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Identifier
Values
=>
Cc0014;cc-rep
([],2)=>1 ([(0,1)],2)=>0 ([],3)=>3 ([(1,2)],3)=>1 ([(0,1),(0,2)],3)=>1 ([(0,2),(2,1)],3)=>0 ([(0,2),(1,2)],3)=>1 ([],4)=>12 ([(2,3)],4)=>6 ([(1,2),(1,3)],4)=>4 ([(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)=>1 ([(1,2),(2,3)],4)=>2 ([(0,3),(3,1),(3,2)],4)=>1 ([(1,3),(2,3)],4)=>4 ([(0,3),(1,3),(3,2)],4)=>1 ([(0,3),(1,3),(2,3)],4)=>3 ([(0,3),(1,2)],4)=>3 ([(0,3),(1,2),(1,3)],4)=>2 ([(0,2),(0,3),(1,2),(1,3)],4)=>2 ([(0,3),(2,1),(3,2)],4)=>0 ([(0,3),(1,2),(2,3)],4)=>1 ([],5)=>60 ([(3,4)],5)=>30 ([(2,3),(2,4)],5)=>20 ([(1,2),(1,3),(1,4)],5)=>15 ([(0,1),(0,2),(0,3),(0,4)],5)=>12 ([(0,2),(0,3),(0,4),(4,1)],5)=>6 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>4 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>3 ([(1,3),(1,4),(4,2)],5)=>7 ([(0,3),(0,4),(4,1),(4,2)],5)=>4 ([(1,2),(1,3),(2,4),(3,4)],5)=>5 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>1 ([(0,3),(0,4),(3,2),(4,1)],5)=>3 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>2 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>2 ([(2,3),(3,4)],5)=>10 ([(1,4),(4,2),(4,3)],5)=>5 ([(0,4),(4,1),(4,2),(4,3)],5)=>3 ([(2,4),(3,4)],5)=>20 ([(1,4),(2,4),(4,3)],5)=>5 ([(0,4),(1,4),(4,2),(4,3)],5)=>2 ([(1,4),(2,4),(3,4)],5)=>15 ([(0,4),(1,4),(2,4),(4,3)],5)=>3 ([(0,4),(1,4),(2,4),(3,4)],5)=>12 ([(0,4),(1,4),(2,3)],5)=>10 ([(0,4),(1,3),(2,3),(2,4)],5)=>8 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>7 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>6 ([(0,4),(1,4),(2,3),(4,2)],5)=>1 ([(0,4),(1,3),(2,3),(3,4)],5)=>4 ([(0,4),(1,4),(2,3),(2,4)],5)=>9 ([(0,4),(1,4),(2,3),(3,4)],5)=>6 ([(1,4),(2,3)],5)=>15 ([(1,4),(2,3),(2,4)],5)=>10 ([(0,4),(1,2),(1,4),(2,3)],5)=>4 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>2 ([(1,3),(1,4),(2,3),(2,4)],5)=>10 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>3 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>2 ([(0,4),(1,2),(1,4),(4,3)],5)=>3 ([(0,4),(1,2),(1,3)],5)=>10 ([(0,4),(1,2),(1,3),(1,4)],5)=>9 ([(0,2),(0,4),(3,1),(4,3)],5)=>2 ([(0,4),(1,2),(1,3),(3,4)],5)=>4 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>1 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>4 ([(0,3),(0,4),(1,2),(1,4)],5)=>8 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>7 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>6 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>3 ([(0,3),(1,2),(1,4),(3,4)],5)=>4 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>3 ([(1,4),(3,2),(4,3)],5)=>2 ([(0,3),(3,4),(4,1),(4,2)],5)=>1 ([(1,4),(2,3),(3,4)],5)=>7 ([(0,4),(1,2),(2,4),(4,3)],5)=>1 ([(0,3),(1,4),(4,2)],5)=>4 ([(0,4),(3,2),(4,1),(4,3)],5)=>1 ([(0,4),(1,2),(2,3),(2,4)],5)=>3 ([(0,4),(2,3),(3,1),(4,2)],5)=>0 ([(0,3),(1,2),(2,4),(3,4)],5)=>3 ([(0,4),(1,2),(2,3),(3,4)],5)=>2 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>1 ([],6)=>360 ([(4,5)],6)=>180 ([(3,4),(3,5)],6)=>120 ([(2,3),(2,4),(2,5)],6)=>90 ([(1,2),(1,3),(1,4),(1,5)],6)=>72 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>60 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>30 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)=>20 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)=>15 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>12 ([(1,3),(1,4),(1,5),(5,2)],6)=>36 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>20 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>24 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>18 ([(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)=>10 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)=>8 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>7 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)=>9 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>4 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)=>5 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)=>15 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)=>10 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)=>10 ([(2,3),(2,4),(4,5)],6)=>45 ([(1,4),(1,5),(5,2),(5,3)],6)=>24 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>15 ([(2,3),(2,4),(3,5),(4,5)],6)=>30 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>6 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>2 ([(1,4),(1,5),(4,3),(5,2)],6)=>18 ([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>14 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>3 ([(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)=>3 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)=>10 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)=>9 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>8 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)=>7 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>6 ([(3,4),(4,5)],6)=>60 ([(2,3),(3,4),(3,5)],6)=>30 ([(1,5),(5,2),(5,3),(5,4)],6)=>18 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>12 ([(2,3),(3,5),(5,4)],6)=>15 ([(1,4),(4,5),(5,2),(5,3)],6)=>6 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>3 ([(3,5),(4,5)],6)=>120 ([(2,5),(3,5),(5,4)],6)=>30 ([(1,5),(2,5),(5,3),(5,4)],6)=>12 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>6 ([(2,5),(3,5),(4,5)],6)=>90 ([(1,5),(2,5),(3,5),(5,4)],6)=>18 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>6 ([(1,5),(2,5),(3,5),(4,5)],6)=>72 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>12 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>60 ([(0,5),(1,5),(2,5),(3,4)],6)=>45 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>3 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>15 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6)=>42 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>30 ([(1,5),(2,5),(3,4)],6)=>60 ([(1,5),(2,4),(3,4),(3,5)],6)=>48 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)=>12 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>8 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>42 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)=>12 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>7 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>36 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>9 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>6 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>10 ([(1,5),(2,5),(3,4),(5,3)],6)=>6 ([(1,5),(2,4),(3,4),(4,5)],6)=>24 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>4 ([(0,5),(1,5),(2,3),(5,4)],6)=>15 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>3 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6)=>9 ([(1,5),(2,5),(3,4),(3,5)],6)=>54 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6)=>12 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6)=>19 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>9 ([(0,5),(1,5),(2,3),(2,4)],6)=>40 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>2 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6)=>14 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>8 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6)=>38 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6)=>9 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)=>5 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>3 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6)=>26 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>7 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>4 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>20 ([(1,5),(2,5),(3,4),(4,5)],6)=>36 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>6 ([(0,5),(1,5),(2,3),(3,4)],6)=>20 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>1 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6)=>6 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>4 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6)=>16 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>10 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>5 ([(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)=>40 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6)=>35 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>32 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>30 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>27 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>24 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>5 ([(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)=>20 ([(2,5),(3,4)],6)=>90 ([(2,5),(3,4),(3,5)],6)=>75 ([(1,5),(2,3),(2,5),(3,4)],6)=>26 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6)=>14 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>5 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>5 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>14 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>2 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)=>7 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>6 ([(2,4),(2,5),(3,4),(3,5)],6)=>60 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>18 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)=>8 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>12 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)=>6 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>5 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>4 ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)=>30 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>4 ([(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)=>3 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)=>14 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>26 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)=>11 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>24 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>15 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)=>16 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>12 ([(1,5),(2,3),(2,5),(5,4)],6)=>18 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6)=>9 ([(1,5),(2,3),(2,4)],6)=>60 ([(1,5),(2,3),(2,4),(2,5)],6)=>54 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6)=>19 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>11 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>14 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>9 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6)=>16 ([(0,5),(1,2),(1,3),(1,4)],6)=>45 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>42 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>10 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6)=>26 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)=>7 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>19 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>6 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>15 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6)=>19 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6)=>12 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>9 ([(1,3),(1,5),(4,2),(5,4)],6)=>12 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)=>5 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>4 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>4 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)=>4 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>3 ([(1,5),(2,3),(2,4),(4,5)],6)=>33 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6)=>6 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>9 ([(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)=>24 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>4 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6)=>12 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>10 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>9 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)=>4 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)=>4 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>11 ([(0,4),(1,3),(1,5),(5,2)],6)=>19 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>7 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6)=>15 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6)=>12 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>2 ([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>15 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>10 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>1 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>5 ([(1,4),(1,5),(2,3),(2,5)],6)=>48 ([(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>42 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>12 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)=>9 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>36 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>12 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)=>8 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>6 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6)=>16 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)=>8 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>7 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6)=>15 ([(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>24 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)=>7 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>5 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>3 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)=>16 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)=>11 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>5 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6)=>11 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)=>5 ([(0,4),(0,5),(1,2),(1,3)],6)=>40 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6)=>35 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>32 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)=>15 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>13 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)=>30 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>27 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>24 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)=>15 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)=>15 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)=>11 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)=>18 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)=>14 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>3 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)=>3 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6)=>14 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>11 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>8 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>8 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)=>9 ([(1,4),(2,3),(2,5),(4,5)],6)=>26 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)=>6 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>18 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>3 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>3 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>9 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>4 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)=>7 ([(0,5),(1,3),(1,4),(5,2)],6)=>20 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>2 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>4 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6)=>12 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)=>10 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>5 ([(2,5),(3,4),(4,5)],6)=>45 ([(1,5),(2,3),(3,5),(5,4)],6)=>8 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>3 ([(1,3),(2,4),(4,5)],6)=>30 ([(1,5),(4,3),(5,2),(5,4)],6)=>8 ([(1,5),(2,3),(3,4),(3,5)],6)=>18 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>4 ([(0,4),(1,5),(5,2),(5,3)],6)=>15 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>6 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6)=>12 ([(1,5),(3,4),(4,2),(5,3)],6)=>3 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>1 ([(1,4),(2,3),(3,5),(4,5)],6)=>18 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>3 ([(0,5),(1,4),(4,2),(5,3)],6)=>10 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>2 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)=>7 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(1,5),(2,3),(3,4),(4,5)],6)=>12 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>6 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>1 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>2 ([(0,5),(1,4),(2,3)],6)=>45 ([(0,5),(1,3),(2,4),(2,5)],6)=>35 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6)=>33 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)=>6 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>4 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>18 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)=>3 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>4 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6)=>15 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)=>28 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>26 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>24 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)=>24 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)=>22 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>20 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>18 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)=>11 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>24 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>15 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>33 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>15 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)=>16 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>12 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>6 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>4 ([(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)=>2 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6)=>19 ([(0,5),(1,3),(4,2),(5,4)],6)=>6 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6)=>3 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6)=>6 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)=>3 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>1 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>4 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>0 ([(0,5),(1,3),(2,4),(4,5)],6)=>19 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6)=>15 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>1 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>7 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>2 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>1 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>4 ([(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)=>15 ([],7)=>2520 ([(5,6)],7)=>1260 ([(4,5),(4,6)],7)=>840 ([(3,4),(3,5),(3,6)],7)=>630 ([(2,3),(2,4),(2,5),(2,6)],7)=>504 ([(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>420 ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)=>360 ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>180 ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)=>120 ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)=>90 ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)=>72 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>60 ([(1,3),(1,4),(1,5),(1,6),(6,2)],7)=>210 ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>120 ([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)=>140 ([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>105 ([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>84 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>12 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)=>45 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)=>42 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>15 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)=>18 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)=>60 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)=>48 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>42 ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>36 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)=>54 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)=>40 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)=>35 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>32 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>30 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>27 ([(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)=>24 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>20 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)=>24 ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)=>30 ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)=>90 ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)=>75 ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)=>60 ([(2,4),(2,5),(2,6),(6,3)],7)=>252 ([(1,4),(1,5),(1,6),(6,2),(6,3)],7)=>140 ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)=>90 ([(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>168 ([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>126 ([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)=>21 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)=>6 ([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)=>70 ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)=>56 ([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>49 ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>42 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)=>9 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>6 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7)=>12 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>7 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)=>10 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)=>12 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>8 ([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)=>63 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7)=>12 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)=>40 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)=>38 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7)=>14 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>8 ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)=>28 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>4 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)=>15 ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7)=>9 ([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)=>35 ([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)=>12 ([(1,4),(1,5),(1,6),(5,3),(6,2)],7)=>105 ([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)=>79 ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)=>70 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7)=>30 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7)=>26 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>24 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>11 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>14 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>10 ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)=>18 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>12 ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)=>18 ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)=>60 ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)=>54 ([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7)=>48 ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>42 ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>36 ([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)=>45 ([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)=>35 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7)=>33 ([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)=>28 ([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>26 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>24 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)=>24 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)=>22 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>20 ([(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)=>18 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>24 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7)=>11 ([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7)=>33 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>15 ([(3,4),(3,5),(5,6)],7)=>315 ([(2,5),(2,6),(6,3),(6,4)],7)=>168 ([(1,5),(1,6),(6,2),(6,3),(6,4)],7)=>105 ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)=>72 ([(3,4),(3,5),(4,6),(5,6)],7)=>210 ([(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>42 ([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)=>14 ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)=>6 ([(2,5),(2,6),(5,4),(6,3)],7)=>126 ([(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>105 ([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>84 ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)=>21 ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)=>8 ([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>14 ([(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)=>6 ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)=>5 ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>4 ([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)=>21 ([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7)=>9 ([(1,5),(1,6),(5,4),(6,2),(6,3)],7)=>70 ([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)=>63 ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7)=>16 ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)=>45 ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)=>42 ([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7)=>56 ([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)=>49 ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>42 ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)=>12 ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>8 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>6 ([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7)=>12 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)=>9 ([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7)=>15 ([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7)=>40 ([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7)=>35 ([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7)=>32 ([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>30 ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7)=>27 ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>24 ([(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>63 ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)=>10 ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)=>3 ([(4,5),(5,6)],7)=>420 ([(3,4),(4,5),(4,6)],7)=>210 ([(2,6),(6,3),(6,4),(6,5)],7)=>126 ([(1,6),(6,2),(6,3),(6,4),(6,5)],7)=>84 ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)=>60 ([(3,4),(4,6),(6,5)],7)=>105 ([(2,5),(5,6),(6,3),(6,4)],7)=>42 ([(1,5),(5,6),(6,2),(6,3),(6,4)],7)=>21 ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)=>12 ([(4,6),(5,6)],7)=>840 ([(3,6),(4,6),(6,5)],7)=>210 ([(2,6),(3,6),(6,4),(6,5)],7)=>84 ([(1,6),(2,6),(6,3),(6,4),(6,5)],7)=>42 ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)=>24 ([(3,6),(4,6),(5,6)],7)=>630 ([(2,6),(3,6),(4,6),(6,5)],7)=>126 ([(1,6),(2,6),(3,6),(6,4),(6,5)],7)=>42 ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)=>18 ([(2,6),(3,6),(4,6),(5,6)],7)=>504 ([(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>84 ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)=>24 ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>420 ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>60 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>360 ([(0,6),(1,6),(2,6),(3,6),(4,5)],7)=>252 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>12 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>72 ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7)=>240 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>180 ([(1,6),(2,6),(3,6),(4,5)],7)=>315 ([(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>21 ([(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>105 ([(0,6),(1,6),(2,6),(3,4),(6,5)],7)=>63 ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)=>9 ([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7)=>33 ([(1,6),(2,6),(3,6),(4,5),(4,6)],7)=>294 ([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7)=>54 ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7)=>102 ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>42 ([(0,6),(1,6),(2,6),(3,4),(3,5)],7)=>210 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)=>6 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7)=>60 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>30 ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7)=>204 ([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7)=>150 ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>120 ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>210 ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>30 ([(0,6),(1,6),(2,6),(3,4),(4,5)],7)=>105 ([(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)=>15 ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)=>45 ([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7)=>90 ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>15 ([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)=>6 ([(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)=>60 ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>210 ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>180 ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>162 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>150 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>144 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>132 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>120 ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)=>18 ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>6 ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>90 ([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7)=>192 ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>180 ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>30 ([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)=>12 ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>6 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>120 ([(2,6),(3,6),(4,5)],7)=>420 ([(2,6),(3,5),(4,5),(4,6)],7)=>336 ([(1,6),(2,5),(3,5),(3,6),(6,4)],7)=>84 ([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7)=>38 ([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>56 ([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7)=>8 ([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)=>26 ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)=>19 ([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>16 ([(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>294 ([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7)=>84 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7)=>36 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7)=>19 ([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>14 ([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>49 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)=>22 ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)=>17 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>252 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>63 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>24 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>42 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)=>18 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7)=>15 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>12 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7)=>126 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)=>12 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)=>6 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7)=>51 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)=>9 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>36 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)=>114 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7)=>42 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>108 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>72 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)=>75 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>60 ([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>70 ([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>26 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7)=>147 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7)=>18 ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7)=>7 ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7)=>12 ([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>66 ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7)=>10 ([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>42 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)=>13 ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7)=>57 ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)=>129 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7)=>45 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>123 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>84 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)=>134 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>56 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>78 ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)=>81 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>66 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)=>90 ([(0,6),(1,5),(2,5),(2,6),(3,4)],7)=>168 ([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)=>144 ([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)=>18 ([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7)=>66 ([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7)=>12 ([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>48 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7)=>144 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)=>118 ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)=>102 ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>101 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)=>112 ([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7)=>56 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>138 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>84 ([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7)=>90 ([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>72 ([(2,6),(3,6),(4,5),(6,4)],7)=>42 ([(2,6),(3,5),(4,5),(5,6)],7)=>168 ([(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>28 ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)=>8 ([(1,6),(2,6),(3,4),(6,5)],7)=>105 ([(1,6),(2,6),(4,5),(6,3),(6,4)],7)=>21 ([(1,6),(2,6),(3,5),(6,4),(6,5)],7)=>63 ([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7)=>13 ([(0,6),(1,6),(2,3),(6,4),(6,5)],7)=>42 ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)=>12 ([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7)=>30 ([(2,6),(3,6),(4,5),(4,6)],7)=>378 ([(1,6),(2,6),(3,4),(3,6),(6,5)],7)=>84 ([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7)=>30 ([(1,6),(2,6),(3,4),(3,6),(4,5)],7)=>133 ([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>63 ([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7)=>31 ([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)=>21 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7)=>68 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7)=>28 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>18 ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)=>34 ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7)=>9 ([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7)=>19 ([(1,6),(2,6),(3,4),(3,5)],7)=>280 ([(1,6),(2,6),(3,4),(3,5),(6,3)],7)=>14 ([(1,5),(2,5),(3,4),(3,6),(5,6)],7)=>98 ([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>56 ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)=>12 ([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7)=>18 ([(0,6),(1,6),(2,3),(2,4),(6,5)],7)=>70 ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)=>8 ([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7)=>38 ([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>26 ([(1,6),(2,6),(3,4),(3,5),(3,6)],7)=>266 ([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7)=>62 ([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7)=>102 ([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7)=>47 ([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)=>68 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>38 ([(0,6),(1,6),(2,3),(2,4),(2,5)],7)=>210 ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)=>6 ([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7)=>68 ([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7)=>36 ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>24 ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>204 ([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7)=>55 ([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7)=>30 ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7)=>18 ([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7)=>142 ([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)=>39 ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)=>24 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)=>15 ([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>110 ([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)=>36 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>20 ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>90 ([(1,6),(2,6),(3,4),(3,5),(5,6)],7)=>182 ([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7)=>32 ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>140 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>20 ([(0,6),(1,6),(2,3),(2,4),(4,5)],7)=>105 ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)=>3 ([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7)=>34 ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)=>24 ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)=>14 ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>8 ([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7)=>50 ([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7)=>40 ([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7)=>24 ([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7)=>87 ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)=>26 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7)=>9 ([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)=>25 ([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7)=>14 ([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7)=>13 ([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7)=>22 ([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12 ([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7)=>11 ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>8 ([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7)=>15 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>5 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7)=>14 ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>9 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7)=>22 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7)=>14 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>3 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7)=>71 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)=>26 ([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7)=>26 ([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>19 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>65 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>45 ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)=>24 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>15 ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7)=>70 ([(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)=>40 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7)=>56 ([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>50 ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)=>6 ([(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)=>30 ([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7)=>55 ([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)=>29 ([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7)=>18 ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)=>18 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>10 ([(2,6),(3,6),(4,5),(5,6)],7)=>252 ([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>42 ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)=>12 ([(1,6),(2,6),(3,4),(4,5)],7)=>140 ([(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>7 ([(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>70 ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)=>10 ([(0,6),(1,6),(2,3),(3,5),(6,4)],7)=>35 ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)=>4 ([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)=>25 ([(1,6),(2,6),(3,4),(4,5),(4,6)],7)=>112 ([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7)=>22 ([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)=>31 ([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7)=>16 ([(0,3),(1,6),(2,6),(3,4),(3,5)],7)=>70 ([(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)=>30 ([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7)=>20 ([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7)=>32 ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>20 ([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7)=>62 ([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7)=>40 ([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>23 ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>15 ([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>30 ([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>18 ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>12 ([(1,3),(2,6),(3,5),(4,6),(5,4)],7)=>17 ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>2 ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)=>7 ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>1 ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>70 ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>10 ([(0,3),(1,6),(2,6),(3,5),(5,4)],7)=>35 ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>1 ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)=>20 ([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7)=>8 ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>4 ([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7)=>25 ([(1,6),(2,6),(3,5),(4,5)],7)=>280 ([(1,6),(2,6),(3,5),(4,5),(4,6)],7)=>245 ([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7)=>65 ([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7)=>35 ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>224 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7)=>62 ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>32 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>44 ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>210 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>48 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>30 ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>189 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7)=>45 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>27 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>39 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>168 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>36 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>24 ([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7)=>53 ([(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>35 ([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)=>14 ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)=>5 ([(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)=>140 ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>20 ([(0,6),(1,6),(2,5),(3,5),(6,4)],7)=>70 ([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7)=>17 ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)=>8 ([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7)=>50 ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7)=>40 ([(0,6),(1,6),(2,5),(3,4)],7)=>210 ([(0,6),(1,6),(2,3),(4,5),(6,4)],7)=>21 ([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7)=>6 ([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7)=>15 ([(0,6),(1,5),(2,5),(3,4),(5,6)],7)=>84 ([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7)=>48 ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>4 ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>24 ([(0,6),(1,6),(2,5),(3,4),(3,6)],7)=>189 ([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7)=>15 ([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7)=>69 ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7)=>99 ([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7)=>12 ([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>54 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7)=>174 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>87 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7)=>155 ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)=>50 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>149 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>105 ([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7)=>120 ([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7)=>90 ([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>75 ([(0,5),(1,5),(2,6),(3,4),(3,6)],7)=>175 ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7)=>136 ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>120 ([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>114 ([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7)=>17 ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7)=>63 ([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7)=>11 ([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7)=>64 ([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)=>44 ([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)=>20 ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)=>5 ([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7)=>14 ([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7)=>80 ([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7)=>164 ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>111 ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7)=>18 ([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7)=>9 ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>75 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7)=>140 ([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7)=>117 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7)=>106 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>96 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>90 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7)=>55 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7)=>104 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>52 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)=>100 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)=>94 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>88 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)=>90 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>84 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>78 ([(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)=>72 ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7)=>62 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7)=>17 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7)=>10 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)=>4 ([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7)=>60 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)=>40 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)=>130 ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>124 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7)=>23 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7)=>10 ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)=>12 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7)=>6 ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)=>5 ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>4 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>80 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)=>18 ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)=>8 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>60 ([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7)=>23 ([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7)=>11 ([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7)=>95 ([(0,6),(1,6),(2,4),(3,5),(5,6)],7)=>126 ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>6 ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>36 ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>90 ([(0,6),(1,5),(2,5),(3,4),(4,6)],7)=>105 ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)=>6 ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)=>15 ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)=>3 ([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7)=>9 ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>60 ([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7)=>81 ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>8 ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>3 ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>45 ([(3,6),(4,5)],7)=>630 ([(3,6),(4,5),(4,6)],7)=>525 ([(2,6),(3,4),(3,6),(4,5)],7)=>189 ([(1,6),(2,3),(2,6),(3,4),(3,5)],7)=>98 ([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7)=>60 ([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7)=>28 ([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7)=>19 ([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>15 ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7)=>42 ([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>35 ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)=>9 ([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)=>30 ([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)=>19 ([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7)=>17 ([(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>105 ([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)=>17 ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)=>5 ([(1,6),(2,3),(2,6),(3,5),(6,4)],7)=>52 ([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7)=>42 ([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)=>25 ([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7)=>21 ([(1,6),(2,3),(2,6),(3,5),(5,4)],7)=>42 ([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>28 ([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)=>4 ([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)=>14 ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)=>8 ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)=>9 ([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)=>20 ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)=>10 ([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7)=>9 ([(3,5),(3,6),(4,5),(4,6)],7)=>420 ([(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>126 ([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>56 ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)=>30 ([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>84 ([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)=>14 ([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)=>42 ([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)=>35 ([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>28 ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7)=>20 ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7)=>18 ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7)=>16 ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7)=>14 ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)=>12 ([(1,5),(1,6),(2,5),(2,6),(3,4)],7)=>210 ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)=>182 ([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)=>54 ([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>38 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>32 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>26 ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>168 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7)=>54 ([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)=>36 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>24 ([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7)=>31 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)=>44 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7)=>52 ([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)=>28 ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)=>10 ([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7)=>9 ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>6 ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7)=>8 ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7)=>7 ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7)=>9 ([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>98 ([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)=>21 ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>70 ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)=>10 ([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7)=>32 ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7)=>28 ([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7)=>18 ([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7)=>14 ([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7)=>63 ([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7)=>15 ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7)=>11 ([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7)=>41 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7)=>42 ([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7)=>26 ([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>22 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)=>182 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7)=>48 ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>77 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7)=>21 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7)=>15 ([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7)=>11 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7)=>53 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7)=>33 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7)=>32 ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)=>18 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>168 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)=>45 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7)=>30 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7)=>62 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7)=>33 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>24 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>105 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7)=>27 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7)=>15 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)=>21 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7)=>65 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7)=>35 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7)=>36 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7)=>26 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7)=>50 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)=>24 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)=>29 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7)=>140 ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7)=>10 ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)=>4 ([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7)=>7 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)=>6 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7)=>58 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>36 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7)=>40 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)=>28 ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>24 ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>20 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7)=>130 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7)=>51 ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7)=>30 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>124 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)=>79 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)=>58 ([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7)=>23 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7)=>12 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7)=>6 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7)=>82 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)=>30 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7)=>64 ([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)=>15 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)=>8 ([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7)=>16 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7)=>9 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7)=>60 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)=>52 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>46 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>40 ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)=>112 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7)=>22 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7)=>31 ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7)=>16 ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>84 ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)=>18 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>12 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7)=>70 ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)=>5 ([(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)=>3 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)=>4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7)=>40 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7)=>30 ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7)=>18 ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>10 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7)=>52 ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7)=>26 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)=>44 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7)=>26 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7)=>30 ([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7)=>10 ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>7 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)=>20 ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)=>10 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>6 ([(2,6),(3,4),(3,6),(6,5)],7)=>147 ([(1,6),(2,3),(2,6),(6,4),(6,5)],7)=>63 ([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7)=>33 ([(2,6),(3,4),(3,5)],7)=>420 ([(2,6),(3,4),(3,5),(3,6)],7)=>378 ([(1,6),(2,3),(2,4),(2,6),(4,5)],7)=>134 ([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7)=>80 ([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7)=>37 ([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7)=>28 ([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>79 ([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7)=>11 ([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7)=>40 ([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7)=>33 ([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)=>98 ([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>63 ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7)=>9 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7)=>30 ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7)=>25 ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7)=>20 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7)=>14 ([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)=>60 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7)=>49 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7)=>23 ([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>19 ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7)=>23 ([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>40 ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>23 ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>18 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7)=>28 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7)=>23 ([(1,6),(2,3),(2,4),(2,6),(6,5)],7)=>112 ([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7)=>50 ([(1,6),(2,3),(2,4),(2,5)],7)=>315 ([(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>294 ([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7)=>120 ([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7)=>65 ([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7)=>80 ([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>51 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7)=>60 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>42 ([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7)=>90 ([(0,6),(1,2),(1,3),(1,4),(1,5)],7)=>252 ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>240 ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)=>60 ([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7)=>150 ([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)=>45 ([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)=>110 ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)=>36 ([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>87 ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>30 ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>72 ([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7)=>102 ([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7)=>62 ([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7)=>45 ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>36 ([(1,3),(1,4),(1,6),(5,2),(6,5)],7)=>70 ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)=>30 ([(1,6),(2,3),(2,4),(2,5),(5,6)],7)=>182 ([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7)=>40 ([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)=>51 ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7)=>8 ([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>133 ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)=>23 ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)=>42 ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>6 ([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>105 ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)=>15 ([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)=>55 ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)=>19 ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>26 ([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)=>51 ([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7)=>69 ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7)=>26 ([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7)=>33 ([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)=>66 ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,1),(5,2)],7)=>19
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Description
The balance constant multiplied with the number of linear extensions of a poset.
A pair of elements $x,y$ of a poset is $\alpha$-balanced if the proportion $P(x,y)$ of linear extensions where $x$ comes before $y$ is between $\alpha$ and $1-\alpha$. The balance constant of a poset is $\max\min(P(x,y), P(y,x)).$
Kislitsyn [1] conjectured that every poset which is not a chain is $1/3$-balanced. Brightwell, Felsner and Trotter [2] show that it is at least $(1-\sqrt 5)/10$-balanced.
Olson and Sagan [3] exhibit various posets that are $1/2$-balanced.
References
[1] Kislicyn, S. S. Finite partially ordered sets and their corresponding permutation sets MathSciNet:0244113
[2] Brightwell, G. R., Felsner, S., Trotter, W. T. Balancing pairs and the cross product conjecture MathSciNet:1368815
[3] Olson, E. J., Sagan, B. E. On the $1/3-2/3$ Conjecture arXiv:1706.04985
Code
def statistic(P):
    l_ext = P.linear_extensions().list()
    max_balance = 0
    for x,y in Subsets(P,2):
        l = [ext for ext in l_ext
             if ext.index(x) < ext.index(y)]
        new_balance = min(len(l), len(l_ext)-len(l))
        max_balance = max(new_balance, max_balance)
    return max_balance
Created
Jun 16, 2017 at 06:35 by Martin Rubey
Updated
Jul 17, 2017 at 07:29 by Martin Rubey