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 9 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 10 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 14 ([(0,4),(1,3),(2,3),(2,4)],5) => 6 ([(0,1),(2,3),(2,4),(3,4)],5) => 7 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 9 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 9 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 9 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 9 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 10 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 10 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 18 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 18 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 18 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 10 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 15 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 22 ([],6) => 6 ([(4,5)],6) => 6 ([(3,5),(4,5)],6) => 6 ([(2,5),(3,5),(4,5)],6) => 6 ([(1,5),(2,5),(3,5),(4,5)],6) => 7 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 10 ([(2,5),(3,4)],6) => 6 ([(2,5),(3,4),(4,5)],6) => 6 ([(1,2),(3,5),(4,5)],6) => 6 ([(3,4),(3,5),(4,5)],6) => 6 ([(1,5),(2,5),(3,4),(4,5)],6) => 6 ([(0,1),(2,5),(3,5),(4,5)],6) => 7 ([(2,5),(3,4),(3,5),(4,5)],6) => 7 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 7 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 9 ([(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(0,5),(1,5),(2,4),(3,4)],6) => 7 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 6 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 7 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 9 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 8 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 7 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 10 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 14 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 14 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,5),(1,4),(2,3)],6) => 8 ([(1,5),(2,4),(3,4),(3,5)],6) => 6 ([(0,1),(2,5),(3,4),(4,5)],6) => 8 ([(1,2),(3,4),(3,5),(4,5)],6) => 7 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 9 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 9 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 9 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 9 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 10 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 10 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 8 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 10 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 15 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 22 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 18 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 10 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 17 ([],7) => 7 ([(5,6)],7) => 7 ([(4,6),(5,6)],7) => 7 ([(3,6),(4,6),(5,6)],7) => 7 ([(2,6),(3,6),(4,6),(5,6)],7) => 7 ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 10 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 11 ([(3,6),(4,5)],7) => 7 ([(3,6),(4,5),(5,6)],7) => 7 ([(2,3),(4,6),(5,6)],7) => 7 ([(4,5),(4,6),(5,6)],7) => 7 ([(2,6),(3,6),(4,5),(5,6)],7) => 7 ([(1,2),(3,6),(4,6),(5,6)],7) => 7 ([(3,6),(4,5),(4,6),(5,6)],7) => 7 ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 7 ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 9 ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 9 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 10 ([(3,5),(3,6),(4,5),(4,6)],7) => 7 ([(1,6),(2,6),(3,5),(4,5)],7) => 7 ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7 ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 7 ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 8 ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10 ([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 9 ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 8 ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7 ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 9 ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 9 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 14 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 21 ([(1,6),(2,5),(3,4)],7) => 8 ([(2,6),(3,5),(4,5),(4,6)],7) => 7 ([(1,2),(3,6),(4,5),(5,6)],7) => 8 ([(0,3),(1,2),(4,6),(5,6)],7) => 9 ([(2,3),(4,5),(4,6),(5,6)],7) => 7 ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 9 ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 9 ([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 9 ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 9 ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 9 ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 10 ([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 10 ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 8 ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 9 ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18 ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18 ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18 ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 10 ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 15 ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 8 ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 22 ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 18 ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => 9 ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 9 ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 10 ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 13 ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 17 ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 11 ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 10 ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 14 ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 11 ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 11 ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 10 ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 18 ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 18 ([(5,6),(5,7),(6,7)],8) => 8 ([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 18 ([(4,7),(5,6),(5,7),(6,7)],8) => 8 ([(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 9 ([(6,7)],8) => 8 ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 22 ([(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 10 ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 10 ([(5,7),(6,7)],8) => 8 ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 14 ([(4,7),(5,7),(6,7)],8) => 8 ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 18 ([(3,7),(4,7),(5,7),(6,7)],8) => 8 ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 21 ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 10 ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 26 ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 11 ([],8) => 8 ([(4,7),(5,6)],8) => 8 ([(4,7),(5,6),(6,7)],8) => 8 ([(3,4),(5,7),(6,7)],8) => 8 ([(3,7),(4,7),(5,6),(6,7)],8) => 8 ([(2,3),(4,7),(5,7),(6,7)],8) => 8 ([(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 8 ([(1,2),(3,7),(4,7),(5,7),(6,7)],8) => 9 ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 10 ([(4,6),(4,7),(5,6),(5,7)],8) => 8 ([(2,7),(3,7),(4,6),(5,6)],8) => 8 ([(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 8 ([(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 8 ([(1,7),(2,7),(3,7),(4,6),(5,6)],8) => 8 ([(3,7),(4,6),(5,6),(5,7),(6,7)],8) => 9 ([(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 8 ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8) => 8 ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 9 ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 9 ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 10 ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 14 ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 18 ([(2,7),(3,6),(4,5)],8) => 8 ([(3,7),(4,6),(5,6),(5,7)],8) => 8 ([(2,3),(4,7),(5,6),(6,7)],8) => 8 ([(1,4),(2,3),(5,7),(6,7)],8) => 9 ([(3,4),(5,6),(5,7),(6,7)],8) => 8 ([(3,6),(4,5),(4,7),(5,7),(6,7)],8) => 9 ([(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8) => 9 ([(3,6),(3,7),(4,5),(4,7),(5,6)],8) => 9 ([(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 9 ([(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8) => 9 ([(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8) => 10 ([(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8) => 10 ([(2,7),(3,6),(4,5),(4,6),(5,7)],8) => 8 ([(1,7),(2,6),(3,5),(4,5),(6,7)],8) => 9 ([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8) => 10 ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => 15 ([(2,6),(2,7),(3,4),(3,5),(4,7),(5,6)],8) => 8 ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => 18 ([(1,2),(3,6),(4,5),(5,7),(6,7)],8) => 9 ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8) => 9 ([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8) => 10 ([(1,6),(1,7),(2,3),(2,5),(3,4),(4,6),(5,7)],8) => 13 ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8) => 17 ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8) => 10 ([(0,7),(1,6),(2,5),(3,4)],8) => 11 ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8) => 11 ([(0,6),(0,7),(1,2),(1,3),(2,5),(3,4),(4,6),(5,7)],8) => 11 ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 21 ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => 11 ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => 9 ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6)],8) => 9 ([(0,1),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 11 ([(0,3),(1,2),(4,7),(5,6),(6,7)],8) => 11 ([(0,1),(2,5),(3,4),(4,6),(5,7),(6,7)],8) => 11 ([(0,1),(2,7),(3,7),(4,6),(5,6)],8) => 10 ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9) => 15 ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9) => 14 ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9) => 11 ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9) => 13 ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9) => 11 ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 11 ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9) => 12 ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 12 ([(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 18 ([(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 18 ([(6,7),(6,8),(7,8)],9) => 9 ([(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 18 ([(5,8),(6,7),(6,8),(7,8)],9) => 9 ([(4,8),(5,8),(6,7),(6,8),(7,8)],9) => 9 ([(7,8)],9) => 9 ([(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 22 ([(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 10 ([(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 10 ([(6,8),(7,8)],9) => 9 ([(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 14 ([(5,8),(6,8),(7,8)],9) => 9 ([(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 18 ([(4,8),(5,8),(6,8),(7,8)],9) => 9 ([(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 21 ([(3,8),(4,8),(5,8),(6,8),(7,8)],9) => 10 ([(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 26 ([(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9) => 11 ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9) => 14 ([],9) => 9 ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9) => 10 ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9) => 9 ([(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9) => 21 ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9) => 26 ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7)],9) => 11 ([(3,4),(5,8),(6,7),(7,8)],9) => 9 ([(5,8),(6,7),(7,8)],9) => 9 ([(4,8),(5,8),(6,7),(7,8)],9) => 9 ([(3,8),(4,8),(5,8),(6,7),(7,8)],9) => 9 ([(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9) => 10 ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9) => 11 ([(1,8),(2,7),(3,6),(4,5)],9) => 11 ([(1,4),(2,3),(5,8),(6,7),(7,8)],9) => 11 ([(1,2),(3,6),(4,5),(5,7),(6,8),(7,8)],9) => 11 ([(1,8),(2,7),(3,4),(3,5),(4,6),(5,7),(6,8)],9) => 11 ([(0,8),(1,7),(2,3),(4,5),(4,6),(5,7),(6,8)],9) => 12 ([(0,3),(1,2),(4,7),(5,6),(6,8),(7,8)],9) => 12 ([(0,5),(1,4),(2,3),(6,8),(7,8)],9) => 12 ([(0,6),(1,5),(2,8),(3,7),(4,7),(4,8),(5,6)],9) => 12 ([(0,1),(2,8),(3,7),(4,6),(5,6),(7,8)],9) => 12 ([(0,1),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9) => 13 ([(5,7),(5,8),(6,7),(6,8)],9) => 9 ([(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9) => 18 ([(4,7),(4,8),(5,6),(5,8),(6,7),(7,8)],9) => 9 ([(0,7),(0,8),(1,5),(1,6),(2,3),(2,4),(3,4),(5,6),(7,8)],9) => 15 ([(4,7),(5,6),(5,8),(6,8),(7,8)],9) => 9 ([(3,7),(3,8),(4,5),(4,6),(5,6),(7,8)],9) => 10 ([(4,5),(6,7),(6,8),(7,8)],9) => 9 ([(3,8),(4,7),(5,6)],9) => 9 ([(5,8),(6,7)],9) => 9 ([(4,8),(5,7),(6,7),(6,8)],9) => 9 ([(1,2),(3,8),(4,8),(5,8),(6,8),(7,8)],9) => 11 ([(3,4),(5,8),(6,8),(7,8)],9) => 9 ([(4,8),(5,8),(6,7)],9) => 9 ([(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9) => 10 ([(2,3),(4,8),(5,8),(6,8),(7,8)],9) => 9 ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7)],9) => 10 ([(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9) => 18 ([(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9) => 14 ([(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9) => 10 ([(3,8),(4,8),(5,7),(6,7)],9) => 9 ([(2,5),(3,4),(6,8),(7,8)],9) => 9 ([(2,3),(4,7),(5,6),(6,8),(7,8)],9) => 9 ([(1,8),(2,8),(3,8),(4,7),(5,7),(6,7)],9) => 9 ([(1,8),(2,6),(3,5),(4,7),(5,6),(7,8)],9) => 11 ([(4,8),(5,6),(5,7),(6,7),(6,8),(7,8)],9) => 10 ([(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9) => 15 ([(3,7),(3,8),(4,5),(4,6),(5,8),(6,7)],9) => 9 ([(4,8),(5,7),(5,8),(6,7),(6,8)],9) => 9 ([(3,8),(4,8),(5,7),(5,8),(6,7),(6,8)],9) => 9 ([(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9) => 11 ([(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 18 ([(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 18 ([(7,8),(7,9),(8,9)],10) => 10 ([(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 18 ([(6,9),(7,8),(7,9),(8,9)],10) => 10 ([(5,9),(6,9),(7,8),(7,9),(8,9)],10) => 10 ([(8,9)],10) => 10 ([(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 22 ([(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 10 ([(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 10 ([(7,9),(8,9)],10) => 10 ([(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 14 ([(6,9),(7,9),(8,9)],10) => 10 ([(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 18 ([(5,9),(6,9),(7,9),(8,9)],10) => 10 ([(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 21 ([(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 10 ([(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 26 ([(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 11 ([(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 14 ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 15 ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 18 ([],10) => 10 ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 13 ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 12 ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 14 ([(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 26 ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10) => 15 ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 30 ([(0,9),(1,8),(2,7),(3,6),(4,5)],10) => 14 ([(0,5),(1,4),(2,3),(6,9),(7,8),(8,9)],10) => 14 ([(0,3),(1,2),(4,7),(5,6),(6,8),(7,9),(8,9)],10) => 14 ([(0,9),(1,8),(2,3),(4,5),(4,6),(5,7),(6,8),(7,9)],10) => 14 ([(1,9),(2,8),(3,4),(5,6),(5,7),(6,8),(7,9)],10) => 12 ([(1,4),(2,3),(5,8),(6,7),(7,9),(8,9)],10) => 12 ([(1,6),(2,5),(3,4),(7,9),(8,9)],10) => 12 ([(2,9),(3,8),(4,7),(5,6)],10) => 11 ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10) => 14 ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10) => 15 ([(6,8),(6,9),(7,8),(7,9)],10) => 10 ([(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10) => 18 ([(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10) => 10 ([(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 21 ([(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 14 ([(5,8),(6,7),(6,9),(7,9),(8,9)],10) => 10 ([(6,9),(7,8),(8,9)],10) => 10 ([(1,8),(1,9),(2,6),(2,7),(3,4),(3,5),(4,5),(6,7),(8,9)],10) => 15 ([(4,8),(4,9),(5,6),(5,7),(6,7),(8,9)],10) => 10 ([(5,6),(7,8),(7,9),(8,9)],10) => 10 ([(4,9),(5,8),(6,7)],10) => 10 ([(6,9),(7,8)],10) => 10 ([(5,9),(6,8),(7,8),(7,9)],10) => 10 ([(0,1),(2,9),(3,7),(4,6),(5,8),(6,7),(8,9)],10) => 14 ([(0,7),(1,6),(2,9),(3,8),(4,5),(4,8),(5,9),(6,7)],10) => 14 ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10) => 14 ([(2,3),(4,9),(5,9),(6,8),(7,8)],10) => 10 ([(3,4),(5,9),(6,9),(7,9),(8,9)],10) => 10 ([(3,9),(4,9),(5,9),(6,8),(7,8)],10) => 10 ([(0,8),(1,9),(2,9),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9)],10) => 13 ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,7),(6,8),(6,9),(7,8)],10) => 13 ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10) => 13 ([(0,1),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 15 ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8)],10) => 13 ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8)],10) => 11 ([(5,9),(6,9),(7,8)],10) => 10 ([(2,5),(3,4),(6,9),(7,8),(8,9)],10) => 11 ([(3,9),(4,8),(5,6),(5,7),(6,8),(7,9)],10) => 10 ([(4,9),(5,8),(6,7),(8,9)],10) => 10 ([(4,8),(4,9),(5,6),(5,7),(6,9),(7,8)],10) => 10 ([(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 10 ([(1,2),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 13 ([(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10) => 11 ([(5,9),(6,9),(7,8),(8,9)],10) => 10 ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 15 ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 18 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 19 ([(9,10)],11) => 11 ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 15 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11) => 18 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11) => 15 ([],11) => 11 ([(8,10),(9,10)],11) => 11 ([(0,9),(1,10),(2,10),(3,10),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 14 ([(0,10),(1,10),(2,10),(3,10),(4,5),(5,9),(6,8),(6,10),(7,8),(7,9)],11) => 14 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,6),(6,8),(7,9),(7,10),(8,9)],11) => 15 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,7),(7,9),(8,9),(8,10)],11) => 15 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11) => 17 ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 33 ([(1,10),(2,9),(3,8),(4,7),(5,6)],11) => 14 ([(1,6),(2,5),(3,4),(7,10),(8,9),(9,10)],11) => 14 ([(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 30 ([(5,10),(6,9),(7,8),(9,10)],11) => 11 ([(0,1),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 17 ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11) => 15 ([(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 11 ([(7,10),(8,9),(8,10),(9,10)],11) => 11 ([(8,9),(8,10),(9,10)],11) => 11 ([(1,4),(2,3),(5,8),(6,7),(7,9),(8,10),(9,10)],11) => 14 ([(6,10),(7,10),(8,9),(8,10),(9,10)],11) => 11 ([(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11) => 14 ([(5,10),(6,10),(7,10),(8,9),(9,10)],11) => 11 ([(0,11),(1,10),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 17 ([(10,11)],12) => 12 ([(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 12 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12) => 19 ([(2,11),(3,10),(4,9),(5,8),(6,7)],12) => 14 ([(0,11),(1,10),(2,9),(3,8),(4,7),(5,6)],12) => 17 ([(0,10),(1,11),(2,11),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 16 ([],12) => 12 ([(8,11),(9,10),(9,11),(10,11)],12) => 12 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 22 ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 38 ([(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 30 ([(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 21 ([(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 14 ([(8,10),(8,11),(9,10),(9,11)],12) => 12 ([(0,7),(1,6),(2,5),(3,4),(8,11),(9,10),(10,11)],12) => 17 ([(0,5),(1,4),(2,3),(6,9),(7,8),(8,10),(9,11),(10,11)],12) => 17 ([(0,3),(1,2),(4,11),(5,9),(6,8),(7,10),(8,9),(10,11)],12) => 17 ([(0,3),(1,2),(4,7),(5,6),(6,10),(7,11),(8,9),(8,10),(9,11)],12) => 17 ([(0,1),(2,7),(3,6),(4,9),(5,8),(6,7),(8,10),(9,11),(10,11)],12) => 17 ([(0,11),(1,10),(2,3),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 17 ([(0,11),(1,9),(2,7),(3,6),(4,8),(5,10),(6,7),(8,9),(10,11)],12) => 17 ([(0,9),(1,8),(2,11),(3,10),(4,5),(4,6),(5,7),(6,8),(7,9),(10,11)],12) => 17 ([(0,11),(1,9),(2,8),(3,10),(4,5),(4,8),(5,9),(6,7),(6,10),(7,11)],12) => 17 ([(1,8),(2,7),(3,6),(4,5),(9,11),(10,11)],12) => 15 ([(2,5),(3,4),(6,11),(7,11),(8,10),(9,10)],12) => 13 ([(4,5),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 12 ([(3,11),(4,11),(5,10),(6,10),(7,9),(8,9)],12) => 12 ([(4,11),(5,11),(6,11),(7,11),(8,10),(9,10)],12) => 12 ([(4,11),(5,11),(6,11),(7,10),(8,10),(9,10)],12) => 12 ([(9,11),(10,11)],12) => 12 ([(0,10),(0,11),(1,7),(1,8),(2,4),(2,5),(3,4),(3,5),(6,7),(6,8),(9,10),(9,11)],12) => 17 ([(0,1),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 19 ([(0,11),(1,11),(2,11),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9)],12) => 14 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,10),(8,10),(9,10)],12) => 15 ([(1,11),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 15 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 19 ([(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 14 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10),(10,11)],12) => 18 ([(4,11),(5,10),(6,9),(7,8)],12) => 12 ([(0,11),(0,12),(1,11),(1,12),(2,11),(2,12),(3,11),(3,12),(4,11),(4,12),(5,11),(5,12),(6,11),(6,12),(7,11),(7,12),(8,11),(8,12),(9,11),(9,12),(10,11),(10,12)],13) => 42 ([(0,10),(1,8),(2,7),(3,9),(4,12),(5,11),(6,11),(6,12),(7,8),(9,10)],13) => 18 ([(5,10),(6,10),(7,10),(8,9)],11) => 11 ([(4,10),(5,9),(6,7),(6,8),(7,9),(8,10)],11) => 11 ([(6,11),(7,10),(8,9)],12) => 12 ([(2,10),(3,10),(4,10),(5,10),(6,7),(7,9),(8,9),(8,10)],11) => 11 ([(7,11),(8,11),(9,10),(9,11),(10,11)],12) => 12 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,12),(9,11),(10,11),(11,12)],13) => 19 ([(1,2),(3,10),(4,8),(5,7),(6,9),(7,8),(9,10)],11) => 14 ([(4,9),(4,10),(5,6),(5,8),(6,7),(7,9),(8,10)],11) => 13 ([(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 11 ([(3,11),(4,11),(5,10),(6,9),(7,8),(7,9),(8,10)],12) => 12 ([(4,9),(5,10),(6,10),(7,10),(8,9),(8,10)],11) => 11 ([(5,8),(5,9),(6,7),(6,9),(7,9),(8,9)],10) => 10 ([(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 14 ([(1,8),(1,9),(2,3),(2,5),(3,4),(4,6),(5,7),(6,8),(7,9)],10) => 17 ([(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 11 ([(0,12),(1,11),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11),(10,12)],13) => 18 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9)],11) => 13 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13) => 23 ([(0,10),(1,10),(2,9),(3,9),(4,8),(5,8),(6,12),(7,11),(11,12)],13) => 17 ([(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10) => 10 ([(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12) => 15 ([(1,10),(2,9),(3,4),(5,6),(5,7),(6,8),(7,9),(8,10)],11) => 14 ([(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 14 ([(4,10),(5,11),(6,11),(7,11),(8,9),(8,10),(9,11)],12) => 12 ([(5,10),(6,10),(7,9),(8,9)],11) => 11 ([(1,7),(1,8),(2,3),(2,4),(3,6),(4,5),(5,7),(6,8)],9) => 11 ([(5,10),(6,10),(7,9),(8,9),(9,10)],11) => 11 ([(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10) => 10 ([(3,7),(4,8),(5,8),(6,7),(6,8)],9) => 9 ([(0,12),(1,12),(2,11),(3,10),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],13) => 18 ([(1,2),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9)],12) => 14 ([(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10) => 11 ([(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 18 ([(2,7),(3,6),(4,5),(8,10),(9,10)],11) => 12 ([(4,5),(6,10),(7,10),(8,10),(9,10)],11) => 11 ([(1,9),(2,8),(3,11),(4,10),(5,7),(5,10),(6,7),(6,11),(8,9)],12) => 15 ([(0,10),(1,9),(2,12),(3,11),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(11,12)],13) => 18 ([(6,9),(6,10),(7,8),(7,10),(8,9),(9,10)],11) => 11 ([(7,9),(7,10),(8,9),(8,10)],11) => 11 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10)],12) => 15 ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9)],11) => 11 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,8),(8,10),(9,10),(9,11)],12) => 15 ([(0,3),(1,2),(4,10),(5,9),(6,8),(7,8),(9,11),(10,12),(11,12)],13) => 18 ([(0,1),(2,7),(3,6),(4,9),(5,8),(6,7),(8,10),(9,10)],11) => 15 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,8),(8,10),(9,11),(9,12),(10,11)],13) => 19 ([(7,8),(9,10),(9,11),(10,11)],12) => 12 ([(5,9),(5,10),(6,7),(6,8),(7,8),(9,10)],11) => 11 ([(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 18 ([(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11) => 11 ([(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12) => 12 ([(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 18 ([(6,10),(7,10),(8,9)],11) => 11 ([(0,12),(1,11),(2,5),(3,4),(6,7),(6,8),(7,9),(8,10),(9,11),(10,12)],13) => 18 ([(4,10),(5,9),(6,7),(8,9),(8,10)],11) => 11 ([(0,10),(1,9),(2,12),(3,11),(4,5),(6,8),(6,11),(7,8),(7,12),(9,10)],13) => 18 ([(2,11),(3,10),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 14 ([(1,11),(2,11),(3,10),(4,9),(5,6),(5,7),(6,8),(7,9),(8,10)],12) => 15 ([(7,11),(8,11),(9,11),(10,11)],12) => 12 ([(0,11),(0,12),(1,2),(1,4),(2,3),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11),(10,12)],13) => 25 ([(2,9),(2,10),(3,7),(3,8),(4,5),(4,6),(5,6),(7,8),(9,10)],11) => 15 ([(0,9),(0,10),(1,2),(1,4),(2,3),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 21 ([(1,10),(2,11),(3,11),(4,11),(5,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 14 ([(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 18 ([(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10)],12) => 13 ([(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,10),(9,10)],11) => 15 ([(5,9),(6,8),(7,8),(7,9),(8,9)],10) => 10 ([(0,10),(1,9),(2,3),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 15 ([(0,10),(1,9),(2,12),(3,11),(4,7),(4,8),(5,6),(5,9),(6,10),(7,11),(8,12)],13) => 18 ([(3,11),(4,11),(5,11),(6,7),(7,9),(8,10),(8,11),(9,10)],12) => 12 ([(4,7),(4,8),(5,6),(5,8),(6,7)],9) => 9 ([(2,9),(3,8),(4,11),(5,10),(6,10),(6,11),(7,8),(7,9)],12) => 13 ([(2,8),(2,9),(3,5),(3,6),(4,5),(4,6),(7,8),(7,9)],10) => 11 ([(6,11),(7,11),(8,11),(9,10),(10,11)],12) => 12 ([(3,10),(4,10),(5,10),(6,10),(7,9),(8,9)],11) => 11 ([(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12) => 14 ([(3,11),(4,11),(5,11),(6,11),(7,11),(8,9),(9,10),(10,11)],12) => 13 ([(0,13),(0,14),(1,13),(1,14),(2,13),(2,14),(3,13),(3,14),(4,13),(4,14),(5,13),(5,14),(6,13),(6,14),(7,13),(7,14),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14)],15) => 50 ([(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10)],12) => 12 ([(8,11),(9,10)],12) => 12 ([(3,10),(4,10),(5,10),(6,9),(7,9),(8,9)],11) => 11 ([(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10)],11) => 11 ([(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 21 ([(0,1),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13) => 21 ([(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9) => 10 ([(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8)],10) => 10 ([(4,11),(5,10),(6,7),(6,8),(7,9),(8,10),(9,11)],12) => 12 ([(2,8),(3,9),(4,9),(5,6),(5,7),(6,8),(7,9)],10) => 10 ([(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9) => 9 ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9)],11) => 13 ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11) => 14 ([(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 26 ([(0,8),(1,7),(2,10),(3,9),(4,6),(5,6),(7,8),(9,11),(10,11)],12) => 16 ([(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,11),(10,11)],12) => 17 ([(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 15 ([(5,11),(6,10),(7,8),(9,10),(9,11)],12) => 12 ([(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 18 ([(2,10),(3,11),(4,11),(5,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 13 ([(0,10),(1,10),(2,9),(3,8),(4,5),(4,6),(5,7),(6,8),(7,9)],11) => 15 ([(1,8),(2,8),(3,7),(4,7),(5,10),(6,9),(9,11),(10,11)],12) => 14 ([(0,11),(1,11),(2,10),(3,10),(4,9),(5,9),(6,8),(7,8)],12) => 15 ([(0,11),(1,12),(2,12),(3,12),(4,12),(5,6),(5,7),(6,8),(7,9),(8,10),(9,11),(10,12)],13) => 17 ([(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 18 ([(0,1),(2,8),(3,7),(4,6),(5,6),(7,10),(8,11),(9,10),(9,11)],12) => 16 ([(2,10),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 12 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,7),(7,9),(8,10),(8,11),(9,10)],12) => 15 ([(2,7),(3,6),(4,5),(8,11),(9,10),(10,11)],12) => 14 ([(0,9),(1,8),(2,11),(3,10),(4,12),(5,12),(6,7),(6,10),(7,11),(8,9)],13) => 18 ([(7,10),(8,9)],11) => 11 ([(4,7),(4,8),(5,6),(5,8),(6,8),(7,8)],9) => 9 ([(1,8),(2,8),(3,8),(4,8),(5,7),(6,7)],9) => 9 ([(0,5),(1,4),(2,3),(6,9),(7,8),(8,11),(9,12),(10,11),(10,12)],13) => 18 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,12),(9,11),(10,11)],13) => 19 ([(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9)],11) => 11 ([(8,11),(9,10),(10,11)],12) => 12 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12) => 18 ([(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 12 ([(2,11),(3,11),(4,11),(5,11),(6,7),(7,9),(8,10),(8,11),(9,10)],12) => 13 ([(0,3),(1,2),(4,10),(5,9),(6,8),(7,8),(9,10)],11) => 15 ([(0,7),(1,6),(2,5),(3,4),(8,10),(9,10)],11) => 15 ([(3,9),(4,10),(5,10),(6,7),(6,8),(7,9),(8,10)],11) => 11 ([(5,8),(6,7),(9,11),(10,11)],12) => 12 ([(0,11),(1,12),(2,12),(3,12),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11),(10,12)],13) => 17 ([(2,8),(3,8),(4,8),(5,7),(6,7)],9) => 9 ([(1,11),(2,9),(3,8),(4,10),(5,7),(6,7),(8,9),(10,11)],12) => 15 ([(2,9),(3,8),(4,11),(5,10),(6,7),(6,10),(7,11),(8,9)],12) => 14 ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,7),(7,9),(8,9),(8,10)],11) => 13 ([(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 18 ([(6,11),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 12 ([(5,11),(6,11),(7,11),(8,10),(9,10)],12) => 12 ([(4,8),(5,7),(6,7),(6,8),(7,8)],9) => 9 ([(1,4),(2,3),(5,8),(6,7),(7,10),(8,11),(9,10),(9,11)],12) => 15 ([(2,9),(3,10),(4,10),(5,6),(5,7),(6,8),(7,9),(8,10)],11) => 12 ([(5,9),(6,7),(6,8),(7,8),(7,9),(8,9)],10) => 10 ([(6,11),(7,11),(8,10),(9,10),(10,11)],12) => 12 ([(5,11),(6,11),(7,11),(8,10),(9,10),(10,11)],12) => 12 ([(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11) => 11 ([(2,10),(2,11),(3,4),(3,5),(4,7),(5,6),(6,8),(7,9),(8,10),(9,11)],12) => 14 ([(1,9),(2,9),(3,9),(4,5),(5,7),(6,8),(6,9),(7,8)],10) => 11 ([(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10),(10,11)],12) => 12 ([(0,1),(2,10),(3,10),(4,9),(5,9),(6,8),(7,8)],11) => 14 ([(5,10),(6,11),(7,11),(8,11),(9,10),(9,11)],12) => 12 ([(6,10),(7,9),(8,9),(8,10),(9,10)],11) => 11 ([(0,8),(1,7),(2,10),(3,9),(4,7),(4,8),(5,6),(5,9),(6,10)],11) => 15 ([(6,11),(7,10),(8,9),(10,11)],12) => 12 ([(6,10),(7,11),(8,11),(9,10),(9,11)],12) => 12 ([(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11) => 13 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,12),(9,12),(10,11),(11,12)],13) => 22 ([(4,10),(5,10),(6,9),(7,8),(8,9)],11) => 11 ([(2,10),(3,10),(4,10),(5,6),(6,8),(7,9),(7,10),(8,9)],11) => 11 ([(1,4),(2,3),(5,10),(6,10),(7,9),(8,9)],11) => 13 ([(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10) => 10 ([(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11) => 18 ([(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 18 ([(3,10),(4,9),(5,8),(6,7)],11) => 11 ([(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 18 ([(0,3),(1,2),(4,10),(5,9),(6,8),(7,8),(9,11),(10,11)],12) => 16 ([(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12) => 18 ([(0,9),(1,8),(2,11),(3,10),(4,12),(5,12),(6,10),(6,11),(7,8),(7,9)],13) => 17 ([(1,2),(3,9),(4,8),(5,7),(6,7),(8,10),(9,10)],11) => 13 ([(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 18 ([(4,10),(4,11),(5,7),(5,8),(6,7),(6,8),(9,10),(9,11)],12) => 12 ([(0,10),(1,11),(2,11),(3,11),(4,11),(5,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 15 ([(0,10),(1,8),(2,7),(3,9),(4,6),(5,6),(7,8),(9,10)],11) => 15 ([(3,10),(4,11),(5,11),(6,7),(6,8),(7,9),(8,10),(9,11)],12) => 12 ([(6,11),(7,11),(8,11),(9,10)],12) => 12 ([(1,2),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 17 ([(6,9),(6,10),(7,8),(7,10),(8,9)],11) => 11 ([(0,10),(0,11),(1,8),(1,9),(2,6),(2,7),(3,4),(3,5),(4,5),(6,7),(8,9),(10,11)],12) => 20 ([(4,5),(6,11),(7,11),(8,10),(9,10)],12) => 12 ([(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 22 ([(0,7),(0,8),(1,2),(1,4),(2,3),(3,5),(4,6),(5,7),(6,8)],9) => 17 ([(3,9),(4,8),(5,7),(6,7),(8,10),(9,10)],11) => 11 ([(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 26 ([(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 18 ([(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 26 ([(3,10),(4,10),(5,10),(6,7),(7,9),(8,9),(8,10)],11) => 11 ([(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(6,7),(6,8)],11) => 13 ([(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9) => 9 ([(7,10),(7,11),(8,9),(8,11),(9,10),(10,11)],12) => 12 ([(2,8),(3,7),(4,10),(5,9),(6,9),(6,10),(7,8)],11) => 12 ([(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10) => 15 ([(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9) => 10 ([(4,10),(5,10),(6,10),(7,9),(8,9)],11) => 11 ([(6,10),(6,11),(7,8),(7,9),(8,9),(10,11)],12) => 12 ([(1,8),(2,7),(3,10),(4,9),(5,6),(5,9),(6,10),(7,8)],11) => 14 ([(3,11),(4,10),(5,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 12 ([(7,10),(8,9),(8,11),(9,11),(10,11)],12) => 12 ([(2,11),(3,10),(4,5),(6,7),(6,8),(7,9),(8,10),(9,11)],12) => 14 ([(2,10),(3,10),(4,9),(5,9),(6,8),(7,8)],11) => 11 ([(0,12),(1,12),(2,11),(3,10),(4,5),(6,7),(6,8),(7,9),(8,10),(9,11)],13) => 18 ([(1,9),(1,10),(2,3),(2,4),(3,6),(4,5),(5,7),(6,8),(7,9),(8,10)],11) => 14 ([(1,8),(2,8),(3,7),(4,7),(5,10),(6,9),(9,10)],11) => 13 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,9),(9,10),(10,11)],12) => 19 ([(0,9),(1,8),(2,11),(3,10),(4,5),(4,6),(5,8),(6,9),(7,10),(7,11)],12) => 16 ([(2,9),(3,9),(4,9),(5,9),(6,8),(7,8)],10) => 10 ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8)],10) => 11 ([(0,8),(1,7),(2,10),(3,9),(4,6),(4,9),(5,6),(5,10),(7,8)],11) => 15 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,11),(8,11),(9,11),(10,11)],13) => 15 ([(0,15),(0,16),(1,15),(1,16),(2,15),(2,16),(3,15),(3,16),(4,15),(4,16),(5,15),(5,16),(6,15),(6,16),(7,15),(7,16),(8,15),(8,16),(9,15),(9,16),(10,15),(10,16),(11,15),(11,16),(12,15),(12,16),(13,15),(13,16),(14,15),(14,16)],17) => 57 ([(5,10),(6,11),(7,11),(8,9),(8,10),(9,11)],12) => 12 ([(0,8),(0,9),(1,2),(1,3),(2,5),(3,4),(4,6),(5,7),(6,8),(7,9)],10) => 14 ([(0,1),(2,12),(3,10),(4,9),(5,11),(6,8),(7,8),(9,10),(11,12)],13) => 18 ([(3,11),(4,11),(5,11),(6,11),(7,10),(8,10),(9,10)],12) => 12 ([(2,3),(4,10),(5,9),(6,8),(7,8),(9,11),(10,11)],12) => 13 ([(2,10),(3,9),(4,5),(6,7),(6,8),(7,9),(8,10)],11) => 12 ([(0,14),(0,15),(1,14),(1,15),(2,14),(2,15),(3,14),(3,15),(4,14),(4,15),(5,14),(5,15),(6,14),(6,15),(7,14),(7,15),(8,14),(8,15),(9,14),(9,15),(10,14),(10,15),(11,14),(11,15),(12,14),(12,15),(13,14),(13,15)],16) => 54 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10)],12) => 17 ([(4,9),(5,10),(6,10),(7,8),(7,9),(8,10)],11) => 11 ([(0,12),(1,12),(2,11),(3,11),(4,10),(5,9),(6,7),(6,8),(7,9),(8,10)],13) => 17 ([(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12) => 12 ([(1,6),(2,5),(3,4),(7,10),(8,9),(9,11),(10,11)],12) => 15 ([(0,5),(1,4),(2,3),(6,12),(7,11),(8,10),(9,10),(11,12)],13) => 18 ([(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 12 ([(4,11),(5,9),(6,8),(7,10),(8,9),(10,11)],12) => 12 ([(4,5),(6,9),(7,9),(8,9)],10) => 10 ([(5,10),(5,11),(6,7),(6,9),(7,8),(8,10),(9,11)],12) => 13 ([(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9) => 9 ([(1,11),(2,11),(3,11),(4,11),(5,6),(6,10),(7,9),(7,11),(8,9),(8,10)],12) => 14 ([(3,6),(4,5),(7,10),(8,9),(9,11),(10,11)],12) => 12 ([(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11) => 11 ([(2,11),(3,11),(4,10),(5,9),(6,7),(6,8),(7,9),(8,10)],12) => 13 ([(6,9),(6,10),(7,8),(7,10),(8,9),(8,10),(9,10)],11) => 11 ([(2,8),(2,9),(3,4),(3,5),(4,7),(5,6),(6,8),(7,9)],10) => 11 ([(7,10),(8,9),(9,10)],11) => 11 ([(4,9),(5,9),(6,8),(7,8),(8,9)],10) => 10 ([(7,11),(8,11),(9,10),(10,11)],12) => 12 ([(6,9),(7,8),(7,10),(8,10),(9,10)],11) => 11 ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,9),(8,9)],10) => 17 ([(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11) => 11 ([(6,7),(8,9),(8,10),(9,10)],11) => 11 ([(2,9),(3,9),(4,9),(5,8),(6,8),(7,8)],10) => 10 ([(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 12 ([(6,10),(6,11),(7,8),(7,9),(8,11),(9,10)],12) => 12 ([(7,10),(8,10),(9,10)],11) => 11 ([(4,11),(5,11),(6,11),(7,11),(8,9),(9,10),(10,11)],12) => 12 ([(5,11),(6,11),(7,10),(8,9),(9,10)],12) => 12 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,10),(7,10),(8,10),(9,10)],12) => 14 ([(3,8),(3,9),(4,5),(4,7),(5,6),(6,8),(7,9)],10) => 13 ([(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12) => 15 ([(1,2),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 15 ([(5,9),(5,10),(6,7),(6,8),(7,10),(8,9)],11) => 11 ([(3,10),(4,8),(5,7),(6,9),(7,8),(9,10)],11) => 11 ([(4,7),(5,6),(8,10),(9,10)],11) => 11 ([(0,1),(2,7),(3,6),(4,9),(5,8),(6,11),(7,11),(8,10),(9,10)],12) => 16 ([(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,9),(9,10),(10,11)],12) => 15 ([(5,8),(5,9),(6,7),(6,9),(7,8)],10) => 10 ([(1,9),(2,8),(3,11),(4,10),(5,8),(5,9),(6,7),(6,10),(7,11)],12) => 15 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,9),(9,11),(10,11),(10,12)],13) => 19 ([(7,11),(8,10),(9,10),(9,11),(10,11)],12) => 12 ([(6,11),(7,11),(8,10),(9,10)],12) => 12 ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,8),(7,8)],9) => 17 ([(1,7),(1,8),(2,4),(2,5),(3,4),(3,5),(6,7),(6,8)],9) => 11 ([(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10) => 10 ([(3,4),(5,11),(6,10),(7,9),(8,9),(10,11)],12) => 12 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,10),(7,10),(8,10),(9,10)],12) => 13 ([(9,10),(9,11),(10,11)],12) => 12 ([(3,8),(4,8),(5,7),(6,7),(7,8)],9) => 9 ([(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 33 ([(0,5),(1,4),(2,3),(6,11),(7,11),(8,10),(9,10)],12) => 16 ([(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9)],10) => 10 ([(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10) => 10 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,9),(9,10),(10,11)],12) => 17 ([(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 11 ([(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 14 ([(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 14 ([(0,1),(2,9),(3,9),(4,8),(5,8),(6,11),(7,10),(10,11)],12) => 16 ([(4,11),(5,10),(6,7),(8,9),(8,10),(9,11)],12) => 12 ([(0,11),(1,12),(2,12),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11),(10,12)],13) => 18 ([(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10),(10,11)],12) => 14 ([(1,10),(1,11),(2,3),(2,5),(3,4),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 21 ([(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11) => 11 ([(0,5),(1,4),(2,3),(6,9),(7,8),(8,10),(9,10)],11) => 15 ([(0,16),(0,17),(1,16),(1,17),(2,16),(2,17),(3,16),(3,17),(4,16),(4,17),(5,16),(5,17),(6,16),(6,17),(7,16),(7,17),(8,16),(8,17),(9,16),(9,17),(10,16),(10,17),(11,16),(11,17),(12,16),(12,17),(13,16),(13,17),(14,16),(14,17),(15,16),(15,17)],18) => 62 ([(5,9),(6,10),(7,10),(8,9),(8,10)],11) => 11 ([(4,8),(5,9),(6,9),(7,8),(7,9)],10) => 10 ([(0,10),(0,11),(1,2),(1,3),(2,5),(3,4),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 17 ([(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 15 ([(1,2),(3,8),(4,7),(5,10),(6,9),(7,8),(9,11),(10,11)],12) => 15 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,6),(6,11),(7,10),(7,12),(8,9),(8,10),(9,11)],13) => 17 ([(2,11),(3,11),(4,11),(5,11),(6,11),(7,8),(8,10),(9,10),(9,11)],12) => 13 ([(1,10),(2,11),(3,11),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 15 ([(7,10),(7,11),(8,9),(8,11),(9,10)],12) => 12 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,6),(6,10),(7,9),(7,11),(8,9),(8,10)],12) => 15 ([(3,4),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 13 ([(2,5),(3,4),(6,9),(7,8),(8,10),(9,10)],11) => 12 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,11),(7,11),(8,11),(9,11),(10,11)],13) => 16 ([(0,7),(1,7),(2,6),(3,6),(4,9),(5,8),(8,10),(9,10)],11) => 14 ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10) => 11 ([(3,11),(4,10),(5,6),(7,8),(7,9),(8,10),(9,11)],12) => 12 ([(1,4),(2,3),(5,11),(6,10),(7,9),(8,9),(10,11)],12) => 15 ([(3,10),(4,9),(5,6),(5,7),(6,8),(7,9),(8,10)],11) => 11 ([(0,7),(1,7),(2,6),(3,6),(4,9),(5,8),(8,10),(9,11),(10,11)],12) => 16 ([(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12) => 12 ([(2,10),(3,10),(4,9),(5,8),(6,7),(6,8),(7,9)],11) => 12 ([(2,9),(3,9),(4,8),(5,8),(6,11),(7,10),(10,11)],12) => 13 ([(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 18 ([(0,3),(1,2),(4,12),(5,12),(6,11),(7,11),(8,10),(9,10)],13) => 17 ([(0,10),(1,9),(2,12),(3,11),(4,5),(6,9),(6,10),(7,8),(7,11),(8,12)],13) => 18 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10),(10,11)],12) => 15 ([(4,7),(5,6),(8,11),(9,10),(10,11)],12) => 12 ([(0,12),(1,11),(2,3),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11),(10,12)],13) => 18 ([(4,10),(4,11),(5,6),(5,7),(6,9),(7,8),(8,10),(9,11)],12) => 12 ([(1,2),(3,9),(4,8),(5,7),(6,7),(8,10),(9,11),(10,11)],12) => 15 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,7),(7,11),(8,10),(8,12),(9,10),(9,11)],13) => 17 ([(1,10),(2,10),(3,9),(4,8),(5,6),(5,7),(6,8),(7,9)],11) => 13 ([(6,10),(7,10),(8,10),(9,10)],11) => 11 ([(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 11 ([(0,12),(0,13),(1,12),(1,13),(2,12),(2,13),(3,12),(3,13),(4,12),(4,13),(5,12),(5,13),(6,12),(6,13),(7,12),(7,13),(8,12),(8,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13)],14) => 46 ([(6,10),(7,8),(7,9),(8,9),(8,10),(9,10)],11) => 11 ([(2,3),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 13 ([(2,5),(3,4),(6,9),(7,8),(8,10),(9,11),(10,11)],12) => 14 ([(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12) => 12 ([(3,8),(4,9),(5,9),(6,7),(6,8),(7,9)],10) => 10 ([(3,8),(4,7),(5,6),(9,11),(10,11)],12) => 12 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9)],11) => 15 ([(2,11),(3,11),(4,11),(5,11),(6,11),(7,10),(8,10),(9,10)],12) => 12 ([(2,3),(4,10),(5,9),(6,8),(7,8),(9,10)],11) => 12 ([(3,4),(5,8),(6,7),(7,9),(8,10),(9,10)],11) => 11 ([(7,11),(8,11),(9,10)],12) => 12 ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11) => 15 ([(3,4),(5,10),(6,10),(7,9),(8,9)],11) => 11 ([(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 11 ([(4,9),(5,9),(6,9),(7,8),(8,9)],10) => 10 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,12),(9,10),(10,11),(11,12)],13) => 21 ([(0,1),(2,9),(3,9),(4,8),(5,8),(6,11),(7,10),(10,12),(11,12)],13) => 17 ([(2,3),(4,9),(5,9),(6,9),(7,9),(8,9)],10) => 11 ([(5,11),(6,10),(7,9),(7,10),(8,9),(8,11)],12) => 12 ([(5,10),(6,9),(7,8)],11) => 11 ([(1,9),(2,10),(3,10),(4,10),(5,6),(5,7),(6,8),(7,9),(8,10)],11) => 13 ([(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 10 ([(0,3),(1,2),(4,9),(5,8),(6,11),(7,10),(8,9),(10,12),(11,12)],13) => 18 ([(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 21 ([(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 26 ([(3,9),(3,10),(4,5),(4,6),(5,8),(6,7),(7,9),(8,10)],11) => 11 ([(5,10),(6,9),(7,8),(7,9),(8,10)],11) => 11 ([(3,10),(3,11),(4,8),(4,9),(5,6),(5,7),(6,7),(8,9),(10,11)],12) => 15 ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10) => 13 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,8),(8,10),(9,10),(9,11)],12) => 17 ([(6,11),(7,10),(8,9),(8,10),(9,11)],12) => 12 ([(3,10),(3,11),(4,5),(4,7),(5,6),(6,8),(7,9),(8,10),(9,11)],12) => 17 ([(3,11),(4,11),(5,11),(6,11),(7,8),(8,10),(9,10),(9,11)],12) => 12 ([(3,9),(4,8),(5,11),(6,10),(7,10),(7,11),(8,9)],12) => 12 ([(5,6),(7,11),(8,11),(9,11),(10,11)],12) => 12 ([(6,10),(7,10),(8,9),(9,10)],11) => 11 ([(4,9),(5,9),(6,8),(6,9),(7,8),(7,9)],10) => 10 ([(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11) => 11 ([(2,9),(2,10),(3,4),(3,6),(4,5),(5,7),(6,8),(7,9),(8,10)],11) => 17 ([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,10),(8,10),(9,10)],12) => 13 ([(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 21 ([(4,11),(5,11),(6,10),(7,9),(8,9),(8,10)],12) => 12 ([(0,3),(1,2),(4,7),(5,6),(6,9),(7,10),(8,9),(8,10)],11) => 15 ([(7,11),(8,10),(9,10),(9,11)],12) => 12 ([(5,10),(6,10),(7,9),(7,10),(8,9),(8,10)],11) => 11 ([(1,11),(2,10),(3,4),(5,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 15 ([(1,9),(2,10),(3,10),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 13 ([(3,6),(4,5),(7,10),(8,9),(9,10)],11) => 11 ([(7,11),(8,10),(8,11),(9,10),(9,11)],12) => 12 ([(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11) => 17 ([(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11) => 22 ([(0,9),(1,8),(2,7),(3,6),(4,5),(10,12),(11,12)],13) => 18 ([(2,7),(2,8),(3,4),(3,6),(4,5),(5,7),(6,8)],9) => 13 ([(2,3),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12) => 15 ([(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12) => 12 ([(3,4),(5,10),(6,10),(7,10),(8,10),(9,10)],11) => 11 ([(0,1),(2,8),(3,7),(4,6),(5,6),(7,9),(8,10),(9,10)],11) => 15 ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9)],11) => 13 ([(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9)],11) => 11 ([(2,10),(3,11),(4,11),(5,11),(6,7),(6,8),(7,9),(8,10),(9,11)],12) => 13 ([(4,10),(5,11),(6,11),(7,9),(7,10),(8,9),(8,11)],12) => 12 ([(3,9),(3,10),(4,6),(4,7),(5,6),(5,7),(8,9),(8,10)],11) => 11 ([(6,10),(7,9),(8,9),(8,10)],11) => 11 ([(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10) => 11 ([(0,12),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,11),(9,11),(10,11)],13) => 17 ([(7,10),(7,11),(8,9),(8,11),(9,11),(10,11)],12) => 12 ([(8,11),(9,11),(10,11)],12) => 12 ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,7),(7,9),(8,10),(8,11),(9,10)],12) => 17 ([(8,10),(8,11),(9,10),(9,11),(10,11)],12) => 12 ([(1,10),(2,10),(3,10),(4,10),(5,6),(6,8),(7,9),(7,10),(8,9)],11) => 13 ([(0,10),(1,9),(2,12),(3,11),(4,5),(4,6),(5,7),(6,11),(7,12),(8,9),(8,10)],13) => 18 ([(0,11),(1,11),(2,10),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10)],12) => 16 ([(0,7),(1,6),(2,5),(3,4),(8,11),(9,10),(10,12),(11,12)],13) => 18 ([(2,3),(4,11),(5,9),(6,8),(7,10),(8,9),(10,11)],12) => 14 ([(0,8),(1,8),(2,7),(3,6),(4,5),(4,6),(5,7)],9) => 12 ([(3,8),(4,7),(5,6),(5,7),(6,8)],9) => 9 ([(1,7),(2,6),(3,5),(4,5),(6,8),(7,8)],9) => 10 ([(2,8),(3,7),(4,6),(5,6),(7,8)],9) => 9 ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6)],9) => 11 ([(1,2),(3,8),(4,8),(5,7),(6,7)],9) => 10 ([(1,8),(2,9),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9)],10) => 12 ([(2,9),(3,8),(4,5),(4,6),(5,7),(6,8),(7,9)],10) => 11 ([(0,9),(1,9),(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],10) => 13 ([(1,9),(2,9),(3,8),(4,7),(5,6),(5,7),(6,8)],10) => 12 ([(2,3),(4,7),(5,6),(6,8),(7,9),(8,9)],10) => 11 ([(4,9),(5,8),(6,7),(6,8),(7,9)],10) => 10 ([(0,7),(1,6),(2,9),(3,8),(4,8),(4,9),(5,6),(5,7)],10) => 13 ([(1,7),(2,6),(3,9),(4,8),(5,8),(5,9),(6,7)],10) => 12 ([(0,1),(2,8),(3,7),(4,6),(5,6),(7,9),(8,9)],10) => 13 ([(2,8),(3,7),(4,6),(5,6),(7,9),(8,9)],10) => 10 ([(3,4),(5,8),(6,7),(7,9),(8,9)],10) => 10 ([(2,9),(3,7),(4,6),(5,8),(6,7),(8,9)],10) => 11 ([(0,7),(1,7),(2,6),(3,6),(4,9),(5,8),(8,9)],10) => 13 ([(1,2),(3,9),(4,8),(5,7),(6,7),(8,9)],10) => 12 ([(3,9),(4,8),(5,7),(6,7),(8,9)],10) => 10 ([(1,9),(2,9),(3,8),(4,8),(5,7),(6,7)],10) => 11 ([(0,3),(1,2),(4,9),(5,9),(6,8),(7,8)],10) => 13 ([(4,9),(5,9),(6,8),(7,8)],10) => 10 ([(3,6),(4,5),(7,9),(8,9)],10) => 10 ([(1,10),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 14 ([(0,10),(1,11),(2,11),(3,11),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12) => 16 ----------------------------------------------------------------------------- Created: May 07, 2016 at 08:53 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 02, 2023 at 19:44 by Martin Rubey